Keywords: felizmente, em permanente contacto, partilhando como sempre todas

First and foremost, I'd like to thank both my supervisors and good friends, Agnès and

Initial remarks

The recent field of oxide spintronics merges the remarkable multifunctionality and strongly correlated character of complex oxide materials, with the ability to exploit the electron spin for highly efficient data storage and transfer [START_REF] Bibes | Oxide Spintronics[END_REF][START_REF] Bibes | Ultrathin oxide films and interfaces for electronics and spintronics[END_REF]. From a materials perspective, complex oxides saw a tremendous boost in popularity with the (re)invention of the pulsed laser deposition technique, which enabled a versatile and flexible way of engineering new and improved phenomena at atomically-precise heterostructures [START_REF] Eason | Pulsed Laser Deposition[END_REF]. Simultaneously, the discovery of high temperature superconductivity in cuprates (copper oxides) [START_REF] Bednorz | Possible high T c superconductivity in the Ba-La-Cu-O system[END_REF] proved that this technique and family of materials had immense potential for future applications.

From a spintronics perspective, spin-based information has been (to this point) recorded by the magnetization direction in a ferromagnetic metal -typically a transition metal alloy based on Co, Fe, and/or Ni -and manipulated by externally applied magnetic fields. This approach led to the first generation of nonvolatile magnetic random-access memories (MRAM), commercialized in 2006. However, their design and very large power consumption prevented higher storage densities. A first technological breakthrough towards denser memories came with the discovery of spin-transfer torque, a mechanism by which a spin-polarized current running through a ferromagnet can switch its magnetization. While this allowed the development of simpler and more compact/efficient designs, the writing energies still remained one to two orders of magnitude above desirable values.

Even though the combination of complex oxides and spintronics is relatively new, several results already confirmed its potential. First, we have multiferroics, a class of materials that became rather appealing for spintronics due to their two (or more) ferroic order parameters (often ferroelectric and magnetic) that can be coupled, providing a route to control magnetism electrically [START_REF] Fusil | Magnetoelectric Devices for Spintronics[END_REF]. Importantly, multiferroics (such as BiFeO 3 ) are insulators, meaning that they are not controlled through the application of electrical currents, but by electric fields, allowing much lower power consumption together with nonvolatility. Second, materials such as SrTiO 3 are starting to be used to convert charge currents in spin currents in very efficient ways, opening new doors for spintronic devices that operate without external magnetic fields [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

Purpose of this thesis and future applications

For the last 50 years, the semiconductor industry has relied on Gordon Moore's prediction that the number of components per integrated circuit doubles every two years [START_REF] Moore | Understanding Moore's Law: Four Decades of Innovation[END_REF]. The trend was mainly possible due to the steady reduction in transistor size and cost (largely as a result of breakthroughs in materials and lithography processes), as well as increasing complexity of computer architectures. Yet, with CMOS technology reaching characteristic sizes of 7 nm, electron tunneling effects start to interfere with the regular functionality of transistors. On top of that, the last 15 years saw a deviation from Dennard's scaling, which states that as transistors get smaller, the power density stays roughly the same [START_REF] Dennard | Design of ionimplanted MOSFET's with very small physical dimensions[END_REF].

In the near future, new technologies beyond-CMOS are required to sustain the increasingly higher demands imposed by the consumer electronics industry. Among the wide range of proposed options, spintronics is considered a leading candidate, backed by recent proposals from Intel for spin-and polarization-based computation [START_REF] Manipatruni | Beyond CMOS computing with spin and polarization[END_REF]. The proposed device consist of two main components: a multiferroic junction, that electrically controls the magnetization of a ferromagnet, and a high spin-orbit coupled interface that efficiently converts spin current in charge currents. Although this type of device will allow the creation of ultra-fast and lowpower logic gates (in the attojoule range), research efforts are still required to perfect both of these components.

In this thesis, we investigate the nature of the 2D electron gas formed in SrTiO 3 , as well as its use for spin-to-charge current conversion. First, we find that, while high temperature pulsed laser deposition is normally required for the creation of these electron gases (for example in the seminal LaAlO 3 /SrTiO 3 interface [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF]), a similar result can be obtained by room temperature deposition of a few nanometers of a reactive metal directly on SrTiO 3 [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF][START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. By studying in detail the mechanisms involved, we provide a simple blueprint and a scalable way of attaining this remarkable 2D system. Second, by carefully engineering these metal/SrTiO 3 structures, we find record values for the spin-to-charge current conversion efficiency, making this system highly desirable for future spin-based electronic devices.

Organization of this thesis

This thesis is composed by four chapters. In the first, we start by introducing basic concepts in spintronics, such as the electron spin, a definition of spin current, and how spins behave in real materials. Then, we review the main consequences of the relation between charge and spin currents in different materials, and how a charge current can be converted in a spin current (and vice-versa). In particular scenarios, the physics of the interconversion follows special symmetry considerations in the framework of the Dressllehaus and Rashba effects, which in turn explain the spin-to-charge current interconversion in 2D electron gases through the direct and inverse Edelstein effect.

In the second chapter, we introduce the main material used throughout this thesis: strontium titanate (SrTiO 3 ). After reviewing its main features, we explore the remarkable 2D elec-tron gas found in the LaAlO 3 /SrTiO 3 system. We discuss in detail the origin of the interfacial conductivity that arises between these two insulators, the critical thickness for conduction of 4 unit cells of LaAlO 3 , and the main mechanisms that lead to the 2D electron gas formation (polar catastrophe, cation interdiffusion, surface reactions and polarity-induced defects).

Then, we thoroughly describe the experimental procedure to obtain such heterostructures, including a comprehensive guide on the surface treatment of SrTiO 3 single crystals, the pulsed laser deposition growth of ultra-thin LaAlO 3 films and magnetron sputtering. In addition, we elaborate on the two main techniques used to evaluate the interfacial properties, X-ray photoelectron spectroscopy and magnetotransport, while showing some results for LaAlO 3 /SrTiO 3 samples. Lastly, we show how a thin deposition of a metallic layer on top of LaAlO 3 /SrTiO 3 can drastically change the interfacial properties, by reducing (if the metal is reactive) or increasing (for noble metals) the critical thickness for conduction. We end this chapter by giving a blueprint that describes how a 2D electron gas can be created in other oxide systems.

In the third chapter we investigate spin-to-charge conversion phenomena. We start by giving an overview on experimental observations of Rashba 2D electron gases, as well as spinto-charge current conversion through the inverse Edelstein effect in semiconductor quantum wells, topological insulators and oxide-based systems. Then, we thoroughly introduce spin pumping, a technique used to generate pure spin currents. Results for spin-to-charge current conversion in the LaAlO 3 /SrTiO 3 and metal-capped SrTiO 3 systems are shown, accompanied by an interpretation of the large and tunable conversion efficiency. For the metal-capped SrTiO 3 case, angle-resolved photoemission spectroscopy and notions of electronic band mixing and topology are introduced to describe the extremely large efficiency.

In the last chapter, we show additional experiments performed on the LaAlO 3 /SrTiO 3 system regarding anisotropic and unidirectional magnetoresistance, while reviewing the scarce bibliography on these effects in 2D electron gases. After that, we introduce a recently discovered effect, the unidirectional spin Hall magnetoresistance, and develop a simple conceptual model for an analogous effect in 2D electron gases: the unidirectional Edesltein magnetoresistance. This effect is based on the expected strong charge-to-spin conversion in 2D electrons gas, and the interaction of the generated spin currents with an adjacent ferromagnet. We finish by very briefly showing preliminary experiments in NiFe/LaAlO 3 /SrTiO 3 heterostructures.

Resumé

Ce travail présente l'étude de la conversion courant de spin en courant de charge dans les gaz d'électrons bidimensionnels à base de SrTiO 3 . Nous commençons par une présentation des concepts de base de la spintronique : le spin, une définition du courant de spin et le comportement des spins dans des matériaux, les principales conséquences de la relation entre les courants de charge et de spin dans différents matériaux, et comment un courant de charge peut être converti en un courant de spin (et vice versa). Dans des scénarios spécifiques, la physique de l'interconversion suit des considérations de symétrie particulières dans le cadre des effets de Dressllehaus et de Rashba, qui expliquent l'interconversion du courant de charge/spin dans les gaz d'électrons 2D via l'effet direct et inverse d'Edelstein. Dans le deuxième chapitre, nous présentons le principal matériau utilisé dans cette thèse: le titanate de strontium (SrTiO 3 ). Après avoir analysé ses principales caractéristiques, nous explorons le gaz d'électrons 2D présent dans le système LaAlO 3 /SrTiO 3 . Nous discutons en détail de l'origine de la conductivité interfaciale entre ces deux isolateurs, l'épaisseur critique de conduction de 4 mailles de LaAlO 3 et des principaux mécanismes conduisant à la formation du gaz électronique 2D (catastrophe polaire, interdiffusion de cation, réactions à la surface et défauts induits par la polarité). Ensuite, nous décrivons en détail la procédure expérimentale pour obtenir des hétérostructures de LaAlO 3 /SrTiO 3 : le traitement de surface des monocristaux de SrTiO 3 , la croissance par ablation laser pulsé de films ultra-minces de LaAlO 3 , et la pulvérisation cathodique. Nous introduisons les deux techniques principales utilisées pour évaluer les propriétés interfaciales, la spectroscopie photoélectronique de rayons X (XPS) et le magnétotransport, avec quelques résultats pour les échantillons de LaAlO 3 /SrTiO 3 . Enfin, nous montrons comment un mince dépôt d'une couche métallique sur LaAlO 3 /SrTiO 3 peut modifier radicalement les propriétés interfaciales en réduisant (si le métal est réactif et possède un travail de sortie inférieur à une valeur critique) ou en augmentant (pour les métaux nobles) l'épaisseur critique de la conduction interfacial. Pour conclure ce chapitre, ous proposons un modèle qui décrit comment un gaz d'électrons 2D peut être créé dans d'autres systèmes à base d'oxydes complexes. Dans le troisième chapitre, nous étudions les phénomènes de conversion spin/charge. Nous commençons par un état de l'art de la littérature concernant des observations expérimentales des gaz d'électrons Rashba 2D, ainsi que de la conversion du courant spin-à-charge par l'effet Edelstein inverse dans les puit de potentiel à base de semi-conducteurs, les isolants topologiques et les systèmes à base d'oxydes. Ensuite, nous introduisons le pompage de spin, une technique utilisée pour générer des courants de spin purs.

Les résultats de la conversion du courant spin-à-charge dans les systèmes LaAlO 3 /SrTiO 3 et metal/SrTiO 3 sont présentés, accompagnés d'une interprétation de la géante et ajustable con-version spin/charge. Dans le cas d'échantillons composés par metal/SrTiO 3 , la spectroscopie photoélectronique résolue en angle (ARPES) et les notions de mélange de bande électronique et de topologie sont introduites pour justifier la conversion charge/spin extrêmement élevé.

Dans le dernier chapitre, nous montrons des expériences supplémentaires réalisées sur le système LaAlO 3 /SrTiO 3 en ce qui concerne la magnétorésistance anisotrope et unidirectionnelle.

Après, nous introduisons un effet récemment découvert, la magnétorésistance de spin Hall unidirectionnel, et développons un modèle conceptuel pour un effet analogue dans les gaz électroniques 2D: la magnétorésistance de Edesltein unidirectionnelle. Cet effet est basé sur la forte conversion charge/spin dans le gaz d'électrons 2D et sur l'interaction des courants de spin générés, avec une couche ferromagnétique adjacent. Nous finissons par montrer les expériences préliminaires sur les hétérostructures NiFe/LaAlO 3 /SrTiO 3 .

| An introduction to spin-to-charge current interconversion

The electron spin

Let us consider an electron revolving around a nucleus. Information regarding the motion of the electron can be acquired through its total angular momentum J , composed of the orbital angular momentum L, that describes the circular motion around the nucleus, and the intrinsic angular momentum S, called spin, that describes the rotation of the electron about his own axis. Unlike the orbital part, which is analogous to the classical notion of angular momentum1 , the intrinsic part is a purely quantum mechanical entity, as inferred by the Stern-Gerlach experiment2 [START_REF] Gerlach | Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld[END_REF]. Due to its quantum mechanical nature, the spin will have a quantized discrete value that needs to be given as a projection along some axis. For convenience, this is usually the z-axis. This means that we are able to represent the spin as the projection S z = m s , where is the reduced Planck constant and m s is the spin quantum number. For an electron, as it follows the Fermi-Dirac statistics (fermion), m s can take one of two discrete values, + 1 2 or -1 2 , usually called "spin-up" and "spin-down". As a fermion, the electron also obeys the Pauli exclusion principle, that states that if two electrons have the exact same quantum numbers n, l and m l , then m s must be different. The spin angular momentum can therefore be generally described as [START_REF] Feynman | The New Millennium Edition: Quantum Mechanics[END_REF]:

S = 2 σ, (1.1)
where σ are the Pauli spin matrices

σ x = 0 1 1 0 , σ y = 0 -i i 0 , σ z = 1 0 0 -1 (1.2)
Due to the difficulty of picturing the electron spin in normal 3D space, these matrices become an especially important tool to manipulate operators and wavefunctions without necessarily knowing what they look like in real space.

From classical electrodynamics, a charged body, such as an electron, rotating about an axis with orbital angular momentum L generates a tiny magnetic moment given by:

µ o = - e 2m e L, (1.3)
where e is the electron charge and m e the electron mass. Even though Eq. (1.3) is true for classical orbital motion, the spin angular momentum S described above also corresponds to a magnetic moment for the electron, so that the spin magnetic moment takes the form of:

µ s = -g e 2m e S = -γS, (1.4)
where γ is the gyromagnetic ratio and g is the dimensionless g-factor that quantum mechanically corrects the classical result of Eq. (1.3), having an expected value of approximately 2 for an electron. Note also, that the magnetic moment of an electron, with orbital angular momentum , can be given as µ B = |e| 2me , known as the Bohr magneton. With this very basic understanding, we can think that, since an electron carries information on both its charge and spin, a flow of charge may result in a flow of spin (under certain conditions). At this point, the concept of spin current starts to gain some meaning.

Understanding charge and spin currents

Theorists have struggled for the last decades with a definition of spin currents. Even though several detailed formulations have been proposed [START_REF] Shi | Proper Definition of Spin Current in Spin-Orbit Coupled Systems[END_REF][START_REF] Vernes | Spin currents, spin-transfer torque, and spin-Hall effects in relativistic quantum mechanics[END_REF][START_REF] An | The universal definition of spin current[END_REF][START_REF] Saitoh | Spin current[END_REF], we will follow the conceptual approach based on a two spin-channel model, further explained in [START_REF] Fabian | The standard model of spin injection[END_REF][START_REF] Rüffer | Non-local Phenomena in Metallic Nanostructures[END_REF][START_REF] Czeschka | Spin Currents in Metallic Nanostructures[END_REF].

We can start by thinking of a charge current as the flow of electrical charged carriers, such as electrons. Since these electrons can either be spin-up or spin-down, the two separate flows, or charge current densities, can be defined as j ↑ = -en ↑ v ↑ and j ↓ = -en ↓ v ↓ , where n σ and v σ represent the carrier densities and velocities for spin σ (up or down) electrons. The total charge current density in a system can therefore be simply put as:

j c = j ↑ + j ↓ = -e(n ↑ v ↑ + n ↓ v ↓ ) (1.5)
If the charge current density is considered as a flow of charge (-e) then the spin current density should be expressed as a flow of spin angular momentum ( /2) so that:

j s = 2 (n ↑ v ↑ -n ↓ v ↓ ) = - 2e (j ↑ -j ↓ ) (1.6)
Notice that if the current density of both spin states j ↑ and j ↓ is equal, then Eq. (1.6) gives j s = 0. This corresponds to charge transport without spin transport, usually called a charge current Adapted from [START_REF] Rüffer | Non-local Phenomena in Metallic Nanostructures[END_REF].

pure charge current. This situation, illustrated in Fig. 1.1a, is usually seen in a conventional paramagnetic conductor. We will see ahead that this might change if spin-orbit coupling is strong. In ferromagnets (FM) however, one current density is larger than the other (j ↑(↓) > j ↓(↑) ), so that the total current density will carry information on both charge and spin. In these cases, an energy splitting is present between the "majority spin" and "minority spin", so that the electrons at the Fermi level (carrying the electrical current) exhibit different conduction properties for opposite spin directions. This is called a spin-polarized current and it generally occurs in FM where an unbalance of spin-up and spin-down is present, as seen in Fig. 1.1b.

In very special cases, a flow of spin angular momentum without any associated net charge transport can be created, so that j ↑ = -j ↓ . This is called a pure spin current (see Fig. 1.1c) and it is achieved with dedicated techniques such as spin pumping.

The whole idea of parallel charge current was first introduced by Mott in 1936, when he formulated that the electrical conductivity in ferromagnetic metals and alloys below the Curie temperature depended on the magnetization state, i.e. the inequivalence of spin up and down populations at the Fermi level [START_REF] Mott | The Electrical Conductivity of Transition Metals[END_REF], as sketched in Fig. 1.2a. Three decades later, Mott's proposition was experimentally confirmed by Fert and Campbell for Ni-and Fe-based alloys, where the ratio between the resistivities of spin-up and spin-down channels was largely increased (up to 20%) by the insertion of impurities with strongly spin-dependent scattering cross-section [START_REF] Campbell | Evidence for two current conduction iron[END_REF][START_REF] Fert | Two-Current Conduction in Nickel[END_REF][START_REF] Campbell | The spontaneous resistivity anisotropy in Ni-based alloys[END_REF][START_REF] Fert | Electrical resistivity of ferromagnetic nickel and iron based alloys[END_REF], meaning that electrical transport in FM was indeed driven by inequivalent spin populations. Solving a system of coupled Boltzmann equations, they created

E F n ↑ (E) n ↓ (E) I ↑ I ↓ ρ ↑ ρ ↓ ρ ↑↓ E (a) (b) Figure 1.2.
Basic concepts of spintronics. (a) Schematic band structure of a ferromagnetic metal, with a dark grey region for majority spin-up carriers and light grey region for minority spin-down carriers. (b) Schematic for a spin-dependent conduction model with spin-up ρ ↑ and spin-down ρ ↓ channels (and respective currents I ↑ and I ↓ ). The spin-mixing term ρ ↑↓ accounts for spin flipping events mainly due to electron-magnon scattering. Adapted from [START_REF] Fert | Historical Overview: From Electron Transport in Magnetic Materials to Spintronics[END_REF].

a model that takes into account spin-up and spin-down currents, as well as a spin mixing term ρ ↑↓ that couples both of them:

ρ = ρ ↑ ρ ↓ + ρ ↑↓ (ρ ↑ + ρ ↓ ) ρ ↑ + ρ ↓ + 4ρ ↑↓ (1.7)
As depicted in the parallel current model of Fig. 1.2b, the spin mixing term ρ ↑↓ represents the exchange of current between the spin-up and spin-down channels, mainly coming from electron-magnon scattering (not to be confused with spin relaxation to the lattice for example). The importance of this term is especially prominent with increasing temperature, where its increase tends to equalize both currents, as seen in most ferromagnetic metals at room temperature. Well below the Curie temperature, spin-flip scattering by magnons freezes out (ρ ↑↓ → 0) so that Eq. (1.7) reduces to 1 ρ = 1 ρ ↑ + 1 ρ ↓ , the parallel model (for two independent spin channels) initially suggested by Mott [START_REF] Mott | The Electrical Conductivity of Transition Metals[END_REF].

Spin-orbit coupling

So far, we have considered the spin as a mere relativistic property of an electron. However, to gain actual control of spin populations in solids we should give the spin an absolute orientation in space, connecting it with the environment where the electron resides. This link is given by the spin-orbit coupling (or spin-orbit interaction) term, and it describes the interaction of the electron spin with its motion inside a potential.

In a classical picture, we can start by imagining an electron orbiting with velocity v around a nucleus. In the rest frame of the nucleus, there is no magnetic field acting on the electron itself. Yet, from the point of view of the electron, the positive charged nucleus appears to be orbiting around it, generating a positive current that translates in an electric field E. Under this electric field, the electron will therefore feel a magnetic (induction-like) field B that will interact with the electron spin magnetic moment µ s , as illustrated in Fig. 1.3a. Its energy will depend on how µ s is oriented relatively to this induction-like field, ultimately explaining the indirect connection between spin S and orbital L angular momentum under the presence of a charged nucleus. As an example, we can see in Fig. 1.3b and 1.3c that for two electrons rotating around the nucleus in the same direction but with opposite spins, the orbital and intrisic momentum can interact either constructively or destructively.

The spin-orbit coupling (SOC) can be more accurately derived from the Dirac equation as a relativistic effect. To account for this coupling, an extra term needs to be added to the Hamiltonian:

H soc = e 4m 2 e c 2 E • (k × σ) = ξL • S, (1.8)
where a spin-orbit coupling constant is given by ξ = (e/2m 2 e c 2 )(1/r)(dV (r)/dr) (r the distance measured from the nucleus), the static electric field in spherical symmetry that the electron feels as E = -∇V (r) = -(r/r)(dV (r)/dr), the orbital angular momentum L = r × k and the spin angular momentum S = ( /2)σ from Eq. (1.1). A fundamental example of this interaction is the fine structure of the hydrogen atom, where an energy splitting is experimentally observed for otherwise degenerate spectral lines [START_REF] Feynman | The New Millennium Edition: Quantum Mechanics[END_REF].

Realistically, even though one must account for the interaction of the electron spin with the electric field generated by all the other electrons and the nucleus, the dominant contributions in Eq. (1.8) come from the strong nuclear electric field, with a stronger effect for electrons in positions r close to the nucleus.

From this, the spin-orbit coupling constant ξ introduced above gives (1/r)(dV (r)/dr) ∼ -Z|e|/r3 , with Z the atomic number. To better visualize this relation, we take the example given by Yafet [START_REF] Yafet | Factors and Spin-Lattice Relaxation of Conduction Electrons[END_REF], for spin-orbit splitting of 3p states of atoms with 11 Z 19. As we start filling the outer shell (increasing Z) the atomic radius shrinks, so that inner p states come closer to the nucleus (decreasing r). In a rather rapid way, both of these contributions will increase the spin-orbit coupling magnitude. This is why, in general, even though spin-orbit interactions are almost negligible for lighter atoms, they become rapidly stronger for heavier atoms 3 . Lastly, given that Eq. (1.8) depends on the orbital angular momentum, s-electrons (having L = 0) will not be affected by spin-orbit coupling. Therefore, this interaction becomes the largest for p-electrons, due to their proximity to the nucleus, and increasingly smaller for d and f orbitals4 .

Spin relaxation and spin dephasing phenomena

In the absence of an external magnetic field, a spin population of a paramagnetic material represents a non-equilibrium state, which tends to relax and become depolarized after a characteristic spin relaxation time. As we saw in Section 1.2, controlling spin currents also involves knowing how far a spin population can propagate until it gets depolarized, a distance called spin relaxation length. Since relatively long spin relaxation times are observed in metals and semiconductors (in the order of nanoseconds), the development of spintronic devices, where spin-encoded information can propagate for modest distances, will revolve around the understading of spin relaxation and dephasing phenomena.

General aspects

The disappearance of an initial non-equilibrium spin polarization can be generally understood as a result of random fluctuating magnetic fields that act on an electron due to spin-orbit coupling 5 . Under this randomly orientated effective magnetic field, the electron spin starts a precessional motion with a Larmor frequency ω 0 during some correlation time τ c . After this period, the direction and magnitude of this field will once again change, leading to precession around the new effective field. After several iterations, the initial spin direction is completely lost.

Phenomenologically, spin relaxation and spin dephasing can be described in the framework of the Bloch-Torrey equations for magnetization dynamics. Following the approach of Fabian and Wu [START_REF] Fabian | Spin Relaxation and Spin Dynamics in Semiconductors[END_REF], the spin dynamics under an external magnetic field B(t) = B 0 u z + B ⊥ (t), with B 0 the static longitudinal component oriented along the z-axis and B ⊥ (t) the time-dependent oscillating component transverse to u z , can be described as:

∂S x ∂t = -ω 0 S y - S x τ 2 , (1.9a
)

∂S y ∂t = -ω 0 S x - S y τ 2 , (1.9b)
∂S z ∂t = S z -S 0 z τ 1 , (1.9c)
where S 0 z is the thermal equilibrium value of the spin in the presence of the static magnetic field B 0 (see Fig. 1.4a). Two characteristic times appear in the equations above: the spin relaxation time τ 1 (also called spin-lattice time), associated with the time it takes for the longitudinal magnetization to reach equilibrium, and the spin dephasing time τ 2 (also called decoherence time), describing how long it takes for an ensemble of transverse electron spins (xand y-axis) to lose their phase while precessing about B 0 . Physically, 1/τ 1 represents the rate at which the spin population reaches thermal equilibrium with the lattice. This process takes place through energy transfer, usually by phonons, from the spin system to the lattice. On the other hand, the loss of phase during time τ 2 occurs due to spatial and temporal fluctuations of the precessing frequencies.

At this point, depending on the strength of the magnetic field, two limiting cases can be considered. In the first, for a weak magnetic field where the inequality ω 0 τ c 1 is satisfied, the spin vector will precess "slowly" around B 0 . For isotropic systems 6 , the model that lead to Eqs. (1.9) predicts in these conditions,

1 τ 1 = 1 τ 2 = ω 2 0 τ c , (1.10)
which culminates in no difference between spin relaxation and dephasing. This leads to τ 1 = τ 2 = τ sf , where τ sf can be defined interchangeably as a unique characteristic time known as spin relaxation time, spin-flip time or spin lifetime. Note that the derivation of Eq. (1.10) for the spin in a fluctuating magnetic field can also be used in a semiquantitative way for the conduction electron spins, since it provides a good estimation on the orders of magnitude of the effects and some useful trends [START_REF] Fabian | Spin Relaxation and Spin Dynamics in Semiconductors[END_REF][START_REF] Žutić | Spintronics: Fundamentals and applications[END_REF].

The second case happens for higher magnetic fields, where ω 0 τ c 1. Here, during the correlation time τ c the spin is able to rotate several times around the magnetic field. During this time, the spin projection transverse to the random magnetic field is (on average) completely destroyed, while the projection along the direction of the field is conserved. Ultimately, the overall result in this regime is τ sf ∼ τ c .

All the considerations made in this section form a rather general picture of spin relaxation and spin dephasing. In fact, if we try to condense all spin relaxation phenomena into a few parameters, we can quickly realize that the underlying physics can vary with material, temperature, etc. In the following section, we focus solely on the effects arising from spin-orbit coupling and the different mechanisms that can generate the fluctuating magnetic fields above mentioned.

Elliott-Yafet mechanism

When an electron gets scattered, the electric field of the charged scatterer is transformed in an effective magnetic field through spin-orbit interaction. This means that momentum relaxation should be accompanied by spin relaxation. Elliot realized that the electron spin can get randomized through momentum scattering processes, typically by phonons at high temperatures and impurities and low temperatures [START_REF] Elliott | Theory of the Effect of Spin-Orbit Coupling on Magnetic Resonance in Some Semiconductors[END_REF]. In the presence of spin-orbit coupling in the form of Eq. (1.8), electron wavefunctions are no longer an eigenstate of σ z , but rather a mixture of spin-up and spin-down states that changes at every scattering event. As depicted in Fig. 1.4b, this means that the spin-state is conserved inbetween collisions, but has a probability of flipping when a scattering event occurs, leading to a change in momentum k. The Elliott relation reads [START_REF] Elliott | Theory of the Effect of Spin-Orbit Coupling on Magnetic Resonance in Some Semiconductors[END_REF]:

1 τ 1 = ξ BM (∆g e ) 2 τ p , (1.11)
where ξ BM is a numerical coefficient later introduced by Beuneu and Monod related to the scattering mechanism [START_REF] Beuneu | The Elliott relation in pure metals[END_REF], ∆g e is the deviation of the g-factor from the free-electron value and τ p is the momentum relaxation time.

Later, Yafet extended Elliott's model to treat the important contribution of electronphonon spin-flip scattering [START_REF] Yafet | Factors and Spin-Lattice Relaxation of Conduction Electrons[END_REF]. The Yafet relation qualitatively connects the temperature dependence of the spin relaxation rate with the resistivity ρ, so that:

1 τ 1 (T ) ∼ ρ(T ) (1.12)
Taking into account the change in spin-orbit coupling strength due to lattice distortion by phonons, Yafet showed that the spin relaxation time follows τ 1 (T ) ∼ T -5 at low temperatures, just like for the resistivity of several metals, a result that was later experimentally observed by Monod and Beuneu [START_REF] Monod | Conduction-electron spin flip by phonons in metals: Analysis of experimental data[END_REF].

When evaluating the spin relaxation times, it is of the upmost importance to consider both Elliott and Yafet's processes, especially at low temperatures where they can have similar magnitudes and interfere destructively. As an example, the Yafet relation alone can be found invalid for silicon, where τ 1 (T ) ∼ T -3 [START_REF] Cheng | Theory of the Spin Relaxation of Conduction Electrons in Silicon[END_REF].

The Elliott-Yafet mechanism dominates spin relaxation of conducting electrons in centrosymmetric conductors with space inversion symmetry. However, in systems lacking this symmetry it competes with the D'yakonov Perel' mechanism. The dominance of one over the other may depend on several variables such as symmetry, type of material, temperature or doping.

D'yakonov-Perel' mechanism

In systems lacking space inversion symmetry7 , a mechanism of spin relaxation due to spinorbit coupling was derived by D'yakonov and Perel' [START_REF] Perel | Spin relaxation of conduction electrons in noncentrosymetric semiconductors[END_REF]. Without inversion symmetry the momentum states of the spin-up and spin-down electrons are not degenerate, E k,↑ = E k,↓ , while the Kramer degeneracy due to time reversal symmetry is preserved,

E k,↑ = E -k,↓ .
The spin splitting introduced by this inversion asymmetry manifests itself as a k-dependent magnetic field B SO (k) around which the electron spin precesses with a Larmor frequency Ω(k) = (eg e /2m e )B SO (k). B SO (k) can also be addressed as the intrinsic spin-orbit field, as it arises from the effect of spin-orbit coupling on the band structure. The momentum B 0 , 0 B ¡ (t), (t) After each scattering event, a new Ω k is defined, so that the spin changes not during, but between collisions. Ultimately, this mechanism results in spin dephasing. (d) Emphasized spin precession changes due to momentum scattering from k to k within the DP mechanism. The large circle represents the momentum position of a carrier (at constant energy) in a two-dimensional electron gas. Panels (a-c) adapted from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF] and panel (d) adapted from [START_REF] Mavropoulos | Spin relaxation in nonmagnetic metals and semiconductors[END_REF].

dependent Hamiltonian term describing the precession of the electron spin is:

H SO = 2 (Ω(k) • σ) (1.13)
The action of B SO (k) can be viewed from the point of view of individual electrons in fluctuating magnetic fields, whose magnitude and direction will change randomly with each scattering event. For a given k, the electron spin will precess with a frequency Ω(k) around B SO (k), until after an average time τ c it gets scattered to k , starting to rotate with different frequency Ω(k ). A representation of this mechanism is depicted in Figs. [START_REF] Bibes | Oxide Spintronics[END_REF].4c and 1.4d. In the limit where τ p Ω ≤ 1, i.e. slow spin precession8 , D'yakonov and Perel' derived the following expression:

1 τ DP s = Ω 2 τ p , (1.14)
where Ω is the average magnitude of the Larmor frequency Ω(k). Here, the spin phase will go through a random walk during a time interval set by the momentum relaxation time τ p , which plays the same role as the correlation time τ p .

In contrast with the Elliott-Yafet mechanism, the spin now rotates not during but between collisions. In this case, the momentum-dependent spin precession described by Eq. (1. [START_REF] Heisenberg | Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[END_REF] together with momentum relaxation time τ p leads to spin dephasing. Counter-intuitively, one realizes that the spin relaxation time τ DP s increases with smaller momentum relaxation times τ p , i.e. slower spin dephasing with increasing scatterer concentration. Fast and random changes of B SO (k) tend to cancel each other out, so that there is not enough time for the spin to precess in any particular direction.

Prominent examples of materials (lacking inversion symmetry) where the above mechanism is relevant are bulk III-V (such as GaAs) and II-VI (ZnSe) semiconductors, as well as 2D

systems where an interface or surface is responsible for breaking inversion symmetry.

Consequences of spin and charge current coupling

As we saw in Section 1.2, an electrical current can carry information regarding both charge and spin degrees of freedom, making these two quantities go hand in hand when evaluating electrical transport. In the presence of spin-orbit interactions, the motion of the electrons gets coupled to their spin, so that a flow of charge current can produce a spin current (and viceversa). This effect is reminiscent of the Magnus effect [START_REF] Johnson | The Magnus Effect-Early investigations and a question of priority[END_REF], where a moving spinning object drags air faster around one side, making its trajectory deviate from the expected straight motion. In a similar fashion, electrons flowing in a conductor with opposite spins will tend to accumulate on opposite sides of a sample, generating a local imbalance of spin populations.

This phenomenon leads to two of the most relevant effects in the field of spintronics, as they unlock the possibility to create and control spin currents: the anomalous Hall effect (AHE)

and the spin Hall effect (SHE).

Anomalous Hall effect

In 1879, Hall discovered that when an out-of-plane magnetic field B z is applied to a conducting material, charged particles in motion will experience a Lorentz force and get deflected [START_REF] Hall | On a New Action of the Magnet on Electric Currents[END_REF],

following the relation F = -e(E + v × B z ), where v is the velocity of the carriers and E is the electric field driving the current.

The Hall effect provided an extremely simple way to measure the carrier concentration n s and mobilities µ s in conductors, by simply probing the transverse (Hall) voltage V H while applying a current I (see Fig. 1.5a):

n s = B z I V H q = B z R xy q = 1 R H q , (1.15a
)

µ s = 1 qR s n s , (1.15b)
where R xy , R H and R s are the transverse resistance, Hall coefficient 9 and sheet longitudinal resistance, respectively.

Later in 1881, Hall also reported that the same effect was ten times larger in ferromagnetic materials than in nonmagnetic conductors [START_REF] Hall | On the "Rotational Coefficient" in nickel and cobalt[END_REF], an effect later known as anomalous Hall effect (AHE). While in nonmagnetic conductors the Hall resistance increased linearly with the applied magnetic field, as exemplified for a Au film in Fig. 1.5b, in ferromagnets the Hall resistance increases abruptly under weak magnetic field, returning to the expected Hall effect behaviour at a given saturation field (see this effect for a Co film in Fig. 1.5d). Kundt observed that the value of this field in Fe, Co, and Ni, was proportional to their magnetization M z [START_REF] Kundt | On the Hall effect in ferromagnetic materials[END_REF].

A few years later, Pugh and Lippert derived an empirical relation between ρ xy , B z and M z [START_REF] Pugh | Hall Effect and the Magnetic Properties of Some Ferromagnetic Materials[END_REF][START_REF] Pugh | and Intensity of Magnetization[END_REF]:

ρ xy = R 0 B z + R A M z (1.16)
The first term represents the well established Hall effect from Eq. (1.15), while the second the anomalous Hall effect contribution due to the spontaneous magnetization, with R A the anomalous Hall coefficient. Interestingly, a finite transverse resistivity can be detected without an external magnetic field, due to the overall spin imbalence present (see sketch in Fig. 1.5c).

Even though the basic features of this effect were theoretically captured early on, a great amount of contradictory theories and results emerged in the following years. Thanks to extensive theoretical and experimental efforts, the AHE is now believed to arise from intrinsic 9 Note that the Hall coefficient RH is the slope usually extracted from experimental Rxy vs. Bz curves. Berry-phase mechanisms (first hinted as an anomalous velocity that could contribute to the

Hall effect [START_REF] Karplus | Effect in Ferromagnetics[END_REF] and much later through notions of topology and geometry [START_REF] Berry | Quantal Phase Factors Accompanying Adiabatic Changes[END_REF]) and extrinsic mechanisms due to disorder, that will be introduced in the next section. For a complete review on the topic, we redirect the interested reader to the work of Nagaosa et al. [START_REF] Nagaosa | Anomalous Hall effect[END_REF].

Spin Hall effect and inverse spin Hall effect

The spin Hall effect (SHE) manifests itself as the conversion of an electrical current passing through a nonmagnetic material with spin-orbit coupling, into a transverse pure spin current, polarized perpendicular to the plane, as sketched in Fig. 1.6a. Reciprocally, the inverse spin Hall effect (ISHE) is characterized by the conversion of an injected spin current in a transverse charge current (Fig. 1.6b). The physics and mechanisms of the SHE are directly extracted from the ones of the AHE, with the main difference being the type of material where it occurs, since the AHE occurs exclusively in magnetic materials while the SHE can occur in magnetic and non-magnetic materials, as well as the method of detection.

D'yakonov and Perel' were the first to theoretically predict the SHE [START_REF] Perel | Possibility of Orienting Electron Spins with Current[END_REF], following the fact that a spin-dependent asymmetric deflection is observed in electron beams due to Mott scattering [START_REF] Mott | The Scattering of Fast Electrons by Atomic Nuclei[END_REF][START_REF] Mott | The Polarisation of Electrons by Double Scattering[END_REF][START_REF] Shull | Electron Polarization[END_REF] and that this type of scattering was believed to be one of the origins of the AHE [START_REF] Nagaosa | Anomalous Hall effect[END_REF]. Both approaches lead to the assumption that spin-dependent electron deflection should occur when an electrical current is injected in a nonmagnet (NM) with spin-orbit coupling. While at first this concept attracted minumum attention, its rediscovery by Hirsh [START_REF] Hirsch | Spin Hall Effect[END_REF] and Zhang [START_REF] Zhang | Spin Hall Effect in the Presence of Spin Diffusion[END_REF] a couple of decades later came with perfect timing, considering that the field of spintronics was starting to grow.

Theories to explain the SHE were naturally borrowed from the apparently similar AHE.

However, a major difference hindered its early development: in FM, the spin-up and spindown populations are not equal, meaning that if spin-dependent deflection occurs, the number of charges that gets deflected to opposite directions is also different. One is therefore able to measure a transverse current, that was generated due to spin-orbit effects. However, in nonmagnets, where the SHE occurs, there is no spin population imbalance, so that even if carriers with different spin get deflected in opposite direction, no transverse electrical signal can be detected. Early on, this spin accumulation without a charge imbalance, imposed a measurement challenge, with the initial successful attempts recurring to optical tools [START_REF] Kato | Observation of the Spin Hall Effect in Semiconductors[END_REF][START_REF] Wunderlich | Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System[END_REF].

Regarding the ISHE, with techniques already available to produce a spin current, the charge current generated was able to be measured by electrical means [START_REF] Saitoh | Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect[END_REF][START_REF] Valenzuela | Direct electronic measurement of the spin Hall effect[END_REF][START_REF] Zhao | Coherence Control of Hall Charge and Spin Currents[END_REF].

Simply put, the relation between spin and charge current can be described, for both effects, as:

j SHE s = - 2e θ SHE (j c × σ s ), (1.17a) j ISHE c = - 2e θ SHE (j s × σ s ), (1.17b)
where σ s is the spin polarization orientation, and θ SHE is called the spin Hall angle, which defines the current conversion efficiency. From Eq. (1.17) we notice that the SHE and ISHE follow the Onsager reciprocity [START_REF] Jacquod | Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way[END_REF], allowing the extraction of θ SHE from both experiments.

The spin Hall angle can be measured through a multitude of different techniques: ferromagnetic resonance spin pumping, where a pure spin current (generated in a FM) gets converted by the ISHE into a charge current in an adjacent NM [START_REF] Saitoh | Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect[END_REF]; modulation of damping and SHE-induced spin-transfer torques, where the spin current produced through the SHE in a NM diffuses to an adjacent FM and changes its dynamic magnetic properties [START_REF] Ando | Electric Manipulation of Spin Relaxation Using the Spin Hall Effect[END_REF][START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF];

spin Hall magnetoresistance, associated with a SHE-induced spin current that is either absorbed or reflected by a FM depending on the direction of its magnetization [START_REF] Nakayama | Spin Hall Magnetoresistance Induced by a Nonequilibrium Proximity Effect[END_REF]; non-local lateral spin valves devices, used to detect a ISHE-induced non-local voltage due to an injected spin-polarized current [START_REF] Valenzuela | Direct electronic measurement of the spin Hall effect[END_REF]. Since all of these techniques carry specific nuances and inherent particuliarities, a huge discrepancy (sometimes of more than one order of magnitude [START_REF] Sinova | Spin Hall effects[END_REF]) can be observed for the calculated θ SHE in the same material.

Mechanisms for current conversion

Spin-dependent Hall effects, such as the ones described previously, can be described using three distinct contributions: the intrinsic mechanism, skew scattering and side-jump mechanism.

The three effects are schematically described in Fig. 1.7.

The intrinsic mechanism was the first to be evaluated in the context of the AHE [START_REF] Karplus | Effect in Ferromagnetics[END_REF], arising solely as a consequence of a spin-splitted band structure in the presence of spin-orbit coupling.

In this context, an additional term to the carrier velocity is introduced, the anomalous velocity, Illustration of the intrinsic and extrinsic (skew scattering and side-jump) mechanisms that drive charge-to-spin current interconversion phenomena. Adapted from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF].

which relates to the Berry curvature [START_REF] Jungwirth | Anomalous Hall Effect in Ferromagnetic Semiconductors[END_REF]. The Berry curvature manifests itself as an effective magnetic field acting in momentum space, and it becomes non-zero for systems with broken time-reversal symmetry or broken inversion symmetry [START_REF] Haldane | Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property[END_REF]. The intrinsic contribution σ int xy that this mechanism introduces in the total spin Hall conductivity can be accurately evaluated, even for materials with rather complex band structures. In fact, when these predictions were cross-checked with experiments, it was observed that this mechanism dominates in materials (particularly in metals) with strongly spin-orbit-coupled bands, where for example a sign change in σ int xy was correctly predicted for Ta and Pt [START_REF] Tanaka | Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals[END_REF]. Besides the influence of the band structure, spin-orbit effects also arise in the presence of impurities. The skew scattering mechanism is related with spin-dependent features which appear within disorder scattering in the presence of spin-orbit coupling. These features were based on Mott's scattering [START_REF] Mott | The Scattering of Fast Electrons by Atomic Nuclei[END_REF][START_REF] Mott | The Polarisation of Electrons by Double Scattering[END_REF] and were later identified in ferromagnets [START_REF] Smit | The spontaneous hall effect in ferromagnetics I[END_REF][START_REF] Smit | The spontaneous hall effect in ferromagnetics II[END_REF] as well as nonmagnetic materials [START_REF] Perel | Spin relaxation of conduction electrons in noncentrosymetric semiconductors[END_REF][START_REF] Hirsch | Spin Hall Effect[END_REF][START_REF] Zhang | Spin Hall Effect in the Presence of Spin Diffusion[END_REF]. In this mechanism, electrons flowing in a material with spin-orbit coupling, will get deflected asymmetrically depending on their spin orientation, in turn yielding a transverse spin Hall conductivity term σ skew xy . The asymmetry can be explained through the (positive or negative) energy contribution of the spin-orbit Hamiltonian, that depends on the relative orientation of the repulsive impurity potential, the electron moment and spin orientation [START_REF] Rüffer | Non-local Phenomena in Metallic Nanostructures[END_REF]. As demonstrated from ab initio calculations [START_REF] Zimmermann | Skew scattering in dilute ferromagnetic alloys[END_REF], this contribution becomes naturally sensitive to the type of impurity introduced, allowing the enhancement of the spin Hall angle.

Lastly, the side-jump mechanism, initially discarded by Smit [START_REF] Smit | The spontaneous hall effect in ferromagnetics I[END_REF][START_REF] Smit | The spontaneous hall effect in ferromagnetics II[END_REF] and reintroduced in the context of the AHE by Berger [START_REF] Berger | Side-Jump Mechanism for the Hall Effect of Ferromagnets[END_REF], suggests that when a particle is scattered in the presence of spin-orbit coupling, its average trajectory (after scattering) will comprise not only of a deflection with angle θ, but also a spin-dependent lateral displacement, ascribed as an additional extrinsic contribution σ s-j xy to the spin Hall conductivity. Putting it all together, the spin Hall conductivity is given by:

σ H xy = σ int xy + σ skew xy + σ s-j xy (1.18)
The controversy around a clear and global interpretation of the AHE and SHE comes from the weight given to each of these mechanisms, which depends on the type of material, crystalline environment, type of scattering impurity, type of measurement and an overall lack of general theories for both weak and strong spin-orbit coupling regimes. Researchers have been additionnaly working on simplified models where the contribution mentioned above might cancel each other in particular cases [START_REF] Nozières | A simple theory of the anomalous hall effect in semiconductors[END_REF][START_REF] Raimondi | Spin-orbit interaction in a twodimensional electron gas: A SU(2) formulation[END_REF], even though, by comparing to experiments, these exact cancellations do not seem to arise.

Additional information regarding the mechanisms of the SHE, spin Hall angles of several materials, experimental studies and device applications can be found in recent reviews [START_REF] Jungwirth | Spin Hall effect devices[END_REF][START_REF] Hoffmann | Spin Hall Effects in Metals[END_REF][START_REF] Sinova | Spin Hall effects[END_REF].

1.6 Consequences of spin and charge current coupling without inversion symmetry

Symmetry considerations

Intuitively, spin-orbit coupling is expected to lift the degeneracy of spin-up and spin-down bands. However, in many metallic systems, such as alkali and noble metals, as well as in the conduction band of diamond-structure semiconductors like Si and Ge, a single branch of the Fermi surface is observed, indicating degeneracy of both spin subbands. In these systems, time-reversal and space-inversion symmetry are preserved.

Time-reversal is represented with the transformation T : t → -t, indicating that a system is halted and "played" backwards. As represented in Fig. 1.8a, reversing the direction of time is equivalent to reversing the momentum and rotational motion (spin) of a particle, so that k → -k and σ → -σ. In a system with time-reversal symmetry, the Kramers degeneracy theorem states that for particles with half integer spin, like an electron, the energy of these two states is the same:

E k,↑(↓) = E -k,↓(↑) (1.19)
In the presence of a magnetic field, an additional Lorentz-force will act on the particle. As the momentum (and velocity) change sign, so does the Lorentz force, changing the trajectory of the particle upon time reversal. In this situation, time reversal symmetry is broken.

Space-inversion symmetry is present in systems that contain an inversion center as one of its symmetry elements. In a crystal, like the one sketched in Fig. 1.8b, for any atom with coordinates (x,y,z) in the unit cell, there is an indistinguishable atom located in (-x,-y,-z). Systems that display space-inversion symmetry are usually called centrosymmetric and the following equality is observed (for both spin-up and spin-down):

E k,↑(↓) = E -k,↑(↓) (1.20)
In this scenario, the band structure is symmetric around the center of the Brillouin zone (k = 0), so that both spin-up and spin-down bands are degenerate.

In the absence of space-inversion symmetry, only Eq. (1.19) holds, and in the presence of spin-orbit coupling, degeneracy of the bands can be lifted. To better illustrate the relation between spin-orbit coupling and space-inversion asymmetry, we elaborate on four different scenarios:

1. Without spin-orbit coupling and without space-inversion asymmetry: In the simplest case, electrons will not have their momentum coupled with their spin, and they will not feel any electric field gradient, since the crystal is centrosymmetric. An example of this case would be electrical transport in bulk Cu, a material with negligible spin-orbit coupling.

2. With spin-orbit coupling and without space-inversion asymmetry: This is the case discussed in Section 1.5.2, where the extra spin-orbit coupling term in the Hamiltonian [Eq.

(1.8)] unlocks k and σ dependent effects, such as the SHE and the ISHE. An example of this is seen in high spin-orbit materials such as bulk Pt or Ta.

3. Without spin-orbit coupling and with space-inversion asymmetry: The lack of spaceinversion symmetry results in the presence of a non-vanishing electric field. As seen previously, an electron moving in an electric field will also experience a magnetic field that acts on its spin. However, since there is no spin-orbit coupling, there is no connection between k and σ, meaning that the electron will not suffer any change in k due to spin canting or spin flipping. Because of this, the bands will stay degenerate.

4. With spin-orbit coupling and with space-inversion asymmetry: In this particular case, the magnetic field arising indirectly from broken space-inversion symmetry, will act on the electron spin. Due to its coupling with k, the equality from Eq. (1.20) no longer holds, resulting in non-degenerate spin-subbands. The interaction between the spin and this "macroscopic" magnetic field leads to an additional coupling term to the Hamiltonian, known as Dresselhaus and Rashba effects.

Dresselhaus and Rashba effects

The combination of spin-orbit coupling and the absence of space-inversion symmetry results in the splitting of the conduction band in two branches, each with its own spin orientation.

Dresselhaus was the first to realize that this effect occurs in non-centrosymmetric bulk semiconductors of the zinc-blende type [START_REF] Dresselhaus | Spin-Orbit Coupling Effects in Zinc Blende Structures[END_REF], such as GaAs or InSb, where two atoms of the unit cell are inequivalent, generating what is known as bulk inversion asymmetry (BIA). In the framework of D'yakonov and Perel' relaxation mechanism introduced in Section 1.4.3, the spinorbit field B SO (to which the spin will precess around with frequency Ω k at each scattering event) will be redefined for each k. The Dresselhaus effect can be modelled by the spin-orbit

Hamiltonian given in Eq. (1.13), where, in cubic momentum space10 , the k 3 -Dresselhaus term is given as [START_REF] Dresselhaus | Spin-Orbit Coupling Effects in Zinc Blende Structures[END_REF][START_REF] Perel | Spin orientation of electrons associated with the interband absorption of light in semiconductors[END_REF]: Adapted from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF] and [START_REF] Soumyanarayanan | Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces[END_REF]. (b) Rashba-split bands experimentally observed through angle-resolved photoemission spectroscopy at the surface of Au(111) [START_REF] Nechaev | Hole dynamics in a two-dimensional spin-orbit coupled electron system: Theoretical and experimental study of the Au(111) surface state[END_REF].

H D = 2 β D 2 2m 3 e E g κ(k) • σ (1.21)
where E g is the band gap, β D is a material-dependent parameter that specifies the strength of the spin-orbit coupling and κ

(k) = [k x (k 2 y -k 2 z ), k y (k 2 z -k 2 x ), k z (k 2 x -k 2 y )
] with k i the momentum component along the main crystal axes.

A similar effect was discovered by Vas'ko [START_REF] Vas'ko | Spin splitting in the spectrum of two-dimensional electrons due to the surface potential[END_REF] and Bychkov and Rashba [START_REF] Bychkov | Properties of a 2D electron gas with lifted spectral degeneracy[END_REF][START_REF] Bychkov | Oscillatory effects and the magnetic susceptibility of carriers in inversion layers[END_REF] in quantum wells and two-dimensional electron gases, where a confining potential E = E z z (with z the unit vector normal to the two-dimensional plane) leads to structural inversion asymmetry (SIA). Similarly to the Dresselhaus case, the Rashba spin-orbit Hamiltonian takes the form of:

H R = α R (z × k) • σ, (1.22)
where the Rashba coefficient α R quantifies the strength of the effect. For each value of k, the energies of two spin-split bands, with opposite spin orientations are:

E ↑,↓ (k) = 2 k 2 2m e ± α R k, (1.23)
where the first term is the free-electron dispersion relation. From this, a momentumdependent splitting of the two spin subbands arises, amounting for a shift of k R = ±α R m/ 2 , as illustrated in Fig. 1.9a for α R > 0. Performing a cut in the band structure at an arbitrary energy, we observe that this splitting leads to two inequivalent Fermi contours with clockwise and counter-clockwise rotation of the spin in the k x , k y plane. We also observe that the coupling introduced by Eq. (1.22) locks the electron spin to its momentum. Lastly, note that in the band structure represented in Fig. 1.9b the equality E k,↑ = E -k,↓ is observed, so that time-reversal symmetry is still present.

The Rashba spin-orbit coupling attracted a lot of attention regarding the manipulation of spins in semiconductor quantum wells, an idea brought forward by Datta and Das with their proposition of a spin transistor [START_REF] Datta | Electronic analog of the electro-optic modulator[END_REF]. In this device, spins could be controlled during their passage from source to drain, due to the tunability of α R with gate voltages. For an extensive analysis on Rashba and Dresselhaus effects, as well as information on theoretical and experimental coefficients α R and β D for several materials and heterostructures, we refer the reader to the work of Ganichev et al. [START_REF] Ganichev | Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells[END_REF] and the review of Fabian et al. [START_REF] Fabian | Semiconductor spintronics[END_REF].

We finish this section by elaborating on the interactions between the Dresselhaus and Rashba effects, as well as on the k-cubic and k-linear terms given by Eqs. (1.21) and (1.22).

In reality, the two effects can coexist in the same system, making the extraction of the relative contributions for both of them quite difficult, as to obtain α R the Dresselhaus coefficient β D is normally neglected. Since both effects lead to k-dependent spin splitting of the bands, the two terms can interfere in such a way that, even if α R and β D are quite large, suppression of macroscopic effects may occur. Among them, the disappearance of antilocalization [START_REF] Knap | Weak antilocalization and spin precession in quantum wells[END_REF],

the absense of spin relaxation in particular crystalographic direction [START_REF] Averkiev | Spin relaxation anisotropy in twodimensional semiconductor systems[END_REF] and lack of beating patterns in Shubnikov-de Hass oscillations [START_REF] Tarasenko | Interference of spin splittings in magneto-oscillation phenomena in two-dimensional systems[END_REF].

Also, for the Dresselhaus effect, given that it arises from BIA, it is intuitively expected that its Hamiltonian is introduced in cubic terms. However, when treating a two-dimensional electron gas in a non-centrosymmetric system, for example in a quantum well formed at the zinc-blende heterostructure InGaAs/GaAs (001), the Dresselhaus Hamiltonian can have an additional linear dependence with k [START_REF] Studer | Role of linear and cubic terms for drift-induced Dresselhaus spin-orbit splitting in a two-dimensional electron gas[END_REF]. Note that in this case, the spin-orbit Hamiltonian comprises both the linear Rashba and Dresselhaus terms [START_REF] Ganichev | Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells[END_REF][START_REF] Gambardella | Current-induced spin-orbit torques[END_REF]:

H 2DEG SO = α R (σ x k x -σ y k y ) + β D (σ x k x -σ y k y ) (1.24)
In addition to SIA and BIA, a third contribution to the spin-orbit interaction called interface inversion asymmetry (IIA) might come in play. For example, at the Fe/GaAs interface, depending on the termination of GaAs one might end up with two possible interfacial configurations: Fe-Ga-As or Fe-As-Ga. These two cases will naturally give different contributions to the overall spin-orbit interactions in the system. Interestingly, at the interface between two centrosymmetric materials, i.e. in the absence of BIA, the Dresselhaus term vanishes, so that only the Rashba spin-orbit coupling and IIA associated terms contribute.

In the same fashion, the Rashba term, given for 2D systems in the presence of SIA, was observed to be cubic in k for hole doped semiconductor quantum wells [START_REF] Winkler | Rashba spin splitting in two-dimensional electron and hole systems[END_REF][START_REF] Moriya | Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGe Quantum Well[END_REF] as well as SrTiO 3 (001) surfaces, a particularly interesting case for the scope of this thesis. In these surfaces, a cubic term was theoretically predicted to arise from heavier bands with d xz /d yz character [START_REF] Shanavas | Theoretical study of the cubic Rashba effect at the SrTiO 3 (001) surfaces[END_REF] (even though it was found to be different from the standard cubic Rashba model) and from the fitting of weak (anti)localization curves [START_REF] Nakamura | Experimental Evidence of Cubic Rashba Effect in an Inversion-Symmetric Oxide[END_REF].

Just like the discovery of high spin-orbit coupling bulk materials lead to the exploration of physical effects such as the spin Hall effect, surfaces and interfaces show extremely promising and advantageous properties for the electrical generation and control of spin currents.

Direct and inverse Edelstein effects

The generation of a charge current by a non-equilibrium spin density was predicted to occur in a 2DEG in the presence of spin-orbit coupling [START_REF] Aronov | Nuclear electric resonance and orientation of carrier spins by an electric field[END_REF][START_REF] Ivchenko | Photocurrent in quantum well structures with optical orientation of free carrier[END_REF][START_REF] Edelstein | Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems[END_REF], an effect later called Edelstein effect [also known as inverse spin galvanic effect [START_REF] Ganichev | Spin-galvanic effect[END_REF]]. At first sight, this effect may simply seem a 2D version of the spin Hall effect. However, some very particular considerations need to be taken into account.

Spin-to-charge current interconversion in a Rashba 2DEG

When a steady charge current driven by an electric field E = E x x is applied, electrons accelerated in the opposite direction induce changes in all k-dependent energy states. From the Boltzmann equation [START_REF] Ziman | Electrons and Phonons[END_REF], the effect of an electric field in k-space is a shift of the Fermi contour (in a single-band picture) by an amount: [START_REF] Fert | Two-Current Conduction in Nickel[END_REF] in the direction opposite to the electric field, with j c the charge current density and n s the sheet carrier density of the 2DEG.

∆k x = eEτ = j c m e n s e (1.
As previously seen, a system with spin-orbit coupling and space-inversion asymmetry unlocks spin-momentum locking, so that each momentum state will see a different effective mag- x and ∆k in x . Carriers unevenly accelerated in opposite directions generate an electric field along x. Modified from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF]. netic field (perpendicular to the momentum vector). In other words, the spin of an electron in k x becomes aligned along y and in -k x aligned along -y. By shifting the Fermi contour with an external electric field, an excess spin density δs ↑ can be generated.

The same reasoning can be extrapolated for a Rashba 2DEG. In this case, the two Fermi contours, with radius k out F and k in F , will shift by the same amount ∆k x , yielding two excess spin densities δs ↑ and δs ↓ , as sketched in Fig. 1.10a. The colored areas representative of these two spin densities are proportional to (k out F ∆k x ) and (k in F ∆k x ), respectively, given that the Rashba constant α R is small and τ is approximately the same for both contours. A key point in the Rashba case is that these two densities are not equivalent, so they will not cancel each other, leading to a finite spin accumulation. This type of conversion between a 2D charge current and a spin current is termed the direct Edelstein effect (DEE).

Similarly to the inverse counterpart of the spin Hall effect, the inverse Edelstein effect (IEE) describes the conversion of a spin current in a 2D charge current. Starting once again from the two Fermi contours of Rashba splitted bands, if a spin current (polarized along y) is injected in a 2DEG, the outer and inner Fermi contour will be displaced by ∆k x in opposite directions, in order to compensate for the excess spin population. As displayed in Fig. 1.10b, the magnitude of the 2D charge current generated will depend on the relative displacement between both contours ∆k total x (which compensate each other) and their radius k in F and k out F (defined by the magnitude of the Rashba splitting).

Conversion efficiency and non-reciprocal Onsager relation

For quantification purposes, it is important to have a figure of merit that evaluates the efficiency of spin-to-charge current interconversion in Rashba systems, similarly to what the spin Hall angle, introduced in Section 1.5.2, does for the spin Hall effect. For the Edelstein effect, assuming that a spin current is polarized along y and a charge current is produced along x, we start by defining a spin current j 3D s as a balance of the total incoming spin density that is being injected in the 2DEG δs , and the relaxation time τ of this out-of-equilibrium spin density distribution in the 2DEG states:

j 3D s = 2e δs τ (1.26)
As we saw above, the injected spin flow δs induces a displacement of the two Rashba splitted Fermi contours in opposite directions. This gives rise to the production of two charge currents, j 2D c out and j 2D c in , associated with the outer and inner Fermi contours:

j 2D c = j 2D c out + j 2D c in 2e m δs 2 (k out F -k in F ), (1.27)
where δs /2 represents, in first approximation, half of the total spin current being injected in each Fermi contour [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF], and k out/in F the radius of the two Fermi contours.

The distance in k, at the Fermi level, between the two contours can be extracted from the Rashba Hamiltonian of Eq. (1.22) as a function of the Rashba coefficient α R :

k out F -k in F = 2m 2 α R (1.28)
Finally, combining Eqs. (1.26), (1.27) and (1.28), we can obtain the ratio between j 2D c and j 3D s , which gives us the efficiency of the spin-to-charge current conversion λ IEE :

λ IEE = j 2D c j 3D s = α R τ (1.29)
Note that since the charge current density produced is 2D (A.m -2 ) and the spin current density injected is 3D (A.m -3 ), λ IEE has the dimension of a length, unlike the spin Hall angle which is dimensionless. Also, it might seem intriguing that λ IEE depends only on a spinindependent type of scattering (like impurity scattering). However, due to spin-momentum locked Rashba bands, anytime an electron that gets scattered from k to k , it experiences spin rotation [START_REF] Zhang | Conversion between spin and charge currents with topological insulators[END_REF].

In regards to the DEE, one would expect its relation with the IEE to follow the Onsager reciprocity, just like discussed for the SHE and ISHE, meaning that λ IEE should also be phenomenologically valid to measure charge-to-spin current conversion efficiency. We argue that in an infinite sample, and only considering the material where the conversion takes place, both the SHE/ISHE and DEE/IEE follow the Onsager reciprocity. However, when considering a realistic case (i.e. finite sample) with an added ferromagnetic layer to generate/detect the spin currents, both effects are not reciprocal, simply because a spin current being injected from a FM to a NM (ISHE or IEE), is not equivalent to spin ejection from the NM to the FM (SHE or DEE).

Nevertheles, the reciprocity of between SHE and ISHE was experimentally observed in Hall-bar devices with Pt wires, where spin-to-charge and charge-to-spin current conversion were observed to drive similar resistance changes [START_REF] Kimura | Spin current absorptions and spin Hall effects in ferromagnetic/nonmagnetic hybrid structures (invited)[END_REF], as shown in Fig. 1.11. We postulate that this equivalence may be misleading, since the geometries used to detect both effects are rather complex and intrinsically non-equivalent.

On the other hand, a discrepancy of about two orders of magnitude between DEE and IEE conversion efficiencies was confirmed at the surface of topological insulator Bi 2 Se 3 [START_REF] Deorani | Observation of inverse spin Hall effect in bismuth selenide[END_REF][START_REF] Wang | Topological Surface States Originated Spin-Orbit Torques in Bi 2 Se 3[END_REF].

To tackle this issue, structures [START_REF] Kim | Evaluation of bulk-interface contributions to Edelstein magnetoresistance at metal/oxide interfaces[END_REF]. They concluded that the conversion mechanism due to DEE and IEE was in fact governed by the ratio of the spin relaxation inside and outside the 2DEG (Rashba 2DEG/TI surface). In several reports regarding the IEE or DEE, a FM material is usually placed close to the 2DEG (normally with a thin barrier between them to suppress exchangecoupling interactions [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF]), and a technique like spin pumping or spin-torque ferromagnetic resonance is used to generate/detect the spin currents. This particular experimental feature implies that while in the IEE the conversion relies on the spin relaxation of an incoming outof-equilibrium spin density inside the 2DEG, in the DEE the conversion also depends on the electron transmission rate between the 2DEG and the FM, so that in the same system j IEE s and j DEE s represent different experimental quantities [START_REF] Zhang | Conversion between spin and charge currents with topological insulators[END_REF][START_REF] Kim | Evaluation of bulk-interface contributions to Edelstein magnetoresistance at metal/oxide interfaces[END_REF]. In other words, the relaxation times associated with both effects are not the same. To further elucidate on this difference, we sketch in Fig. 1.12a and 1.12b what the effects look like in a FM/NM/2DEG system. We observe that in the IEE, a spin current is pumped towards the 2DEG, where spins will relax with a characteristic relaxation time τ s , present in Eq. (1.29). For the DEE case, the spin Note that the variation of the extracted resistance for positive and negative applied field, ∆R c and ∆R s , is the same in both SHE and ISHE experiments, seemingly confirming their Onsager reciprocity. However, due to the intrinsic differences between both geometries, this reciprocity may need a more careful investigation.

accumulation is lost inside the 2DEG after a characteristic spin-flipping time τ s but it also relaxes (independently) across the barrier into the bulk FM, with a spin relaxation time τ b .

With this in mind, the DEE efficiency q DEE can be evaluated by [START_REF] Kim | Evaluation of bulk-interface contributions to Edelstein magnetoresistance at metal/oxide interfaces[END_REF]:

q DEE = α R 1 τ b + 1 τ s , (1.30)
which compared to Eq. 1.29 essentially explains the experimental disparity between the DEE and IEE.

As an additional note, recent theoretical calculations of spin-to-charge conversion experi- ments considering the barrier thickness revealed an important balance between spin transmission through the barrier and spin relaxation back to the FM layer [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF], which in turn adds an additional relaxation term to the model developed by Zhang and Fert [START_REF] Zhang | Conversion between spin and charge currents with topological insulators[END_REF]. Increasing the thickness of the barrier placed between the FM and the 2DEG/TI, leads to a decrease of spin current transmission. Simultaneously, electron exchange between the 2DEG/TI and the FM decreases due to more efficient "protection" of the 2DEG/TI states. Therefore, a compromise should be found so that λ IEE can be maximized. We also note that similar conclusions were drawn by Chauleau et al., where spin-to-charge conversion experiments in NiFe/LaAlO 3 /SrTiO 3 samples as a function of the LaAlO 3 thickness (5, 6 and 7 uc) showed little difference regarding the estimated λ IEE , emphasizing the importance of this balance [START_REF] Chauleau | Efficient spin-to-charge conversion in the 2D electron liquid at the LAO/STO interface[END_REF].

Finally, non-local experiments performed in the 2DEG formed at the LaAlO 3 /SrTiO 3 interface introduce a third scenario to this discussion [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF]. Using a double Hall bar geometry, a charge current injected in a first branch induces a perpendicular spin current through the DEE. The spin current propagates in the 2DEG channel and gets reconverted into a charge current (through the IEE) in the second branch, where it is nonlocally detected. Even though this effect occurs in a 2D system, we believe that it may be more accurately approached as a 2D spin Hall effect, rather than a reciprocal Edelstein effect. Summarizing, while the SHE/ISHE and DEE/IEE should theoretically follow the Onsager principle (in an infinite sample), different relaxation processes need to be considered experimentally, necessarily disproving their reciprocity in a realistic case.

An extended overview of spin-to-charge current interconvertion experiments performed, up to this point, on several Rashba systems and topological insulators will be presented further ahead in Section 3.1. We will then continue to elaborate on this topic by presenting spin-tocharge conversion experiments performed on SrTiO 3 -based Rashba 2DEGs.

|

Tuning the properties of LaAlO 3 /SrTiO 3 interfaces through in situ deposition of metal overlayers Following the great advances in semiconductor research, the last 20 years saw a tremendous development in the rich field of complex oxides. The first breakthrough came with the growth of oxides with unit-cell precision, lead by the demonstration of epitaxially grown LaTiO 3 /SrTiO 3 (LTO//STO) heterostructures [START_REF] Ohtomo | Epitaxial growth and electronic structure of LaTiO x films[END_REF][START_REF] Ohtomo | Artificial charge-modulationin atomic-scale perovskite titanate superlattices[END_REF]. From there, the field continued to attract even more attention with the discovery of interfacial conductivity at the interface between insulating LaAlO 3 and SrTiO 3 (LAO//STO) [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF], as well as its superconducting phase observed a few years later [START_REF] Reyren | Superconducting Interfaces Between Insulating Oxides[END_REF]. Concurrently, a new class of materials where magnetism and ferroelectricity are coupled -multiferroics -opened doors for the idealization of magnetoelectric devices [START_REF] Ramesh | Multiferroics: progress and prospects in thin films[END_REF][START_REF] Bibes | Towards a magnetoelectric memory[END_REF]. To this day, the list of new and improvement physical effects found in precise atomicscale-designed oxide heterostructures continues to grow.

The key ingredient allowing such a wide range of different phenomena is driven by oxygen itself. As pointed out by professor Tokura, "oxygen tends to pull electrons away from other atoms in the compound, resulting in strong electrical fields at the interatomic scale. These fields can give rise to substantial correlations in behavior between the electrons of one atom and those of its neighbors." [START_REF] Heber | Materials science: Enter the oxides[END_REF]. Indeed, besides the tunability provided by the cation size (which alters its relative distance to oxygen atoms), the majority of the effects mentioned above can be tuned by the films' oxygen stoichiometry.

A common way to control this, is by changing the growth parameters, i.e. fabricating heterostructures under very specific oxygen pressures to achieve very specific outcomes. This is notably seen in the growth of LAO//STO, where small deviations from the ideal conditions may render the interface insulating [START_REF] Liu | Origin of the Two-Dimensional Electron Gas at LaAlO 3 /SrTiO 3 Interfaces: The Role of Oxygen Vacancies and Electronic Reconstruction[END_REF]. In this chapter, we describe a different approach for controlling oxygen content in complex oxides, specifically at their surfaces. Inspired by the critical thickness reduction achieved in our lab by capping LAO//STO with a Co layer [START_REF] Lesne | Suppression of the critical thickness threshold for conductivity at the LaAlO 3 /SrTiO 3 interface[END_REF], and the conductivity found at surface of STO when capped with an amorphous LAO thin film [START_REF] Chen | Metallic and Insulating Interfaces of Amorphous SrTiO 3 -Based Oxide Heterostructures[END_REF], we control the q2DEG formed in LAO//STO (and bare-STO) heterostructures by depositing different metallic overlayers. Depending on the metal chosen, we tune the properties of the q2DEG, namely carrier densities, mobilities and spacial extension, and show the ability to turn conduction on or off [START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. Importantly, we describe this tunability with an hybrid electrostatic/chemical mechanism, which in principle can be used universally as a blueprint for the creation of 2DEGs (or even 2D holes gases) in oxide materials at room temperature (as opposed to the required high T growth of LAO for example). Moreover, we show in Chapter 3, a successful implementation of this study, through the creation of a highly efficient spin-to-charge current conversion platform, pushing forward the use of metal/oxide interfaces in the next generation of spin-based electronic devices [START_REF] Manipatruni | Beyond CMOS computing with spin and polarization[END_REF].

2.1 SrTiO 3 : a playground of physical phenomena 2.1.1 Structural and electronic properties STO is often considered one the most versatile and surprising materials in the complex oxides family [START_REF] Pai | Physics of SrTiO 3 -based heterostructures and nanostructures: a review[END_REF]. At room temperature, it exhibits a cubic perovskite structure with a lattice parameter a = 0.3905 nm. The (001), [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF] and [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] crystallographic orientations are the most commonly studied, with the first one being non-polar (most stable) and the other two polar. As displayed in Fig. 2.1a, in the (001)-direction, the STO crystal consists of a stack of TiO 2 and SrO layers, so that two possible surface terminations are available. Importantly, the termination can be experimentally controlled through chemical methods, which plays a critical role in surface-related effects.

Structurally, STO is known to possess two types of distortions, driven by stress or temperature changes: ferroelectric-type (FE) displacement or antiferrodistortive (AFD) rotation.

At around 105 K, STO exhibits a cubic-to-tetragonal AFD phase transition, characterized by rotation of oxygen octahedra and slight elongation of the c parameter. Also, ferroelastic domains along different axis are known to appear(disappear) below(above) this AFD transition temperature, so that new domains can form with temperature cycling. STO is also known to be one the few materials exhibiting quantum paraelectricity. Even though bulk STO remains paraelectric at any finite temperatures, quantum fluctuations avoid the formation of ferroelectric order at low temperatures. The proximity to a ferroelectric phase is manisfested through a drastic increase of the dielectric constant from ST O (300K) ∼ 300 to ST O (4K) ∼ 20000, which was found to be heavily dependent on temperature and electric field applied [START_REF] Müller | SrTiO 3 : An intrinsic quantum paraelectric below 4 K[END_REF][START_REF] Christen | Dielectric properties of sputtered SrTiO 3 films[END_REF].

Regardless of its paraelectric nature, ferroelectricity can still be induced in STO through strain [START_REF] Haeni | Room-temperature ferroelectricity in strained SrTiO 3[END_REF], large electric fields [START_REF] Hemberger | Electric-fielddependent dielectric constant and nonlinear susceptibility in SrTiO 3[END_REF], cation substitution (Sr → Ca, for example) [START_REF] Bednorz | Sr 1-x Ca x TiO 3 : An XY Quantum Ferroelectric with Transition to Randomness[END_REF], isotope substitution (O 16 → O 18 ) [START_REF] Wang | Suppression of the quantum fluctuation in 18 O-enriched strontium titanate[END_REF] or oxygen deficiency [START_REF] Kim | Observation of room-temperature ferroelectricity in tetragonal strontium titanate thin films on SrTiO 3 (001) substrates[END_REF].

In its stoichiometric form, STO is a band insulator with a band gap of 3.25 eV [START_REF] Van Benthem | Bulk electronic structure of SrTiO 3 : Experiment and theory[END_REF], separating oxygen 2p orbitals (valence band) from empty Ti 3d orbitals (conduction band) [START_REF] Tilley | [END_REF], as observed in Fig. 2.1b and 2.1c. The cubic crystal field lifts the degeneracy of the empty 3d orbital, splitting them into a degenerate triplet t 2g and degenerate doublet e g . The t 2g triplet, composed of d xy , d yz and d xz orbitals lies approximately 2 eV below the e g doublet, so that the conduction band minimum is composed of t 2g states. STO can develop a bulk conducting state at carrier densities as low as ∼ 8.5 × 10 15 cm -3 [START_REF] Spinelli | Electronic transport in doped SrTiO 3 : Conduction mechanisms and potential applications[END_REF]. Electron doping may be achieved through (Sr 2+ → La 3+ ) or (Ti 4+ → Nb 5+ ) substitution O and double-ionized V ++ O oxygen vacancies in STO within the band gap. The displacement effect described in panel (a) is reduced for vacancies with lower ionization states. Adapted from [START_REF] Mitra | Electronic structure of oxygen vacancies in SrTiO 3 and LaAlO 3[END_REF].

(both donating 1 electron), as well as oxygen removal (donating 2 electrons). Upon doping, the Fermi level moves into the conduction band and the added electrons induce a valence change from Ti 4+ to Ti 3+ [START_REF] Shanthi | Electronic structure of electron doped SrTiO 3 :SrTiO 3 -δ and Sr 1-x La x TiO 3[END_REF]. As we will see in this chapter, this mixed valence state is the core property that makes STO such an interesting electrical conductor. In contrast, Sr atoms maintain a stable 2+ valence state.

Lastly, STO can acquire a superconducting phase at a critical temperature of T c = 300 mK, with T c exhibiting a dome-shaped behaviour as a function of the carrier concentration [START_REF] Schooley | Dependence of the Superconducting Transition Temperature on Carrier Concentration in Semiconducting SrTiO 3[END_REF]. Recently, it was demonstrated that STO exhibits superconductivity down to carrier concentrations of 5.5 × 10 17 cm -3 , making it the most dilute superconductor known to date [START_REF] Lin | Fermi Surface of the Most Dilute Superconductor[END_REF].

Oxygen vacancies

Oxygen vacancies are the most common and important defect in STO. On one hand, they have a tremendous impact on the structural, transport, magnetic and optical properties of STO; on the other, they are easily created, removed and manipulated, making them a great "knob" to tune said properties.

Assuming a two-fold ionization of the oxygen vacancy (since they can release up to two electrons in the lattice), its formation reaction is described as:

O L ↔ VO + 2e -+ 1/2O 2 (2.1)
with O L the lattice oxygen sites, VO the doubly ionized oxygen vacancy (using Kroger-Vink notation [START_REF] Kröger | Relations between the Concentrations of Imperfections in Crystalline Solids[END_REF]) and e -the free electrons.

The (forward) reaction above usually occurs when heating the STO crystal at high temperatures and in oxygen-deficient atmospheres, resulting in increased concentration of VO and e -. In this process, the oxygen starts by desorbing from the surface, while Ti ions diffuse inwards into the bulk, resulting in Sr-rich surfaces. The diffusion constant of oxygen is about ∼ 10 14 cm 2 .s -1 at room temperature, but may depend on the oxygen pressure, electric field, illumination, existence of high mobility paths such as dislocations or twin walls, among others [START_REF] Pai | Physics of SrTiO 3 -based heterostructures and nanostructures: a review[END_REF]. We note however that, due to its smaller atomic size, the diffusivity of oxygen is orders of magnitude larger than that of Sr or Ti [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF].

After the vacancy is formed, the electrons released may remain localized, therefore not contributing to conduction. In contrast, if the vacancy becomes positively charged (V + O and V ++ O , with the double-ionized form being the most stable [START_REF] Mitra | Electronic structure of oxygen vacancies in SrTiO 3 and LaAlO 3[END_REF]), the e -released in the lattice may render the STO conducting, while the surrounding cations are pushed away (see Fig.

2.2a

). The Ti and Sr atoms in the vicinity will therefore relax away from the vacancy site, pushing the defect state closer to the conduction band, due to weaker Ti-Ti bonding, as displayed in Fig. 2.2b [START_REF] Mitra | Electronic structure of oxygen vacancies in SrTiO 3 and LaAlO 3[END_REF].

LaAlO 3 : a wide bandgap insulator

LaAlO 3 (LAO) has a rhombohedral perovskite structure, with a pseudo-cubic lattice paramenter of a = 0.379 nm, composed of polar (AlO 2 ) -and (LaO) + stacked layers (see Fig.

2.3a

). Structurally, it goes through a rhombohedral-to-cubic phase transition at ∼ 820 K [START_REF] Hayward | Order parameter saturation in LaAlO 3[END_REF].

LAO is a band insulator with a large band gap of 5.6 eV, separating filled O 2p valence bands (hybridized with Al p bands) and empty Al 3s -3p and La 5d conduction bands. In contrast with STO, none of the cations in LAO can access a mixed valence state, making it an extremely robust insulator.

Regarding defects, the formation energies of neutral and charged oxygen vacancies were calculated through DFT [START_REF] Mitra | Electronic structure of oxygen vacancies in SrTiO 3 and LaAlO 3[END_REF][START_REF] Dicks | Spectroscopic properties of oxygen vacancies in LaAlO 3[END_REF]. While slightly different values were calculated by different groups, mainly due to the size of the cell used, V 0 O and V ++ O were found to be the most stable defects, with V ++ O having the lowest formation energy, if the Fermi level is not higher than 3.6 eV above the valence band (see Fig. 2.3b and 2.3c) [START_REF] Dicks | Spectroscopic properties of oxygen vacancies in LaAlO 3[END_REF]. Similarly to STO, positively charged oxygen vacancies induced outward displacement of Al and La species in the lattice, as displayed in Fig. 2.3d.

As we will see ahead, even though LAO is a rather stable material, the formation of oxygen vacancies plays an important role when combined with other complex oxides, such as STO. leads to outward displacement of the neighboring La and Al cations. Adapted from [START_REF] Dicks | Spectroscopic properties of oxygen vacancies in LaAlO 3[END_REF].

We also note that, the values shown in Fig. 2.2b and 2.3c are estimates made from bulk calculations, and do not take into account additional mechanisms that might be at play.

2.3

The LaAlO 3 /SrTiO 3 system

Emerging interfacial conductivity

Ohtomo and Hwang continued to explore the foundations laid by their previous breakthroughs regarding epitaxial growth of complex oxide materials. Following their discovery of charge transfer in unit-cell precise LTO//STO heterostructures [START_REF] Ohtomo | Epitaxial growth and electronic structure of LaTiO x films[END_REF][START_REF] Ohtomo | Artificial charge-modulationin atomic-scale perovskite titanate superlattices[END_REF], they reported in 2004, a for samples grown between 10 -4 and 10 -6 mbar of oxygen partial pressure. The dashed line represent a sample grown at 10 -6 mbar that was additionally post-annealed for 2 h at 400 • C under 1 atm of oxygen. Adapted from [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF].

high-mobility electron gas between LAO and STO(001) [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF].

Due to the band gap insulating nature of LAO, unlike LTO which is a Mott insulator, the conduction found at the LAO//STO interface came to a great surprise. Its discovery is considered a landmark, as it proved that novel phenomena could be exploited at engineered oxide heterointerfaces.

Similarly to the LTO//STO case, LAO was epitaxially grown using pulsed laser deposition (PLD) at 800 • C. When grown on top of STO, LAO is subjected to a tensile strain, due to the lattice mismatch of about -2.9%. To control the growth with atomic precision, reflection high energy electron diffraction (RHEED) was implemented during growth, with each oscillation representing one unit cell grown, as shown in Fig. 2.4a. Interestingly, conduction was only observed when LAO was grown on TiO 2 -terminated STO (see Fig. 2.5a), while the stack remained insulating using SrO-terminated substrates. For LAO thicknesses between 0 and 3 unit cells, the heterostructure is found to be insulating. At a critical thickness t c of 4 uc, finite conductivity σ s is detected [START_REF] Thiel | Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures[END_REF].

The temperature dependence of the sheet resistance for the conducting samples was observed to be strikingly different depending on the oxygen environment used during film growth, as observed in Fig. 2.4b. From Hall effect measurements, electron mobilities of about 10 4 cm 2 .V -1 .s -1 and carrier densities in the range of n s ∼ 10 16 -10 17 cm -2 were found below 10 K. Knowing how sensitive STO can be to high temperature, especially regarding defect formation, the values achieved point out to an oxygen-deficient STO, where oxygen was simply removed during the high temperature and low oxygen pressure (10 -6 mbar) growth, resulting in a conducting substrate. In contrast, samples grown in high oxygen pressures (10 -4 mbar) or annealed in oxygen showed much lower mobilities, in the order of 50 cm 2 .V -1 .s -1 , supporting this scenario.

In the following years, the debate between 3D oxygen-vacancy driven conduction and quasi-2D interfacial conduction began to be resolved. through spectroscopy studies that the large Ti 3+ signature found in non-annealed samples could be suppressed after high temperature treatment in rich oxygen atmosphere [START_REF] Siemons | Origin of Charge Density at LaAlO 3 on SrTiO 3 Heterointerfaces: Possibility of Intrinsic Doping[END_REF].

Superconductivity and traces of magnetism

In addition to the 2D-like conductivity, the q2DEG formed at LAO//STO interfaces was found to become superconducting for a given range of carrier densities below 300 mK [START_REF] Reyren | Superconducting Interfaces Between Insulating Oxides[END_REF], with possible traces of magnetism [START_REF] Brinkman | Magnetic effects at the interface between non-magnetic oxides[END_REF], a particularly interesting combination that has not yet been reported in other 2D systems. Right after the first observation of superconductivity, Caviglia et al. showed that the superconducting ground state could be electrostatically tuned through back-gate field effect [START_REF] Caviglia | Electric field control of the LaAlO 3 /SrTiO 3 interface ground state[END_REF] (see Fig. 2.7a). As the doping level of the q2DEG was modulated, the T c showed a dome-like behavior, reminiscent of what was priorly observed in oxygen deficient bulk STO [START_REF] Schooley | Dependence of the Superconducting Transition Temperature on Carrier Concentration in Semiconducting SrTiO 3[END_REF]. The major difference between both cases is that the thickness of the superconducting layer in LAO//STO was estimated to be at most 10 nm, much smaller than the in-plane superconducting coherence length of 70 nm, implying that the superconductivity is indeed 2D [START_REF] Reyren | Superconducting Interfaces Between Insulating Oxides[END_REF]. Some reports have also linked the behavior of T c with the Rashba spin-orbit strength, due to the existence of a superconducting dome that coincides with a weak anti-localization regime (derived from transport experiments [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF]), where the SOC is known to be stronger. Even though this connection is still puzzling and unclear, it may, for example, enable interesting possibilities for the experimental observation of the elusive Majorana fermions [START_REF] Beenakker | Search for Majorana Fermions in Superconductors[END_REF]. In recent years, a superconducting phase was also observed at the [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF] and ( 111) LAO//STO interface [START_REF] Herranz | Engineering two-dimensional superconductivity and Rashba spin-orbit coupling in LaAlO 3 /SrTiO 3 quantum wells by selective orbital occupancy[END_REF][START_REF] Monteiro | Two-dimensional superconductivity at the (111) LaAlO 3 /SrTiO 3 interface[END_REF], which was correlated with the selective orbital occupancy and spatial extension of the q2DEG.

T (mK)
Regarding magnetism, results have been rather diffuse and apparently inconsistent, but may just hint for a non-trivial magnetic phase forming at the interface. In the recent review by Pai et al., magnetism observed at the LAO//STO interface was separated into two main categories: a ferromagnetic or Kondo liquid phase emerging from local magnetic moments coupled by exchange interactions with itinerant electrons, and a metamagnetic phase arising from a combination of the band structure of d orbitals, spin-orbit coupling and electron pairing [START_REF] Pai | LaAlO 3 /SrTiO 3 : a tale of two magnetisms[END_REF].

Brinkman et al. were the first to report on magnetism at the LAO//STO interface, where an hysteretic behavior of the longitudinal magnetoresistance was observed at temperatures below 300 mK [START_REF] Brinkman | Magnetic effects at the interface between non-magnetic oxides[END_REF]. This observation was backed by an upturn of the resistance when decreasing the temperature below 50 K, implying a Kondo-like effect between conduction electrons and localized magnetic moments. Importantly, the samples used in this study were grown at rather low oxygen pressure (10 -3 mbar) and were not post-annealed. The origin of the magnetic moments can therefore be linked with the formation of oxygen vacancies in the STO, as suggested by Rice et al. [START_REF] Rice | Persistent optically induced magnetism in oxygen-deficient strontium titanate[END_REF]. Other authors have observed ferromagnetic-like hysteresis loops, obtained from SQUID measurements [START_REF] Ariando | Electronic phase separation at the LaAlO 3 /SrTiO 3 interface[END_REF], randomly distributed magnetic dipoles oriented in-plane (see Fig. 2.7b) [START_REF] Bert | Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO 3 /SrTiO 3 interface[END_REF] and finite magnetic moment density obtained from torque magnetometry, with no evidence of hysteretic behavior [START_REF] Li | Coexistence of magnetic order and two-dimensional superconductivity at LaAlO 3 /SrTiO 3 interfaces[END_REF]. In contrast, using polarized neutron reflectom-etry, Fitzsimmons et al. saw no magnetism in a variety of LAO//STO samples grown by different groups [START_REF] Fitzsimmons | Upper Limit to Magnetism in LaAlO 3 /SrTiO 3 Heterostructures[END_REF]. Also, subsequent experiments using scanning SQUID microscopy failed to reproduce the initial observations of magnetic dipoles [START_REF] Bert | Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO 3 /SrTiO 3 interface[END_REF], in apparent similar conditions [START_REF] Wijnands | Scanning Superconducting Quantum Interference Device Microscopy[END_REF]. The second category, related with a metamagnetic state, is mainly backed by transport experiments performed at low temperature (but above T c ), where the observation of effect such as giant negative magnetoresistance [START_REF] Diez | Giant Negative Magnetoresistance Driven by Spin-Orbit Coupling at the LaAlO 3 /SrTiO 3 Interface[END_REF], anisotropic magnetoresistance [START_REF] Joshua | Gate-tunable polarized phase of two-dimensional electrons at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Annadi | Fourfold oscillation in anisotropic magnetoresistance and planar Hall effect at the LaAlO 3 /SrTiO 3 heterointerfaces: Effect of carrier confinement and electric field on magnetic interactions[END_REF] and anomalous Hall effect [START_REF] Joshua | Gate-tunable polarized phase of two-dimensional electrons at the LaAlO 3 /SrTiO 3 interface[END_REF], are only observed above the Lifshitz point [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF], where multiple bands are being simultaneously populated.

Among the many unanswered questions, the coexistence of superconductivity and magnetism seems to be the most puzzling. First, the magnetic dipoles initially observed by Bert et al. were inferred to coexist with a spatially inhomogeneous superconducting phase. In a seperate work, they also saw that, unlike the superconductivity, the density of these magnetic dipoles was insensitive to the magnitude of an applied gate voltage, suggesting that the two may exist in different spatial regions [START_REF] Bert | Gate-tuned superfluid density at the superconducting LaAlO 3 /SrTiO 3 interface[END_REF]. A critical thickness (of 3 uc) for the appearance of magnetic dipoles was also reported by Kalisky et al. [START_REF] Kalisky | Critical thickness for ferromagnetism in LaAlO 3 /SrTiO 3 heterostructures[END_REF]. Intriguingly, a large density of magnetic moments was also observed in electrically insulating p-type LAO//STO heterostructures, regardless of the LAO thickness. This result is supported by the model proposed by Yu and Zunger [START_REF] Yu | A polarity-induced defect mechanism for conductivity and magnetism at polar-nonpolar oxide interfaces[END_REF], which accounts for magnetism due to thermodynamically-driven Ti-on-Al cation substitutions at the interface, but may however imply that the magnetism in LAO//STO is not directly related with the existence of a q2DEG.

Interfacial q2DEG formation mechanisms

After the first successful experiments regarding its quasi-2D nature, the discussion regarding the origin of the quasi-2D electron gas (q2DEG) was far from being resolved. In the following sections, we discuss the "polar catastrophe" scenario initially proposed by Ohtomo and Hwang [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF], followed by other possible scenarios based on defects and surface interactions.

Polar catastrophe

In the (001) direction, while both planes composing an STO unit-cell are neutral, Sr

2+ O 2-
and Ti 4+ O 2- 2 , LAO is composed of alternated charged planes, (LaO) + and (AlO 2 ) -, so that an electric field is introduced within each unit cell. When LAO is grown on STO, an abrupt polar discontinuity occurs at the interface, with an electric potential building up in LAO as its thickness increases. To avoid a so-called polar catastrophe and to release this electrostatic build-up, the whole system can go through electronic reconstruction, where 0. (a) On the left side, the unreconstructed n-type LaO/TiO 2 interface. Along the (001) direction STO shows neutrally charged planes (Q=0) while LAO planes have an associated alternated charge of Q=1 and Q=-1. The electrostatic potential V builds up from the interface and keeps increasing with LAO film thickness. On the right side, a "polar catastrophe" is avoided through the transfer of half an electron to the interface. The potential remains finite since the electric field oscillates around E = 0. (b) Energy band diagram of the LAO/STO interface. The increasing thickness raises the internal potential allowing the LAO valence band (VB) to tilt until it reaches the STO conduction band (CB). At a given critical thickness t c , Zener breakdown occurs and electrons are able to be transferred from the LAO surface towards Ti 3d states at the interface, where a q2DEG appears. Adapted from [START_REF] Vaz | Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures[END_REF]. Ti 2p t 2g conduction bands), inducing metallic behavior at the interface [START_REF] Nakagawa | Why some interfaces cannot be sharp[END_REF]. The electrostatic state of an LAO//STO heterostructure before and after reconstruction is sketched in Fig. 2.8a.

Although this scenario is valid for an n-type interface, i.e. LAO grown on a TiO 2 -terminated STO, p-type interface (grown on SrO-terminated STO) should undergo a similar mechanism, with an electrostatic potential building up with an opposite sign. In this case, hole conduction at the interface should be expected. However, this has not been experimentally observed 11 , most likely due to the difficulty of Ti to accommodate holes (Ti 4+ → Ti 5+ ).

Several experimental findings have confirmed the validity of the polar catastrophe scenario.

For example, the critical thickness first observed by Thiel et al. and replicated by many other groups can be viewed in the light on the electrostatic build-up in LAO. As sketched in Fig. 2.8b, with increasing thickness, the bands of the LAO start to tilt, due to the presence of an increasingly large internal electric field. At a critical thickness of 4 uc, the LAO valence band maximum reaches the energy level of the STO conduction band minimum, allowing charge transfer from the surface towards the STO. This scenario was experimentally backed by Reinle-Schmitt et al., where the critical thickness for conduction was systematically manipulated by altering the polarization of the LAO film, as sketched in Fig. 2.9a [START_REF] Reinle-Schmitt | Tunable conductivity threshold at polar oxide interfaces[END_REF]. Using scanning-tunneling microscopy on the cross-section of LAO//STO samples, Huang et al. directly observed the tilted LAO bands, confirming the existence of a built-in electric field (see Fig. 2.9b) [START_REF] Huang | Mapping Band Alignment across Complex Oxide Heterointerfaces[END_REF]. Lastly, since LAO is a dielectric, an internal electric field should also give rise to electrostriction, which deforms the lattice. Cancellieri et al. observed an expansion of the c-axis by 2%, plotted in Fig. 2.9c, which vanished when the critical thickness is reached, indicating that electronic reconstruction took place [START_REF] Cancellieri | Electrostriction at the LaAlO 3 /SrTiO 3 Interface[END_REF].

On the other side of the spectrum, many other results raised inconsistencies regarding the polar catastrophe scenario. Several spectroscopy studies focused on the La, Sr, Al and Ti core level energy shifts within the LAO//STO heterostructure, revealing no evidence of the strong potential gradient in the LAO film [START_REF] Berner | Band alignment in LaAlO 3 /SrTiO 3 oxide heterostructures inferred from hard x-ray photoelectron spectroscopy[END_REF]. The energy offsets found below and above the critical thickness were much smaller than what was initially predicted [START_REF] Slooten | Hard x-ray photoemission and density functional theory study of the internal electric field in SrTiO 3 /LaAlO 3 oxide heterostructures[END_REF] and they did not increased monotonically with increasing LAO thickness. In some cases, no dependence regarding substrate termination was seen [START_REF] Segal | X-ray photoemission studies of the metal-insulator transition in LaAlO 3 /SrTiO 3 structures grown by molecular beam epitaxy[END_REF]. Other spectroscopy studies also found a Ti 3+ componenent below the critical thickness, signaling for localized/mobile electrons at the interface before the critical thickness is reached [START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF][START_REF] Berner | Band alignment in LaAlO 3 /SrTiO 3 oxide heterostructures inferred from hard x-ray photoelectron spectroscopy[END_REF].

Additionally, from transport experiments the carrier density found in the q2DEG was in the order of 10 13 cm -2 , as opposed to the 0.5 e -/uc required to avoid a polar catastrophe, Schematic of the potential build-up as a function of the thickness t for a pure LAO film (light blue) and a LASTO:0.5, a LAO layer diluted with 50% of STO (dark blue). Altering the composition of the LAO film translates in a modulation of its formal polarization, so that the critical thickness for conduction can be increased. Adapted from [START_REF] Reinle-Schmitt | Tunable conductivity threshold at polar oxide interfaces[END_REF]. (b) Quantitative spectroscopic construction of the evolution of band alignment across the LAO/STO interface, confirming the existence of a built-in electric field E in the LAO layer. Adapted from [START_REF] Huang | Mapping Band Alignment across Complex Oxide Heterointerfaces[END_REF].

V c t t c (2) t c (1) V (a) (b) (c)
(c) Expansion of the LAO c-axis parameter with increasing film thickness, supporting the idea of an increasing internal potential within LAO. The dashed horizontal line indicates the pseudocubic LAO bulk lattice constant. Adapted from [START_REF] Cancellieri | Electrostriction at the LaAlO 3 /SrTiO 3 Interface[END_REF].

which should lead to n s = 3×10 14 cm -2 . A possible explanation relies on the existance of two different electron populations, one closer to the interface where electrons are more likely to become localized due to impurities and defects, and a second one deeper in the bulk where electrons are more mobile [START_REF] Fete | Magnetotransport experiments at the LaAlO 3 /SrTiO 3 interface[END_REF]. However, we note that some oxide-based heterostructures, e.g.

GdTiO 3 /SrTiO 3 , exhibit full charge transfer [START_REF] Moetakef | Quantum oscillations from a two-dimensional electron gas at a Mott/band insulator interface[END_REF]. Lastly, other q2DEG were found in similar systems without charged layers, such as the LAO//STO grown in the [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF] direction, where all the planes within the STO and LAO are neutral [START_REF] Han | Two-dimensional superconductivity at (110) LaAlO 3 /SrTiO 3 interfaces[END_REF]. In this case, a critical thickness is still found, which adds even more questions to the whole debate.

Cation interdiffusion

The LAO//STO case is in fact reminiscent of a well studied semiconductor system: the GaAs/Ge(001) heterostructure. Here, the polar/non-polar interface was found to result in atomic reconstruction, in which intermixing of species compensates the electric field buildup [START_REF] Harrison | Polar heterojunction interfaces[END_REF]. This emphasized that, in a real system, interfaces are never as abrupt as initially idealized, and cationic intermixing should be considered.

As demonstrated in Fig. On the left, the high-angle annular dark-field STEM image reveals the crystalline epitaxial growth. On the right, the concentration map of La and Ti shows small amount of intediffusion at the interface. Modified from [START_REF] Warusawithana | LaAlO 3 stoichiometry is key to electron liquid formation at LaAlO 3 /SrTiO 3 interfaces[END_REF].

in the vicinity of the interface through x-ray diffraction (SXRD) [START_REF] Willmott | Structural Basis for the Conducting Interface between LaAlO 3 and SrTiO 3[END_REF], medium-energy ion spectroscopy (MEIS) [START_REF] Kalabukhov | Cationic Disorder and Phase Segregation in LaAlO 3 /SrTiO 3 Heterointerfaces Evidenced by Medium-Energy Ion Spectroscopy[END_REF] and electron energy loss spectroscopy (EELS) [START_REF] Nakagawa | Why some interfaces cannot be sharp[END_REF]. It was generally concluded that an La 1-x Sr x TiO 3 compound forms near the interface, on the STO side, which due to its metallic behaviour could possibly be the origin of the q2DEG. In opposition to this scenario, Warusawithana et al. grew LAO//STO samples using molecular beam epitaxy (MBE), a much gentler technique to grow epitaxial heterostructures, to find through scanning tunneling electron microscopy (STEM) and EELS almost no interdiffusion at the interface, as shown in Fig. 2.10b [START_REF] Warusawithana | LaAlO 3 stoichiometry is key to electron liquid formation at LaAlO 3 /SrTiO 3 interfaces[END_REF]. In these experiments, the samples were still conducting, undermining the credibility of the intermixing scenario.

Returning to the GaAs/Ge case, we point out a crucial difference when comparing it to the LAO//STO system. In the semiconductor stack, since each ion has a fixed charge, atomic reconstruction is the most favorable relaxation mechanism. In contrast, the mixed valence state of the Ti atoms in STO, also allows electronic reconstruction, so that even if interdiffusion is present, it may not be as severe as in other fixed valency systems.

Surface reactions

While in traditional semiconductor devices, the conducting channel is buried several hundreds of nanometers within the stack, in LAO//STO the conducting interface is a few uc away from the surface. Therefore, surface reactions could potentially play an important role on the Sketch of the nanowire writing/erasing procedure in LAO(3uc)/STO samples (at the verge of conduction), using a biased tip. Adapted from [START_REF] Bi | Water-cycle mechanism for writing and erasing nanostructures at the LaAlO 3 /SrTiO 3 interface[END_REF]. (b) Ti 3+ /Ti 4+ spectral weight ratio and relative Al 2p core level shift from XPS measurements performed in LAO/STO samples in different conditions (information in the x-axis in chronological order). Adapted from [START_REF] Scheiderer | Surface-interface coupling in an oxide heterostructure: Impact of adsorbates on LaAlO 3 /SrTiO 3[END_REF]. (c) Water dissociation at AlO 2 -terminated LAO surface. Adsorption of dissociated/molecular water bonds with the surface, releasing electrons that contribute to the conduction at the LAO/STO interface. Adapted from [START_REF] Adhikari | Charge Transfer to LaAlO 3 /SrTiO 3 Interfaces Controlled by Surface Water Adsorption and Proton Hopping[END_REF].

properties of the buried q2DEG.

This feature was first exploited by Cen et al., where a biased AFM tip was used to "write" and "erase" nano-scale conducting paths in LAO//STO heterostructures [START_REF] Cen | Nanoscale control of an interfacial metal-insulator transition at room temperature[END_REF]. The concept was simple: if the insulator-to-metal transition occurs at 4 uc, a sample with 3 uc should, in principle, be at the verge of conductivity. By locally altering the chemical and electrostatic properties of the surface, for example creating/filling oxygen vacancies at the LAO surface, conductivity could be reversibly induced at the interface. The ability to generate nano-wires in a system with such a rich physical spectrum, unleashed exciting prospects for the exploration of single-electron effects or even quasi-1D superconductivity [START_REF] Cen | Oxide Nanoelectronics on Demand[END_REF]. This technique was readily utilized by other groups, who analyzed in more detail the physical and chemical aspects of this patterning method. Xie et al. associated the effect of the biased AFM tip with the control of free surface charges [START_REF] Xie | Charge Writing at the LaAlO 3 /SrTiO 3 Surface[END_REF][START_REF] Xie | Tuning the Electron Gas at an Oxide Heterointerface via Free Surface Charges[END_REF]. Bi et al. went further and described a "water-cycle" mechanism, which took into consideration the presence of OH -and H + ions from dissociated water molecules at the LAO surface [START_REF] Bi | Water-cycle mechanism for writing and erasing nanostructures at the LaAlO 3 /SrTiO 3 interface[END_REF]. It was concluded that a biased tip could locally control the concentration ratio of these two species, to turn the interfacial conductivity on or off. Note that the effect was suppressed when the experiments were performed under vacuum or a dry inert gas atmosphere.

In the following years, a great amount of work was dedicated into the understanding of chemical reactions at the LAO surface. Xie et al. achieved a carrier density tunability of ∼ 2 × 10 13 cm -2 by submerging LAO//STO samples in different polar solvents, emphasizing the discrepancy in results between in-situ and ex-situ measurements within the LAO//STO community [START_REF] Xie | Control of electronic conduction at an oxide heterointerface using surface polar adsorbates[END_REF]. Using DFT calculations, Bristowe et al. predicted a stabilization of surface redox reactions at 4 uc, which lead to the formation of oxygen vacancies at the LAO surface [START_REF] Bristowe | Surface defects and conduction in polar oxide heterostructures[END_REF]. Soft x-ray angle resolved photoelectron spectrocopy (SX-ARPES) by Berner et al. were also consistent with the formation of oxygen vancancies, which induced in-gap states at the LAO surface [START_REF] Berner | Band alignment in LaAlO 3 /SrTiO 3 oxide heterostructures inferred from hard x-ray photoelectron spectroscopy[END_REF]. These vacancies would then release electrons that were transferred to the interface by the LAO polar field. Scheiderer et al. showed through x-ray photoelectron spectroscopy (XPS) that controlled dosing of H and H 2 O in the measuring chamber can effectively tune the Ti 3+ signature [START_REF] Scheiderer | Surface-interface coupling in an oxide heterostructure: Impact of adsorbates on LaAlO 3 /SrTiO 3[END_REF]. In a similar fashion, Adhikari et al. studied the role of surface protonation in the q2DEG properties [START_REF] Adhikari | Charge Transfer to LaAlO 3 /SrTiO 3 Interfaces Controlled by Surface Water Adsorption and Proton Hopping[END_REF]. Lastly, surface reactions were successfully used as non-destructive and reversible patterning methods, through the use of optical illumination [START_REF] Brown | Giant conductivity switching of LaAlO 3 /SrTiO 3 heterointerfaces governed by surface protonation[END_REF] and oxygen plasma treatment [START_REF] Dai | Tailoring LaAlO 3 /SrTiO 3 Interface Metallicity by Oxygen Surface Adsorbates[END_REF].

Polarity-induced defects

In general, the different mechanisms described above (polar catastrophe, oxygen vacancies at the interface, cation intermixing and oxygen vacancies in LAO) were able to successfully explain specific experimental observations of the LAO//STO interface. However, they failed to provide a unified theory that could describe all the physical phenomena simultaneously. In 2014, Yu and Zunger formulated a polarity-induced defect mechanism that could, in principle, explain several puzzling features of the q2DEG, for both n-type and p-type interfaces [START_REF] Yu | A polarity-induced defect mechanism for conductivity and magnetism at polar-nonpolar oxide interfaces[END_REF].

They started by discarding a purely electrostatic and defect-free scenario. Firstly, since it was previously observed that the internal electric field of the LAO layer is much weaker than initially thought by the polar catastrophe model [START_REF] Segal | X-ray photoemission studies of the metal-insulator transition in LaAlO 3 /SrTiO 3 structures grown by molecular beam epitaxy[END_REF][START_REF] Huang | Mapping Band Alignment across Complex Oxide Heterointerfaces[END_REF][START_REF] Slooten | Hard x-ray photoemission and density functional theory study of the internal electric field in SrTiO 3 /LaAlO 3 oxide heterostructures[END_REF], band bending of the LAO valence band maximum over the STO conduction band minimum (see Fig. 2.8b) was considered highly unlikely. Secondly, the formation of the q2DEG due to interfacial substitution (La-on-Sr and Ti-on-Al) or oxygen vacancy formation V O was also considered improbable.

Below the critical thickness t c < 4 uc, the Fermi level E F lies around the middle of the STO band gap (see Fig. 2.12a), and the formation energy of interfacial antisite defects, such as La 0 Sr (I) and T i 0 Al (I), was observed to be energetically favorable (see their negative energy of formation in Fig. 2.12b). Even though this indeed promotes cation intermixing, both defects are stable in their charge neural states, therefore contributing with no free carriers to the system. Charged defects can also form at the surface of LAO due to Ti-on-Al substitutions 2.12a, as both defect states are located deep in the band gap, electrons remain bonded on the interfacial deep acceptor states, leading to an insulating interface.

[T i + Al (S)
Oxygen vacancies at the interface V O (I) show an opposite behavior, but a similar outcome.

As seen in Fig. 2.12b, V O (I) were observed to be energetically stable in their charged state V ++ O , but their formation energy is rather high, leading to very low concentration of these defects. In addition, even if these defects form, they are easily removed by the usual high temperature and rich oxygen pressure annealing process (see Fig. 2

.6).

Above the critical thickness t c ≥ 4 uc, oxygen vacancies at the surface of LAO V O (S) were observed to be thermodinamically favorable. First, and as observed in Fig. 2.12d, the formation energy of these defects decreases linearly as the thickness of the LAO film increases, so that at t > 3-4 uc, V O (S) are able to form spontaneously. Concomitantly, E F is now pinned around the conducting band minimum of STO 12 , so that shallow donor levels at the surface are formed. Due to the polar field, electrons released by these defects are driven towards the interface, to form the q2DEG, and to the Al - T i (I) defect states, where they become trapped, hence explaining the "missing electrons" observed in transport experiments.

Both below and above the critical thickness, the T i Al and Al T i defect pairs and V O (S) allow the transfer of electrons to the interface and contribute as the two main sources of polar field cancellation, supporting the weak polar field observed experimentally [START_REF] Segal | X-ray photoemission studies of the metal-insulator transition in LaAlO 3 /SrTiO 3 structures grown by molecular beam epitaxy[END_REF][START_REF] Huang | Mapping Band Alignment across Complex Oxide Heterointerfaces[END_REF][START_REF] Slooten | Hard x-ray photoemission and density functional theory study of the internal electric field in SrTiO 3 /LaAlO 3 oxide heterostructures[END_REF][START_REF] Berner | Band alignment in LaAlO 3 /SrTiO 3 oxide heterostructures inferred from hard x-ray photoelectron spectroscopy[END_REF].

As shown in Fig. 2.12b, Al T i defects prefer to stay in a negative charge state, meaning they will essentially act as interfacial electron traps. Below t c , all electrons are transferred to the interface, to partially cancel the polar field and become trapped. Above t c , with the spontaneous formation of V O (S), the energy formation of Ti-on-Al defects increases to positive values (see Fig. 2.12e). The reduced concentration of Al T i defects is not sufficient to trap all electrons coming for V O (S), and only some of them stay available for conduction.

The insulating character of the p-type interface is justified by the absence of any shallow electron donors. The polar discontinuity present is accommodated through the creation of La + Sr (I) defects, that generate deep donor levels at the interface. The electrons are driven by the polar field towards the LAO surface, where they become trapped in deep levels due to Sr - La (S) defects and La vacancies V - La (S). Summarizing, even if the q2DEG formation is concluded to arise from polarity-induced defect formation, electrostatics, especially related to the polar field, as still an essential ingredient. In fact, the polar field plays a crucial role, as it allows electron transfer to the interface and lowers the formation energy of V O (S) as the thickness increases. As we will see in the sections ahead, altering the surface conditions should, in principle, change the formation energy of V O (S), so that the critical thickness, vacancy formation and expected free electrons at the q2DEG become tunable properties that should change drastically when adding a capping layer on top of the LAO//STO heterostructure [START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. ,c) adapted from [START_REF] Fete | Magnetotransport experiments at the LaAlO 3 /SrTiO 3 interface[END_REF] and (b) adapted from [START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF].

Electronic properties and band structure

As we described in Section 2.1, the conduction band of STO is composed of empty Ti 3d orbitals that, due to the cubic crystal field, split into a degenerate doublet e g and degenerate triplet t 2g states (see Fig. 2.1b). In the LAO//STO heterostructure, the interface confinement and SOC further split the t 2g states in d xy and d xz /d yz orbitals [START_REF] Fete | Magnetotransport experiments at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF]. As displayed in Fig. In bulk STO, due to the different overlaps between neighboring Ti 3d orbitals, the band structure of the t 2g triplet consists of three ellipsoids with a long axes along the three main directions, as displayed in Fig. 2.13b. The d xy orbitals are oriented along the (x, y) plane, so that they overlap equally with each other along both x and y directions (see Fig. In LAO//STO, the heavy d x z/yz bands are essentially pushed to higher energies. This can be observed in the cross-section of the band structure of Ti 3d states at the LAO//STO interface, along the xz and xy plane, as displayed in Fig. 2.14a and 2.14c, respectively. Notice also the elongation along the least favorable hopping directions. In addition, angle-resolved photoemission spectroscopy (ARPES) has been extensively used to image the band structure at STO surfaces [194,[START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF][START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF][START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF] and LAO//STO interfaces [START_REF] Cancellieri | Polaronic metal state at the LaAlO 3 /SrTiO 3 interface[END_REF]. To exemplify this, the ARPES data collected for the band structure of the q2DEG at the surface of STO is displayed in Fig. 2.13b and 2.13d, exhibiting remarkable similarity to the theoretical predictions.

Given the effective masses of the three bands, their relative positions (in energy) within the q2DEG potential well can be understood. In the z direction, the d xy bands have an higher effective mass, so that they will lie at a lower energy, when compared to DFT calculations [START_REF] Popović | Origin of the Two-Dimensional Electron Gas Carrier Density at the LaAlO 3 on SrTiO 3 Interface[END_REF][START_REF] Delugas | Spontaneous 2-Dimensional Carrier Confinement at the n-type LaAlO 3 /SrTiO 3 Interface[END_REF][START_REF] Khalsa | Theory of the SrTiO 3 surface state two-dimensional electron gas[END_REF][START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF]. We add that all of these properties can be changed by multiple effects. Applying an external electric field leads to changes in the carrier density of the q2DEG, shifting the E F up/down in energy, and leading to transitions between single and multiband transport [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF]. Simultaneously, at low temperature the dielectric constant of STO sees an enourmous increase, which leads to alterations in the depth profile [START_REF] Reich | Accumulation, inversion, and depletion layers in SrTiO 3[END_REF].

d
Lastly, SOC also plays an important role regarding the band structure, especially through Adapted from [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF].

strongly mixed. Joshua et al. argued that the strongest effect in the system is the atomic SOC, which is especially prominent when d -bands are degenerate [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. They calculated that, while adding carriers to the interface (shifting the E F up in energy), a maximum of spin-orbit strength (L.S product) is observed at these avoided crossing points. Other authors confirmed this, predicting an increase of the Rashba splitting by one order of magnitude (linked to the atomic SOC), when reaching these special points [START_REF] Khalsa | Theory of the SrTiO 3 surface state two-dimensional electron gas[END_REF][START_REF] Zhong | Theory of spin-orbit coupling at LaAlO 3 /SrTiO 3 interfaces and SrTiO 3 surfaces[END_REF][START_REF] Shanavas | Theoretical study of the cubic Rashba effect at the SrTiO 3 (001) surfaces[END_REF].

Due the extremelly small energy scales at play, directly observing this phenomena has been quite a challenge. In fact, ARPES measurements regarding SOC in STO have been nothing but controvertial. Santander-Syro et al. observed a giant Rashba splitting on STOcleaved surfaces, with a distance between the two band minima of 0.1 Å -1 , when the expected found [START_REF] Walker | Absence of giant spin splitting in the two-dimensional electron liquid at the surface of SrTiO 3 (001)[END_REF]. Regardless, the Rashba SOC enhancement was still found to be consistent with several magnetotransport experiments [START_REF] Caviglia | Electric field control of the LaAlO 3 /SrTiO 3 interface ground state[END_REF][START_REF] Fête | Rashba induced magnetoconductance oscillations in the LaAlO 3 -SrTiO 3 heterostructure[END_REF][START_REF] Fête | Large modulation of the Shubnikov-de Haas oscillations by the Rashba interaction at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Liang | Nonmonotonically tunable Rashba spin-orbit coupling by multiple-band filling control in SrTiO 3 -based interfacial d-electron gases[END_REF].

ε c -V 0 n = 1 n = 2 n = 3 ε c -V(z) ε z z n n(d xy ) n(d xz / d yz ) (a)
Since these Rashba SOC maxima are observed at the crossing between bands with different orbital character, it is naively expected that the effect is driven by inter-orbital hopping, where delocalization in the z direction increases (hybridization between d xy and d xz/yz bands).

King et al. also predict exotic coupled spin-orbital textures in these regions [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF]. While one expects Rashba-like perpendicular spin-momentum locking, they observed spin alignment perpendicular to the Fermi surface for large sections of the d xz/yz bands, in addition to the finite orbital angular momentum for the isolated d xy and d xz/yz bands (which should be quenched).

In Chapter 3, we will exploit this feature of the q2DEG to perform spin-to-charge current conversion, while shedding some light on the fascinating inter-band interactions.

Experimental procedure

In the following section, we describe the full procedure for the growth, morphological, electrical and chemical analysis of our LAO//STO and metal/LAO//STO samples. To do this, we take advantage of a system, shown in Fig. 2.16, which combines pulsed laser deposition, magnetron sputtering and x-ray photoelectron spectroscopy, all connected in vacuum through a cluster (at the center). This allows us to perform several different experiments in situ, i.e.

without breaking vacuum; an extremely important feature in the analysis of surface sensitive phenomena.

We start by giving a brief introduction of each technique, followed by the step-by-step procedure. During this experimental section, we will also provide several details regarding what went wrong during each step, as well as usefull "tricks and tips", which usually get neglected in most scientific articles. In principle, this section can be used as a guide to reproduce all of the results attained in this section. This experimental procedure may also be found in video form in Ref. [START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF]. atomically flat SrO-terminated STO (001) substrates after a 72h annealing at 1300 • C (in air) [START_REF] Bachelet | Atomically flat SrO-terminated SrTiO 3 (001) substrate[END_REF]. Lastly, SrO-termination was also found to be less stable than TiO 2 -termination [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF].

However, in both cases the termination can degrade in a matter of days/weeks by simply leaving the substrates exposed to air. We start by filling an ultrasonic cleaner and heat it to 60 • C. We fill a borosilicate glass beaker with acetone, and place an out of the box mix-terminated single-side polished (001)oriented STO single-crystal substrate (55 mm 2 in lateral size, 0.5 mm in thickness with a miscut angle between 0.01°and 0.02°) inside the borosilicate glass beaker. We proceed to sonicate the substrate in acetone for 3 min and dry it using a nitrogen blow gun. We then repeat this procedure but using isopropanol and then deionized water, to ensure that the surface is as clean as possible.

Then, we place the clean substrate in a sample holder made of polyvinylidene fluoride, PVDF, with a "dipper" shape (see Fig. 2.17a). It is important to choose a dipper made of a material that sustains the acidic HF solution. We then fill a large borosilicate glass beaker with running deionized water (see Fig. 2.17b). After placing the substrate in the dipper, we fill a beaker, typically made of Polytetrafluoroethylene, PTFE, to about 20% of its maximum volume, with a buffered hydrofluoric (HF) solution (HF:NH 4 F = 1:7) 13 . Then, we submerge the dipper in HF for exactly 30 s and immediately move it into the deionized running water to stop any subsequent chemical reactions. After 2 min, we remove the sample holder from the deionized water, and dry the substrate with a nitrogen blow gun.

We follow the chemical treatment with a high-temperature annealing step under rich oxygen environment. After inserting the sample in an appropriate furnace (see Fig. 2.17c), we ramp the temperature to 1000 • C at a rate of 20 • C/min, and leave it for 3 hours at that temperature. After this, we let the sample cool down to 20 • C.

To ensure the quality of the surface, we perform atomic force microscopy scans in tapping mode, before and after this procedure, as displayed in Figs. 2.18a and 2.18b, respectively.

Note the random corrugations at the surface of the untreated STO, with an average height of about 0.70 nm. After treatment, we attain the "terrace-like" surface with steps with an average length of ∼ 200 nm, and a height of 0.48 ± 0.07 nm, approximately 1 uc of STO. Note that the length of the steps depends solely on the initial miscut angle.

During substrate termination, one should be extra careful with the submerging time in HF solution. We observed over-etched surfaces by varying just 5 s with regard to the original recipe. Additionally, we observed a dependence between substrate step size and submerging time. For smaller step sizes (less than 100 nm) submerging 30 s might lead to over-etching, even though afterwards the annealing procedure might be sufficient to properly reconstruct the surface.

Pulsed laser deposition and reflection high-energy electron diffraction

Pulsed laser deposition (PLD) is a physical vapor deposition technique that enables the growth of thin-films at an atomic scale. The technique gained popularity in the later 1980's, after its successful implementation on the epitaxial growth of high temperature superconducting films [START_REF] Inam | As-deposited high T c and J c superconducting thin films made at low temperatures[END_REF], which required a very specific stoichiometry in order to achieve the superconducting state.

In PLD, a pulsed laser is focused and shot onto a target of the material to be deposited.

If the laser energy density is large enough, each pulse will ablate a small amount of material, generating a plasma plume, as shown in Fig. 2.19a. A substrate is usually placed in front of the target, so that the species within the plume get deposited on it, slowly forming an atomic sized thin-film.

There are several features for which PLD gained so much popularity, especially within the complex oxides community. First, it enables stoichiometric transfer of ablated material from a target with multiple species. The transfer of material will depend heavily on the energy density (or fluence) of the laser used, as well as on the absorption properties of the target. For a low laser fluence (or low target absorption), the laser pulse will simply heat the target, leading to potential thermal evaporation of species. When the fluence is increased, an ablation threshold is reached, and a small volume of material can be effectively ablated. The laser wavelength should also be carefully chosen, having in mind the type of material to be ablated. For an excessively large fluence, the laser might penetrate deep inside the target, resulting in the ablation of micron-sized particles, which naturally imposes a problem on the growth of fine multilayer structures. Second, the technique is compatible with background pressures ranging from ultra high vacuum (UHV) up to 1 bar. In fact, the introduction of a background gas during growth serves two purposes. On one hand, the growth of thin-films often require reactive species (oxygen in the case of complex oxides), which defines the desired phase of the grown film. From a chemical perspective, one might therefore grow completely different thin-films, using the same target and different oxygen pressures. On the other hand, it can be used to reduce the kinetic energies of the ablated species. Lastly, experimentally speaking, PLD is a rather simple technique, even though the many parameters can make optimization a arduous process.

In principle, each ablation pulse will only provide enough material for the deposition of a submonolayer, with the specific amount depending on factors like fluence, pressure, target-tosubstrate distance and laser spot size. Precise control of the growth speed can be achieved using reflection high-energy electron diffraction (RHEED). In this technique, an electron beam, with energies typically ranging between 10-100 keV, irradiates the substrate surface at grazing angle, resulting in forward scattered diffraction patterns, that can be emitted and monitored using a phosphor screen and a camera. From the intensity, arrangement and profile of the diffraction patterns, one is able to obtain valuable information on the surface condition: the periodicity of the atomic arrangements, flatness of the surface, potential growth of thin-films vs. islands, among others. Particularly, one can also learn about the growth mode. For example, if the laser fluence is too large, species at the surface might not have enough time to propagate and reorganize at the surface, so that 3D islands are favorably formed. See Fig.

2.19b

for some examples. However, in an ideal layer-by-layer growth, we expect to see the intensity of the diffraction spots to oscillate, as shown in Fig. 2.19c. Maximum intensity is achieved when the surface is fully covered (or before growth). As species arrive to the surface, the morphology becomes more irregular, which lowers the spot intensity. As a new layer is starting to form, the intensity goes back up towards another maximum.

In the next few paragraphs, we describe the growth of LAO//STO heterostructures using a combination of PLD and RHEED, in a chamber designed by SURFACE GmbH & Co. KG (see Figs. 2.20a and 2.20b). We start by preparing the single-crystal LAO target (provided by CrysTec GmbH) with 1-inch diameter. To do this, the surface of the target is mechanically polished using a soft sandpaper and isopropanol as lubricant. The target is normally polished every 15 to 20 growth processes, to ensure surface uniformity. We advise the use of single crystal targets to avoid the possible preferential ablation of specific species, which might occur for example in ceramic/sintered targets. In our case, samples grown with a ceramic target resulted in insulating LAO//STO samples, most likely due to off stoichiometry of the grown films [START_REF] Warusawithana | LaAlO 3 stoichiometry is key to electron liquid formation at LaAlO 3 /SrTiO 3 interfaces[END_REF].

Protocol -LAO target preparation

After drying the target with a nitrogen blow gun, we mount it in a carousel. The carousel is inserted inside the loadlock chamber and transferred in vacuo to the PLD chamber. Note that, in Fig. 2.20c, the whole carousel allows rotation between different targets, as well as rotation of each target.

Before pre-ablating the LAO target, i.e. "cleaning" the surface by ablating it several times, we inspect the laser energy with an energy meter (Coherent J-50MUV-248). In our The laser path can be seen in Fig. 2.21a and 2.21b. Right after exiting the source, the size of the beam is modulated using a slit. Depending on its size and shape, we are able to perform ablation at different energy ranges and spot sizes. The intensity of the beam is then modulated by a variable attenuator (Metrolux ML 2100) at constant operation voltage (∼ 21 kV). The laser beam is finally focused on the surface of the target, using two converging lenses. Placing the energy meter between the quartz window and the second converging lens, we calibrate the laser energy to find a desired rate and intensity (similar to the parameters used during growth, as discussed in the paragraphs ahead). Even though the absolute values may change over time, we aim at a fluence of about 1 J/cm 2 , where the fluence = energy/spot area [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF].

We start the rotation of the target. As shown in Fig. 2.21c, the custom target rotation allows ablation in consecutively smaller semi-circles, to avoid two consecutive overlapping shots, which could potentially lead to some local overheating or melting of the target and subsequent off-stoichiometry. We insert oxygen in the chamber, until a partial pressure of 2 × 10 -4 mbar is achieved (same as during growth). After removing the energy meter, the laser rate is set to 3 or 4 Hz and the target is pre-ablated for 20000 pulses. At first, the long pre-ablation step might seem overly long. However, we observed that the transport properties of conducting LAO//STO deteriorate extremely quickly by overlooking this step. Notably, pre-ablating with less than 10000 pulses repeatedly showed insulating LAO//STO interfaces.

Protocol -LAO film growth

After assuring that the STO substrate is clean, we glue it, with the terminated surface pointing upwards, to a special holder using silver paste (DuPont 4929N Conductive Silver Composite). The holder is heated in a hotplate at 100 • C for about 10 min so that the solvent evaporates and the silver pastes solidifies. After letting it cooldown, we insert it in the loadlock and transfer it to the PLD chamber. At this stage, the substrate's surface should be facing down towards the target, as shown in Fig. 2.22a.

Oxygen is inserted in the chamber until a partial pressure of 2 × 10 -4 mbar is reached.

Then, the temperature of the holder is raised to 730 • C at a rate of 25 • C/min, using an infrared laser heater, positioned above the holder. The high temperature used is essential for three main reasons, which together allow 2D layer-by-layer growth: the increased diffusivity of the adatoms as they reach the surface of the substrate, reduction of nucleation densities and recrystallization of the thin film grown. At room temperature, the species simply adhere to the surface the moment they touch it, which naturally drives the formation of 3D island and non- crystalline films. Even though this is clearly undesirable for epitaxial growth of LAO//STO, it can be used to grow amorphous films of LAO (a-LAO).

With both pressure and temperature stabilized, we set the RHEED gun to a source voltage of 30 kV and an average current of 40 µA, and align it at a grazing angle with the substrate's surface (1°to 3°), so that the diffraction spots are observed on the phosphor screen (see Figs.

2.22a and 2.22b

). On the other side of the phosphor screen, a CCD camera is used to monitor in real-time the intensity of each spot. The RHEED gun alignment is made so that the targetto-substrate distance is 63 mm. As mentioned before, this parameter is essential to achieve the correct stoichiometry, and should therefore be thoroughly optimized depending on the geometry of the PLD used.

Similarly to the laser calibration procedure performed for the target pre-ablation, we place the energy meter in the path of the laser to measure its intensity, aiming for a fluence of approximately 1 J/cm 2 . Practically, since the laser energy measurement is done outside the chamber and the inner side of the laser entrance window gets coated over time, which yields to a loss of transmission, we guide ourselves by targeting a constant growth rate value instead.

After about 15 growths, the window can differ up to 20 mJ from the energy measured outside.

The optimized growth rate for LAO was found to be approximately 25 pulses/uc for our specific PLD growth process, equivalent to an (outside) energy of about 60 mJ.

The laser is set to a repetition rate of 1 Hz. With a rotating target and the RHEED spot intensity being recorded, we start the growth. Immediately, the RHEED signal intensity, shown in Fig. 2.22b, drops, as new La and Al species start to arrive at the substrate's surface.

As observed, the intensity after one oscillation, i.e. one uc grown, does not go back to the initial value. This indicates that the growth may not be 100% layer-by-layer, and some small islands may form during the growth of the film. However, as demonstrated ahead, TEM imaging showed good uniformity, and confirmed, together with standard X-ray diffraction, the correct corresponding number of LAO unit cells. Additionally, we can see in Fig. 2.22c the rather weak and purple plume created through ablation of the LAO target.

Following the growth of the desired LAO film thickness, we perform a post-annealing step, where the temperature is lowered to 500 • C, and the oxygen partial pressured is raised to 300 mbar. The sample is left in these conditions for 1 hour. After that, it is cooled to room temperature under the same pressure, at about 25 • C/min. This step is of extreme importance in order to fill oxygen vacancies at the STO substrate, which are favorably formed due to the high temperatures and can induce bulk conductivity. It was observed that, after post-annealing in a rich oxygen environment, the only conducting path left is the q2DEG formed at the LAO//STO interface [START_REF] Basletic | Mapping the spatial distribution of charge carriers in LaAlO 3 /SrTiO 3 heterostructures[END_REF]. For clarity, we show in Fig. 2.23, the time evolution of the whole growth procedure.

We end this section by mentioning that the fabrication of LAO//STO structures has also been successfully achieved by molecular beam epitaxy (MBE). Even though both techniques require a high level of optimization, MBE should be particularly used when the interface quality is critical for the experiment, as it provides high quality heterostructures with a great control of layer thickness and very low defect concentration [START_REF] Schlom | Perspective: Oxide molecular-beam epitaxy rocks![END_REF]. Yet, it possesses slower deposition rates and involves a larger financial investment. PLD on the other hand also provides the means to create high quality samples. It has the benefits of being versatile, cost-efficient, fast (growth itself may last less than 2 min) and conceptually simple. It might however lead to a slightly larger concentration of defects, since it is based on the ablation of high energy species against the substrate. As an example, a comparative study of LaNiO 3 /LaAlO 3 heterostructures grown by PLD and MBE is shown in Ref. [START_REF] Wrobel | Comparative study of LaNiO 3 /LaAlO 3 heterostructures grown by pulsed laser deposition and oxide molecular beam epitaxy[END_REF]. Note also that while MBE has been implemented before for large scale deposition of different materials, PLD is now also being considered as a possible candidate for industrial applications [START_REF] Blank | Pulsed laser deposition in Twente: from research tool towards industrial deposition[END_REF].

For an extensive review on the physics and application of PLD and RHEED, we refer the reader to Ref. [START_REF] Eason | Pulsed Laser Deposition[END_REF] and [START_REF] Braun | Applied RHEED: Reflection High-Energy Electron Diffraction During Crystal Growth[END_REF].

Magnetron sputtering

Sputtering is a physical vapor deposition process, commonly used for the growth of thin films.

As shown in Fig. 2.24a, when a target is bombarded with energetic ions generated by a discharge plasma, surface atoms are removed, i.e. sputtered. If a substrate is placed near the plasma region, the ejected species may condense at the surface, forming a thin film of the target material. The plasma is usually created through a high voltage or RF power source, and can be maintained due to secondary electrons that are emitted from the target surface during ion bombardment. The classic sputtering process is quite versatile, but is limited by low deposition rates, low ionization efficiencies in the plasma, and substrate heating effects [START_REF] Kelly | Magnetron sputtering: a review of recent developments and applications[END_REF].

Magnetron sputtering (and other variations) were developed to circumvent some of these issues. By placing magnets all around the target forming a ring shape (see Fig. 2.24b) and a magnet with opposite polarity at the center, the magnetic field created constrains the secondary electrons to the vicinity of the target, increasing ionization efficiency of the plasma, which in turn yields higher sputtering rates. Consequently, the plasma discharge can be maintained at much lower operating pressures and voltages. Adapted from [START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF].

For our experiments, we use a sputtering system built by PLASSYS (displayed in Fig.

2.24c

), which is composed of five different targets and an automated mechanism that places the substrate holder in the specified position. The system is exclusively equipped with metallic targets with about 2 inches of diameter and 5 mm thick 14 , sintered and provided by Neyco S.A.

Protocol

Starting from either a bare STO substrate or an LAO//STO heterostructure, we place it inside the sputtering chamber with the surface facing down, towards the target. Ar, which will serve as the reactive gas, is inserted in the chamber with a flow of about 100 sccm, until a pressure of 4.5 × 10 -4 mbar is reached. The substrate-to-target distance is adjusted depending on the target used. Naturally, a calibration procedure is priorly performed for each target. To do this, we deposit the desired material for several arbitrary periods of time, and inspect the thickness using X-ray reflectometry, so that the growth rate can be defined for the parameters used. As an example, for the growth of Co, the substrate-to-target distance is 7 cm.

With the shutter closed, we ramp the DC current to about 100 mA (36 W) so that the plasma is ignited. After stabilizing, the current is lowered to 80 mA (deposition current) and the inflow of Ar is reduced to 5.2 sccm 15 . With a stable plasma, we wait about 5 min (presputtering step), in order to remove any oxide phase that might have formed at the surface of the target. After this time, the shutter is open for a given time, usually a few tens of seconds for very thin layer (<2 nm) and a few minutes for thicker films, and the deposition is performed. See Fig. 2.24d for the interior of the chamber during this step. If the sample will be used for transport experiments, a protective Al capping layer is usually deposited (at the end of the experiment) to prevent oxidation of the layers underneath. Finally, the current and Ar flow are lowered to zero and the chamber is pumped back to UHV.

We emphasize that different metals have different wetting behaviors on top of oxide substrates [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF]. We advise increasing the thickness accordingly to achieve full coverage, since films under a few nm thick might result in non-percolated layers. Usually, this can be checked through AFM or scanning electron microscopy characterization, to verify good uniformity.

Using slower deposition rates and less energetic incoming species is also recommended, to finely control the film's thickness and avoid possible penetration of sputtered species into the sample. To do this, one might increase the substrate-to-target distance and/or reduce the plasma excitation current.

In the following section we fabricate LAO//STO samples capped with metals such as Al, Ti, Ta, Co, Nb, NiFe, Pt, Pd and Au. Interestingly, depending on their chemical and electronic properties all materials have a different influence on the q2DEG formed. Illustration of the photoelectron emission process from a solid material. The photoelectron loses energy on the solid itself (white circles) or on adsorbate at the surface (grey circles).

Adapted from [START_REF] Van Der Heide | X-ray Photoelectron Spectroscopy[END_REF].

2.4.2 Chemical and electronic analysis 2.4.2.1 X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy (XPS) is the most used electron emission technique for defining the element composition of surfaces of solids, allowing identification and quantification of elements, chemical states and electronic states within 10 nm of a solid surface (assuming that the element exists in a concentration above 0.1 atomic %). Its origins can be traced back to 1887, when Hertz noted that sparks would form when an electrically isolated metal was exposed to light [START_REF] Hertz | Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung[END_REF]. Later in 1905, Albert Einstein explained this phenomenon as an energy transfer between incident photons and electrons bound to the atoms of the metallic material [START_REF] Einstein | Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen[END_REF], granting him the Nobel prize in Physics in 1921. It took however 50 years for these concepts to be practically used in what is now known as XPS. Siegbhan et al. were the first to build an instrument that could analyze core photoelectron emissions with enough resolution to allow elemental detection and analysis [START_REF] Siegbahn | ESCA Atomic, Molecular and Solid State Structure Studies By Means of Electron Spectroscopy[END_REF], which also granted him the Nobel prize in Physics in 1981. Up to this date, the understanding and technical improvement of XPS has not stopped.

In regards to elemental detection, H and He are exceptionally not easily detected with this technique, due to their extremely small photoelectron cross-section 16 . Also, since XPS is optimized for the analysis of core electrons, an element like H, that needs to share its only electron in forming compounds, cannot be detected. These setbacks can be overcome with extremely long collection times or specific variations of the technique itself. For example, valence electrons may be efficiently detected through Ultraviolet photoelectron spectroscopy (UPS). Also, Auger electron spectroscopy (AES) can be used when increased spatial resolution is needed (at the cost of sensitivity) and Wavelength-dispersive X-ray analysis (WDX) or Energy-dispersive X-ray analysis (EDX) for enlarged depth of analysis to about 1 µm (or more) below the surface.

Photoelectrons can be described as a one step process where an electron initially bounded to an atom or ion is ejected by a photon. Since photons are massless entities, they are annihilated when photon-electron interaction occurs. If the energy transfer that occurs from this interaction is large enough, the electron is able to escape and be emitted out of the atom/ion (depending on its position in the solid). The electron's remaining kinetic energy (K.E.), once it exits the solid, depends therefore on the amount of energy required to unbound the electron, as well as on the incident photon energy.

In Fig. 2.25a, we show a schematic example of the photoelectron emission process in an oxygen atoms. On the left, we observe the emission of a core electron (1s) due to the incident X-ray energy, described above. On the right, we notice that the vacancy formed when an inner-shell electron (1s) is ejected from an atom can also be filled by an electron from a higher energy shell (2s). This process results in an additional release of energy. While this energy is usually emitted as a photon, it can also be absorbed by another electron (2p) which is then ejected from the atom. This subsequent emitted electrons are called Auger electrons. The kinetic energy of an Auger electron corresponds to the difference between the energy of the initial electronic transition and the ionization energy of the ejected electron's shell.

XPS analysis is usually carried out by preliminary energy sweep over all accessible energies, as shown in Fig.

K.E. = E ph -φ XP S -B.E., (2.2)
where E ph is the incoming photon energy, defined by the type of X-ray source used, and φ XP S the work function of the instrument, since there is an associated energy cost to transport an electron from the sample to the analyzer. Note that Eq. 2.2 does not apply to Auger electrons since these are only related to internal atomic relaxations and thus are photon energy independent (fixed K.E.). For core electrons the K.E. is dependent on this photon energy, so that the B.E. is fixed. Changing the energy of the X-ray source is therefore a powerful way to distinguish between a Auger and a photoelectron peak. For different photon energies, if the B.E. of the peak moves, then it can be identified as an Auger electron peak.

Technical Features

There are several prerequisites that ensure effective data collection in XPS. Among them, the most important are the vacuum system, the X-ray source and energy analyzer. After collection, the data needs to be carefully analyzed, with the help of reference books with peak positioning and other special features of each element [START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF].

First, the quality of the vacuum during XPS analysis should not be overlooked. On one hand, electrons ejected from the sample need to travel a short distance until they reach the detector. Naturally, under poor vacuum conditions, their mean free path is strongly reduced, since electrons are deflected and attenuated by gaseous particles inside the chamber. Under these conditions, the fine details of relevant peaks may be completely destroyed. On the other hand, being a surface sensitive technique, the quality of the data collected will depend heavily on the state of the sample's surface. Even in samples that were thoroughly cleaned prior to the analysis, particles will still be adsorbed at the surface, forming a thin layer that interferes with the ejected electrons. This can be schematically seen in Fig. 2.25c, where electrons from By adjusting the electron take-off angle, with respect to the analyser, a different sampled volume may be attained (normally with smaller volume probed for higher take-off angles). Adapted from [START_REF] Van Der Heide | X-ray Photoelectron Spectroscopy[END_REF].

deeper layers completely lose their kinetic energy due to adsorbates. One peak that is normally seen in any XPS spectra is the C 1s peak, which in carbon-free samples gives a good idea of how clean the surface is.

Second, the X-ray energy source should be powerful enough to excite core electrons. There are three main types of X-ray sources: standard, monochromatic and synchrotron, with the first two the most commom and commercially available and the third exclusive to dedicated facilities. The standard source is the most versatile, since it can be used with any anode material. Different anode materials allow different energies and have different energy spreads, with the two most commom being Mg and Al. Other materials can be found in Ref. [START_REF] Van Der Heide | X-ray Photoelectron Spectroscopy[END_REF].

The monochromated source consists of the same elements of the standard source, with an additional concave single crystal that produces a focused X-ray beam with a spot size (on the sample) as low as 10 µm. Even though it normally requires a larger investment, the focused beam allows greater photon flux per unit area, leading to higher yield of ejected electrons, and a narrower energy spread of the generated X-rays. Synchrotron-based sources provide any photon energy and even higher photon flux, however they induce greater sample degradation and normally require costly and time limited beam-time in dedicated facilities.

Third, electrons ejected are collected by an energy analyzer. The two main configurations are the cylindrical mirror analyzer (CMA) and hemispherical sector analyzer (HSE). The latter, schematically represented in Fig. 2.26a, is by far the most utilized, as it enables improved energy resolutions (in the order of 0.01 eV). Interestingly, this resolution is much higher than the X-ray source energy spread (0.7 eV for a Mg source, for example), meaning that the bottleneck of energy resolution is primarily defined by the X-ray source. Additionally, the XPS energy spectrum can be collected in two main modes: constant retard ratio (CRR) and constant analyzer energy (CAE), with the latter being the most commonly used (also referred to as pass energy). Lower pass energies, i.e. lower energy of the electrons entering the analyzer, result in improved resolution, normally at the cost of sensitivity.

If the solid analyzed is an insulator, positive charge will accumulate over the area where electron emission occurs. Any positive charge build up will lead to reduced K.E. of the ejected electrons, leading to a higher apparent B.E. This charging effect can be compensated through co-irradiation of the sample with low energy electrons (< 10 eV), usually using what is known as a charge neutralizer, which self-compensates the positively charged surface with new electrons.

In conductive samples this does not occur, since electrons from a grounded terminal will gradually compensate this charge loss.

Lastly, the area and depth of the sample probed can be easily modified for an extended and more detailed analysis. In contrast with experiments performed with a monochromated source, where the X-ray beam can be focused on a specific and rather small region of the sample, the spot size, using standard sources, can be tuned using an aperture with variable size. As exemplified in Fig. 2.26b, even though electrons are ejected from the whole sample, only some of them are allowed to pass towards the detector. Regarding the probing depth, one may aim for a more or less surface sensitive measurement by simply changing the electron takeoff angle, i.e. the angle between the electron ejection direction and the analyzer. As shown on the left side of Fig. 2.26c, if the electron ejection has a 90°takeoff angle (sample's surface parallel to the detector), maximum probing depth is achieved. By tilting the sample, the effective length that electrons can travel inside the sample stays the same, meaning that the available probing depth is reduced (see right side of Fig. 2.26c). As we will see ahead, this In the following paragraphs, we describe a standard procedure to perform XPS analysis on STO, LAO//STO and metal-capped LAO//STO heterostructure. We use a custom XPS system built by Omicron (displayed in Fig. 2.27a), equipped with a non-monochromated Twin Anode X-ray source DAR 400 (with a Al-Kα and Mg-Kα anode) and an energy analyser EA 125.

The experiment starts by placing the sample holder, positioning the substrate/sample surface towards the energy analyzer, as displayed in Fig. 2.27b. Since the X-ray gun is non-monochromated (standard), we approach it as much as possible to the sample, without making contact. Almost all experiments were carried out with the Mg-Kα source, with the Al-Kα being used when additional probing depth was needed. The X-ray gun is turned on, by applying an emission current to the filament of 20 mA, at an anode voltage of 15 kV.

Regarding the analyzer's electron-optics, a circular entrance slit of 2 mm of diameter and an exit slit with rectangular shape of 5x11 mm were used. As stated above, the slit size simply defines the area of the sample's surface to be probed. It can also be used to reduce, since some systems have an upper limit regarding counts/second, or increase the electron count when the signal has poor resolution.

After assuring that UHV condition is met (∼ 10 -10 mbar), we start collecting a survey spectra, between 1200 and 0 eV, with a selected step of 0.05 eV, a dwell time of 0.5 s (i.e. the collection time at each step) and a pass energy of 30 eV. Normally, the lens mode can also be controlled. Since electrons exit the sample with different angles (in regard to the surface), the lens mode allows for a more spread or directional electron collection. Naturally, setting this mode on "low" (preferential collection of electrons exiting the sample perpendicularly), drives the electron count (intensity) down.

As an example, we can see in Fig. 2.27c a survey spectrum for an STO substrate. After identifying the position of each relevant peak, we perform a finer scan with lower step and longer dwell times. For improved statistics, we capture the same peak several times in a row and average the collected spectra. The data is then carefully analyzed in the software CasaXPS. See Section 2.4.2.3 and 2.5.2.2 for more details.

Basics of magnetotransport

In 1958, van der Pauw proposed a method of measuring the resistivity and Hall effect of samples with an arbitrary shape, as long as the sample is flat, solid and the contacts are sufficiently small and placed on its perimeter [START_REF] Van Der Pauw | A method of measuring specific resistivity and Hall effect of discs of arbitrary shape[END_REF]. Unlike the linear four point probe, which was placed on one of the sides of the sample, the four point van der Pauw method provided an average resistivity of the sample. We show in Fig. 2.28a a generic van der Pauw configuration.

When sourcing a current through contacts a and b and measuring the voltage in contacts c and d, the resistance is given as:

R ab,dc = V dc I ab (2.3)
From the reciprocity theorem, R ab,cd = R cd,ab . Switching the polarity of both current and voltage probes, one can obtain the average values in both x and y directions so that R xx = (R ab,dc + R dc,ab )/2 and R yy = (R ad,bc + R bc,ad )/2. With this in mind, van der Pauw derived the following relation for an arbitrary shaped sample:

exp - πt ρ R xx + exp - πt ρ R xy = 1, (2.4)
where t is the thickness of the sample, and ρ its resistivity. As a function of ρ, Eq. 2.4 can be written as:

ρ t = π ln(2) R xx + R yy 2 f, (2.5)
with f the van der Pauw correction factor. f takes values between 1 and ∼ 0.2, and is given as a function of the ratio R xx /R xy . When R xx = R xy , meaning that the sample is perfectly isotropic, f = 1 and Eq. 2.5 reduces to:

R s = R xx π ln(2) , (2.6)
with R s the sheet resistance, given in Ω/ (loosely translated as ohm per aspect ratio).

Hall effect

The Hall effect, introduced in Section 1.5.1, may also be evaluated using the van der Pauw method. Since this effect relies on the in-plane deflection of carriers due to an out-of-plane magnetic field, a current sourced in contacts a and c should, in principle, generate a voltage drop across contacts b and d. With increasing magnetic field, more carrier get deflected and the voltage drop increases (positive or negatively, depending on the type of carriers).

The transverse resistivity measured in a 2D or 3D conductors can be expressed as:

ρ 2D xy = ρ 3D xy t = V - H -V + H I , (2.7)
where I = (I --I + ) is the sourced current and V H the transverse Hall voltage detected.

See the sketch in Fig. 2.28c for more details. Since ρ 2D xy gives the resistivity of a quasi-2D sheet, where the width is much larger than the thickness t, we refer to it simply as R xy . Modified from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF] and [START_REF] Vaz | Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures[END_REF].

Historically, the Hall effect has been used as a powerful tool to determine the doping type, carrier density and mobility in semiconductors. Here, the Hall constant R 2D H can be defined as:

R 2D H = R xy B , (2.8)
which translates, in practice, to the experimental slope of a B vs. R xy curve. This value readily gives the type of (majority) carrier in the system, with positive slope for holes and negative slope for electrons. Moreover, the sheet carrier density n s ≡ n 2D can be expressed as:

n s = 1 qR 2D H (2.9)
The longitudinal resistivity of a semiconductor can also be written as a function of the carrier density n and the mobility µ, assuming that there are only one type of carriers contributing to transport or the concentration of one is orders of magnitude larger than the other:

ρ 3D xx t = 1 qn 3D µ (2.10)
Assuming once again a quasi-2D sheet, the mobility is given as:

µ = 1 qR s n s , (2.11)
where n s is given in electrons per cm 2 (or cm -2 ), and µ in cm 2 .V -1 .s -1 . The puck where the sample is mounted comes with 3 channels, each with 4 pads (V + ,V -,I + ,I -).

Protocol

Since the Dynacool runs the measurement sequentially, i.e. a single internal source applies current to one channel at a time, we bond the first channel in Hall geometry, and the second in longitudinal van der Pauw configuration, as observed in 2.29a and schematically shown in Fig. 2.29b.

Before measuring, the contacts are checked with a multimeter. To ensure that the sample is uniform, we verify if the resistance measured in different directions is roughly the same, so that the van der Pauw R xx ≈ R yy condition is satisfied. If R xx and R yy are significantly different, the van der Pauw measurement should be performed in both directions (following Ref. [START_REF] Van Der Pauw | A method of measuring specific resistivity and Hall effect of discs of arbitrary shape[END_REF]). The importance of this step was elevated by some reports on strong anisotropic electric transport properties in LAO//STO [START_REF] Brinks | Anisotropic electrical transport properties of a two-dimensional electron gas at SrTiO 3 -LaAlO 3 interfaces[END_REF].

The puck is finally mounted inside the cryostat. Measurements were usually performed with an applied DC current of 10 to 100 µA, without any signs of heating.

XPS and magnetotransport analysis of LaAlO 3 /SrTiO 3 interfaces

Since its discovery, the LAO//STO interface has been intensively investigated using X-ray photoelectron spectroscopy. The great majority of these studies relied either on the evaluation of possible valence changes of interfacial Ti atoms, which would signal the formation of a q2DEG, or on La and Al core level shifts, which could be connected to the predicted built-in polar field in the LAO layer. For the 15 uc sample, the signal arising from the buried Ti atoms in STO is almost fully suppressed.

While the error bars were rather large, they estimated a maximum depth for Ti 3+ -related spectral weight of about 3 uc [for an LAO(5uc)//STO sample] and a carrier density of 2 × 10 14 cm -2 , still smaller than the 3.3 × 10 14 cm -2 expected within the polar catastrophe picture.

More recently, spectroscopy studies were also performed in similar STO-based systems, such as NdGaO 3 /SrTiO 3 and LaGaO 3 /SrTiO 3 [START_REF] Treske | Universal electronic structure of polar oxide hetero-interfaces[END_REF] and under the application of gate-voltage [START_REF] Minohara | Dielectric collapse at the LaAlO 3 /SrTiO 3 (001) heterointerface under applied electric field[END_REF].

In Fig. 2.31a, we show the in situ XPS spectra collected (at the Ti 2p level) for LAO//STO samples with different LAO thicknesses, using a Mg Kα X-ray source and a take-off angle of 0°. For comparison purposes, all spectra were normalized to the same integrated intensity and shifted in binding energy so that the Ti 2p 3/2 peak maxima coincide in energy 18 . For both the STO substrate and the LAO(1uc)//STO sample, we observe the spin splitted Ti 2p peak composed only of a Ti 4+ component, indicating the absence of additional electrons at the surface/interface, and revealing the insulating nature of these samples. For the LAO(4uc)//STO sample (in blue) we notice that a small additional component emerges at around -2 eV from the main Ti 4+ component. This is attributed to the Ti 3+ contribution, due to additional electrons hosted in the otherwise empty Ti 3d shell of Ti atoms in STO. The formation of a q2DEG in this sample is later confirmed through transport experiments (shown in Section 2.4.2.3), which reveal finite conductivity. Additionally, we show in Fig. 2.31b similar spectra, collected for LAO//STO samples with 1, 4 and 15 uc of LAO. Due to the large thickness (15 uc ∼ 5.7 nm) the latter was observed to be the absolute limit with which Ti was still measurable, even though the signal was already quite noisy (as shown in the inset). Nevertheless, we roughly estimate a maximum probing depth of about 5 nm for our experimental system.

£ (cm -2 .V -1 .s -1 ) (a) (b) (d) (c) T = 2 K
We conclude this section with magnetotransport experiments performed on uncapped LAO(5uc)//STO samples, i.e. above the critical thickness for conduction, grown using PLD in the conditions described in Section 2.4.1.2. First, the temperature dependence of the sheet resistance R s , measured in van der Pauw geometry, is shown in Fig. 2.32a. A reduction of about two orders of magnitude is observed, with a low temperature resistance of about 70 Ω/ , in good agreement with typical values found in the literature for the q2DEG in LAO//STO. In Fig. 2.32b, we show the transverse (Hall) resistance R xy measured at 2 K, with an applied magnetic field (perpendicular to the sample's surface) ranging from -9 to 9 T. Even though the Hall trace shows a slight non-linearity (a feature that will be discussed further ahead), we are able to use Eq. 2.9 to estimate the sheet carrier density n s . By fitting each Hall curve at different temperatures (not shown), we plot in Fig. 2.32c the temperature dependence of n s in the q2DEG. Unlike the major increase in resistance, n s suffers little change with decreasing temperature. Also, the values obtained are in the range of 3 × 10 13 cm -2 , consistent with other results found in the litterature [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Smink | Gate-Tunable Band Structure of the LaAlO 3 -SrTiO 3 Interface[END_REF] and one order of magnitude smaller than initially predicted by the polar catastrophe scenario. This discrepancy may however be justified due to localized carriers, that may be trapped in defect states [START_REF] Yu | A polarity-induced defect mechanism for conductivity and magnetism at polar-nonpolar oxide interfaces[END_REF], and are not detectable through transport experiments.

In turn, the drastic change in resistance can be ascribed to the large increase in carrier mobility. In Fig. 2.32d, we show the temperature dependence of the carrier mobility µ, calculated using Eq. 2.11. The drastic drop in mobility, from 4000 cm 2 .(V -1 .s -1 ) to about 5 -10 cm 2 .(V -1 .s -1 ) at room temperature, evokes the behavior found in reduced STO crystals, where mobility values were suspected to be limited by electron-phonon scattering processes at higher temperatures (> 100 K) and by impurity scattering at lower temperatures [START_REF] Frederikse | Hall Mobility in SrTiO 3[END_REF].

Hence, one may attempt to engineer low-defect interfaces in order to increase the mobility at low temperatures.

Regarding sample-to-sample reproducibility, changes in carrier density and mobility in the order of ± 1 × 10 13 cm -2 and ± 1000 cm 2 .(V -1 .s -1 ) (low T ), respectively, were normally observed among samples grown in similar conditions. First, several experimental nuances may lead to this small disparity. For example, if the surface of the STO substrate possesses higher concentration of defects or adsorbed particles, the carrier mobility at the LAO//STO interface may be affected. Same thing goes for the quality of the TiO 2 termination or the size of the steps. Second, after growth and removal of the sample from vacuum, the LAO surface becomes exposed to adsobates that were observed to alter the carrier density at the interface (see Section 2.3.3.3). Additionally, photo-excited carriers may be induced by simply exposing the sample to ambient light. Both of these issues may be surpassed by adding an appropriate capping layer to the heterostructure.

Finally, the non-linear Hall trace, mentioned above, can be attributed to a multi-band regime, where two types of carriers in lighter d xy and heavier d xz,yz bands contribute to conduction. In this case, while Eq. 2.9 can be used to roughly estimate an (average) carrier concentration, a two-band model is usually implemented to gain further knowledge on the carrier densities and mobilities for each type of carrier:

R xy (H) = H 1 e (n 1 µ 2 1 + n 2 µ 2 2 ) + (n 1 + n 2 )(µ 1 µ 2 H) 2 (n 1 µ 1 + n 2 µ 2 ) 2 + (n 1 + n 2 ) 2 (µ 1 µ 2 H) 2 , (2.12a) R xx (H) = 1 R 1 + 1 R 2 + u 2 1 R 2 + u 2 2 R 1 H 2 1 R 1 + 1 R 2 2 + u 1 R 2 + u 2 R 1 2 H 2 (2.12b)
with n 1 , n 2 and µ 1 , µ 2 the carrier densities and mobilities for the two different bands, R 1 , R 2 the longitudinal resistances of each carrier type, H the applied magnetic field and e the electron charge. In LAO//STO samples, the transition between single-band and multi-band transport regime, known as Lifshitz transition, was observed to occur around 1.6 × 10 13 cm -2

[162], accompanied by clear modification of the q2DEG properties [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. We shall elaborate on the implication of this transition, in particular to the Rashba SOC at the interface, in Section 3.3 and 3.4.

2.5

Tuning the critical thickness of LaAlO 3 /SrTiO 3 with metal overlayers

Previous studies

As introduced in Section 2. 3.3.3, what occurs at the surface of the LAO//STO heterostructures playes a critical role on the properties of the buried q2DEG. The first few studies regarding this surface-interface interaction were focused on the onset of conductivity itself, with the clear example of the induced q2DEG in (otherwise insulating) LAO(3uc)//STO using a biased AFM tip [START_REF] Cen | Nanoscale control of an interfacial metal-insulator transition at room temperature[END_REF]. From this point forward, chemically and/or electrostatically alteration of the surface became a powerful tool to tune the interfacial conductivity.

Besides the many works on the influence of surface adsorbates, density functional theory (DFT) calculations revealed that a metallic overlayer on LAO//STO could significantly alter the Ti 3d band occupancy depending on the nature of the metal overlayer [START_REF] Arras | Tuning the two-dimensional electron gas at the LaAlO 3 /SrTiO 3 (001) interface by metallic contacts[END_REF]. Interestingly, the polar field within the LAO film was also modified, in some cases even suppressed. While most metals tested reduced the LAO polar field and induced interfacial conductivity through the creation of gap states near the topmost AlO 2 layer, metals like Au were observed to enhance the polar field.

This prediction was extremely relevant for multiple reasons: first, when compared to the adsorbates-related or light-induced methods, a metallic capping offers a much more stable and durable way of modulating the properties of the q2DEG; second, any scenario could, in principle, be induced by carefully choosing an adequate metal, i.e. turning on/off the q2DEG, tuning up/down the carrier density, adjusting the LAO polar field, among others; third, the reduction of the critical thickness for conduction of 4 uc imposes an excellent opportunity device-wise, as it favors, for example, the detection of spins due to a smaller tunnel barrier resistance [START_REF] Bibes | Towards electrical spin injection into LaAlO 3 -SrTiO 3[END_REF].

With these advantages in mind, the first experimental observation of a q2DEG below the 4 uc critical thickness was achieved in our lab, for Co-capped LAO(x)//STO samples, with x = 1 and 2 u.c. [START_REF] Lesne | Suppression of the critical thickness threshold for conductivity at the LaAlO 3 /SrTiO 3 interface[END_REF]. As observed in Fig. 2.33a, DFT calculations predict, as expected, an insulating interface for LAO(1uc)//STO heterostructures, with the Fermi level E F lying at the top of the valence band (see green square). Adding just one monolayer of Co shifts the Fermi level to the bottom of the conduction band, leading to partially occupied Ti 3d states, as displayed in Fig. 2.33b. These prediction were confirmed through transport experiments on Co(2nm)/LAO(x)//STO samples, with x = 1,2,4 uc, where the Hall effect curves collected for these samples resemble the ones for uncapped LAO//STO samples above the critical thickness (see Fig. In attempt to justify the suppression of the critical thickness, the authors postulated that, while considering the potential within the LAO layer, if the work function of the metal φ M was small enough, i.e. if the E F on the metal side was higher in energy than the E F on STO (prior to contact), charge transfer should be induced towards the STO, so that both Fermi levels align and the whole system could find an equilibrium state [START_REF] Arras | Tuning the two-dimensional electron gas at the LaAlO 3 /SrTiO 3 (001) interface by metallic contacts[END_REF][START_REF] Lesne | Suppression of the critical thickness threshold for conductivity at the LaAlO 3 /SrTiO 3 interface[END_REF]. Even though this idea worked relatively well to explain the basic features of the initial observations, several questions remained unanswered. Could a trend be found between work function and carrier density of the q2DEG? Would noble metals with large work functions render the interface insulating? And most importantly, a purely electrostatic approach might explain the theoretical predictions, but in reality, chemical reactions should also be considered, especially between highly reactive metals and complex oxides. Could these chemical interactions also play a role in the formation of the q2DEG?

In the following sections, we answer these questions by extensively studying the properties of LAO//STO samples, below the critical thickness, capped with a variety of metals (Ti, Ta, Co, Nb, Al, NiFe, Pt, Pd and Au). We use transport experiments to evaluate the carrier density and mobility of the q2DEG formed, as well as XPS to understand the chemical interactions occurring at the metal/LAO and LAO//STO interfaces. To top it all off, we present a model based on electron transfer and oxygen vacancy formation, that explains most features of this system. Surprisingly, we also find that the critical thickness can not only be reduced, but also increased, by using a specific set of metals.

Reactive metals on LaAlO

3 (<4uc)/SrTiO 3

Transport properties and parallel conduction model

We start by reporting the magnetotransport response of LAO(2uc)//STO structures capped with different metallic capping layers (Co, Ti, Ta, Nb, NiFe), with thickness ranging from 2 to 3 nm (depending on the wetting properties of the metal). For this first set of samples, we show in Fig. 2.34a the temperature dependence of the sheet resistance, using van der Pauw configuration (see inset). Since the resistance of the metallic layer itself is expected to show a small dependence with temperature (in the order of a few Ω [START_REF] Lesne | Suppression of the critical thickness threshold for conductivity at the LaAlO 3 /SrTiO 3 interface[END_REF]), the drop in sheet resistance observed reveals that a second conducting channel starts to contribute at lower temperatures.

We attribute this new conducting channel to a q2DEG formed at the LAO//STO interface. As shown previously in Fig. 2.32a, the sheet resistance of the q2DEG drops from the kΩ range at room temperature, to a few tens of Ω below 10 K (where it plateaus). In this metal/LAO//STO structure, conduction is dominated by the metal at room temperature (R M s R q2DEG s ). As temperature decreases, the q2DEG starts to become less resistive, to a point (at low T ) where separated by a thin LAO layer 19 . Here, R q2DEG can be expressed as:

R q2DEG = R M R T OT AL R M -R T OT AL , (2.13)
where R T OT AL is the longitudinal resistance of the whole M/LAO//STO stack.

In Hall configuration, besides the two resistances, the Hall voltages generated in each layer must be considered (see Fig. 2.35b). The circuit shown can be simplified using Millman's theorem [START_REF] Millman | A Useful Network Theorem[END_REF], so that the Hall resistance of the q2DEG alone is given by: In the inset, the zoomed Hall data for a reference Ta metallic layer. Adapted from [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

LAO R q2DES V- V+ R M V H,M V H,q2DES -
R H,q2DEG = R H,T OT AL R q2DEG R M + 1 2 -R H,M R q2DEG R M 2 , (2.14)
with R H,T OT AL the transverse (Hall) resistance of the whole M/LAO//STO stack.

In Fig. 2.35c and 2.35d, we demonstrate the extraction of the isolated q2DEG transport response for a Ta/LAO(2uc)//STO sample. Disentanglement of the longitudinal resistance R s is performed as follows: R T OT AL is the symmetrized magnetoresistance data collected in transport for the whole Ta/LAO//STO stack (black curve); R M is the transport data collected for the Ta layer only, which is essentially the measurement of the full stack at room temperature (grey curve) 20 . Combining both curves, we calculate R q2DEG (as a function of H) using Eq. 2.13 (red curve). The same procedure is utilized to disentangle the transverse (Hall) resistance, as shown in Fig. 2.35d, where Eq. 2.14 gives a similar tilted trace but larger

Hall resistances for the q2DEG at the Ta/LAO//STO interfaces.

Taking this simple parallel conduction model, we extract the M R and Hall traces for the q2DEG formed at the interface of the several M/LAO//STO samples, as shown in Fig. 2.36a and 2.36b, respectively. We note that the extracted Hall curves are rather similar when compared to the ones measured in uncapped LAO(5uc)//STO (dashed curve). However, the MR curves show a larger value at high fields when compared to the uncapped LAO//STO case, possibly due to the role of oxygen vacancy formation within the STO (discussed ahead).

M/LAO(2 uc)//STO n total s × 10 13 (cm -2 ) n 1 n 2 µ 1 (cm 2 .(V.s) -1 ) µ 2 (cm 2 .(V.s) -
In Table 1 we show the carrier densities and mobilities extracted from a simultaneous 2-band model fitting (Eq. 2.12) of both Hall and MR curves. Notably, the values extracted along with the precise shape of the Hall and MR curves varies with the metallic capping layer, suggesting different metal-LAO/STO interactions.

Ti 4+

Ti 2p, Mg Ka, q = 0°Ti 2p, Mg Ka, q = 0°T i 4+ The difference between the grey and colored curves, shown below the spectra, highlights the presence of Ti 3+ after Co and Ta deposition. In the insets, angle dependence of the spectral weight in the Ti 3+ region before and after metal deposition. (c,d) Expanded view of the Ti 2p 3/2 core-level spectra (dots) fitted with both Ti 4+ (grey area) and Ti 3+ contributions (colored area). All data was collected in-situ. Adapted from [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

Intensity

XPS analysis

To gain additional insight into these interactions, we studied M/LAO(1 uc)//STO samples using in situ XPS. As reported in several previous studies (see Section 2.4.2.3), XPS can be used to probe the possible existence of a q2DEG. Indeed, the presence of a conducting layer in the STO is associated with a valence change of the Ti 3d ions from 4+ (in the 3d 0 bulk insulating state) towards 3+, detectable through a spectral intensity increase at the lower binding energy side of both spin-orbit split Ti 2p peaks. In Fig. 2.37a and 2.37b, we show the systematic XPS analysis of two LAO(1 uc)//STO samples capped with 3 Å of Co and Ta.

Similarly to the XPS data presented for uncapped LAO//STO samples in Section 2.4.2.3, all spectra were normalized to the same integrated intensity and shifted in binding energy so that the Ti 2p 3/2 peak maxima coincide in energy.

For both samples, we started by measuring the Ti 2p core level spectra intensity for a bare TiO 2 -terminated STO substrate, which was priorly annealed at high temperature and in high oxygen pressure, to remove undesired adsorbates21 (black curve). As expected, the spectra shows fully Ti 4+ features, confirming the insulating nature of the substrate. The substrate was then transferred, in vacuo, to the PLD chamber, where 1 uc of crystalline LAO was grown (details on the PLD growth procedure in Section 2.4.1.2). A second XPS scan was then performed (grey curve) on this LAO(1uc)//STO sample, revealing once again no valence change of the interfacial Ti atoms, consistent with the absence of a q2DEG for an LAO thickness smaller than the critical thickness [START_REF] Thiel | Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures[END_REF] and with other spectroscopy studies [START_REF] Treske | Universal electronic structure of polar oxide hetero-interfaces[END_REF]. Finally, the sample is transferred, in vacuo, to the magnetron sputtering chamber, where 3 Å of Co or Ta are deposited at room temperature. Details on the sputtering procedure can be found in Section 2.4.1.3. One last XPS study is performed on these M/LAO//STO samples, which exhibited profound differences depending on the metal overlayer chosen.

First, we show in Fig. 2.37a the results for a Co-capped structure (green curve), for which a small Ti 3+ contribution arises at around -2 eV from the main Ti 4+ peak. For clarity, the intensity difference between the LAO(1uc)//STO and the Co/LAO(1uc)//STO spectra is shown below the main spectra. The small additional weight at -2 eV is compensated by a decrease of the Ti 4+ . Due to the rather small nature of this effect, the same feature cannot be seen in the Ti 2p 1/2 (smaller peak at around 6 eV). This result is reminiscent of the one obtained for the uncapped LAO(4uc)//STO, shown in Fig. 2.31a, suggesting that a q2DEG is formed in this sample.

To assess the depth distribution of the Ti 3+ , we performed angle-dependent XPS experiments, shown in the inset of Fig. 2.37a. While the 0°spectrum corresponds to the maximum probing depth, increasing the probing angle leads to a more interface sensitive measurement.

We observe that at 50°, the Ti 3+ component is about twice as large as at 0°, which indicates that the relative concentration of Ti 3+ is higher near the interface. This result is in line with what is reported in the literature for thick and uncapped LAO//STO [START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF], and matches with our transport experiments (Fig. 2.36) where the Hall traces of both Co/LAO(2uc)//STO and LAO(5uc)//STO are rather similar. In addition, we show in Fig. 2.37c the fit of the Ti 2p 3/2 peak with Ti 3+ and Ti 4+ components, from which we estimate a Ti 3+ /Ti 4+ peak area ratio of 1%.

A strikingly different result was obtained for the Ta-capped heterostructure, shown in Fig. Fitted Ta 4f core-level spectrum of a Ta(3Å)/LAO(1uc)//STO sample with multiple Ta oxide peaks, following Ref. [START_REF] Moo | An XPS depth-profile study on electrochemically deposited TaO x[END_REF]. No Ta metal peak is discernable (usually located 5 eV away from the oxide peak) which indicates that the Ta capping is nearly fully oxidized. Adapted from [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

2.37b (red curve). A much stronger Ti

below the main spectra). The magnitude of the Ti 3+ contribution clearly exceeds what has been observed for standard and uncapped LAO//STO above the critical thickness. This suggests that the STO hosts an unusually large electron density after Ta deposition. In contrast with the Co-capped structure, the angle-dependent data (see inset) does not show a significant Ti 3+ intensity variation, indicating that the conducting region formed in these Ta/LAO//STO structures extends deeper than the XPS maximum probing depth and is thicker than in standard LAO//STO or Co-capped LAO//STO samples. We present in Fig. 2.37d the fit performed on the Ti 2p 3/2 peak with two components, which yielded a Ti 3+ /Ti 4+ peak area ratio of about 20%.

To attain further knowledge on the origin of the q2DEG in M/LAO//STO structures, we performed XPS analysis on the relevant peaks of each metallic capping layer. Due to their reactive nature, i.e. their easiness to oxidize when exposed to air, the metals used as capping layers should in principle react with the oxygen present in LAO and STO. If this occurs, indications of oxidized metal should be observed in these sample 22 . In Fig. 2.38a and 2.38b, we show the XPS spectra collected at the Co 2p and Ta 4f core levels, respectively. For the first case (Co), we compare the spectra collected on the Co/LAO(1uc)//STO sample (dark green curve) with references of pure metallic Co (black curve) and fully oxidized Co (light green curve) 23 . The Co/LAO//STO data deviates from that of the metallic Co reference and shows signatures of oxidation. Using linear combinations of the metallic and oxidized Co reference spectra, we estimated that 45±5% of the Co in the capping layer on top of the LAO//STO heterostructure was oxidized.

For the Ta/LAO//STO sample, the Ta 4f spectrum, displayed in Fig. 2.38b, was successfully fitted with a mixture of Ta 2 O 5 , TaO 2 and TaO oxide peaks, taking into consideration their relative distance (in energy) and weight [START_REF] Moo | An XPS depth-profile study on electrochemically deposited TaO x[END_REF]. We found no indications of any metallic Ta phase, thus suggesting that nearly 100% of the Ta was oxidized. To verify this result, we perform XPS experiments on the Ti 2p and Au 4f core levels on a Au/LAO(1uc)//STO sample. First, we observe in Fig. 2.40a that upon deposition of about 3 Å of Au (dark yellow curve), no sign of an additional Ti 3+ component is observed.

The only visible difference between the capped and uncapped sample is a slight broadening of the Ti 2p 3/2 peak (easily observed in yellow area below the main spectra) which may be ascribed to potential structural damage induced by the deposition of heavy species such as Au. Additionally, no Ti 3+ signal is evidenced through the angle-dependent XPS experiments (see inset). The XPS data suggests that this sample does not host a q2DEG, consistent with the Hall trace measured for this sample. As shown in Fig. 2.40b, the Ti 2p 3/2 peak can be fitted with a single component corresponding to Ti 4+ , so that the Ti 3+ /Ti 4+ peak area ratio is ∼0. We add that it is likely that, due to the poor wetting properties of Au, 3 Å is not In the inset, the magnetoresistance M R for the same samples. Adapted from [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

enough to form a continuous film. From AFM, we have however observed a rough but uniform surface. This may be due to formation of Au nanoparticles at the surface of LAO, which are not observable due to the resolution of the AFM.

Similarly to the previous experiments with Co and Ta, we analyzed the Au 4f core level to look for any traces of chemical interaction within the Au layer. As displayed in Fig. 2.40c, the Au capping layer spectra appears identical to a metallic Au reference 24 , implying that no chemical reaction occurred with the LAO//STO structures.

In the following sections, we investigate the nature of metal-oxide interactions, mainly following the review from Fu and Wagner [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF], in order to further understand the conductive/insulating behavior found in metal-capped LAO//STO samples.

Metal-oxide interactions 2.5.4.1 Electrostatic interactions: charge redistribution

The interfacial contact between a metal and an oxide may result in charge redistribution, which is essentially driven by the principles of system energy minimization. Depending on the nature of the metal, electronic interactions can occur as localized charge redistribution among 24 Analysis performed on a Au(50nm)/SiO2/Si sample, prepared in situ. Relative Binding Energy (eV the atoms in layers close to the interface and/or as long-range delocalized charge transfer between the metal and the space charge region within the oxide.

) Au 4f, Mg Ka, q = 0°T i 2p 3/2 , Mg Ka, q = 0°T i 2p, Mg Ka, q = 0° Au/LAO/STO 50° 0°L AO/STO 50° 0°+ q (a) (b) (c)

Localized charge redistribution

Local charge redistribution is governed by electrostatic and van der Walls interactions (with the latter being, in general, much weaker). Macroscopically, Stoneham and Tasker proposed that metal-oxide interactions originate from the attractive forces between ions in the oxide and induced "image charges" on the metal side [START_REF] Stoneham | Metal-non-metal and other interfaces: the role of image interactions[END_REF], which accounted for rather large adhesion energies between both materials. In ultra-thin metal layers, interactions are dominated by distortions of the valence band of the metal due to the electrostatic field of the oxide, an effect called the polarization effect. Noguera and Bordier also introduced the concept of metal-induced gap states (MIGS) [START_REF] Noguera | Theoretical approach to interfacial metal-oxide bonding[END_REF]. The idea was that after contact, some states originally in the valence or conduction bands of the oxide could be pulled into the gap, generating donor-like or acceptor-like states. The density of these gap states is predicted to decay over several Å within the oxide, depending on the size (in energy) of the band gap. Formation of chemical bonds between the metal atoms and surface oxygen ions also plays an important role within charge transfer mechanisms. An ionic bond at a metal-oxide interface is formed through electron donation from one atom to the other, leading to a redox reaction.

Naturally, this type of bonding strongly depends on oxide's surface properties, such as surface termination, surface impurities, surface defects, among others. This process has severe implication on mass transport at the interface, as we will see in the next section.

Long-range delocalized charge transfer An especially relevant case for the scope of this chapter is the interaction of metals with small band-gap oxides, such as STO, where intrinsic or extrinsic dopants may generate free carriers within the material, causing them to behave as n-type or p-type semiconductors. In this particular case, interface formation is not driven by interface states, but by charge transfer between the metal and the charge transfer region generated at the oxide surface.

This process can be described by Schottky contact theory, shown in Fig. 2.41a. After contact, the energy bands of a metal and a semiconductor in contact adjust, so that both E F aligns. For this readjustment to occur, the Fermi level E F is required to "bend" to higher or lower energies, forming a barrier at the interface due to the space charge layer at the semiconductor surface (see Fig. 2.41b) [START_REF] Grundmann | The Physics of Semiconductors[END_REF]. The barrier height φ B can be simply estimated by the relation between the work function of the metal φ M and the electron affinity of the semiconductor χ S :

φ B = φ M -χ S (2.15)
In essence, long-range charge transfer occurring at metal/oxide interfaces is responsible for space charges and band bending at the oxide surface. 2. Alloy formation. In some cases, a stable intermetallic compound may be formed at a metal/oxide interface. Here, cations are expected to be physically extracted from the oxide substrate to become incorporated in the metallic overlayer, following (for example):

M e I M e II O x → M e I M e II y M e II O z (2.17)
As an example, when Pt nanoparticles were deposited on SiO 2 substrates and subjected to high temperature reduction process, a Pt-rich Pt 3 Si alloy phase was identified [START_REF] Penner | Platinum nanocrystals supported by silica, alumina and ceria: metal-support interaction due to high-temperature reduction in hydrogen[END_REF].

3. Encapsulation. In this very peculiar case, metal particles are physically encapsulated by a thin layer of the oxide underneath, following the reaction:

M e I M e II O x → M e II O x-σ M e I M e II O x (2.18)
Note that in this case the metallic capping M e I does not form an oxide or alloy phase.

This can be experimentally observed in noble metals (such as Pt or Pd) on TiO 2 [START_REF] Diebold | The surface science of titanium dioxide[END_REF].

4. Interdiffusion. Lastly, metals may tend to diffuse into the oxide substrate (or vice-versa).

This normally leads to the formation of interdiffusion zones or oxide solid solutions near the interface. This process can be described by:

M e I M e II O x → M e I M e II O y (2.19)
An example of this is the formation of NiAl 2 O 4 at Ni/Al 2 O 3 interfaces [START_REF] Zhong | Surface science studies on the Ni/Al 2 O 3 interface[END_REF].

The most straightforward way to predict each of these interactions is through thermodynamical considerations. In first approximation, the enthalpy of formation of oxides ∆H O f , in kJ/mol O, can be used to explain several experimental results observed at metal/oxide systems. However, additional thermodynamical interface terms may help understand some reaction processes, such as oxidation and encapsulation. In general, if the metal surface energy γ M e is much larger than the oxide surface energy γ M eO , 3D metal islands and encapsulation effects are favored, especially for low surface energy oxides such as TiO 2 or STO. Yet, if the metal is highly reactive, it may simply reduce its own γ M e through an oxidation process, leading to the formation of uniform films or 2D-like structures.

Cabrera-Mott theory

Initially proposed to explain the low temperature oxidation of metal surfaces, the Cabrera-Mott theory was the first to take into consideration the interplay between both electronic and chemical interactions at metal/gas interfaces [START_REF] Cabrera | Theory of the oxidation of metals[END_REF]. This theory can be explained in the following step-by-step process: first, when a thin layer of (ambient) oxygen is adsorbed at the metal surface, oxidation occurs at the first few metallic monolayers, leading to the formation of a thin metal oxide layer; then, assuming that electrons can pass through this thin layer, charge transfer occurs between the metal and adsorbed oxygen atoms; this charge transfer is considered to be much faster than ionic motion, which leads to the appearance of a quasi-stable electric field E 0 whose magnitude depends on, what is known as, the Mott potential (simply given by the difference between the work function of the metal φ M and O 2p energy levels); the generated E 0 across the metal oxide barrier, with thickness L(t), lowers the required energy for ionic motion (which is normally facilitated with increased temperature) so that oxygen anions can diffuse towards the metallic region; finally, after a very rapid initial growth rate, L(t) starts to become too large for electron transfer and ionic motion to be possible, resulting in a very slow growth rate at L(t) ∼ 5 -15 nm. The whole process is schematically shown in in hand, with high φ M metals being less likely to oxidized, and low φ M metals being the most reactive (in general) [START_REF] Pomonis | Electron density and work function dependence of the enthalpy of formation of metal oxides[END_REF]. This behavior is demonstrated in Fig. 2.44, where we plot the evolution of ∆H O f as a function of φ M for several metals.

Explaining the q2DEG formation in M/LAO//STO heterostructures

In this section, we use the Cabrera-Mott theory to better understand the electrostatic and chemical interactions between different metals and the LAO//STO heterostructure.

Following the theoretical work by Arras et al., introduced in Section 2.5.1, it appears reasonable to assume that, for ideally stoichiometric heterostructures, the key parameter determining the formation of a q2DEG in metal-capped LAO//STO samples is the φ M [START_REF] Arras | Tuning the two-dimensional electron gas at the LaAlO 3 /SrTiO 3 (001) interface by metallic contacts[END_REF].

Indeed, for metals with a low φ M , the E F of the metal will initially be located higher in energy than the bottom of the conduction band of the STO, so that it is energetically favorable to transfer electrons from the metal to the STO, in turn leading to the q2DEG formation.

On the other hand, for metals with a higher φ M , the E F of the metal lies in the gap of the STO, so that no charge transfer towards the interface occurs. Without the detailed insight brought by the in situ XPS experiments, this scenario appears to be sufficient to justify our findings, since for low φ M metals a q2DEG is clearly formed, while for high φ M metals (Au, Pt, etc) no interfacial conductivity is detected. However, XPS clearly displays signatures of metal oxidation for Co and Ta, signaling chemical reactions between the metal and the oxide structure. Just like it was initially proposed by Cabrera and Mott, the physics and chemistry of these types of systems cannot be fully described by a purely electrostatic model, meaning that defect formation and ionic diffusion must also be taken into account [START_REF] Cabrera | Theory of the oxidation of metals[END_REF][START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF].

Let us now focus on the M/LAO//STO samples where magnetotransport (M = Au, Co, NiFe, Ta, Nb, Ti) and XPS experiments (M = Au, Co, Ta) were performed. In Fig. 2.45 we plot the total sheet carrier density of the q2DEG n total s (from magnetotransport), the Ti 3+ /Ti 4+ peak area ratio and percentage of oxidized volume within the metallic capping M OX (from XPS) as a function of the φ M and ∆H O f . First, in Fig. 2.45a, we observed a striking linear dependence between n total s (taken from Table 1) and ∆H O f , with the exception of Nb, which induces a 2DEG with abnormally large n s . The amount of metal oxide deduced from Fig. 2.38 also scales linear with ∆H O f . Given the thicknesses of the metal capping used in the XPS experiments (∼ 3 Å), saturation of metal-oxide formed is achieved for Ta. Naturally, for metals with even higher ∆H O f , full oxidation is expected. Regarding the Ti 3+ /Ti 4+ ratio, its magnitude is observed to increases with ∆H with φ M , as displayed in Fig. 2.45b. However, we observe that a linear trend may be present regarding the Ti 3+ /Ti 4+ ratio. More points would be needed to confirm this. Intriguingly, heterostructures capped by metals with very different φ M have rather similar n s (compare for example Ti-and Co-capped samples).

We conclude that due to the observed trends, the φ M seems to have a large impact on the total amount of carrier transferred to the interface, therefore controlling the Ti 3+ /Ti 4+ ratio. On the other hand, the ∆H O f seems to strongly influence the n s of the 2DEG formed, as well as the amount of oxide formed, consistent with a scenario related with oxygen vacancy formation in the STO and the Cabrera-Mott theory [START_REF] Cabrera | Theory of the oxidation of metals[END_REF], respectively.

In an attempt to combine both electrostatic and chemical interactions, we propose the scenario summarized in Fig. 2.46, which explains our experimental finds for the Co-and Tacapped samples. Prior to the metal deposition onto the LAO//STO, band tilting occurs due to the internal polar field in the LAO. When the metal is deposited, if the pure electrostatic criteria described previously is satisfied (i.e. the E M F higher in energy than the E ST O F ) carriers are transferred from the metal towards the STO (so that both E F align) and the q2DEG is formed. Smaller φ M translates in higher energy differences with respect to the , electrons are transferred from the metal to the STO, generating a space charge electric field E SC opposing the polar field E P in LAO. Due to the oxidation of the metal at the interface with LAO, oxygen vacancies (pink squares) are formed in the LAO, providing more electrons which are also transferred to the STO. Electron transfer from the metal and due to oxygen vacancies formation to the STO are represented as dark green arrows. E C is the field in the q2DES region due to the band bending. The bottom part sketches the spatial profiles of the concentration of oxygen vacancies [V O ] after diffusion. For the Ta case, the total amount of oxygen vacancies is much larger than for Co so that, due to the confining electric field E C , [V O ] are pushed towards the STO bulk. This process generates a depolarizing field E D , which opposes E C . CB and VB denote the conduction band minimum and the valence band maximum, respectively, vac is the vacuum level and F is the Fermi energy. Adapted from [START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. that larger charge transfer is promoted. This charge transfer creates a space charge electric field, E SC , opposite to the polar field E P in the LAO, and which partially cancels the latter (depending on the amount of charge transferred). Indeed, when comparing Co (φ Co = 5.1 eV) with Ta (φ T a = 4.05 eV), the highest carrier density and the Ti 3+ /Ti 4+ peak area ratio occurs for the Ta capped sample, consistent with the mechanism proposed. However, our XPS data show that while for Co the amount of transferred charge and the q2DEG properties are comparable to those of reference (uncapped) samples, for Ta, oxidation is much more severe. Thus, the amount of transferred charge is much larger and, importantly, the q2DEG has a larger spatial extension. This latter point is crucial, since in a purely electrostatic picture, a higher carrier density in the q2DEG implies a stronger electric field in the STO and thus a stronger confinement [START_REF] Copie | Towards Two-Dimensional Metallic Behavior at LaAlO 3 /SrTiO 3 Interfaces[END_REF], which is inconsistent with a thicker q2DEG observed from angle dependent XPS (see inset of Fig. 2

E ST O F , so (a)

.38b).

A way to reconcile these apparently contradictory observations is to assume that the extension of the q2DEG is larger in the Ta-capped sample due to the presence of oxygen vacancies in the STO, a very likely scenario for an interface between a highly reactive metal and STO [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF]. This effect may in fact be reminiscent of the mechanism proposed by Yu and Zunger for uncapped LAO//STO [START_REF] Yu | A polarity-induced defect mechanism for conductivity and magnetism at polar-nonpolar oxide interfaces[END_REF], which states that at 4 uc of LAO, oxygen vacancies spontaneously form at the LAO surface, while the electrons associated with their formation are transferred to the STO to yield a q2DEG. Here, we argue that the deposition of a reactive metal gives the system enough energy so that these oxygen vacancies are favorably formed. If the oxidation of the metal is moderate, as for the Co case, only a small amount of oxygen vacancies will be created in the LAO, where they will largely remain. The few electrons thus released will then be transferred to the STO and contribute carriers to the q2DEG. Note that this is most likely the dominant effect, since the φ Co places the E F at almost the same energy level as the E F of STO.

For the Ta case, since the oxidation of the metal is very severe (with a ∆H O f (Ta) twice as large) the amount of oxygen vacancies created in the LAO will be much larger (as will the corresponding number of extra carriers transferred to the STO). For such high concentrations, these neutral oxygen vacancies will tend to diffuse through the LAO layer and eventually reach the STO. There, because of the electric field present in the q2DEG region, they may be ionized and thus drift away deep into the STO, eventually generating an opposing electric field E D (see Fig. 2.46b). This depolarization field should weaken the confinement of the carriers in the STO near the interface, yielding an increase of the q2DEG thickness. Proof of the existence of oxygen vacancies in the LAO//STO structure is shown in Fig. 2.47. While in situ XPS measurement revealed a Ti 3+ signature, removing the sample from the chamber and putting it back in completely suppresses this Ti 3+ contribution. We believe that by exposing the sample Ti 2p core-level spectra collected for an LAO(1uc)//STO (black curve) and Ta(3Å)/LAO(1uc)//STO sample (colored curve). The Ti 3+ feature observed in-situ and appearing after Ta deposition is suppressed when the sample is taken out of the chamber for a few minutes and then re-measured, signaling oxygen refilling by simple exposure to air.

to air, these superficial oxygen vacancies (not very well protected by the thin 3Å Ta layers) are filled and the q2DEG disappears. However, if the Ta thickness is 2.5 nm, like the samples used for magnetotransport measurements, the oxygen vacancies created by Ta deposition remain in the STO, giving additional stability to the q2DEG formed.

Lastly, for the Au-capped LAO//STO no hint of a q2DEG was detected from transport or XPS, as well as no oxidation of the metallic overlayer. The weak electrochemical interactions between oxides and noble metals have previously been thoroughly investigated (see Ref.

[140]), and mainly attributed to the high work function of the metals (φ Au > 5 eV) and their reduced tendency to oxidize (∆H O f ∼ 0 kJ/mol O). Ultimately, Au tends to not react with the underlying oxide, so that Au species arriving at the surface of LAO, most likely contribute to the formation 3D islands or nano-sized particles, while still wetting relatively well [START_REF] Silly | Bimodal Growth of Au on SrTiO 3 (001)[END_REF].

We add that, among the noble metals family, Au has a relatively small surface energy (γ Au ∼ 1.6 J.m -2 on TiO 2 ), which was observed to be insufficient for the reduction of Ti 4+ or to go through an encapsulation process. However, its counterparts Pd and Pt show higher φ M (5.45 and 5.65 eV, respectively) and larger γ (∼ 2 and 2.7 J.m -2 on TiO 2 , respectively) [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF]. This combination of properties was observed to allow oxidation of Ti 3+ to Ti 4+ in Pd/TiO 2 and Pt/TiO 2 samples, accompanied by thermodynamical relaxation through encapsulation. In the next Section, we take these interesting features and perform a more in-depth study on the and after (black lines) Pt/LAO interface formation, where E SC represents the space charge electric field generated by the electron transfer towards the Pt layer. Adapted from [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

effect of these metals on the conducting properties LAO//STO interface.

Increasing the critical thickness with a Pt-capping

In Fig. To explain this puzzling result for the 5 and 7 uc samples, we postulate that prior to Pt deposition, a q2DEG actually forms, assuming that electronic reconstruction already took place. Due to its high φ M , the E F of Pt lies inside the gap of the STO. After Pt deposition and band alignment (as sketched in Fig. 2.48d), charge may be promoted from the STO towards the Pt, depopulating the q2DEG to the point where the interface becomes insulating.

A similar effect has been reported for Pt//reduced-TiO 2 [START_REF] Schierbaum | Electronic structure of Pt overlayers on (1 × 3) reconstructed TiO 2 (100) surfaces[END_REF] and Pt//STO [START_REF] Chung | Surface spectroscopy studies of the SrTiO 3 (100) surface and the platinum-SrTiO 3 (100) interface[END_REF], where the Ti 3+ component of the substrate was substantially reduced after Pt deposition, and a Schottky barrier with a height of 0.4 eV (for one monolayer of Pt) was formed at the interface.

At a larger LAO thickness (≥ 9 uc), signatures of the q2DEG eventually appear, as deduced from the change in the shape of the Hall, MR and normalized resistance versus T curves.

Although the very low resistance of the Pt with respect to the q2DEG precludes a proper determination of the carrier density and mobility, the data suggest that n s may be lower than for all the reactive metal-capped heterostructures discussed earlier.

The same line of thought proposed to explain the behavior of the 5 and 7 uc samples may be applied to the 9 and 10 uc samples. However, one of two things may occur. When increasing the LAO thickness, electron transfer towards the Pt may be hampered and therefore not sufficient to completely depopulate the q2DEG, only leading to a reduction in the sheet carrier density. Alternatively, it is possible that as the LAO thickness increases from 5 to 9 uc, the electric field within the LAO also builds up sufficiently for it to favor the transfer of electrons from the Pt to the STO, hence placing the E F pf Pt above the E F of STO.

Conclusions

In this chapter, we started by thoroughly introducing the 2D electron gas formed at the interface between LAO and STO. Then, we gave a step-by-step protocol regarding STO surface termination, the PLD growth of ultra-thin LAO films and deposition of metallic overlayers using magnetron sputtering. Along with X-ray photoelectron spectroscopy and magnetotransport experiments, we investigate the electrostatic and chemical properties of metal/LAO//STO heterostructures, where metal = Co, Ta, Ti, Al, Nb, NiFe, Au, Pd and Pt. The collected data is interpreted in the framework of the Cabrera-Mott theory. The main conclusions of this study are the following:

1. The initial critical thickness of 4 unit cells of LAO for 2DEG formation can be modulated by room temperature deposition of a thin metallic overlayer.

2. The critical thickness is observed to decrease when the overlayer is composed of a reactive metal, i.e. metals that tend to form an oxide rather easily (Co, Ta, Ti, Al and Nb), and to increase when the overlayer is composed of a noble metal, i.e. metals that normally do not form an oxide phase (Au, Pd and Pt).

3. For the reduction of the critical thickness, the effect is associated with electron transfer from the metal towards the LAO/STO interface, when the position of the E F of the metal is higher than the E F of STO (prior to contact), and with oxygen vacancy formation in the LAO//STO heterostructure, that release additional electrons in the lattice. As these metals react with air to form an oxide phase, in this case the metal pulls oxygen the oxide structure, becoming itself oxidized in the process.

4. For the increase of the critical thickness, the position of the E F of the metal is lower than the E F of STO (prior to contact), leading to electron transfer from the LAO/STO interface towards the metal. In this scenario, the 2DEG is depopulated, rendering an insulating LAO/STO interface for LAO thicknesses up to 7 unit cells. The 2DEG is once again detected above this thickness due to either E F (of the metal) positioning above the E F of STO, due to the increasing LAO polar field that tilts the bands, or reduced electrostatic interaction between metal and STO due to the increased thickness of LAO.

5.

In general, a q2DEG with more carriers is expected for capping layers with higher tendency to oxidize (given by the enthalpy of oxide formation ∆H O f ) and lower work functions. We find a linear trend between ∆H O f and the carrier density n s of the formed q2DEG. Another (less clear) linear trend is observed between the work function of the metal and the amount of Ti 3+ /Ti 4+ extracted from XPS measurements.

6. The formation of a q2DEG in STO with a simple room temperature sputtering deposition of a metal opens great prospects for larger scale applications, which were, up until this point, limited by a high temperature pulsed laser deposition procedure.

We add that, while the metals were used to tune the properties of the q2DEG at the LAO/STO interface, they can also be used to induce a q2DEG directly on STO. In terms of q2DEG formation, the LAO layer serves two purposes: first, it creates a "barrier" for the process of oxygen removal directly from the STO, since the diffusivity of oxygen in LAO is expected to be smaller than in STO. Note that the oxygen vacancy formation process will initially start from the top of LAO layer, so that it only allows extraction directly from the STO if its thickness is thin enough. For example, in a Ta/LAO(10uc)//STO sample, we expect oxygen vacancies to be present only in the LAO layer. Second, from an electrostatic point of view, it facilitates charge transfer from the metal towards the STO. This can be observed in Fig. 2.46. If we consider that the LAO layer is for example 3 uc (instead of 1 uc), the position of the E F of Co will actually be much higher than the E F of STO, solely due to the increased band tilting induced by the LAO polar field. Above 4 uc, we assume that the polar cathastrophe may take place, and the band tilting is reduced due to charge transfer from the surface of the LAO. investigate the spin-polarized 2DEG formed in EuO//STO heterostructures (note that here, after a deposition of metallic Eu, oxygen is pulled from the STO resulting in a EuO layer) [START_REF] Kormondy | Large positive linear magnetoresistance in the two-dimensional t2g electron gas at the EuO/SrTiO 3 interface[END_REF]; and lastly, Mattoni et al. engineered an extremelly high mobile 2DEG (µ = 80,000 cm 2 .V -1 .s -1 ) with strong magnetoresistance (∼ 900 %) in WO 3 /LAO//STO heterostructures [START_REF] Mattoni | Insulator-to-Metal Transition at Oxide Interfaces Induced by WO 3 Overlayers[END_REF].

Expanding to other systems -how band alignment and interfacial oxygen deficiency unlock 2DEGs in complex oxides

We conclude this chapter with a simple blueprint that can be used to unlock 2DEGs in other complex oxides. The single requirement is that the metallic capping has a high tendency to oxidized ∆H O f (see Fig. 2.44) and a work function that is small enough so that, in direct contact with the complex oxide, the position of E metal F is higher than E ox F . In this scenario, oxygen vacancies are created at the surface of the complex oxide, releasing electrons to the lattice, and charge transfer is promoted from the metal towards the interface. This unlocks extremely interesting opportunities for 2DEGs with additional intrinsic properties from the complex oxide itself. One can for example picture a ferroelectric 2DEG in BaTiO 3 , a high spin-orbit coupling 2DEG in KTaO 3 , or a multiferroic 2DEG in BiFeO 3 .

Simultaneously, one might use the properties of the metallic capping to induce proximity effects in the 2DEG. Special attention should be taken to the fact that the metal overlayer oxidizes in the process, so that ultimately the proximity effect takes place at a metaloxide/complex oxide interface. Among the many possibilities, we suggest the coupling between magnetic capping layer and the 2DEG (recently explored in EuO//STO heterostructures [START_REF] Kormondy | Large positive linear magnetoresistance in the two-dimensional t2g electron gas at the EuO/SrTiO 3 interface[END_REF]), coupling between superconducting layers and the superconducting 2DEG [START_REF] Giaever | Magnetic Coupling Between Two Adjacent Type-II Superconductors[END_REF] or the exploration of proximity interactions between heavy metals with high-spin orbit coupling and the 2DEG [START_REF] Marchenko | Giant Rashba splitting in graphene due to hybridization with gold[END_REF]. In 2D systems without inversion symmetry, the band degeneracy can be lifted as a consequence of spin-orbit coupling. As introduced in Section 1.6.2, the spin-dependent splitting of the bands described by Bychkov and Rashba [START_REF] Bychkov | Properties of a 2D electron gas with lifted spectral degeneracy[END_REF], unlocks a fantastic platform to study the interactions between charge and spin [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF]. One of the first experimental realizations of this type of Rashba system were 2D quantum wells (QWs), created in doped semiconductor hetererostructures lacking inversion symmetry, such as InGaAs/InAlAs [START_REF] Das | Evidence for spin splitting in In x Ga 1-x As/In 0[END_REF][START_REF] Koga | Rashba Spin-Orbit Coupling Probed by the Weak Antilocalization Analysis in InAlAs/InGaAs/InAlAs Quantum Wells as a Function of Quantum Well Asymmetry[END_REF], InGaAs/InP [START_REF] Schapers | Effect of Rashba spin-orbit coupling on magnetotransport in InGaAs/InP quantum wire structures[END_REF], SiGe/Si [START_REF] Wilamowski | Evidence and evaluation of the Bychkov-Rashba effect in SiGe/Si/SiGe quantum wells[END_REF] and AlGaN/GaN [START_REF] Lo | Spin splitting in modulation-doped Al x Ga 1-x N/GaN heterostructures[END_REF], to name just a few (see Fig. 3.1a for an example). To quantify the magnitude of the Rashba effect in these systems, magnetotransport experiments were performed to evaluate both the weak (anti)localization transport regimes and the beating patterns of Shubnikov-de Haas oscillations. As shown in Fig. 3.1b and 3.1c, through different fitting procedures, both approaches lead to a value of the Rashba coefficient α R that could be correlated with how well these systems would perform on a real device. Overall, α R was found to be in the order of 10 -12 eV.m, with small but finite modulation by application of a gate voltage [START_REF] Nitta | Gate Control of Spin-Orbit Interaction in an Inverted In 0.53 Ga 0[END_REF][START_REF] Engels | Experimental and theoretical approach to spin splitting in modulation-doped In x Ga 1-x As/InP quantum wells for B→0[END_REF] (see Fig. 3.1d).

| Spin-to-charge current conversion in SrTiO

While the search for platforms with strong and tunable Rashba effects intensified in semiconductor QWs, at roughly the same time another approach using surfaces of metals started to gain some traction [START_REF] Bihlmayer | The Rashba-effect at metallic surfaces[END_REF]. Surface states can be viewed as a particular case of a 2DEG, since the surface always breaks inversion symmetry and is associated with an effective potential that leads to a finite gradient along the surface normal. On top of that, these surface states can be probed with surface sensitive spectroscopy techniques, such as angle resolved photoelectron spectroscopy (ARPES), allowing a direct evaluation of the splitted bands. LaShell et al.

were the first to evidence this for Au [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] surfaces, where the surface state doublet observed through ARPES was correctly interpreted to arise as a consequence of spin-orbit coupling [START_REF] Lashell | Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy[END_REF]. Not only that, but the band-splitting observed in these surfaces was much larger than for semiconductors QWs, with an estimated α R = 3.3 × 10 -11 eV.m. It is worth to understand that, at a surface, the electric field cannot be simply described by the gradient of the surface potential. By considering the work function of Au (which defines the surface potential) and using this value in a nearly free electron model, a splitting of 10 -6 eV is calculated [START_REF] Blügel | Magnetism in Reduced Dimensions[END_REF], orders of magnitude lower than expected. However, this value is corrected when the large atomic spin-orbit coupling of Au (Z Au = 79) and the asymmetry of the wavefunction25 are taken into account [START_REF] Petersen | A simple tight-binding model of spin-orbit splitting of sp-derived surface states[END_REF], which leads to a value close to the experimental splitting of 0.1 eV, obtained in

Ref. [START_REF] Lashell | Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy[END_REF]. This result stresses not only the importance of spin-orbit effects in these surface states, but also their orbital character.

Studies of Rashba effects in metal surfaces were later extended to Ag [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] and Cu [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF].

In the first case, it was indeed calculated [START_REF] Bihlmayer | The Rashba-effect at metallic surfaces[END_REF] and recently observed with spin-ARPES [START_REF] Yaji | Rashba spin splitting of L -gap surface states on Ag(111) and Cu(111)[END_REF] 0.0 k x (Å -1 that the splitting in Ag( 111) surfaces is about 20 times smaller than in Au [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF], with a α R = 3 × 10 -12 eV.m. Even though a smaller splitting is expected from the atomic number difference between both elements, with Z Ag = 47, the huge discrepancy can be closely associated with the orbital predominance of surface states with p z character, which ultimately reduce the asymmetry of the wavefunction. Note that for Au, there is a much larger admixture of surface states with d z 2 character, strongly enhancing this asymmetry of the wavefunction and consequently the spin-splitting. In the second case, Cu shows an even smaller atomic number, with Z Cu = 29. Surprisingly, the spin-splitting was calculated and observed with laser-ARPES [START_REF] Tamai | Spin-orbit splitting of the Shockley surface state on Cu(111)[END_REF] and spin-ARPES [START_REF] Yaji | Rashba spin splitting of L -gap surface states on Ag(111) and Cu(111)[END_REF] to be only 4-6 times smaller than in Au [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF], once again due to increased asymmetry of the wavefunction.

On the other side of the spectrum there is Bi, a much heavier atom with Z Bi = 83 and semimetal 26 properties. The ∼ 0.3 eV splitting (α R = 5.6×10 -11 eV.m) observed at the surface of Bi [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] [START_REF] Ast | Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy[END_REF][START_REF] Koroteev | Strong Spin-Orbit Splitting on Bi Surfaces[END_REF], Bi(110) [START_REF] Agergaard | The effect of reduced dimensionality on a semimetal: the electronic structure of the Bi(110) surface[END_REF] and Bi(100) [START_REF] Hofmann | Electronic structure and Fermi surface of Bi(100)[END_REF] was so large that it needed to be confirmed by DFT calculations as a spin-orbit related effect, and not simply two different surface states.

Following these discoveries, an even higher splitting was observed in √ 3× √ 3BiAg(111) surface alloys [START_REF] Ast | Giant Spin Splitting through Surface Alloying[END_REF], which came as a surprise due to the much lower splitting observed in Ag [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF].

Once again, the Rashba splitting may change drastically due to different orbital characters present. It is known that for Bi [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF], surface states are not only localized at the interface but also form bonds with atoms in the closest layers beneath the interface. As calculated in [START_REF] Bihlmayer | Enhanced Rashba spin-orbit splitting in Bi/Ag(111) and Pb/Ag(111) surface alloys from first principles[END_REF], in an hypothetically flat Ag/Bi [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] surface alloy, the Rashba splitting shows values in the range of Bi(111) surfaces. However, when in contact with a Ag layer, Bi atoms can slightly relax, leading to rapid changes of the ratio between orbitals with s and p z character (and even the addition of p (x,y) ), thus increasing the splitting and giving a giant α R = 3.05 × 10 -10 eV.m [START_REF] Ast | Giant Spin Splitting through Surface Alloying[END_REF]. To summarize, we show in Fig. 3.2 the splitted bands, collected through ARPES experiments at the surfaces of Au, Ag, Cu and Bi/Ag in the (111) direction.

Edelstein effect in semiconductor QWs and metallic surfaces

Besides the general phenomenological interest for the Rashba effect, most research done in the field had one goal in mind: systems with large Rashba coefficients to devise a spin-field effect transistor (spin-FET) [START_REF] Datta | Electronic analog of the electro-optic modulator[END_REF]. During a decade investigating a multitude of different combinations of materials, it all came down to the ability of these systems to actually "handle" spin currents.

To do this, the analogous to the spin Hall effect would be utilized to interconvert charge and spin current: the direct Edelstein (DEE) and inverse Edelstein effects (IEE) (see Section 1.6.3 for an in-depth description).

Simply put, just like the spin Hall in bulk systems, the DEE and IEE allow the conversion of charge currents in spin current (and vice-versa) in 2D Rashba systems lacking inversion symmetry. Early in 2002, Ganichev et al. demonstrated for the first time the inverse Edelstein effect (in their article termed spin-galvanic effect) in n-type GaAs/AlGaAs semiconductor QWs at low temperatures [START_REF] Ganichev | Spin-galvanic effect[END_REF]. In this experiment, an in-plane oriented non-equilibrium population of electron spins (controlled by an external magnetic field) was optically-induced in the QW, generating a finite charge current that was electrically detected. Following these results, the reciprocal effect, i.e. manipulation of the spin orientation by injection of an electrical current in a QW, was also achieved in semiconductor QWs, such as GaAs/AlGaAs [START_REF] Ganichev | Can an electric current orient spins in quantum wells?[END_REF][START_REF] Sih | Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases[END_REF] and InGaAs/InAlAs [START_REF] Yang | Spectral Dependence of Spin Photocurrent and Current-Induced Spin Polarization in an InGaAs/InAlAs Two-Dimensional Electron Gas[END_REF]. The latter was especially interesting since both the direct and inverse effect were achieved using Kerr rotation experiments, even at high temperature (even though the signal vanished at room temperature). While the realization of these effects represented a step forward towards the idealized spin-FET, the QWs utilized showed a rather small α R , in the order of 10 -12 eV.m. It was clear that there was a lot of room for improvement through the exploration of new systems with larger Rashba coefficient, which would ultimately lead to more efficient spin-to-charge conversion phenomena.

With this goal in mind, the giant Rashba splitting found in Bi [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF] and The top panels represent the ferromagnetic resonance spectra. At resonance, the injected spin current drives a current peak I, which is presented in the bottom panels. Modified from [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF].

√ 3× √ 3BiAg (
the Ag/Bi interface, as sketched in Fig. 3.3a. The spin current generated induces a potential drop at the interface, that can be detected as a voltage peak using a simple two point electrical probe. In this particular case, since both Ag and Bi layers (alone) also show surface states with Rashba properties, the experiment was performed separately on NiFe/Ag and NiFe/Bi samples, which showed a voltage peaks much smaller than for the NiFe/Ag/Bi structure (see Fig. 3.3b). By estimating the spin current generated with the NiFe ferromagnetic layer through spin pumping and normalizing the detected voltage, the authors used Eq. 1.29 to estimate a λ IEE , which was found to range between 0.2 to 0.33 nm. Being the first few results regarding quantification of spin-to-charge conversion in a Rashba system, the λ IEE obtained could not be qualified as efficient or inefficient. The authors attempted a derivation of a spin

Hall angle θ SHE by considering the interface as a 2D system with finite thickness (smaller than the spin diffusion length). Having achieved an unphysical value of 1.5, roughly meaning that one spin could generate more that one charged carrier, they concluded that the comparison between the two effects could not be correctly made, emphasizing the importance spin-orbit effects induced at the Ag/Bi interface. Nevertheless, this work unlocked the door for several other experiments using more exotic materials such as topological insulators and oxide-based 2DEGs, where larger efficiencies could be potentially found.

Edelstein effect in topological insulators

Since the first observations in the mid 2000s, topological insulators (TIs) brought a wide range of physical phenomena displaying properties that are topologically distinct from all other known states of matter up until this point [START_REF] Qi | Topological insulators and superconductors[END_REF]. TIs show conducting surface states (or edge states) that emerge due to strong spin-orbit coupling, and are protected by time-reversal symmetry, so that "symmetry-protected" 2D conduction becomes available at the surface of a 3D insulating material. Among their many interesting use cases, such as hosts of quantum spin Hall effect [START_REF] Konig | Quantum Spin Hall Insulator State in HgTe Quantum Wells[END_REF] and possibly the elusive Majorana fermions [START_REF] Fu | Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator[END_REF], this class of materials is also particularly attractive for spintronics applications. Similarly to what is seen in Rashba systems, the carriers in these surface states have their spin coupled orthogonally with their momentum, a feature called spin-momentum locking, allowing the generation spin-polarized currents. However, while the Rashba spin-orbit coupling leads to momentum-dependent spinsplitting of the bands (see Fig. Regardless of their differences, the conducting surface states found in topological insulators can be viewed as yet another particular case of a 2D system where spin currents can be created and manipulated. The spin-to-charge conversion mechanisms discussed in Section 1.6.3.1 can be (with a few small changes) applied for the case of a singular Fermi circular contour in a TI, as seen in Fig. 3.4c. The main difference is the fact that while in the Rashba case, shifting both Fermi contours leads to the generation of two inequivalent spin densities (with opposite spin direction), in TIs the shift in momentum leads to a single spin density, with sign depending on the chirality and orientation of the injected current. More information can be found in the useful article by Zhang and Fert, regarding several spin transport properties for spin-to-charge interconversion in TIs [START_REF] Zhang | Conversion between spin and charge currents with topological insulators[END_REF].

Charge-to-spin conversion though the DEE has been demonstrated at room temperature in TIs such as Bi 2 Se 3 [START_REF] Mellnik | Spin-transfer torque generated by a topological insulator[END_REF][START_REF] Wang | Topological Surface States Originated Spin-Orbit Torques in Bi 2 Se 3[END_REF] and at low temperature for (Bi 1-x Sb x ) 2 Se 3 [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF]. Using spintorque ferromagnetic resonance (ST-FMR), a charge current driven in the conducting surface of the TI gets converted into a spin current that, through the direct Edelstein effect (DEE), exerts spin-transfer torque on an adjacent metallic ferromagnet 27 . By calculating the change 27 Usually NiFe, CoFeB or the magnetic insulator Y3Fe5O12 (YIG). The plot shows the conversion efficiency q ICS (equivalent to what we previously called q DEE ) as a function of the Sb doping level, which modulates the position of the E F above/below the Dirac point. Adapted from [START_REF] Soumyanarayanan | Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces[END_REF][START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF]. (e) Spin-to-charge current conversion in Fe/Ag/α-Sn heterostructures. The plot shows the detected charge current (at FMR resonance). Note that when Fe is in direct contact with α-Sn, the topological surface states are destroyed, suppressing any spin-to-charge current conversion effects. Adapted from [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF].

in damping of the ferromagnetic material, and estimating the charge current injected, the conversion efficiency q DEE can be estimated (see Section 1.6.3.2 for more details). Notably, in the work of Kondo et al. for NiFe/Cu/(Bi 1-x Sb x ) 2 Se 3 trilayer system 28 , the E F position was tuned by changing the relative quantities of Bi and Se, so that charge-to-spin conversion was achieved above and below the Dirac point [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF]. The charge-to-spin current conversion efficiency q DEE is displayed in Fig. 3.4d, as a function of the Se concentration. The chargeto-spin current conversion efficiency q DEE is displayed in Fig. 3.4d, as a function of the Se concentration. Even though the chirality of the Fermi contour changes sign when crossing the Dirac point, so does the type of carriers, i.e. n-type above and p-type below the Dirac point. The resulting spin current produced should therefore have the same orientation in both regions, matching the unchanged positive sign of the detected spin-current induced FMR and confirming the geometrical formulation of the Edelstein effect. Finally, q DEE was estimated to be within the range of 0.47-0.51 nm -1 . Spin-to-charge conversion through the inverse Edelstein effect was also achieved in Bi-based topological insulators, with efficiencies on the 0.01 nm range [START_REF] Deorani | Observation of inverse spin Hall effect in bismuth selenide[END_REF], way below the initially expected values. As pointed out by several authors [START_REF] Shiomi | Spin-Electricity Conversion Induced by Spin Injection into Topological Insulators[END_REF][START_REF] Deorani | Observation of inverse spin Hall effect in bismuth selenide[END_REF], due to an imperfect insulation of the bulk states, current shunting effects lead to spin-to-charge conversion signal that includes contributions from both the bulk and surface states, a setback that may prevent this family of materials from reaching higher conversion efficiencies.

The exploration of these effects continued with other topological insulators such as α-Sn [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF] and SmB 6 [START_REF] Song | Spin injection and inverse Edelstein effect in the surface states of topological Kondo insulator SmB 6[END_REF]. As shown in Fig. 3.4e, Rojas-Sanchez et al. used spin pumping to injected a spin current in the surface states of α-Sn while measuring the charge current produced, similarly to their previous work on Ag/Bi interfaces [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF]. However, this time the λ IEE found was 2.1 nm, at least one order of magnitude larger than in the best metallic Rashba systems. SmB 6 shows a particularly interesting feature, where below 3K the bulk states becomes highly insulating, ensuring current conversion exclusively through surface states. Even though a λ IEE was not calculated, the produced voltage rapidly degraded above 10 K, reiterating the importance of having insulating bulk states to maximize the conversion efficiency. Recently, Noel et al. found a large λ IEE = 2.0 ± 0.5 nm at room temperature in strained HgTe protected by a HgCdTe layer [START_REF] Noel | Highly Efficient Spin-to-Charge Current Conversion in Strained HgTe Surface States Protected by a HgCdTe Layer[END_REF]. Optimization of the conversion efficiency obtained was found to be heavily dependent on the HgTe layer thickness, which needed to be thick to decouple the top and bottom surface, but thin enough to avoid the relaxation within the bulk states.

Edelstein effect in oxide-based 2DEGs

In the search for alternative systems to explore 2D Rashba physics, oxide interfaces emerge as yet another prominent candidate, for their exotic and unusual electronic properties. The acclaimed LaAlO 3 /SrTiO 3 system, introduced in Chapter 2, serves as a great example of an all-oxide system that exhibits fascinating properties such as interfacial conductivity with high mobilities [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF], superconductivity [START_REF] Reyren | Superconducting Interfaces Between Insulating Oxides[END_REF], and traces of magnetism [START_REF] Bert | Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO 3 /SrTiO 3 interface[END_REF]. Additionally, Caviglia et al. showed that the quasi 2D electron gas (q2DEG) formed at the interface also shows strong gate-tunable Rashba spin-orbit coupling [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF], ideal for further exploration of spin-to-charge interconversion [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

In 2016, we observed for the first time the inverse Edelstein effect in an oxide-based Rashba 2DEG at low temperatures [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF], using spin pumping technique to inject a spin current in the 2DEG and measuring the produced charge current with a simple two-point probe, similarly to what was previously done in metallic interfaces [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] and the surface of topological insulators [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF] (see Fig. 3.5a). The approach taken to increase the spin-to-charge conversion efficiency in LAO//STO was to play with the much larger relaxation times observed in the confined 2DEG.

As a reminder, even though λ IEE is usually associated only with α R , according to Eq. 1.29 it also depends on the momentum relaxation time τ s . Indeed, although the Rashba coefficient for this interface is rather small, compared with other systems (α [START_REF] Walker | Carrier-Density Control of the SrTiO 3 (001) Surface 2D Electron Gas studied by ARPES[END_REF][START_REF] Hurand | Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO 3 /SrTiO 3 devices[END_REF][START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF] vs. α Bi R = 5.6 × 10 -11 eV.m for example), the relaxation time is several orders of magnitude larger, with an estimated τ LAO/ST O s = 1.4 × 10 -12 s vs. τ Bi s = 5 × 10 -15 s. Due to this massive difference, a record value of λ IEE = 6.4 nm was achieved, mainly due to the fact that the 2DEG in LAO//STO is "encapsulated" between two insulating materials, assuring that conduction takes place exclusively at the interface (a major setback for topological insulators due to conducting bulk states [START_REF] Shiomi | Spin-Electricity Conversion Induced by Spin Injection into Topological Insulators[END_REF][START_REF] Deorani | Observation of inverse spin Hall effect in bismuth selenide[END_REF]). Moreover, external gate voltage was used to tune the conversion efficiency, leading to not only a modulation of the effect but even a sign change of λ IEE , as shown in Fig. 3.5b.

LAO/ST O R = 3 × 10 -12 eV.m
From this seminal work, several other groups have investigated spin-to-charge conversion at oxide interfaces, even up to room temperature. At 300 K, the dielectric constant of STO becomes as low as 300, compared with 20000 below 4 K, hampering the generation of large electric fields at the interface. Also, the mobility of charge carriers in the LAO//STO 2DEG is known to be 1000-5000 cm 2 .V -1 .s -1 at low temperature, but two orders of magnitude lower at higher temperatures, driving the relaxation time to lower values. Chauleau et al. found that λ IEE drops to 1 nm at 75 K and about 0.15 nm at room temperature [START_REF] Chauleau | Efficient spin-to-charge conversion in the 2D electron liquid at the LAO/STO interface[END_REF]. In contrast, other groups have found an increase in the detected IEE voltage with increasing temperature [START_REF] Song | Observation of inverse Edelstein effect in Rashba-split 2DEG between SrTiO 3 and LaAlO 3 at room temperature[END_REF]. In view of the decrease in the momentum relaxation time with increasing temperature, For larger lengths, the spin current is eventually lost (inset). Adapted from [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF].

(eV.m) 10 -10 10 -11 10 -12 10 -13 10 -14

Spin current generation and charge current detection

Exploring the physics of spin-to-charge current conversion will naturally involve both the creation of spin currents and the detection of charge currents. As introduced in Section 1.2, there are generally two types of currents containing spin information: spin-polarized and pure spin currents. Since we want to detect the charge currents produced by the injection of a spin current, having an extra charge component in the injected signal is undesired, and would make the quantification of the effect quite difficult. For this reason, just like in most works cited in the last section, we will perform spin pumping experiments to generate a pure spin current from a ferromagnetic material towards a Rashba 2DEG. In this section, we give a very brief introduction on two important pieces to generate these currents; ferromagnetic resonance and spin pumping. Then, we describe the experimental apparatus used, as well as important aspects regarding charge current detection and spin-rectification effects.

Ferromagnetic resonance

In ferromagnets, even in the absence of external magnetic fields, magnetic moments of atoms and ions tend to align in a particular direction in space, resulting in finite magnetization.

Alignment of these moments is driven by the exchange interaction, making it possible to approximately describe a whole spin system as one macrospin with magnetization M . In equilibrium, M saturates to a maximum value M s , so that the magnetic state can be described as a unit vector order parameter m(r, t) = M /M s .

Due to the large exchange energy costs involved, altering the magnetic state of a ferromagnetic material is not easy, and normally low-energy excitations can only induce a modulation of the magnetization direction. However, upon application of an external magnetic field H, m tends to be realigned in the new imposed direction, by precessing around H until a new equilibrium state is achieved, as sketched in Fig. 3.7d.

The magnetization dynamics involved in this process can be described by the Landau-Lifshitz-Gilbert (LLG) equation, given as:

∂m ∂t = -γ(m × H ef f ) + α G m × ∂m ∂t (3.1)
The first part of the LLG equation describes the precessional motion around H ef f , the effective magnetic field comprising all external and internal sources of magnetic fields, with γ the gyromagnetic ratio introduced in Eq. 1.4. The second part of the equation is connected with relaxation of the magnetization toward its equilibrium configuration, usually due to interaction of the spins with its environment (conduction electrons, lattice vibrations, etc).

The Gilbert damping constant α G is introduced, describing how fast the spins become aligned with H ef f .

If the damping force drives the alignment of the magnetization along H ef f , the precessional motion may be maintained by supplying enough energy to the system through an oscillating or rotating source. The principle of ferromagnetic resonance (FMR) technique is to find the "sweet-spot" to which the precessional motion is steadily sustained, allowing an evaluation of the magnetic properties of a ferromagnetic system.

The application of a static magnetic field H yields an energy splitting of the eigenstates called Zeeman splitting. As depicted in Fig. Modified from [START_REF]Ferromagnetic Resonance -Theory and Applications[END_REF]. (d) Illustration of the magnetization relaxation process after the rf field in turned off. Notice how a damping-like effect aligns m with H ef f . Adapted from [START_REF] Czeschka | Spin Currents in Metallic Nanostructures[END_REF].

the application of a radio-frequency (rf) microwave h rf . The resonance condition for these transitions to occur is therefore given by:

ω = g e µ B µ 0 H res (3.2)
When this condition is met, the macrospin will keep a steady precessional motion around the applied magnetic field. When H and h rf are applied in the film's plane (and H • h rf = 0), the dispersion relation of H res with angular frequency ω = 2πf is also known to follow Kittel's relation:

ω γ 2 = H res (4πM ef f + H res ), (3.3)
where M ef f is the effective saturation magnetization and 4πM ef f = 4πM s + H u⊥ is the shape anisotropy in a ferromagnetic polycrystalline film, with H u⊥ representing other perpen-dicular uniaxial anisotropy29 [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF].

Experimentally, multiple combinations of ω and H res may satisfy Eq. (3.2). However, it is usually more practical to fix ω and sweep H. As it is increased, the microwave absorption and dispersion properties of the dynamic magnetic susceptibility χ = χ + iχ are monitored (through its imaginary and real part, respectively) and plotted as a function of the applied magnetic field, as depicted in Fig. 3.7b and 3.7c. Since there are typically more electrons in the lower energy state (according to Maxwell-Boltzmann distribution), as we approach H res , transitions from m J = -1/2 to m J = +1/2 start to occur, and a resonant absorption peak with a characteristic Lorentzian lineshape emerges, as exemplified in Fig. 3.7b. Here, the full width half-maximum is denoted 2∆H. Additionally, since the usual FMR detection is performed with a lock-in technique, instead of χ , the measurement gives its first field derivative, so that dχ /dH(H) is often known as the FMR signal (see Fig. 3.7c). From this curve, we are able to extract the resonance field H res (at the inflection point), as well as the peak-to-peak linewidth ∆H pp , which follows the relation ∆H pp = (2∆H)/ √ 3. Its dependence with ω can also be used to calculate the damping constant α G , through the relation:

∆H pp (ω) = ∆H 0 + ∆H G = ∆H 0 + 2 √ 3 ω γ α G , (3.4)
where the term ∆H 0 accounts for the frequency-independent contributions due to inhomogeneities in the FM layer, and ∆H G the FMR linewidth due to Gilbert damping [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF]. Since defects tend to accumulate at the surface, ∆H 0 is usually in the order of a few Gauss in thick FM layers.

Alternatively, M ef f and α G can be extracted from out-of-plane (OOP) angular dependence measurements, as thoroughly discussed in Ref. [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF]. Although this method is in many ways more arduous (in terms of analysis), the main idea is to perform FMR experiments as a function of the angle θ H with respect to the surface, i.e. θ H = 90°for in-plane field and θ H = 0°for out-of-plane field. M ef f and the effective g-factor g * e can be extracted by fitting the H res vs. θ H curve with a least square function, while α G is obtained by fitting the ∆H pp vs. θ H curve with:

∆H pp = ∆H G + ∆H θ = 2 √ 3 ω γ α G cos(θ H -θ M ) + dH res dθ H ∆θ (3.5)
In the first term of Eq. 3.5, ∆H G represents the FMR linewidth due to Gilbert damping, similarly to Eq. 3.4, but with an additional cos dependence of the difference between the angle θ H of the applied field and the actual angle of the magnetization with the FM layer θ M . The second term is composed of ∆H θ , the angular dispersion of the perpendicular anisotropy and demagnetizing field (4πM ef f ) due to inhomogeneities in the FM layer. Here, ∆θ = θ H -θ M , and for thick FM films it is usually in the order of 0.1°.

The OOP angular dependence analysis is normally convenient to confirm the α G and M ef f extracted from the simple H res and ∆H pp dependence with the applied RF frequency. However, it ultimately gives a more precise value of α G , for the simple fact that the effective g-factor g * e can also be extracted, which means that the gyromagnetic ratio γ, entering in both Eqs. 3.4 and 3.5, can be more precisely calculated (see also Eq. 1.4).

Spin pumping

When the magnetization direction m starts to rotate with angular frequency ω around H ef f , the time dependence of the scattering matrix in spin space can induce spin currents in adjacent nonmagnetic layers, leaving the electron system in an out of equilibrium state. To better explain this phenomenon, we recur to the concept of spin battery, initially proposed by Brataas et al. [START_REF] Brataas | Spin battery operated by ferromagnetic resonance[END_REF] and schematically shown in Fig. 3.8.

While in a conventional charge battery, charge current conservation implies the existence of two poles, positive and negative, with two possible polarity states, a spin battery only requires one pole, the ferromagnetic source, where the polarity is defined by a three-dimensional vector.

As long as the magnetization is kept in precession (and some other requirements discussed ahead are met), the ferromagnet will pump its own spin angular momentum towards any adjacent metallic layer, hence the name spin pumping.

Given that the ferromagnet is thicker than the ferromagnetic coherence length (few Å for Co, Ni, or Fe) the spin current emitted towards the metallic layer is determined by g ↑↓ , a complex30 quantity called spin-mixing conductance (given in m -2 ). g ↑↓ can be viewed as the interface transparency, as it controls the transport of spins across the interface between the ferromagnet and the adjacent metallic layer.

The spin current produced by the ferromagnetic source can be written as [START_REF] Brataas | Spin battery operated by ferromagnetic resonance[END_REF]:

I source s = 4π {g ↑↓ } m × dm dt -{g ↑↓ }m (3.6)
In reality, Eq. (3.6) gives the maximum spin current that can be generated in a spin battery.

If the spin relaxation rate is smaller than the spin injection rate, spin accumulation builds is pumped towards the normal metal (NM), inducing spin s flips and ultimately spin accumulation ∆µ N s at the interface, that dissipates towards bulk. In turn, this accumulation may drive a diffusive spin current backflow I back s towards the FM. Adapted from [START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF].

incoming pumped current from the ferromagnet, a perpendicular component survives:

I back s = {g ↑↓ } 4π (m × ∆µ N s × m) (3.7)
where ∆µ N s is the spin accumulation in the metallic layer. The total (renormalized) spin current pumped is therefore given by I s = I source s + I back s . Note that, the spin currents given by Eq. (3.6) and (3.7) are given in units of mechanical torque. In the following chapters we shall introduce a way to quantitatively estimate the pumped spin current density, allowing a comparison with the charge current density generated through the IEE.

Lastly, the fact that a new spin relaxation channel is provided in a FM/NM structure implies a change in the magnetization dynamics of the ferromagnet. If we consider an isolated FM, magnetization relaxation is mainly provided by its lattice, yielding a magnetization damping in the form of the Gilbert damping constant α G , introduced in Eq. (3.1). In a FM/NM structure, the metallic layer serves a reservoir that opens up an additional channel for relaxation. Interestingly, we realize that in Eq. (3.6), the real part of the spin-mixing conductance {g ↑↓ } takes the same form as α G in Eq. (3.1), so that the pumped spin current leads to an additional damping of the magnetization precession. On the other hand, in the second half of Eq. (3.6), {g ↑↓ }m acts as an additional magnetic field that results in a shift of the resonance position. Experimentally, the enhanced damping of the magnetization trans-lates in a broading of the FMR linewidth ∆H (see Fig. 3.7b) and can be given by its effective value [START_REF] Tserkovnyak | Enhanced Gilbert Damping in Thin Ferromagnetic Films[END_REF][START_REF] Azevedo | Spin pumping and anisotropic magnetoresistance voltages in magnetic bilayers: Theory and experiment[END_REF]:

α ef f α G + γ {g ↑↓ }/(4πM s V) 1 + [ √ tanh(t N /t N sf )] -1 , (3.8)
with V the volume of the FM layer, t N and l N sf the thickness and spin-diffusion length of the NM layer, and the ratio between momentum and spin-flip scattering time in the NM layer.

In this small introduction, we only covered the very basics of FMR and spin pumping, which should serve as a toolbox for the experimental results shown in the following sections.

For more information regarding magnetization dynamics in ferromagnetic heterostructures, we refer the reader to the extentive review of Tserkovnyak et al. [START_REF] Tserkovnyak | Nonlocal magnetization dynamics in ferromagnetic heterostructures[END_REF].

Experimental setup

In this section, we describe the experimental apparatus used in our spin pumping experiments.

Geometrical considerations are of extreme importance for a proper understanding of the voltages detected at resonance. As we will see, many different contributions may arise besides the IEE generated charge current. FMR-driven spin pumping experiments were conducted in a Brüker ESP300E X-band CW spectrometer with a loop gap Brüker ER 4118X-MS5 cavity contained in a cryostat. A sketch of the setup is depicted in Fig. 3.9a. The sample is mounted in a support that is suspended inside the cavity and allows the magnetic field H dc to be applied in-plane. A microwave radiation h rf with fixed frequency is generated by a Gunn diode and then guided into the loop gap microwave resonator. The coupling between the waveguide and the resonator is achieved through a tunable iris. While normally the incident microwave is entirely absorbed by the resonator, at resonance the sample partially absorbs the rf power. This will in turn detune the cavity, through partial reflection of microwave radiation, so that calibration of the iris is required at the beginning of each set of measurements.

The samples are glue to a thin PCB sample holder and electrical detection is performed with aluminum wires bonded on two sides of the sample, so that the detected voltage is parallel to h rf and perpendicular with H dc . An additional contact is placed on the back-side of the sample, using silver paste, enabling the application of a back-gate voltage.

A second sketch is presented in Fig. 3.9b showing the orientation of each physical component. The in-plane magnetic field aligns the magnetization m of the FM with the y-axis.

The microwave radiation along the x-axis drives the magnetization into precession, so that a pure spin current is pumped along the z-axis across the barrier and towards the 2DEG. Note A key detail regarding the geometry of our experiment is that the voltage probes are bonded across the whole heterostructure (similarly to the transport experiments shown in Section 2.5.2.1), meaning that magnetoresistance effects originating in the FM will also be detected. We shall consider the different elements composing the detected voltage in the following section.

Voltage contribution from spin rectification and Edelstein effects

Under microwave excitation, two contributions arise in the ferromagnetic material: an rf electric field E rf , generating an rf current j rf , and an rf magnetic field h rf that exerts a field torque on the magnetization, inducing precession around its equilibrium direction. The oscillating magnetization drives time-dependent magnetoresistance effects in the ferromagnet, so that the precessional motion itself causes an rf resistance. Simply put, spin rectification is the generation of a dc voltage/current due to non-linear coupling between j rf and the oscillating resistance driven by the precessing magnetization of the magnetic structure [START_REF] Harder | Analysis of the line shape of electrically detected ferromagnetic resonance[END_REF].

Spin rectification can originate from magnetoresistance effects such as the anisotropic magnetoresistance (AMR), the anomalous Hall effect (AHE) and planar Hall effect (PHE). Even though they present a powerful tool to probe magnetization dynamics in magnetic samples, for the purpose of our experiments these effects are undesirable, as they add up to the Edelstein signal. Ideally, the sample is placed right at the center of the loop gap cavity (see Fig. 3.10a),

where E rf is minimized and the h rf is maximized. However, in practical terms there is always some non-vanishing E rf at the sample level, so that spin rectification effects occurring at the resonance must be properly evaluated.

Given the geometry of our experiment (see Fig. 3.10b) with a j rf produced within the sample due to E rf along the y-axis, the voltage being detected along the x-axis is in the transverse Hall geometry, so that, in addition to Edelstein signal, a PHE and AHE contribution arising from the FM will be detected. As pointed out by Harder et al. [START_REF] Harder | Electrical detection of magnetization dynamics via spin rectification effects[END_REF] and Azevedo et al.

[315], the measured voltage curve in FMR experiments can be phenomenologically described by a symmetric and antisymmetric component, so that [START_REF] Harder | Analysis of the line shape of electrically detected ferromagnetic resonance[END_REF][START_REF] Azevedo | Spin pumping and anisotropic magnetoresistance voltages in magnetic bilayers: Theory and experiment[END_REF]:

V = V of f set + V s ∆H 2 (H -H res ) 2 + ∆H 2 + V as -∆H(H -H res ) (H -H res ) 2 + ∆H 2 ,
(3.9) with V of f set a nonresonant offset voltage, and V s and V as the symmetric and antisymmetric contributions. Even though rectification effects may take both symmetric and antisymmetric forms, as displayed in Fig. 3.10c, the latter usually is dominant in FM films, as observed for example in CoFeB [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF] and NiFe [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]. One the other hand, voltage produced by ISHE or IEE is always symmetric (with respect to the resonance field). This means that, in order to properly quantify the voltage being generated due to spin-to-charge conversion effects, one must be sure that the FM alone is not generating a large V sym . The simplest way of scrutinizing these two contributions is by measuring a reference sample. We take the example of the measurements performed by Rojas-Sanchez et al. in Ta/CoFeB/MgO/Ge and (reference) Ta/CoFeB/MgO/SiO 2 samples [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF]. First, FMR experiments on the reference sample revealed a practically fully antisymmetric signal. The same experiment on the "real" sample revealed a large symmetric peak, attributed solely to the ISHE. Additionally, the OOP angular dependence of V sym for both samples showed striking differences, once again signaling that the symmetric signal is dominated by the ISHE. A similar procedure will be utilized in the sections ahead, to evaluate the voltage generated in NiFe/LAO//STO samples. We add that the spin-to-charge converted voltages should also be perfectly reversed with inversion of field direction (i.e. rotating it by 180°). Since j c ∝ (j s × σ), flipping the spin direction σ of the spin density that is pumped into the 2DEG leads to an opposite shift of the Fermi contours, which generates a current in the opposite direction (see Section 1.6.3.1 for more details). As an additional note, both symmetric and antisymmetric voltage contributions in Eq. (3.9) exhibit a linear dependence with the microwave power P (∝ to h 2 rf )). However, increasing the power over a certain threshold can lead to unwanted heating effects, destroying this linear behavior.

An additional source of V sym may arise due to heating effects such as the spin Seebeck effect (SSE). In fact, due to microwave radiation absorbed by the sample at resonance, heating effects are likely to occur, even though they are expected to be rather small. To exclude this contribution from the collected signal, one can simply perform the FMR experiment using H in both directions (parellel and antiparallel). In both cases, the microwave-driven heating should produce a similar voltage peak with the same sign, so that if a large difference between both curves is observed, heating effects may be relevant. We note that Seebeck-related effects normally give voltages in the range of 50-100 nV.K -1 . In order for these to be relevant in spin-to-charge conversion experiments, which normally give µV and mV signals, the sample would need to see a raise in temperature of about 100 K, a scenario that seems highly unlikely and that would additionally inflict large shifts in the H res .

Inverse Edelstein effect in LaAlO 3 /SrTiO 3 heterostructures

In Section 2.3, we shed some light on the properties of LAO//STO interfaces and how they can be exploited to perform spin-to-charge current conversion. Despite its low Rashba coefficient, (c) Scanning TEM cross-section. Modified from [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

the combination of large relaxation times and the possibility to tune the effect through gate voltage make this system particularly interesting for a much broader study of Rashba physics in confined systems, as well as some possible device applications.

With this in mind, the conversion of a spin current to a charge current in an oxide-based 2DEG through the inverse Edelstein effect was for the first time experimentally observed in our lab, using NiFe/LAO//STO heterostructures [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

Sample fabrication and electrical characterization

The NiFe/LAO//STO samples were grown in a setup combining pulsed laser deposition (PLD) and a magnetron sputtering chamber with in vacuo sample transfer, as demonstrated previously in Fig. 2.16. Similarly to the concept presented in Chapter 2, the critical thickness of LAO for 2DEG formation was reduced to 2 uc by deposition of a thin layer of metallic NiFe, so that the barrier for spin pumping is reduced, while the 2DEG is kept confined between two insulating materials. We start with a TiO 2 -terminated (001)-oriented STO substrate, terminated by the procedure described in Section 2.4.1.1. A single-crystal LAO target is ablated by a KrF (248 nm) excimer laser at a repetition rate of 1 Hz and a fluence of about 1 J.cm -2 .

During deposition, the oxygen partial pressure inside the PLD chamber was kept at 2 × 10 -4 mbar, the substrate at a temperature of 730 °C, and the substrate-to-target distance at 63 mm. As observed in Fig. 3.11a, the growth was accompanied by RHEED, where the intensity oscillation indicate layer-by-layer growth of 2 uc. After this, the samples were annealed for 30 where the massive drop in resistance due to the q2DEG is observed at lower temperatures.

The parallel conduction model, introduced in Section 2.5.2.1, was used to extract the q2DEG contribution (light blue curve).

Additionally, MR and Hall measurements confirm the existence of a 2DEG. As displayed in Fig. 3.12b and 3.12c, after extracting the isolated 2DEG contribution, we fitted both MR and Hall curves (in purple) with a 2-band model (see Eq. 2.12), yielding two bands with carrier densities of n 1 = 1.54 × 10 13 cm -2 , n 2 = 1.07 × 10 13 cm -2 and mobilities of µ 1 = 3300

cm 2 V -1 s -1 , µ 2 = 160 cm 2 V -1 s -1 .
Here, we note that even though the Hall curve extracted appears to be linear, which might indicate the population of only one band, a single-band model fails to provide a good fit for both MR and Hall curves simultaneously31 .

FMR and spin pumping experiments

Using the FMR technique introduced in the previous section, we characterize the dynamic magnetic response of our samples32 . Measurements were performed at room temperature, using a broadband technique involving a co-planar waveguide. The main difference between this setup and the X-band cavity is the h rf field orientation with respect to the sample. While in cavity, the microwave field lines minimize undesired rf electric fields E rf (see Fig. 3.10a), in a co-planar waveguide geometry the sample is placed directly on the rf stripline, so that the h rf is poorly defined at the sample level, which in turn leads to larger rectification effects.

However, this geometry normally allows frequency modulation (unlike in the cavity), making it quite useful to study the properties of FM layers.

The sample is mounted in a Au stripline (waveguide) placed at the center of an electromagnet which provides an in-plane dc magnetic field and an rf field, supplied by a microwave The black lines represent the fits (using Eq. 3.4) which allow the extraction of the damping constant α G . Adapted from [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

field shifts when changing the rf frequency. Each curve is then fitted with:

dχ dH (H) = -2 A abs (H -H res ) [∆H 2 + (H -H res ) 2 ] 2 + 4A dis (H -H res ) 2 [∆H 2 + (H -H res ) 2 ] 2 , (3.10)
where ∆H is the half-width at half-maximum of the Lorentzian lineshape, A abs and A dis are the prefactors which correspond to the dispersion and absorption contributions 33 (χ and χ , respectively). By fitting each curve, we obtain the resonance field H res as well as the peak-to-peak linewidth ∆H pp = (2∆H)/ √ 3, which are plotted as a function of the frequency, as displayed in Fig. 3.13b and 3.13c, respectively. From the dependence with H res we are able to use Kittel's equation [Eq. (3.3)] to extract the effective saturation magnetization M ef f of the NiFe film, which shows roughly the same value for the NiFe layer on LAO//STO and on LAO.

From the dependence with ∆H pp we extract the effective damping constant 34 We then proceed to the spin pumping experiments, where, at the ferromagnetic resonance condition, the NiFe layer is expected to pump a pure spin current towards the interfacial q2DEG. The samples are cut in a 2.4 mm × 0.4 mm slab geometry, and are wire-bonded and mounted inside a loop gap cavity, as described in Section 3.3.2. A third wire was placed under the sample, using conducting silver paste, to allow the application of a back gate voltage.

Unlike the FMR experiments, spin pumping was performed at a temperature of 7 K (using the helium-flow cryostat) to exploit the low resistance of the q2DEG (∼ 100 Ω).

We start by aligning the sample with H dc , by performing FMR tests at different angles θ H until the minimum H res is found. Then, voltage measurements are performed in parallel (P) and antiparallel (Q) mode, i.e. H dc and -H dc , to confirm that the signal is well reversed. A power dependence can also be performed, to verify its linearity with the detected signal. The sample is then initialized by sweeping the back-gate voltage from +200 V to -200 V, and then back to +200 V, at which the first measurement is made. The importance of this "initialization step" is discussed in detail in the next section, but can be linked with the filling/spilling of carriers in the 2DEG quantum well [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF].

At a given gate voltage, we sweep the external in-plane magnetic field, around values close to the expected resonance field while measuring the voltage. The rf frequency and power are fixed at ∼9.66 GHz and 2 mW, respectively. A sketch of the experiment is also displayed in Fig. 3.14a. We show in Fig. 3.14b the first-field derivative of the absorption peak dχ /dH, phenomenologically introduced in Section 3.2.1, indicating that the resonance condition is met at about 97 mT. Under an applied back-gate voltage of 125 V, we observe a large voltage peak (normalized to the microwave power, i.e. V = V raw /h 2 rf ), indicating that charge current is being produced in the q2DEG due to the injection of a spin current (thick red curve). Moreover, as discussed in Section 3.2.4, the peak is mostly symmetric, indicating that the voltage produced essentially comes from the IEE. A very small antisymmetric contribution is also displayed (thin red line), associated with rectification effects. Note that each contribution can be extrapolated from the raw voltage curve using Eq. (3.9). To discard possible contributions due to heating effects, we reverse the polarity of the applied magnetic field (same as rotating it 180°in-plane). The blue curve in Fig. 3.14c shows a well reversed voltage peak with similar magnitude. In this case, the direction of the injected spins σ is flipped, so that the spin density injected in the q2DEG drives a displacement of the Fermi contours in the opposite direction in k-space, as described in Section 1.6.3.1. Ultimately, a voltage with opposite sign is generated.

In the inset, we show similar data collected at room temperature. The gate voltage in this case is practically ineffective, due to the large temperature dependence of the dielectric constant of STO (see the next section for more details). However, we notice that the signal

T = 7 K V g = 125 V H dc <0 H dc >0
dc''/dH (arb.

u.)

T = 7 K V g = 0 V H dc <0 H dc >0
dc''/dH (arb.

m 0 H (mT) H dc <0 H dc >0 Vraw 80 90 100 110 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 90 100 110
-0 ,0 0 2 0 ,0 0 0 Each curve is disentangled in a symmetric (dotted line) and antisymmetric (thin line) component using Eq. 3.9. The inset shows similar data collected at room temperature. (d,e,f ) Same as the previous panels but for a reference NiFe//LAO sample. Partially adapted from [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]. (b) Peak-to-peak linewidth ∆H pp and contributions due to the Gilbert damping ∆H G and perpendicular anisotropy dispersion due to inhomogeneities in the FM layer ∆H θ , extracted from the fit (red curve) described by Eq. 3.5. In the inset, the equilibrium angle of magnetization θ 0M as a function of the angle of the applied magnetic field θ H . (c) Normalized symmetric voltage and fit (red curve) using a numerical function proportional to sin(θ 0M ). Adapted from [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF] (supplementary). is mostly antisymmetric, meaning that (almost) no spin-to-charge current conversion takes place. At room temperature, the resistance of the q2DEG is orders of magnitude larger than at 7 K, which drives the momentum relaxation time τ to much lower values. From Eq. (3.5), due to its dependence with τ , the conversion efficiency given by λ IEE follows the same trend, plummeting to much lower values.

0 ,0 0 2 300K Vraw T = 7 K V g = 125 V H dc <0 H dc >0 Vraw Vsym V/h rf (mV.G -2 ) m 0 H (mT) Vasym 2 H dc <0 H dc >0 Vraw Vsym STO LAO NiFe j c 2D j s V m h rf H dc V g σ NiFe/LAO(2uc)//STO NiFe//LAO (reference) (b) (c) (e) (f
0M H V s /h rf (mV.G -2 ) 2 μ 0 ¡ H pp (mT)
£ G =0.0077 T=7 K V g =+100 V ¤H G ¥H θ 0 -
Lastly, we show similar experiments for a reference NiFe(20nm)//LAO sample, as sketched in Fig. 3.14d. For this case, the data presented in Fig. 3.14f reveals an almost perfectly antisymmetric voltage contribution, reversible by switching the polarization of the applied magnetic field. We conclude that rectification effects arising from the NiFe layer contribute very little to the symmetric signal, thus strengthening our previous conclusions regarding IEE signal arising in this Rashba 2DEG.

To further confirm this result we perform OOP angular dependence, as displayed in Fig. 3.15, where θ H = 0°corresponds to the magnetic field applied out-of-plane. First, we numerically fit the angular dependence of H res (red curve) to obtain the effective g-factor g * e and M ef f , as shown in Fig. 3.15a. We find g * e = 2.07 at 7 K, slightly lower than that taken in broadband analysis for NiFe at room temperature (g * e = 2.11). The ∆H pp angle dependence is also fitted using Eq. 3.5, where α G = 0.0077 is obtained (see Fig. 3.15b). Remarkably, we have found roughly the same value as the one obtained at room temperature. It is worth noting that for another Rashba interface, namely at the metallic Ag/Bi interface, it was found that α G and g * e were almost temperature-independent [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF]. Finally, we analyze the angular dependence of the detected voltage as shown in Fig. 3.15c. We observe that all the features agree very well with the spin-to-charge conversion mechanism, i.e. the symmetric signal changes sign (but not in magnitude) upon reversing H dc , and drops to zero when H dc is applied perpendicular to the plane (θ H = 0°).

Spin-to-charge current conversion modulation

One of the most attractive features of the LAO//STO system is the possibility to tune the properties of the 2DEG using back-gate voltage, mainly due to the extremely large dielectric constant and insulating nature of STO at low temperature. This feature becomes absolutely essential for the prospects of manipulating spin currents electrically, something that is possible in semiconductor-based Rashba 2DEGs but much more difficult for all-metallic system, where spin-related effects were observed to be much larger.

Early on, electrostatic doping of the 2DEG became a quite popular way to tune its carrier densities and mobilities, allowing researchers to take advantage of the complex multiband transport properties of this 2D Rashba system to study some of its most exotic physical effects, such as superconductivity [START_REF] Caviglia | Electric field control of the LaAlO 3 /SrTiO 3 interface ground state[END_REF], Shubnikov-de Haas oscillations [START_REF] Fête | Large modulation of the Shubnikov-de Haas oscillations by the Rashba interaction at the LaAlO 3 /SrTiO 3 interface[END_REF] or weak (anti)localization regimes [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF]. From the latter, it was found that α R increased with positive back-gate voltage, an effect driven by a drastic change in the ratio between momentum and spin relaxation times, which in the framework of D'yakonov and Perel' points towards a strong spin-orbit coupling regime [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF]. Since then, several other authors have confirmed the gate tunability of the Rashba SOC through magnetotransport [START_REF] Shalom | Tuning Spin-Orbit Coupling and Superconductivity at the SrTiO 3 /LaAlO 3 Interface: A Magnetotransport Study[END_REF][START_REF] Fête | Rashba induced magnetoconductance oscillations in the LaAlO 3 -SrTiO 3 heterostructure[END_REF][START_REF] Hurand | Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO 3 /SrTiO 3 devices[END_REF][START_REF] Gopinadhan | Gate Tunable In-and Out-of-Plane Spin-Orbit Coupling and Spin-Splitting Anisotropy at LaAlO 3 /SrTiO 3 (110) Interface[END_REF] and theory [START_REF] Zhong | Theory of spin-orbit coupling at LaAlO 3 /SrTiO 3 interfaces and SrTiO 3 surfaces[END_REF][START_REF] Shanavas | Electric Field Tuning of the Rashba Effect in the Polar Perovskite Structures[END_REF][START_REF] Bucheli | Phase diagrams of voltage-gated oxide interfaces with strong Rashba coupling[END_REF], using both the LAO//STO interface as well as other STO-based systems [START_REF] Liang | Nonmonotonically tunable Rashba spin-orbit coupling by multiple-band filling control in SrTiO 3 -based interfacial d-electron gases[END_REF].

Ultimately, all of these results lead to one question: can we efficiently use this gate effect to manipulate spin and charge currents?

H > 0 V sym /V asym 0.05 T = 7 K -200 V +200 V H > 0 T = 295 K V sym /V asym 0.3 -200 V +200 V H > 0 T = 7 K V g (V) +200 +150 +100 +50 0 -200 -150 -100 -50 V (μV) 0 1 2 -1 -

Estimation of λ IEE

We start by looking at the gate dependence of the (raw) voltage detected in the NiFe//LAO reference sample, at low temperatures. We observe in Fig. 3.16a that sweeping the back-gate voltage between +200 and -200 V hardly changes the shape or magnitude of the antisymmetric curve. On one hand, the stability of the signal and absence of modulation assures us that applying rather large gate voltages on a 0.5 mm substrate of LAO does not perturb the cavity (not shown here but also evidenced by the almost unaltered FMR spectra) and that no spinto-charge conversion occurs due to the NiFe/LAO interface.

For the NiFe/LAO(2uc)//STO sample, we performed similar experiments both at room and low temperature, as displayed in Figs. 3.16b and 3.16c, respectively. Regarding the room temperature case, we observe very similar behavior to that of the reference sample, i.e. mostly antisymmetric signal and absence of gate modulation. It is however important to realize that, in this case, a q2DEG exists at the LAO//STO interface. The lack of modulation is associated with the low dielectric constant of STO at room temperature ( ST O ∼ 300), which, as we will see ahead, hampers any efficient modulation of the properties of the q2DEG.

In striking contrast, the raw voltage (normalized by the microwave power) detected at low temperature shows values two orders of magnitude larger than the ones observed at room temperature. The curves collected, with an applied back-gate voltage between +200 V to -200 V and a step of 50 V, also go through several sign and symmetric/antisymmetric shape changes, in an apparent non-monotonic fashion.

At this point, it is of interest to calculate the spin-to-charge current conversion efficiency,

given by λ IEE in Eq. 1.29. This efficiency can be simply estimated through a ratio between the 2D charge current generated in the 2DEG and the 3D spin current injected through spin pumping, λ IEE = j 2D c /j 3D s . First, taking the symmetric component of the generated raw voltage (associated with IEE) we use Ohm's law to calculate the equivalent 2D current density normalized by the microwave power:

j 2D c = V sym wRh 2 rf , (3.11)
where w = 0.4 mm is the sample width and R the two-point resistance of the NiFe/LAO//STO heterostructure.

The resulting charge current density spectra generated at low temperature through the IEE, for different back-gate voltages, is shown in Fig. 3.17a. Here, we clearly see that the produced current not only changes magnitude, but also changes sign at about V g = 0 V.

Remarkably, we achieve a maximum value of

j 2D c = 53.3 mA.m -1 .G -2 at V g = +125 V, one
order of magnitude larger than in previous reports (1.5 mA.m -1 .G -2 for Ag/Bi [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] and 5.9

mA.m -1 .G -2 for α-Sn [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF]). Additionally, we show in Fig. 3.17b that, when turning the magnetic field by 180°, hence injecting spins oriented along -y axis instead of y, the IEE signal is well reversed for the range of gate voltages applied.

Then, we turn to the estimation of the spin current density being injected through spin pumping across the LAO barrier and into the 2DEG, given by [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]:

j 3D s = {g ↑↓ }γ 2 (µ 0 h rf ) 2 8πα 2 N iF e/2DEG µ 0 M ef f γ + (µ 0 M ef f γ) 2 + 4ω 2 (µ 0 M ef f γ) 2 + 4ω 2 2e , (3.12)
where the real part of the spin-mixing conductance g ↑↓ is:

{g ↑↓ } = 4πM ef f t F g e µ B (α N iF e/2DEG -α N iF e ), (3.13)
with t F the thickness of the NiFe layer and α N iF e/2DEG -α N iF e the Gilbert damping constant difference between the NiFe/LAO//STO and NiFe//LAO (reference) samples.

In Table 2, we present the parameters used in Eq. (3.12) and (3.13) to extract a spin current density of j 3D

s = 8.4 × 10 6 A.m -2 .G -2 .
Using the calculated spin current density and charge current density for each applied gate voltage, we plot in Fig. 3.17c the calculated λ IEE . A maximum is achieved at +125 V, where a λ IEE = 6.4 nm is achieved, in great contrast with the much lower values of 0.1-0.4 nm found in Ag/Bi [START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] and 2.1 nm found in α-Sn [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF].

Using the simple approximation of circular contours introduced in Section 1.6.3.1, we .G -

-150 V -100 V -50 V 0 V +75 V +125 V +175 V T = 7 K H dc > 0 μ 0 H (mT) (a)
H dc > 0

H dc < 0 0 20 40 60 -20 -40 -60 j c (mA.m -1 .G -2
) Table 2: Relevant parameters for the estimation of the spin current j 3D s injected through spin pumping and experiments/equations that allow their quantification. is promoted, introducing a "faster" relaxation mechanism that drives τ to lower values [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF].

0 100 200 -100 -200 V g (V) 0 100 200 -100 -200 V g (V) ¡ IEE (nm) 0 2 -2 -4 -6 T
Having an insulator in contact with the Rashba system (in our case the LAO barrier) essentially reduces/removes this relaxation channel, allowing longer τ and subsequently larger conversion efficiencies.

2DEG under electrostatic gating

Only a few years after the discovery of the 2DEG in LAO//STO, the possibility to tune its carrier density was demonstrated by Thiel et al. [START_REF] Thiel | Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures[END_REF], by taking advantage of the very large dielectric constant displayed by STO at low temperatures. At 4 K, applying a back-gate voltage of +200 V to an STO substrate with a thickness of L = 0.5 mm (an electric field of E = 0.4 MV.m -1 ) corresponds to a dielectric constant of ST O 16000 [START_REF] Christen | Dielectric properties of sputtered SrTiO 3 films[END_REF], at least two orders of magnitude larger than at room temperature.

For a parallel-plate capacitor composed of a back-gate metallic layer and a top contact (to the 2DEG), the capacitance is given as:

C(V ) = 0 (V )(S/L), (3.14)
where 0 is the vacuum permittivity, V the applied voltage, S the area of the sample, L the separation between the back-contact and the 2DEG (i.e. the substrate thickness).

The equivalent charge induced at the interface by application of a back-gate voltage V g can be written as: Starting from an as-grown sample and at V g = 0 V (state I), applying a positive V g fills the quantum well up until electrons start to spill out, i.e. irreversibly escaping from it (state II). Applying a negative V g depletes the quantum well (state III). The process of filling/depletion is considered reversible, as long as the V g applied is below the (previous) maximum V g . (e) Sheet resistance of an LTO//STO sample (comparable to LAO//STO) measured for several positive ∆V G > 0 and negative ∆V G < 0 sweeps. The equivalent regions for states I, II and III (from the previous panels) are also identified. Modified from [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF].

∆Q = Vg 0 C(V )dV (3.15) LaAlO 3 V G e -
III V G = 0 V V G < 0 V V G > 0 V (a) (b) (c) (d) (e)
From Eq. (3.14) and (3.15), we can estimate the carrier density that can be injected/removed from the interface:

∆n s = 1 eS ∆Q = 0 eL Vg 0 (V )dV (3.16)
Given the geometry of a usual STO substrate (L = 0.5 mm), a maximum gate voltage of about +200 V and ST O 16000 at low temperatures, we are able to modulate the carrier density of the 2DEG to ∆n s 2 × 10 13 cm -2 . Since the usual carrier densities found in these types of sample are in the order of 10 12 -10 13 cm -2 range, electrostatic field effect proves itself as a very efficient way to tune the properties of the 2DEG. Notice that at room temperature ST O 300, so that the ∆n s allowed is practically ineffective.

In addition to the efficient modulation, electrostatic gating induces a very peculiar behaviour in the electronic properties of the 2DEG, as demonstrated by Biscaras et al. for LAO//STO and LTO//STO heterostructures at low temperatures and shown in Fig. 3.18 [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF]. In their work, the application of a positive or negative gate voltage was used to either fill or deplete the potential well located at the interface, driving a modulation of the electron density. It was found that when starting with a virgin sample, the application of a positive gate voltage up until +200 V (which introduces carriers in the potential well) led to very weak modulation of the interfacial resistance. Decreasing the gate voltage, immediately drove the resistance to higher values, which continued to increase until the minimum gate voltage (-200

V) was applied. When the gate voltage is once again increased to +200 V, it follows almost perfectly the previous polarization. The behavior of the sheet resistance as a function of gate voltage is displayed in Fig. 3.18e.

It was concluded that, in the first positive polarization, after cooling down, the E F lied very close to the top of the potential well (Fig. 3.18b). Adding more carriers (positive gate voltage) shifts the E F to higher energies, to a point where carriers start to spill out of the well and into the STO substrate, where they end up trapped on localized states (Fig. 3.18c). At this point, changing the gate voltage between -200 V and +200 V only empties and fills the well (Fig. 3.18d), leading to a reversible modulation of the resistance. Naturally, if at any point the gate voltage is increased above the previous maximum, the resistance is irreversibly changed.

It is for this reason that, prior to all of our spin pumping experiments, an "initialization step" is performed, so that no electron spilling occurs during the experiment.

We observe a very similar behavior when measuring the sheet resistance of our NiFe/LAO//STO heterostructures as a function of gate voltage, with the added issue regarding shunting of the NiFe metallic layer. We observe in Fig. 3.19a that the dependence between 0 to +200 V and +200 to 0 V is very similar to the one described by Biscaras et al. However, in the second polarization, below V g = 0 V conduction is almost entirely dominated by the NiFe, even though the 2DEG resistance itself is expected to increase further. This imposes a rather intricate problem when attempting to use the parallel conduction model described in Section 2.5.2.1 to extract relevant properties of the 2DEG alone, at least for negative gate voltages.

Nevertheless, we plot in Figs. 3.19b and 3.19c the magnetoresistance and Hall curves as a function of the applied back-gate voltage, respectively. As expected, below V g = 0 V, the curves are characteristic of a ferromagnetic layer. Yet, at V g = +200 V, the 2DEG appears to be dominating the parallel conduction. Using the two-band model (Eq. 2.12), we extract a carrier density of n total = 3.41 × 10 13 cm -2 (n 1 = 2.39 × 10 13 cm -2 and n 2 = 1.02 × 10 13 cm -2 ) and mobilities of µ 1 = 120 cm -2 .(V.s) -1 and µ 2 = 3500 cm -2 .(V.s) -1 , as shown in Fig.

3.19d.

In essence, the combination of the gate-dependent transport properties above mentioned, together with the modulation of the SOC strength observed in previous reports [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF], allows us to draw an explanation for the gate-dependence of λ IEE with regards to the E F position, the complex band structure of the 2DEG in STO and orbital occupancy.

m 0 H (T) Vg = 200 V T = 5 K (a) (b) (c) (d)

Fermi level position and orbital occupancy

In bulk STO, the cubic crystal field lifts the degeneracy of the 3d orbitals, so that the energy of the t 2g triplet is lowered with respect to the e g doublet. The t 2g triplet, forming the conduction band minimum, is composed of three degenerate ellipsoidal Fermi surfaces centered in the Γ point and aligned along the main lattice directions. At the LAO/STO interface, when a q2DEG is formed, the degeneracy is lifted due to the perpendicular confining electric field that breaks inversion symmetry. In this scenario, represented in Fig. 3.20a, a light d xy band is split towards lower energy with respect to the other two heavier d xz and d yz bands. At low carrier densities, hence, low E F , only the d xy band is occupied. In this regime, transport is carried out with only one type of carrier and the spin splitting is expected to be rather small, giving a calculated Rashba constant of α R = 3 × 10 -12 eV.m [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF][START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF][START_REF] Walker | Carrier-Density Control of the SrTiO 3 (001) Surface 2D Electron Gas studied by ARPES[END_REF]. By increasing the carrier density, the d xz and d yz bands become populated and their α R is calculated to have a sign opposite to one of the d xy band [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Shanavas | Electric Field Tuning of the Rashba Effect in the Polar Perovskite Structures[END_REF]. At an energy level close to the crossing of both light and heavy bands, α R increases about one order of magnitude as a result of the strong mixing between both orbital characters.

Joshua et al. found that, in regular growth condition 35 , several LAO//STO samples show a universal Lifshitz transition between single-band (d xy ) and multi-band (d xz and d yz ) at a critical density of n c =1.68 × 10 13 cm -2 . From the transport experiments under electrostatic gating performed in the previous section, at +200 V the q2DEG formed in NiFe/LAO(2uc)//STO heterostructures is found to have a carrier density of n t = 3.41 × 10 13 cm -2 . Also, from a gate-modulation between +200 and -200 V, while assuming a rigid band structure, i.e. the distribution in momentum space is unaffected by the carrier density itself plus the large electric fields generated, we expect a carrier density modulation of ∆n s 4 × 10 13 cm -2 . From this, we estimate the energy range that is swept in our gate voltage experiment, drawn over the band structure in Fig. 3.20a.

Let us now focus on Figs. 3.20a and 3.20b. At negative gate voltages, the Fermi level lies below the Lifshitz point, where only the d xy band with weak α R is populated. A small increase of the gate voltage to about -100 V gives a constant and rather modest λ IEE , consistent with the weak energy dependence of α R for this band. Continuing to increase V g , the Lifshitz transition is crossed, and the λ IEE drops to almost zero at V g = 0 V. Given that the α R is expected to change sign for the heavier bands, we expect that at V g = 0 V spin-to-charge conversion averages out to zero, due to similar but opposite λ IEE given by each band individually. For positive gate voltages, we observe that the λ IEE changes sign, due to the dominance of the α R given by the heavier bands. Not only that, but the signal increases steeply up until +125 V, where the Fermi level reaches the avoided crossing points, a region of strong orbital mixing where α R reaches its maximum value. Indeed, as shown in Figs. cm -2 (Lifshitz transition [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]) the heavy d xz,yz bands start to be occupied. Above that, at the region where the heavy and light bands cross each other, large spin-orbit effects are predicted [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF]. The highlighted area represents the expected gate voltage region swept. (b) In this range, the λ IEE sign change (at V g ∼ 0 V) is attributed to the onset of occupation of heavy bands, which contribute with an opposite sign to the overall "effective" Rashba coefficient.

The maximum observed at V g = 125 V is linked to the avoided band crossing region. (c) Calculated band structure including atomic spin-orbit coupling, which induces band splitting at the Γ point. On the right, calculated spin-orbit strength (L.S product) as a function of energy. Modified from [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. (d) Spin splitting ∆ and k-cubic Rashba coefficient α 3 as a function of the 2DEG carrier density. A maximum is found for n 3 × 10 13 cm -2 (slighly above the expected Lifshitz transition) matching the avoided band crossings region. Modified from [START_REF] Liang | Nonmonotonically tunable Rashba spin-orbit coupling by multiple-band filling control in SrTiO 3 -based interfacial d-electron gases[END_REF].

increasing the gate voltage to +200 V, we see λ IEE dropping back to lower values, possibly due to the contribution of additional bands coming in play at higher energies that drive α R down (see once again Liang et al. calculations in 3.20d).

We would like to note that, although consistent with previous works, the interpretation given above is rather qualitatively and naive. In general, several nuances need to be taken into consideration for an improved analysis.

First, we should understand that, when introduced theoretically in Section 1.6.2, α R represents a constant and intrinsic value of the band structure, regardless of the position of the Fermi level. Even though the claim that this value is changing in our experiments may be counter-intuitive, it can be easily explained by the several band transitions that occur during modulation of the Fermi level. When populating several bands, each of them will contribute accordingly their own α R , so that the λ IEE calculated is nothing but an average of multiple Edelstein effects. While for the d xy band this effect can be simply described by a circular Fermi contour approximation, the ellipsoidal shape the d xz/yz bands introduces complex spin configurations that complicate a global interpretation.

Second, the rigid band structure approximation used is too crude, as it does not take into account the potential well modulation due to external electric fields. As reported by McKeown Walker et al., with increasing carrier density the electric field at the interface increases, deforming the potential well and changing the energy splitting between light and heavy bands [START_REF] Walker | Carrier-Density Control of the SrTiO 3 (001) Surface 2D Electron Gas studied by ARPES[END_REF][START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF]. The picture described by Joshua et al. is therefore valid for carrier densities in the 2 × 10 13 cm 13 range [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. However, the universality of the Lifshitz transition might not hold for samples with much larger or much lower carrier densities.

To address both of this issues and gain further knowledge regarding spin-to-charge conversion phenomena in STO-based structures, we expand the study in Section 3.3 to a broader set of samples, which allows the exploration of a larger range of carrier densities, subsequently unraveling in more detail the intricate physics at play.

LAO thickness dependence

In addition to the spin-to-charge current conversion analysis performed in NiFe/LAO(2uc) //STO, we investigated the role of the LAO barrier thickness.

We start by showing in Fig. 3.21 the results of transport experiments performed on NiFe(2.5nm)/LAO(x)//STO samples, where x = 0, 1 and 2 uc. Immediately, we notice the weak R s dependence with temperature and bulk-metal-like Hall and MR coming from the NiFe layer for the 0 and 1 uc samples, suggesting the absence of a q2DEG. This result is reminiscent of the result discussed in Section 2.5.1 for Co-capped LAO(x)//STO samples, where conductivity was only present for x ≥ 1 uc. We attributed this behavior to the fact that, given The spectra for the NiFe//STO sample is additionally collected at 50°(light blue).

T = 7 K V/h rf (mV.G -2 ) V g (V) 2 uc 1 uc 0 uc 2 STO NiFe j c 2D j s V m h rf H dc V g σ (d) (e)
We perform spin-to-charge current conversion experiments on these three samples, similarly to Section 3.3.2 (see experimental sketch in Fig. 3.21d and results in Fig. 3.21e). Strikingly, we detect a voltage signal arising from the IEE on all of them, even though from transport the samples with 0 and 1 uc of LAO showed no sign of a q2DEG. Not only that, but the dependence of the detected voltage displays a completely different behavior, with at least two sign changes and larger maxima at -125 V and -175 V. In the following paragraphs, we propose a tentative explanation for these puzzling results.

To investigate further the chemical interactions involved at the NiFe/oxide interface, we perform in situ XPS experiments on NiFe(6Å)//STO samples. In Fig. 3.22a, we show the survey spectra of the STO substrate (prior to NiFe deposition) and the spectra of a NiFe(6Å)//STO sample. We observe that while the Ni-related peaks (at about 400 and 70 eV) are quite prominent, Fe is harder to observe due to lower concentration, with the largest feature at around 700 eV. In Fig. 3.22b, we show the Ti 2p core level spectra collected on the same two samples. When comparing the STO curve (black) with the NiFe//STO curve (blue), additional spectral weight is present on both lower and higher binding energy sides of the Ti 4+ peak, which prohibits a reasonable conclusion regarding a Ti 3+ component. Additional weight is also introduced at both sides when changing the electron take-off angle to 50°. Note that in the bibliography, a broadening of the peak is usual attributed to surface damage, instrumental broadening effects or photoelectron emission-induced phonons (lattice vibrations) [START_REF] Van Der Heide | X-ray Photoelectron Spectroscopy[END_REF]. Since little information can be extracted from the Ti 2p core level analysis, we investigate the chemical states of Ni and Fe within the ultrathin film deposited. Although the mechanisms of alloy deposition are known to be quite complex [START_REF] Byun | Composition and process dependence of sputtered NiFe thin films[END_REF], we have confirmed an approximate Fe/Ni ratio of 28% ± 5%, with similar peak features for both thick and ultra-thin films (not shown).

The Ni 2p core level spectra is presented in Fig. 3.23a, for a reference sample of metallic NiFe (on the left), a reference sample for oxidized (in air) NiFe (on the right) and our sam- When spin pumping is performed in NiFe//STO heterostructres, conversion may occur locally on these puddles, which generates a charge current that flows through the NiFe layer and is detected by the two voltage probes. From an electrical transport perspective, the inhomogeneous 2DEG cannot be detected.

ple composed of NiFe//STO (at the center). While the reference metallic spectra exhibits two main spin-splitted peaks (Ni 2p 1/2 and Ni 2p 3/2 ), with two smaller satellite features next to them (at the higher binding energy side), the oxide reference shows two additional peaks developing at lower binding energy. Comparatively, the spectra collected on the NiFe//STO sample is mostly composed of a metallic phase, with small features on the lower binding energy side possibly indicating slight oxidation. Previous spectroscopy reports on Ni/TiO 2 [START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF] revealed that, above a thickness of 1 monolayer, lateral interaction between Ni adatoms was predominant, which inhibited electron transfer towards the substrate [START_REF] Onishi | Photoelectron spectroscopic study of clean and CO adsorbed Ni/TiO 2 (110) interfaces[END_REF]. Along with its high work function, this result indicated that little electrochemical interaction occurs between Ni and the STO surface.

Similar experiments were performed for the Fe 2p core level, as shown in 3.23b. We observe that for the metallic reference, Fe 2p is composed of two spin-splitted peaks (Fe 2p 1/2 and Fe 2p 3/2 ), with a "tail" at higher binding energies connected to a distribution of unfilled oneelectron levels (conduction electrons) [START_REF] Van Der Heide | X-ray Photoelectron Spectroscopy[END_REF]. The oxide reference sample is composed of large Fe oxide peaks that appear shifted by a few eV (towards higher binding energy) in regards to the metallic ones. Although difficult to notice (due to the low concentration of Fe in the ultra-thin layer) a good indication for formation of an oxide phase is the absence of the metallic "tail".

On the NiFe//STO sample, we indeed notice a peak developing at the high binding energy side of the main metallic peaks, suggesting that an oxide phase forms. Indeed, theoretical and experimental reports on Fe/TiO 2 (110) structures confirmed the oxidation of Fe for extremely low coverages, accompanied by a reduction of Ti cations at the interface [START_REF] Diebold | Electronic structure of ultrathin Fe films on TiO 2 (110) studied with soft-x-ray photoelectron spectroscopy and resonant photoemission[END_REF].

Assuming that during the sputtering deposition both Ni and Fe species are randomly arriving at the surface of STO, at least 20% of it will be covered by Fe (given the initial composition of the target and the 80-to-20 ratio obtained in previous experiments). Due to the high reactivity of Fe, conducting nano-regions (or puddles) may form randomly at the STO surface, due to local reduction of Ti cations or phase separation [START_REF] Scopigno | Phase Separation from Electron Confinement at Oxide Interfaces[END_REF]. In turn, from a transport point of view, these non-percolating regions will not contribute to the longitudinal transport, with conduction being dominated by the NiFe layer. Yet, if a spin density is pumped towards these conduction regions, conversion may occur, and the charge current produced can flow through the NiFe metallic overlayer and be detected. This scenario is sketched in Fig. 3.24.

Note that in this case, the non-percolating regions might have larger local carrier densities, which depend on the strong Fe//STO interactions, leading to a rather efficient IEE.

We add that, besides the scenario involving local reduction due to Fe clusters, intrinsic electronic inhomogeneities and inhomogeneous distribution of oxygen vancacies have been reported in oxides. On one hand, an energy reduction was calculated when the electron density in LAO//STO q2DEG is increased, favoring agglometration of electrons in regions of enhanced densities [START_REF] Bovenzi | Possible Mechanisms of Electronic Phase Separation in Oxide Interfaces[END_REF]. On the other hand, electronic phase separation was evidenced at the surface of oxygen depleted STO surfaces, attributed to clustering of oxygen vacancies [START_REF] Dudy | In Situ Control of Separate Electronic Phases on SrTiO 3 Surfaces by Oxygen Dosing[END_REF].

Inverse Edelstein effect in metal-capped SrTiO 3

In the following section, we expand the spin-to-charge current conversion experiments to a broader set of samples, where the principles introduced in Chapter 2 are utilized to generate a q2DEG at the surface of STO, through the deposition of different metallic layers. The main idea is simple: by removing completely the crystalline LAO layer, we use instead an ultra-thin layer (few Å) of reactive metal directly of STO, which leads to the formation of a q2DEG. The oxidizing metal forms a thin barrier, which is usefully used to protect and "encapsulate" the q2DEG formed, allowing, in principle, efficient spin-to-charge conversion phenomena. A NiFe layer is then deposited, for the FMR and spin pumping experiments, with an added AlOx capping layer to protect it from surface oxidation. For the following study, we focused on two metals, Ta and Al, with rather different oxygen-getter properties and work functions.

This new type of system can be extremely advantageous for two mains reasons: first, it enables an extended range of possible carrier densities in the q2DEG, which in turn should allow more efficient spin-to-charge conversion effects for higher energy regions of the band structure (see Section 3.3.3.3 for more details); second, the growth of the metals and FM can be performed at room temperature with a simple sputtering procedure, which technically reduces immensely the complexity of previous experiments involving high temperature and PLD grown LAO//STO heterostructures. We believe that this might also open exciting possibilities for larger scale applications.

However, additional considerations need to be taken. Changing the tunneling barrier through which spins will be injected may result in different spin injection efficiencies, mainly due to changes in the tunneling resistance. At first, lower injection efficiency might seem detrimental to the overall spin-to-charge conversion phenomena, but it may in fact be the exact opposite, since the spins that arrive at the q2DEG are much less prone to scatter back towards the FM, which boosts the overall effect [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF]. Additionally, the large amount of oxygen vacancies present in this metal-capped structures may very well play a role in the conversion effect. Throughout this section, we examine some of these ideas in more detail.

XPS and magnetotransport experiments

Similarly to what was performed in Section 2.5.2.2, we evaluate both the Ti 2p core level spectra (before and after metal deposition) as well as the relevant metal peaks. As displayed in Fig. 3.25, we carefully look at the effect of Ta and Al, directly in contact with STO. In Section 2.6 we discussed how the LAO barrier (and the internal polar electric field) facilitates electron transfer from the metal towards the STO, by increasing the relative position of the E F of the metal in regards to the E F of STO (before contact). In this case, the direct contact between metal and STO makes things simpler. First, charge transfer is expected to occur for low work function metals such as Ta and Al, generating a space-charge region close to the STO surface, and hence lowering the conduction band minimum. We observe in Fig. 3.25a and 3.25c that a rather large Ti 3+ component arises at the lower binding energy side of main Ti 2p peaks (at around 4 and -3 eV). Interestingly, this feature appear to be broader for the Ta case, which might be related to the inherent differences between Ta and Al atomic properties (Al being much smaller), as well as their chemical interactions with STO (assuming interactions at the surface and within the first few layers of STO). We also observe a slight angle dependence of this Ti 3+ feature, which shall be carefully evaluated in the next section.

Regarding the metallic overlayer, for Ta//STO (Fig. 3.25b) we observe similar features to the ones previously obtained at Ta/LAO(1uc)//STO samples (see Section 2.5.2.2), where the Ta 4f core level spectrum can be fully fitted with Ta oxide peaks [START_REF] Moo | An XPS depth-profile study on electrochemically deposited TaO x[END_REF]. Similar experiments were performed for the Al//STO sample (Fig. 3.25d). From the literature [START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF], the main difference between the Al and Al 2 O 3 peaks is a shift towards higher binding energies (from 72.6 to 74.7 eV) and a slight peak broadening (with the characteristic metallic "tail" at higher binding energies vanishing for Al 2 O 3 ). From our data we only observe one peak, which naturally we expect to be Al 2 O 3 . However, severe charging effects due to the insulating nature of the sample and the rather noisy data make this analysis more complicated. To solve this issue, we look at the Sr 4s and Sr 4p peaks (displayed in the inset of Fig. 3.25d). We notice a shift 153 In situ XPS study of metal//STO heterostructures. (a) Ti 2p core level spectra of a Ta(3Å)//STO sample, before (black) and after (red) Ta deposition. The grey and orange curves represent data collected at a take-off angle of 50°. The Ti 4+ and Ti 3+ components are indicated for both spin-split Ti 2p peaks. (b) Ta 4f core level spectra for a Ta(3Å)//STO sample. The spectra resembles the one collected in Fig. 2.38 for Ta(3Å)/LAO//STO heterostructures, where the Ta layer was found to be fully oxidized [START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. (c) Same as panel (a) but for an Al(3Å)//STO sample. (d) Al 2p core level spectra for a Al(3Å)//STO sample. Due to severe charging effects and ambiguity regarding the nature of the Al peak observed (metallic or fully oxidized), the magnitude of the binding energy shift for Sr 4s and Sr 4p peaks is investigates (see inset). Shifting the Al peak by the same amount (∼ -12 eV), we find its effective binding energy to be 74.5 eV, which correspods to the position attributed for oxidized Al [START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF].

AlOx/NiFe/M//STO n total s × 10 13 (cm -2 ) µ 1 (cm 2 .(V.s) -1 ) µ 2 (cm 2 .(V.s) and mobilities µ 1 , µ 2 for the q2DEG formed in AlOx/NiFe/M//STO samples. Values were obtained from the simultaneous 2-band model fitting of the Hall and longitudinal magnetoresistance displayed in Fig. 3.26 (green curves). Error bars for n s and µ were never above ± 0.10×10 13 cm -2 and ± 10 cm 2 .(V.s) -1 , respectively. of about 12 eV from the expected values from Ref. [START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF]. Shifting the Al peak by the same amount, we obtain a binding energy of 74.5 eV, coincident with the expected position of the Al 2 O 3 , therefore confirming the oxidized state of this capping layer.

In Fig. 3.26, we display the magnetotransport experiments performed on AlOx/NiFe(2.5nm)/M//STO samples, where M = Al(0.3nm), Al(0.9nm), Ta(0.3nm) and Ta(0.9nm). On the left, we display the temperature dependence of the sheet resistance R s , on the center the longitudinal sheet magnetoresistance R xx , and on the right the Hall effect R xy . For all samples the q2DEG properties were isolated using the method introduced in Section 2.5.2.1, where a characteristic tilted Hall shape is observed [START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. The longitudinal magnetoresistance and Hall curves were fitted using a 2-band model (Eq. 2.12), which allowed us to extract the sheet carrier densities n s and mobilities µ of the q2DEGs formed. The results are displayed in Table 3.

Interestingly, we observe in Fig. 3.27, higher carrier density for thicker metallic layer thickness (red squares with grey fill are higher than red squares with light grey fill) and generally higher carrier densities for Al-capped samples, which possesses larger enthalpy of oxide formation ∆H O f . We can interpret this results by considering that oxygen vacancies are formed more efficiently when capping STO with Al, which leads to higher concentration of free electrons in the STO lattice. In blue, we also plot the mobilities for the four samples. For Ta, we observe that for a thicker layer, mobilities are reduced, consistent with the existence of more oxygen vacancies which contribute to increased scattering within the q2DEG. This trend is however not observed for the Al case, where the mobilities are practically not affected with increasing concentration of oxygen vacancies.

Overall, we conclude two main points: first, metals with larger enthalpies of oxide formation (i.e. larger oxygen getter capabilities) induce more vacancies at the STO surface, which increases the carrier density but lowers the mobility; second, from transport experiments (blue curves in the middle plots of Fig. 3.26) we observe an oddly large magnetoresistance for the (c,f,i,l) transverse resistance R xy (Hall effect) as a function of applied out-of-plane magnetic field H for AlOx/NiFe/M//STO samples, where M = Al(0.3nm), Al(0.9nm), Ta(0.3nm) and Ta(0.9nm). On the middle and right panels, the transport properties for the total stack (black), the metallic reference (red), the extracted isolated q2DEG contribution (blue) and the simultaneous 2-band fitting (green) are shown, following the procedure described in Section 2.5. q2DEG, which ranges between 10 % < MR < 40 %. In contrast, the MR usually obtained in uncapped LAO//STO samples is around a few % (see Fig. 2.36). We believe that this increase in MR for these metal//STO heterostructures might be due to ferromagnetic order induced by oxygen vacancies at the STO surface [START_REF] Pai | LaAlO 3 /SrTiO 3 : a tale of two magnetisms[END_REF]. As reported by Rice et al., induced magnetization (by magnetic circular dichroism) was observed to persist in reduced-STO samples, but not in Nb-doped STO. Also, the magnetic imprint vanished when the oxygen vacancies were filled (by re-oxygenation of the reduced-STO samples) [START_REF] Rice | Persistent optically induced magnetism in oxygen-deficient strontium titanate[END_REF]. DFT calculations provided by Choi et al. also revealed that magnetic moments are induced due to neutral oxygen vacancies V 0 O leading to unpaired spins of Ti (but not for doubly charged vacancies V ++ O , which are most favorably formed but remove the two unpaired 3d-orbital electron spins from the neighboring Ti atom) [START_REF] Choi | Correlated Visible-Light Absorption and Intrinsic Magnetism of SrTiO 3 Due to Oxygen Deficiency: Bulk or Surface Effect? Inorganic[END_REF]. We suspect that even though a larger concentration of the oxygen vacancies formed at the STO surface become ionized, hence releasing electrons to form the q2DEG, an unknown amount might stabilize in a neutral state, which in turn gives rise to a ferromagnetic phase that plays a role in the large MR observed.

Spin-to-charge current conversion experiments

We now present the spin-to-charge conversion experiments performed on similar samples. Here, after depositing the ultra-thin layer of metal, a thick NiFe with 20 nm (followed by an AlOx capping layer) was added. An illustration of the samples and experiment is shown in Fig. 3 nm (top panels) and 0.9 nm (bottom panels), as a function of the back-gate voltage V g . On the left, the raw voltage peaks (dashed lines) and symmetric (thick lines)/antisymmetric (thin lines) at FMR resonance are shown for a positive applied dc magnetic field H dc . On the right, the peak charge current produced as a function of V g for positive H dc (red circles). Additionally, the antisymmetric part (light grey circles) is shown. Even though this contribution comes from the NiFe (which is practically not affected by V g ), its change can be possibly related with the changes in the rf field lines due to the large modulation of the dielectric constant in STO with applied V g , which destabilizes the cavity. calculated current density (normalized by the rf field power) j c /h 2 rf , calculated using Eq. 3.11 and considering a 2-point resistance R T a0.3nm = 42 Ω, R T a0.9nm = 55 Ω, R Al0.3nm = 37.1 Ω and R Al0.9nm = 47.5 Ω, an rf power P = 10 mW, and a sample width of w = 0.4 mm.

Comparatively to the NiFe/LAO//STO data shown in Fig. 3.17, we observe that the gate voltage dependence for these four samples is strikingly different, with multiple sign changes at different gate voltages and different peak maxima suggesting the influence of the carrier density and oxygen vacancy formation modulation through insertion of different metallic layers in direct contact with STO. However, the Ta(0.3nm) brings interesting questions regarding the validity of the simple picture used to describe the NiFe/LAO//STO with regards to the carrier density, the Fermi level position and the band structure in the (001) direction. Even though we believe this interpretation gives a good overall understanding of the spin-to-charge conversion effect, both of these samples have roughly the same carrier density, but their gate dependence is rather different.

Realistically, we identify several effects that need to be considered for a proper evaluation of spin-to-charge conversion effect: the elevated concentration of oxygen vacancies at the STO surface, the non-rigidity of the band structure when applying gate voltage, additional features of the band structure not captured in the (001) direction of the Brillouin zone, the efficiency of spin injection through a metal-oxide ultra-thin barrier, the scattering mechanisms within this vacancy-induced q2DEG and possible spin-to-charge current conversion at the NiFe/TaOx interface (which competes with conversion occuring in the 2DEG).

To try to gain further understanding of some of this features, we focus over the next few sections on the spin-to-charge conversion experiments on the Al(0.9nm) sample, which interestingly shows an exceedingly large charge current densities (both for positive and negative values). Al. An XPS study, similar to the one presented in Section 3.4.1, is performed before and after the metal deposition. As shown in Fig. 3.31a, the spectra collected for the Al//STO sample (orange area) shows two additional features at lower binding energy (-2.4 and -4.5

eV) corresponding to Ti 3+ and Ti 2+ components. As discussed before, the Ti 3+ feature can be connected to the formation of a q2DEG at the surface of STO. However, in this case the appearance of an even more reduced Ti component reveals the particularly severe oxidation occurring in this heterostructure. We attribute this to the large enthalpy of oxide formation of Al, which is the largest for all the metals tested within this thesis (∆H O f = -558 kJ/mol O), and to the increased thickness of Al. Note that for the thinner Al insertion (0.3 nm) evaluated in Fig. 3.25c, no sign of a Ti 2+ valence state is observed. Also, from Fig. 3.25d, the whole 0.3 nm deposited become oxidized, while in the present case only 75 % of the 0.9 nm deposited are observed to be oxidized, as displayed in the inset of Fig. 3.31a. According to the Cabrera-Mott theory, introduced in Section 2.5.4.3, the reduction of the STO and subsequent oxidation of the metallic layer occurs at the interface. This oxidation/reduction effect will take place until the newly formed metal-oxide phase is so thick that electron and oxygen transport is halted.

For this specific interface, we derive that this point occurs at around 0.7 nm of AlOx. In principle, depositing more than 0.9 nm should therefore not contribute to the properties of the q2DEG.

In addition, we estimate the spatial distribution of the Ti 3+ /Ti 2+ -rich layer, by angledependent XPS experiments, as displayed in Fig. 3.31b. To do this we estimated the ratio between the weights of the Ti 3+ /Ti 2+ peaks and the Ti 4+ peak as a function of the electron take-off angle (see Section 2.4.2.1 for more details). Increasing the take-off angle allows the evaluation of a volume of the sample closer to the interface, which can be used to estimate the extension of these newly formed Ti 3+ and Ti 2+ states. The data collected from the several Ti core level spectra at different take-off angles (see inset) can be fitted with the model developed As shown in yellow, the spectra is fitted with three components, Ti 4+ , Ti 3+ and Ti 2+ , using the relative areas and peak distance constrains from XPS bibliography [START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF]. In the inset, the Al 2p core level spectra revealing a metallic (25%) and oxidized (75%) Al components within the capping layer. (b) Ratio between the sum of the peak areas from Ti 3+ and Ti 2+ and the peak area from Ti 4+ for different take-off angles. The error bars come from the fitting process in the software CasaXPS, using a Monte Carlo procedure [START_REF]Uncertainty Estimates in XPS[END_REF]. The green dashed line represents the best fit using the model from Sing. et al [START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF], shown in Eq. 3.17. The experimental Ti 2p core level spectra as a function of the take-off angle are shown in the inset.

by Sing et al. [START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF]: 0.9 nm. The element chemical mapping of Sr, Ti, Al and O, displayed in Fig. 3.32c-f, has been acquired using Electron Dispersive X-ray Spectroscopy (EDX). Almost no interdiffusion is observed between STO and the Al. Regarding the oxygen, we observe large detected signal from within the STO, but also extending over to the Al layer, which confirms our oxidized Al layer scenario when in direct contact with STO. (c) Carrier densities n derived from fitting the extracted Hall traces with a linear model (from -175 V to 0 V, n linear ) or with a two-band model (from 25 V to 175 V, where n LM and n HM stand for the density of low-mobility and high-mobility carriers, respectively). n total is estimated from the gate voltage dependence of capacitance measurements.

I(3+) + I(2+) I(4+) = p[1 -exp(-d/λcosθ)] 1 -p[1 -exp(-d/λcosθ)] , (3.17

Magnetotransport under back-gate voltage

The temperature dependence of the sheet resistance R s for a NiFe/Al//STO sample and a NiFe//STO reference sample is displayed in Fig. 3.33a. Three curves are displayed: for the reference sample without the Al metallic layer (brown curve), the resistance shows practically no change over the whole range of temperatures, pointing towards conduction only at the NiFe layer; in the full stack (black curve) a drop in resistance is observed below 100 K, signaling an additional conduction path corresponding to the q2DEG; following the method described in Section 2.5.2.1, the isolated 2DEG contribution is extracted (red curve) [START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF]. We hypothesize that the smaller R s observed at room temperature (when compared to ≈ 10 4 Ω in uncapped LAO//STO -see Fig. 2.32) is due to the much higher carrier concentration of the formed q2DEG, as well as some residual metallic Al at the NiFe/Al interface (after Al oxidation), which is not accounted for in the reference sample.

In Fig. 3.33b, we display the Hall curves extracted for the q2DEG at T = 7 K while applying a back-gate voltage V g . While a non-linear Hall trace is obtained for large positive gate voltages, decreasing V g promotes a more linear dependence, suggesting that a transition between multi-band to single-band transport occurs. The curves for V g < 0 V were hidden for clarity, since they remain linear and practically unchanged. We fit this set of curves with a 2-band model, to obtain the mobile carrier densities in both regimes. Note that for additional precision of this fitting, we used capacitance C measurements as a function of V g . As described by Biscaras et al., measuring the time-dependent resistivity for a given step of the gate voltage ∆V g , allows us to extract the corresponding modification of the carrier density ∆n s = C∆V g /e [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF]. By adding this constrain to the 2-band fitting of the Hall traces, we calculate the total carrier density n total as a function of gate voltage, as displayed in Fig. 3.33c. For negative V g , where the Hall trace is linear, we extract n linear from the slope of the curve. Approaching V g = 0 V a single to multiband transition occurs, for a total carrier density of 8.5 × 10 13 cm -2 , and n LM and n HM (for a low and high mobility band, respectively) are obtained. The black curve n total represents the constrained carrier density expected from the capacitance measurements. At large and positive V g , the total carrier density reaches about 1.05 × 10 14 cm -2 . In these samples, the Lifshitz transition thus occurs for carrier densities larger than what was previously reported for LAO//STO heterostructures [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. This result also reinforces the non-ridigity of the band structure, where the increased carrier density drives a stronger confining electric field, which alters the shape of the q2DEG quantum well.

Spin-to-charge conversion efficiency

In Fig. We repeated the experiments shown in the bottom panel of Fig. 3.30, for a smaller step of V g (every 10 V instead of every 25 V). The voltage peaks collected, as well as the FMR signal, for three V g are displayed in Fig. 3.34c. In the three bottom panels, we plot the raw, symmetric and antisymmetric voltage components (represented as circles, thick line and thin line, respectively). In addition, we show that by reversing the polarity of the magnetic field H dc (red and blue data), the signal can be well reversed, in agreement with the IEE theory. Then, we took each symmetric voltage peak maximum and calculated the conversion efficiency ) λ IEE . The results are displayed in Fig. 3.34d. Besides the several sign and magnitude changes already observed in the previous section, the conversion efficiency at maximum values is extremely high, for both positive and negative values (λ IEE = +33 nm, -25 nm). These are much higher than in any other spin-orbit system previously measured [START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF]. In fact, it is even 5 times larger than the previous record found in LAO//STO interfaces [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

H dc > 0 V g = 120 V V g = 0 V V g = -170 V V raw V sym
Additionally, we show in Fig. 3.35 the two separate measurements performed on NiFe/Al(0.9nm)//STO samples. Both experiments were performed in difference samples (of the same batch) with an interval of 6 months between them. As observed the main features (sign changes and magnitude) of the initially captured data can be well reproduced, highlighting the robustness of these spin-to-charge current conversion experiments. Similar results regarding reproducibility were obtained for the NiFe/LAO//STO case [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]. STO samples, with an integrated carrier densities in the 10 14 cm -2 range36 . As displayed in Fig. 3.36a, we start by evaluating the Fermi surface of the q2DEG stabilized at the (001) surface of STO. We are able to resolve three concentric circular contours with d xy character and two ellipsoidal Fermi surface sheets with major axes along the k x and k y direction, with d xz and d yz character, respectively. These heavier bands have lower intensity due to the light polarization chosen for this experiment [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF].

As explained in Section 3.3.3.3, in our previous interpretation of the gate dependence of IEE in NiFe/LAO//STO, we attributed the large effects to specific points in the band structure [in the [START_REF] Ivchenko | Photocurrent in quantum well structures with optical orientation of free carrier[END_REF] direction] where the light and heavy bands crossed each other, forming avoided crossing points, where it was previously calculated that the spin-orbit strength (L.S product) reached large values [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF] and where orbital mixing and local orbital angular momentum were significantly induced [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF]. However, the Edelstein effect should occur due to the sum of all interactions between bands over the whole Brillouin zone. This means that, for a given energy, even though in the (100) direction nothing relevant might seem to contribute to the Edelstein effect, interactions between bands in other crystallographic directions may play an important role. For this reason, we display in Figs. 3.36b-d, the energy dispersion in the original [START_REF] Ivchenko | Photocurrent in quantum well structures with optical orientation of free carrier[END_REF] direction, as well as the (110) and ∆ direction. Particularly in the latter, special points just below the E F were recently theoretically predicted to exhibit inversion of the electronic wave functions, which lead to the appearance of topological 1D states (see Fig. 3.36e) [START_REF] Vivek | Topological states at the (001) surface of SrTiO 3[END_REF].

Certainly, this feature should also play a role in the spin-to-charge conversion efficiency.

The band inversion predicted by Vivek et al. are expected to give rise to metallic 1D edge states with topological properties, previously invoked to describe the quantum spin Hall effect [START_REF] Kane | Quantum Spin Hall Effect in Graphene[END_REF][START_REF] Hsieh | A topological Dirac insulator in a quantum spin Hall phase[END_REF]. Considering that there are two edge states at each boundary of the sample, with spin up flowing in one direction and spin down flowing on the opposite direction, the contribution arising from two opposite boundaries should average to zero when a measurement is performed over the whole sample. Technically, the edge states should not contribute directly to the Edelstein effect. Yet, while band inversion itself may render the 2DEG topological, it is its effect on the morphology of the band structure that might contribute to the Edelstein effect.

To understand this relationship better, we evaluate the Edelstein effect using the semiclassical Boltzmann transport theory37 . To do this, we calculate the spin density (per unit cell)

s/A as a response to an applied electric field E, so that:

s A = E, (3.18)
Note that in this case, we are estimating the charge-to-spin current conversion, i.e. the direct Edelstein effect. Even though we extensively discussed in Section 1.6.3.2 the non-Onsager reciprocity of the direct and inverse Edelstein effect, in theoretical terms we only consider an isolated 2DEG where extra relaxation channels due to proximity to a FM layer or a tunneling barrier are not included, hence, both effects can be reciprocally evaluated. In Eq.

3.18, the Edelstein tensor can be written as:

ij = e A k σ i k Λ j k δ(E k -E F ), (3.19)
where A is the area of the system, e the electron charge, σ k the spin expectation value of the state at wave vector k and energy E k and Λ k = τ 0 v k the mean free path as a function of the relaxation time τ 0 and the group velocity v k . The tensor is calculated over all k-points and all bands, for a fixed τ 0 = 1 ps and at T = 0 K, where only the states at the Fermi level E F contribute to the Edelstein effect. We start by overlaying an 8-band tight-binding model onto the energy dispersion data in Figs. 3.36, to which we find a rather good agreement (similarly to the 6-band model presented in Ref. [START_REF] Vivek | Topological states at the (001) surface of SrTiO 3[END_REF]). Due to the limiting energy resolution, some features, such as the avoided crossing points in the (100) direction and the topologically non-trivial points in the ∆ direction, cannot be resolved experimentally through ARPES. Using this model, we estimate the Edelstein tensor over all k-points as a function of E k for each pair of Rashba splitted bands. These results (and the total sum of all effects in red) are presented in Fig. 3.37a.

Accompanying the results from the theoretical model, we display in Figs. these heavy bands exhibit opposite spin helicity, which in turn leads to an opposite sign of the Rashba splitting. Accordingly, we observe that bands (5 + 6) give a negative contribution to the overall Edelstein signal, which counters the effect given by the previous pairs of bands and drives the total xy to zero (zone III). At -52 meV we reach the first avoided crossing points between bands (3 + 4) and (5 + 6) in the (100) direction. Here, orbital mixing and a significant local orbital angular momentum unlock a strongly enhanced splitting of the bands, despite the modest atomic spin-orbit coupling in STO [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF], which drive the Edelstein effect to larger values and results in a plateau around zone IV. At -43 meV the last pair of bands start to be occupied (7 + 8). These contribute with the same sign as bands (1 + 2), so that the overall signal approaches zero and changes sign once again. Closer to the E F , at -14 meV the band inversion in the ∆ direction between bands (3 + 4) and (5 + 6) region is reached, where a second positive maximum of the overall tensor is observed (zone V). From the zoom in Fig. 3.37f, the splitting is observed to be smaller than in the first avoided crossings in the (100) direction, meaning that the enhancement of the Edelstein effect in this region does not come primarily from spin splitting of the bands. For energies closer to E F , the total signal is observed to decrease once again, due large compensation between bands (5 + 6) and (7 + 8) (zone VI). In these regions the 8-band model starts to be insufficient to capture the effect of understand that for larger splittings (arising from larger α R ), λ IEE is boosted, since the compensation between displaced contours is reduced. However, a similar effect may arise from uncompensated spin textures of neighboring bands. Imagining that an electric field is applied in the Rashba 2DEG with small splitting but very different spin textures, the displacement may lead to abnormally low compensation between contours, which in turn drives the conversion efficiency up. This scenario is precisely what we observe in the topological non-trivial points.

As displayed in Figs. 3.38a and 3.38b, although the splitting between bands is relatively small in the (110) direction, the spin textures are extremely different, explaining the large Edelstein efficiency in this region (zone V in Fig. 3.37a). In contrast, as displayed in Figs. 3.37c and 3.37d, the spin polarization calculated at -38 meV shows rather similar interband features.

We finish this section by comparing the theoretical prediction with the gate voltage dependence of λ IEE . As we can observe in Fig. 3.39, most features can be well reproduced, including the several changes of sign and magnitude. However, several questions are left unanswered: does the energy range used in the calculations matches the modulation attained by gate voltage experiments? Is an electronic structure analysis sufficient to extract the complete picture of the IEE? These and other open questions are addressed in the following section, where we also discuss the next steps required to fully understand the nature of spin-to-charge conversion effects and their application in real devices.

Conclusions

In are, in general, due to the highly-doped q2DEG formed, with carrier densities in the 10 14 cm -2 range [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF], while the usual q2DEG in LAO//STO shows n s 3 × 10 13 cm -2 .

The higher carrier density implies that the E F is positioned higher in the 2DEG band structure, where, for example, the special topologically non-trivial points were predicted [START_REF] Vivek | Topological states at the (001) surface of SrTiO 3[END_REF].

Prospects and the future of nanoelectronics

Several unanswered questions arise after studying the spin-to-charge current conversion in the Al//STO system. First, the theoretical model developed does not take into account the changes in the band structure when applying a back-gate voltage. One can think that, while doping(depleting) the quantum well close to the STO surface, the confining electric field increases(decreases). This means that the shape of the potential well is inevitably altered, which should lead to changes in the band structure itself (for example the energy splitting between light and heavy bands at the Γ point). Therefore, the connection between Fermi contours at the E F and gate voltage modulation of the 2DEG will need, in the future, to include the non-rigidity of the band structure. This can be eventually linked to a better comparison between carrier density swept with gate voltage, and the energy range used in the theoretical calculations (see Fig. 3.39). Further Poisson-Schrodinger simulations are required to give more accurate values regarding the quantum well filling levels, i.e. the required carrier densities to reach specific points in the band structure. From the gate voltage dependent transport experiments, we also obtain a one-band to multi-band transition at around n s 9 × 10 13 cm -2 , very far from the "universal" Lifshitz transition found at n c 1.6 × 10 13 cm -2 in LAO//STO [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. We argue that this transition is only universal for the range of carrier densities usually found in LAO//STO heterostructures. For the highly-doped regime of the 2DEG in Al//STO, the band structure and associated energies are largely altered, which pushes this transition to higher n s and emphasizes the importance of taking into account the non-rigidity of the band structure.

Further experiments are also required to confirm the effective thickness of the q2DEG present in Al//STO. While the angle-dependent XPS study (shown in Fig. 3.31) gives an approximate value, a more accurate analysis could be performed using high-resolution EELS, which could help discriminate Ti atoms in a 4+ and 3+ valence state. Additionally, a major difference between the q2DEG in LAO//STO and Al//STO is the amount of oxygen vacancies.

The role of these defects in regards to the spin-to-charge current conversion efficiency is still unknown. Since they are predicted (in very specific cases) to induce magnetism in STO [START_REF] Pai | LaAlO 3 /SrTiO 3 : a tale of two magnetisms[END_REF],

X-ray magnetic circular dichroism experiments may help to answer this question.

Regarding the spin pumping experiments, two main issues still need to be resolved.

| Anisotropic and unidirectional magnetoresistance effects in SrTiO 3 -based 2D electron gases

The resistivity of materials can be severely altered under an externally applied magnetic field.

The most basic evidence of this is the Hall effect, where charged carries accelerated by an electric field E, are deviated from their original trajectory through a Lorentz force that acts on them due to an out-of-plane magnetic field H. In ferromagnets, where the anomalous Hall effect is observed due to their inherent magnetized state, extra terms to the regular Hall effect need to be introduced to explain the much larger magnetoresistance effects.

Yet, another effect caused by the intrinsic magnetization of a ferromagnetic material (FM) can be observed depending on the relative orientations of E and H. In 1856, William Thomson (later known as Lord Kelvin) wrote the following: "I found that iron, when subjected to magnetic force, acquires an increase of resistance to the conduction of electricity along, and a diminution of resistance to the conduction of electricity across, the lines of magnetization. By experiments more recently made, I have ascertained that the electric conductivity of nickel is similarly influenced by magnetism, but to a greater degree, and with a curious difference from iron in the relative magnitudes of the transverse and longitudinal effects" (from [START_REF] Thomson | On the Electro-Dynamic Qualities of Metals:-Effects of Magnetization on the Electric Conductivity of Nickel and of Iron[END_REF]). The effect described by Thomson was later coined anisotropic magnetoresistance (AMR), and is now known to be related with spin-dependent scattering mechanisms within the FM.

Very recently, an extension to this effect was observed in bilayers composed of a high spin-orbit coupling material and a FM [START_REF] Avci | Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers[END_REF]. Here, a combination of spin Hall effect and AMR allows for two different resistance states depending on the relative orientation of the FM magnetization and direction of an applied charge current. This effect, coined spin Hall magnetoresistance (SMR), brings exciting prospects for the development of new spintronics devices.

In the following chapter, we will start by presenting an extensive introduction to these effects, followed by experimental evidence on how they can be exploited in Rashba systems.

Note that the results presented here are all preliminary, and will require a more careful analysis in the future.

Anisotropic MR in magnetic materials

To give a clear description of the AMR, we follow the approach proposed by Campbell possible scattering events dependending on the magnetization direction M and an applied current J . Adapted from [START_REF] O'handley | Modern Magnetic Materials: Principles and Applications[END_REF].

the schematic of Fig. We now realize that while spin-orbit coupling introduces new scattering channels, they are essentially controlled by the electron momentum k, which is dictated by the direction of acceleration of the electrons within the FM (i.e. current J direction), and the magnetization M , which can be modulated by the application of an external magnetic field H. In Fig. 4.1d, we display two examples that illustrate the different scattering channels depending on the relative orientation between J and M . On the top, when J M the empty d states have orbital angular momentum L orthogonal to M , so that their d xy orbitals are compatible with the conduction electrons in k x , leading additional available scattering channels and increased resistivity. On the bottom, when J ⊥ M the unoccupied d states are placed in planes not compatible with conduction electrons in k x , so that this scattering channel is hampering and resistivity drops. Moreover, the new spin-orbit scattering process ρ s ↑ d ↓ , displayed in Fig. 4.1c, can be represented as [START_REF] O'handley | Modern Magnetic Materials: Principles and Applications[END_REF]:

ρ s ↑ d ↓ = δcos 2 θ, (4.1)
where δ is the scattering strength, given by a ratio of spin-orbit and Coulomb interactions between conduction electrons, and θ the angle between J and M . Note that the angular dependence is quadratic, since the effect is equivalent whether J and M are parallel or antiparallel. This can be experimentally evidenced in Fig. 4.2 for AMR experiments of a thick NiFe film at room temperature, where a current is applied in a fixed direction and a magnetic field is rotated in-plane. Here, AMR = R ⊥ -R R ⊥ . For an extensive discussion on the physics and implication of AMR in FM, we redirect the interested reader to Refs. [START_REF] Campbell | The spontaneous resistivity anisotropy in Ni-based alloys[END_REF][START_REF] O'handley | Modern Magnetic Materials: Principles and Applications[END_REF][START_REF] Mcguire | Anisotropic magnetoresistance in ferromagnetic 3d alloys[END_REF][START_REF] Bechthold | Galvanomagnetic Transport: from Hall Effect to AMR[END_REF].

Anisotropic MR in 2D electron gases

With the recent advances regarding a possible intrinsic contribution to both the anomalous Hall effect (AHE) and spin Hall effect (SHE), a band structure related origin of the AMR was brought to the table. Velev et al. analyzed the AMR in constrained environments, such as FM nanowires, where electron transport becomes balistic rather than diffuse [START_REF] Velev | Ballistic Anisotropic Magnetoresistance[END_REF]. In this scenario, dimensions are reduced to less than the mean free path of the electrons, and an AMRlike phenomena is observed, not due to selective electron scattering observed in bulk materials, but from the effect of spin-orbit interactions on the band structure, which leads to different band crossings when the magnetization direction was changed. They also predicted that this effect could be either positive or negative, and that the angular dependence would be very different from the conventional AMR. Schliemann and Loss also investigated the anisotropic transport in constrained environments, this time in a 2D electron gas in the presence of spinorbit coupling [START_REF] Schliemann | Anisotropic transport in a two-dimensional electron gas in the presence of spin-orbit coupling[END_REF]. They found that charge transport becomes anisotropic if both Rashba α r and Dresselhaus β D spin-orbit coupling are present (for |α r | β D ) and hypothesized that through gate voltage one might be able to effectively investigate spin-orbit interactions in these systems. Using the same methods applied to study the AHE and SHE, Kato et al. also found an intrinsic AMR arising from spin-polarized Rashba-split 2DEG [START_REF] Kato | Intrinsic anisotropic magnetoresistance in spin-polarized two-dimensional electron gas with Rashba spin-orbit interaction[END_REF]. A schematic of their results in shown in Fig. 4.3, where a displacement of the Fermi contours and additional band crossings are observed depending on the direction of the magnetic field applied. high fields and low temperatures [START_REF] Annadi | Fourfold oscillation in anisotropic magnetoresistance and planar Hall effect at the LaAlO 3 /SrTiO 3 heterointerfaces: Effect of carrier confinement and electric field on magnetic interactions[END_REF]. However, they simply attributed this effect to magnetic interactions at the interface. Using gate-voltage to tune the properties of the 2DEG, Fete et al. observed AMR oscillations but no additional features reported by previous authors, even at high magnetic fields and well above the Lifshitz point [START_REF] Fête | Rashba induced magnetoconductance oscillations in the LaAlO 3 -SrTiO 3 heterostructure[END_REF]. A similar work was performed on LAO//STO(110) interfaces, where the existence of magnetic order was discarded and spinorbit coupling alone was considered sufficient for the appearance of AMR [START_REF] Ma | Giant crystalline anisotropic magnetoresistance in nonmagnetic perovskite oxide heterostructures[END_REF].

Additional theoretical work has been developed by Trushin et al., taking into consideration spin-orbit coupling effects to the spin textures of the band structure and elastic scattering due to polarized magnetic impurities [START_REF] Trushin | Anisotropic magnetoresistance of spin-orbit coupled carriers scattered from polarized magnetic impurities[END_REF]; in contrast, Bovenzi and Diez focused on transport effects driven by spin-orbit coupling, while intentionally neglecting the controversial localized magnetic moments at the LAO//STO interface [START_REF] Bovenzi | Semiclassical theory of anisotropic transport at LaAlO 3 /SrTiO 3 interfaces under an in-plane magnetic field[END_REF]. In this work, by calculating the resistivity tensor as a function of the magnitude and orientation of an externally applied in-plane magnetic field, a transition was observed to occur from weak anisotropy (at the low-field regime) to a strong anisotropy with multiple maxima and minima away from the main crystalline axes (at the high-field regime and above n c ), recalling the experimental observation of complex AMR [START_REF] Joshua | Gate-tunable polarized phase of two-dimensional electrons at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Annadi | Fourfold oscillation in anisotropic magnetoresistance and planar Hall effect at the LaAlO 3 /SrTiO 3 heterointerfaces: Effect of carrier confinement and electric field on magnetic interactions[END_REF]. These features were also observed to be especially large at the vicinity of avoided crossing points between d xy and d xz,yz bands, where intraband and interband scattering are extremely sensitive to the magnitude and direction of the magnetic field. While rotating an in-plane external magnetic field H ext , the effective magnetic field H ef f seen by the 2DEG is different when the angle between j c and H ext is either 90°or 270°. This discrepancy leads to a unidirectional term in these specific orientations.

H ext 90° -j c H R E z Rashba 2DEG 270° 180° 0° x y θ H ext -j c H R E z Rashba 2DEG H ext H eff (90°) ≠ H eff (270°)

Unidirectional MR in 2D electron gases

In the framework of the Rashba effect in a 2DEG, electrons moving in a confining electric field experience a magnetic field H R [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF]. Naively, one might assume that this static H R , which depends on the electron momentum k, may interfere with an external applied magnetic field H ext . In the case of a regular FM, considering that the current J is applied along -x, and that θ is the angle between J and H ext , we obtain the same resistance state at 90°and 270°.

However, if in a Rashba system a static H R (dependent on the direction of J ) is present, the previous equality fails, giving rise to a unidirectional component. A simple illustration of this effect is shown in Fig. 4.6.

Evidence of this unidirectional component in Rashba 2DEGs is still rather unexplored territory, with one report on LAO//STO [START_REF] Narayanapillai | Current-driven spin orbit field in LaAlO 3 /SrTiO 3 heterostructures[END_REF] and one on InAs quantum wells [START_REF] Choi | Spin-polarization-induced anisotropic magnetoresistance in a twodimensional Rashba system[END_REF], as displayed in Fig. 4.7a,b and 4.7c-e, respectively. In LAO//STO, a difference in resistance was detected by positioning an external in-plane field at θ = 90°and 270°. The sign of this difference was reversed upon inverting the polarity of the applied current I, which in principle flips H R and inverts the sign of the unidirectional component. The authors also attempted to extract the magnitude of the H R as a function of I, even though this field should depend exclusively on the confining electric field E z and the electron momentum k [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF]. In InAs quantum wells, a similar effect was observed, with the unidirectional component (∆V A in Fig. We then grow 5 uc of crystalline LAO at high temperatures, using the procedure described in Section 2.4.1.2. The growth is followed by an oxygen-rich post-annealing process, where the oxygen vacancies formed due to the high temperature growth and the direct contact between As shown in Fig. 4.9, we then measure the longitudinal resistance R xx (in a Quantum Design's Dynacool system, using an in-plane rotation probe and an external Keithley 2400

SourceMeter) as a function of the angle θ between the applied dc current I c = 50 µA and an external in-plane magnetic field H, for different magnitude of H and a fixed temperature of T = 2 K. In each plot, we can also see the data collected while applying a positive current (black) and negative current (red). With H = 0 T, no dependence is observed as expected, yet we do see a resistance difference between both data sets (constant for the whole experiment), which we attribute to an experimental artifact. In Fig. 4.9b, by applying H = 0.5 T, we start seeing a small but finite angle dependence, with minima at 90°and 270°. Readily, we notice that a magnitude difference between these two positions is present, which is then observed to increase further for larger H (up until 9 T), just like the overall size of the AMR.

To better evaluate the evolution of the AMR magnitude, we plot in Fig. simple sinusoidal function, which, similar to the field dependence, shows a linear evolution with respect to the applied current. Interestingly, we do not observe the increased asymmetry between R uni at 90°and 270°observed before, indicating that its origin could be related with the increasing H. Also, from the fitted curve (dotted line in Fig. 4.11b) it appears that a finite unidirectional component is present in the absence of an applied current, which naturally seems unphysical.

Very recently, extremely similar behavior has been observed for an ultra-thin layer of topological insulator Bi 2 Se 3 [START_REF] He | Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states[END_REF]. The main results are shown in Fig. 4.12. Here, the mea- surement is performed with an ac current of fixed frequency where R ω , the first harmonic resistance (equivalent to the conventional R xx ) and R 2ω , the second harmonic resistance (that include current-dependent changes to the resistance), are detected with lock-in amplifiers at difference phases. Both (ac) R 2ω and (dc) R uni were shown to be equivalent in the supplementary information of Ref. [START_REF] He | Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states[END_REF], with the only difference being the lower noise achieved in ac measurements (due to the intrinsic filtering properties of the lock-in amplifiers). We notice that in Figs. (current) and magnetic field. In the future, a similar model needs to be adapted for the slightly more complex Rashba case, so that this linear dependence can also be confirmed.

Spin Hall MR in FM/NM heterostructures

The spin Hall effect (SHE) in materials with high spin-orbit coupling is known to allow the interconversion of charge currents in spin currents. For the direct effect, an applied charge current induces two spin densities (with opposite spin) at opposite edges of the sample. If a FM is placed in contact, the spin density may be transferred to it, possibly altering its magnetic state. This was the reasoning behind the work by Miron et al., where the SHE in Pt was used to switch the perpendicular magnetization of an adjacent Co layer at room temperature [START_REF] Miron | Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection[END_REF]. By driving a positive or negative current in Pt, the orientation of the spin accumulation at the interface with Co was reversed, changing the magnetization direction in the FM layer. This experiment unlocked new and exciting possibilities regarding the control of magnetization without the use of external magnetic fields [START_REF] Awschalom | Spintronics without magnetism[END_REF]. This transfer of spin torque was further investigated by Liu et al., by performing spin-torque ferromagnetic resonance (ST-FMR) to analyze the magnetization dynamics induced in a NiFe layer on top of Pt [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF]. The work was followed by magnetization switching in Co/Pt [START_REF] Liu | Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect[END_REF], as well as in more efficient Ta/CoFeB bilayers [START_REF] Liu | Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum[END_REF].

generated, with spin polarization σ parallel to the surface (see Fig. 4.13a). When a FM layer (like YIG) is placed on top of Pt, interfacial spin mixing occurs in the form of spinangular momentum exchange between the magnetization M of YIG and the spin polarization σ induced by the SHE in Pt. Depending on the relative orientation of these two components, two effects may arise: if M ⊥ σ, spin-angular momentum is transfer to the FM layer, so that the spin current generated in Pt is "absorbed", leading to a high resistance state R ⊥ (Fig. 4.13b); if M σ, the spin current is essentially reflected back to the Pt, where it is reconverted in a charge current through the ISHE (Fig. 4.13c). This resistance state R is lower than R , which unlocks an AMR-like behavior within the paramagnetic Pt layer. The effect can be experimentally evidenced in Fig. 4.13d. Notice the change in resistance when an external magnetic field switches the magnetization of the YIG layer. Also, to exclude possible induced ferromagnetism in Pt due to its proximity with YIG, a Cu layer is inserted between them. While the effect is still observe in these conditions, it can be fully suppressed when an insulating SiO 2 is inserted.

At the same time, a theory of SMR was formulated by Chen et al., who associated the effect with different degrees of spin accumulation in the normal metal (NM) depending on the orientation of M in the FM, leading to a modulation of spin flip events in the NM, as well as spin transfer at the NM/FM interface [START_REF] Chen | Theory of spin Hall magnetoresistance[END_REF].

The SMR was later explored in YIG/Pt interfaces [START_REF] Althammer | Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids[END_REF], as well as YIG/Ta [START_REF] Hahn | Comparative measurements of inverse spin Hall effects and magnetoresistance in YIG/Pt and YIG/Ta[END_REF]. Another approach using ferromagnetic metals also started to be studied, even though it imposed additional concerns regarding the AMR from the FM, which naturally overlaps with the SMR effect [START_REF] Lu | Hybrid magnetoresistance in the proximity of a ferromagnet[END_REF][START_REF] Cho | Large spin Hall magnetoresistance and its correlation to the spin-orbit torque in W/CoFeB/MgO structures[END_REF].

Unidirectional spin Hall MR in FM/NM heterostructures

Regardless of the overlaping AMR and SMR signal, another effect was identified in these all-metallic samples, which dealt with the difference in resistance between a parallel and antiparallel M σ configurations [START_REF] Avci | Magnetoresistance of heavy and light metal/ferromagnet bilayers[END_REF][START_REF] Avci | Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers[END_REF] (see Fig. 4.14a and 4.14b). The effect was coined unidirectional SMR (USMR) and showed an amplitude of only 0.005% (orders of magnitude smaller than the 0.5% observed in conventional SMR for YIG/Pt). Interestingly, the sign of this effect was changed when using Ta or Pt. These two materials possess spin Hall angles with opposite signs, meaning that the polarization direction σ of the spin current flowing towards the interface is also different (see Fig. 4.14c and 4.14d). Lastly, the USMR showed the exact same angle-dependent resistance behavior as the unidirectional AMR addressed before in Rashba 2DEGs and TI, although its origin is expected to be different.

The nature of the USMR was suggested to arise from the different spin-dependent electrochemical potential alignment at the NM/FM interface [START_REF] Avci | Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers[END_REF]. The main conclusion was that depending on the relative orientation of M and σ, an additional spin-dependent interface resistance was added or subtracted from the total resistance of the bilayer. This idea can be more clearly understood through the theoretical model by Zhang and Vignale, shown in Fig. 4.15 [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF]. First, by sourcing a current in the bilayer, the SHE in the NM will induce a spin accumulation µ s oriented along y or -y depending of the current direction (E ext ). Note that the spin accumulation is simply characterized by an excess density of electrons with one specific spin orientation and a corresponding depletion of electrons with the opposite spin, so that globally, no charge accumulation is created. This balance assures that the conductivity of the NM layer is not altered, and the mobility of the electrons remains spin independent.

However, the conductivity of the FM layer can indeed be modified by a spin accumulation induced due to the SHE in the NM, which leads to the formation of an artificial FM layer at the interface (see Fig. 4.15). Ultimately, the difference in longitudinal resistance of the bilayer on both configurations (parallel and antiparallel) is simply produced by different spin-dependent mobilities in the FM layer, similar to the concept of current in-plane GMR [START_REF] Fert | Historical Overview: From Electron Transport in Magnetic Materials to Spintronics[END_REF]. Schematic of the USMR theoretical model for high spin-orbit coupling metal (HM)/ferromagnet (FM) bilayers [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF]. (a) For an external electric field E ext applied in the HM (along the x axis), the spin Hall effect drives a spin accumulation with polarization σ aligned with the -y axis. Close to the interface, the spin accumulation µ s created can be viewed as an artificial FM layer within the original FM layer. A change in longitudinal resistance arises from the spin dependence of the mobility in the FM layer, similar to the concept of current-in-plane GMR [START_REF] Fert | Historical Overview: From Electron Transport in Magnetic Materials to Spintronics[END_REF]. (b) When E ext is instead applied along -x axis, the µ s in the FM has the same orientation as its initial magnetization M , leading to small modulation of the longitudinal resistance. Adapted from [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF].

Unidirectional spin Hall MR in exotic systems

Similarly to how the SHE in 3D bulk materials was shifted towards the more efficient surfaces of topological insulators and Rashba 2DEGs, where the Edelstein effect is observed, researchers started to look for SMR effects using more exotic systems.

Olejnik et al. first investigate USMR behavior (in their work called linear SMR, or LSMR) in paramagnetic-(Ga,Mn)As/ferromagnetic-(Ga,Mn)As bilayers, which exhibited a resistance ratio two orders of magnitude larger than in FM/normal metal bilayers [START_REF] Olejník | Electrical detection of magnetization reversal without auxiliary magnets[END_REF]. It was suggested that the p-type paramagnetic-(Ga,Mn)As (which was shown to possess a large spin Hall angle of ∼ 1%) could generate a much larger non-equilibrium spin density. By interacting with the magnetization direction of the ferromagnetic-(Ga,Mn)As layer, the USMR was expected to be much larger. On top of that, due to the lower carrier density in the p-type semiconductor (when compared to a bulk metal), a significantly larger spin density was expected to be generated for the same applied charge current density, which ultimately results in stronger USMR. The same conclusion was drawn in the therotical model of Zhang and Vignale, where the USMR was calculated to increase for lower carrier densities [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF].

In a similar fashion, Yasuda et al. investigated Cr x (Bi 1-y Sb y ) 2-x Te 3 /(Bi 1-y Sb y ) 2-x Te 3 (CBST/BST for short) topological insulator heterostructure, where CBST is ferromagnetic [START_REF] Yasuda | Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator[END_REF]. They observed extremelly large UMR, where the difference in resistance between parallel and antiparal- components from the total R 2ω signal, as a function of temperature. Adapted from [START_REF] Lv | Unidirectional spin-Hall and Rashba-Edelstein magnetoresistance in topological insulator-ferromagnet layer heterostructures[END_REF].

lel states M J was observed to be two orders of magnitude larger than in the semiconductor heterostructures (at low temperatures). While in FM/NM the USMR was attributed to an in-plane GMR-like effect, here, the spin-momentum locked states at the surface of the TI may require a more careful look at the intrinsic spin-dependent scattering mechanisms. The authors attributed the large effect to the asymmetric scattering of surface electrons by magnons, since the UMR was surprisingly suppressed for large magnetic fields, reminiscent of what is observed for the spin Seebeck and magnon Hall effect (see [START_REF] Yasuda | Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator[END_REF] for more details). We note that this particular study is actually closer to the UMR phenomena discussed in Section 4.3

(for an isolated TI surface/Rashba 2DEG) than to a USMR effect, since the UMR observed arises from within the ferromagnetic TI layer, and not due to the interaction between FM/NM interface. Proof of this comes from the suppression of the effect above the Curie temperature of CBST, with the UMR effect being largely attenuated above 30 K. Naturally, this imposes massive constrains to the practical applicability of this system.

To go around this issue while still harnessing the interesting properties of TIs, Lv et al.

performed similar experiments but for simpler systems: (Bi,Sb) 2 Se 3 /CoFeB and Bi 2 Se 3 /CoFeB bilayers [START_REF] Lv | Unidirectional spin-Hall and Rashba-Edelstein magnetoresistance in topological insulator-ferromagnet layer heterostructures[END_REF]. As shown in Fig. 4.16a,b, the main result was a USMR-like effect originating from charge-to-spin current conversion arising from the high spin-orbit coupling TI (bulk), and the Edelstein effect occuring at the TI surface. The authors called this effect unidirectional spin-Hall and Rashba-Edelstein magnetoresistance (USRMR). After measuring the second harmonic resistance R 2ω (similarly to the FM/NM case in Section 4.4) and carefully extracting the contribution from heating-related effects (such as anomalous Nerst effect and spin Seebeck effect), the authors estimated a maximum R U EM R /j c of 1.00±0.11 mΩ MA -1 cm 2 at T = 70 K (Fig. 4.16d,e), slightly larger than the best result found using Ta/Co bilayers at room temperature [START_REF] Avci | Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers[END_REF] (after re-normalization to the total resistance of each system). We start by recalling that, as introduced in Section 1.2, a spin current is solely a flow (in opposite directions) of electrons with opposite spins, so that no net charge current is involved in the process (see Fig. 4.17a). As illustrated in Fig. 4.17b, by sourcing a charge current j c in a strong spin-orbit coupling material (in red), charge-to-spin conversion takes place due to SHE, described in Section 1.5.2. A spin current j s perpendicular to the plane is produced, which is dissipated in the FM. When a spin current flows towards the FM, an electron density with spin up(down) accumulates in the FM, while another electron density with spin down(up) accumulates in the NM (see the interface region in Fig. 4.17c). On the FM side, an artificial FM layer close to the interface is created (in blue), with an effect on the overall resistivity of the FM due to a current in-plane GMR-like effect [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF]. On the NM side, if a spin density was efficiently ejected in the first place, the subsequent backflow (with opposite spin orientation) leads to the partial re-injection of a spin current j s into the NM, which through the ISHE is re-converted back in a charge current j c , that opposes the original sourced j c . For the case when a spin current cannot be dissipated in the FM, i.e. M parallel to σ, the initial j c is unnafected by the generated spin densities at opposite edges of the NM, as illustrated in Fig. dissipate in the FM, leaving the initial j c unaltered. The contrast between the two resistance states for the UEMR is found to be much larger, as illustrated in Fig. 4.18f, simply because the current compensation in the antiparallel case is much more severe.

Summarizing this second part, we identify the three key differences between the USMR and UEMR. First, the charge-to-spin current conversion efficiency is expected to be larger in the DEE than the SHE, which leads to the creation of a more pronounced artificial FM layer within the FM. This effect was already hinted by Olejnik et al. for p-type semiconductors with large spin Hall angles (when compared to Ta or Pt, for example) [START_REF] Olejník | Electrical detection of magnetization reversal without auxiliary magnets[END_REF]. Second, the carrier densities found in Rashba 2DEGs are orders of magnitude smaller than in a bulk NM, which accordingly to the model by Zhang and Vignale should also boost the USMR [START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF]. Third, the spin-to-charge current re-conversion process is necessarily more efficient in spin-momentum locked contours, for the simple fact that an electron in k with spin orientation σ ↑ is necessarily exchanged with an electron in -k with σ ↓ . Ultimately, the spin current ejected implies a larger compensation (in terms of displacement of the contours), leading to an overall increase of the resistance at the TI/Rashba 2DEG (much higher than in FM/NM heterostructures). as well as the orientation of the applied magnetic field H can be seen in Fig. 4.19a. Note that unlike the experiments in LAO//STO, the initial magnetic field (at 0°) lies perpendicular to the applied current, so that (comparatively) all plots from here on are considered to be shifted by +90°.

We start by performing AMR experiments at T = 2 K, while sourcing a current of 500 39 To assure straight current lines along the sample. 40 Although it may seem an overly large current, the equivalente calculated charge current density jc ∼ 1 × 10 4 A.cm -2 is similar to the one used for the previous AMR experiments in LAO//STO Hall bars. Additionally, no notable heating effects were observed during the experiment (even though this needs to be more carefuly evaluated in the future. , respectively. Since the respective current densities for the two cases are comparable (j ∼ 1 × 10 4 A.cm -2 ), we conclude that the total unidirectional component is quite similar for both cases, so that, in principle, no UEMR is present in the NiFe/LAO//STO heterostructure. Future experiments to confirm this results are discussed in the conclusion. We add that the spin exchange at the FM/2DEG may be blocked by the insulating LAO barrier. Even though efficient spin pumping was previously observed towards the 2DEG, the efficiency of a spin accumulation from the 2DEG towards the FM is still unknown.

We finish this preliminary study with temperature dependence measurement, as observed in Fig. 4.22, where the unidirectional component was only observed at low temperature, similar to the results in TI [START_REF] Yasuda | Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator[END_REF]. The spin-to-charge current interconversion is also strongly reduced in the 2DEG with increasing temperature [START_REF] Chauleau | Efficient spin-to-charge conversion in the 2D electron liquid at the LAO/STO interface[END_REF], suppressing any possible UEMR effects.

Conclusions and prospects

In this chapter, we investigated anisotropic magnetoresistance (AMR) and unidirectional magnetoresistance (UMR) in magnetic bulk materials and 2D electron systems. While the AMR in magnetic materials is associated with spin dependent scattering events, which creates a resistance variation depending on the relative orientations of the applied current and an external in-plane magnetic field, in 2D electron system the effect is expected to arise from intrinsic band structure effects. Additionally, UMR is only observed in the second case, where the presence of a fixed Rashba-induced magnetic field adds up to the total externally applied field and drives specific resistance changes in apparently similar configurations. We perform an experimental study in the LAO//STO system, revealing that the AMR and UMR scale quadratically and linearly as a function of an external magnetic field, respectively. Additionally, the UMR was also observed to scale linearly as a function of the applied current. While these results are reminiscent of very recent data shown for the topological insulator Bi 2 Se 3 [START_REF] He | Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states[END_REF], the interpretation provided (involving hexagonal warping with fnite out-of-plane spin textures) may not be applicable to a Rashba 2DEG. Further modeling is therefore required in this regard.

as previously reported in YIG on Pt experiments [START_REF] Chang | Sputtering growth of Y 3 Fe 5 O 12 /Pt bilayers and spin transfer at Y 3 Fe 5 O 12 /Pt interfaces[END_REF]. While in these samples ferromagnetic resonance experiments still showed a small signal, the 2DEG initially present at the interface of LAO//STO disappeared, most likely due to the high temperature treatment. Further experiments are needed in the future to achieve this all-oxide spin-to-charge current interconversion platform.

Also, the LAO barrier present in our experiments may be hampering proximity effects between the 2DEG and the FM, which were shown to play an important role in USMR and possibly in UEMR experiments. A possible solution might be to remove the crystalline LAO and the metallic NiFe layer, and replacing it with an alternative magnetic oxide, such as Fe3O4

or EuO. Note that in this case, one could deposit Eu directly on STO, which will in turn form oxygen vacancies and unleash a 2DEG in STO [START_REF] Lömker | Two-dimensional electron system at the magnetically tunable EuO/SrTiO 3 interface[END_REF][START_REF] Kormondy | Large positive linear magnetoresistance in the two-dimensional t2g electron gas at the EuO/SrTiO 3 interface[END_REF], while at the same time forming an insulating ferromagnetic layer.

Figure 1 . 1 .

 11 Figure 1.1. Illustration of different types of currents. (a) Charge current composed of a flow of charged carriers with equal spin-up and spin-down densities. (b) Spin-polarized current (usually found in ferromagnetic materials) where unbalanced spin-up and spin-down densities leads to finite spin transport. (c) Pure spin current composed strictly of a flow of spin angular momentum. These can be generated through dedicated techniques such as spin pumping.Adapted from[START_REF] Rüffer | Non-local Phenomena in Metallic Nanostructures[END_REF].

Figure 1 . 3 .

 13 Figure 1.3. Spin-orbit coupling. (a) From the point of view of an electron, a positively charged nucleus (orbiting around it) generates an electric field which translates into an induction-like magnetic field B, that will interact with the spin magnetic moment of the electron. Depending on the orbiting direction of the electron around the nucleus, and on its spin, L and S may be (b) parallel or (c) antiparallel, leading to two energy-split states.

Figure 1 . 4 .

 14 Figure 1.4. Spin relaxation and spin dephasing phenomena. (a) Model of an electron spin S precessing around a static magnetic field B 0 along u z . A time dependent fluctuating magnetic field B ⊥ leads to spin precession and spin dephasing. (b) Elliot-Yafet mechanism. Each momentum scattering event, caused by phonons or impurities, may probabilistically lead to spin flipping. Within this mechanism, the spin is conserved during a characteristic momentum relaxation time τ p , i.e. inbetween collisions. (c) D'yakonov-Perel' mechanism for τ p Ω ≤ 1, with Ω the average magnitude of the precessing frequency. The spin slowly precesses around a k-dependent effective spin-orbit field Ω k between two scattering events.After each scattering event, a new Ω k is defined, so that the spin changes not during, but between collisions. Ultimately, this mechanism results in spin dephasing. (d) Emphasized spin precession changes due to momentum scattering from k to k within the DP mechanism. The large circle represents the momentum position of a carrier (at constant energy) in a two-dimensional electron gas. Panels (a-c) adapted from[START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF] and panel (d) adapted from[START_REF] Mavropoulos | Spin relaxation in nonmagnetic metals and semiconductors[END_REF].

Figure 1 . 5 .

 15 Figure 1.5. (a) Schematic of the Hall effect. Under the application of an out-of-plane magnetic field B ext , charge carriers flowing in a material are deflected towards the edges of the sample. An increasingly large transverse resistance R xy is detected with increasing B ext . (b) Example of Hall data collected for a Au film (∼ 5 nm), at room temperature. The negative slop indicates that transport is carried out by electrons. (c) Schematic of the anomalous Hall effect (AHE). Under an out-of-plane magnetic field, the injection of a current in a ferromagnetic sample, with the magnetization M (out-of-plane), results in deflection of carriers with opposite spins in opposite direction. The charge imbalance at each edges of the sample leads to the generation of an orthogonal charge j c and spin j s current. (d) An abrupt increase of the transverse resistance R xy is observed in a Co film (∼ 3 nm) at room temperature due to the AHE. At a given saturation field, the signal returns to the regular Hall effect expected from a metal (see inset).

Figure 1 . 6 .

 16 Figure 1.6. Schematic of the spin Hall effect (SHE). (a) The direct SHE is described by the deflection of carriers with opposite spins towards opposite edges of a sample with sizable spin-orbit coupling. This effect generates a pure spin current j s , orthogonal to the initial charge current j c injected. Note that the spin current generated cannot be directly measured through electrical means, ∆V = 0V . (b) Conversely, in the inverse SHE (ISHE) the injection of a pure spin current j s in a high spin-orbit coupling material results in the production of a transverse finite charge current j c .

  Figure 1.7. Illustration of the intrinsic and extrinsic (skew scattering and side-jump) mechanisms that drive charge-to-spin current interconversion phenomena. Adapted from [40].

Figure 1 . 8 .

 18 Figure 1.8. Symmetry considerations. (a) Time-reversal symmetry is present when reversing the direction of time t is equivalent to reversing the momentum k and spin σ of a particle. (b) Space-inversion symmetry is present in systems containing an inversion center, so that relative to this point, an atom with coordinates (x,y,z) always has an identical counterpart in (-x,-y,-z). Materials with space-inversion symmetry are usually called centrosymmetric. (c) Energy dispersion of carriers with different momentum k for a centrosymmetric system.

Figure 1 . 9 .

 19 Figure 1.9. Band structure of a Rashba system lacking space-inversion symmetry. (a) Bottom: Energy dispersion for Rashba-split bands with opposite spin configurations. Top: At the Fermi level, two contours with different sizes and spin chiralities are observed. Right: 3D representation of the band structure. Adapted from [40] and [82]. (b) Rashba-split bands experimentally observed through angle-resolved photoemission spectroscopy at the surface of Au(111) [83].

Figure 1 . 10 .

 110 Figure 1.10. Illustration of spin-to-charge current interconversion in 2D Rashba systems. (a) Direct Edelstein effect (DEE). In the presence of a charge current j c applied along -x (electron flow along x), both Rashba split Fermi contours are displaced in the same direction and by the same amount ∆k x , yielding two uncompensated spin densities δs ↑ and δs ↓ , and hence a finite spin accumulation. (b) Inverse Edelstein effect (IEE). Upon injection of a steady source of a non-equilibrium spin density along z, with spin direction σ along y, both Fermi contours are displaced in opposite direction by ∆k outx and ∆k in x . Carriers unevenly accelerated in opposite directions generate an electric field along x. Modified from[START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF].

Figure 1 . 11 .

 111 Figure 1.11. Onsager reciprocity of spin Hall and inverse spin Hall effects [106]. (a) Schematic representation of the spin Hall effect (SHE), where an injected spin current I s is converted in a charge current I c in a high spin-orbit coupling bulk material (Pt). (b) Normalized voltage non-locally detected in a Pt wire, as a function of an in-plane magnetic field H, upon injection of a spin-polarized current using a NiFe pad. Note that the spin polarized current is sourced between the NiFe pad and a Cu wire, but does not go through the Pt wire (schematic of the experiment in the inset). (c) Schematic representation of the inverse spin Hall effect (ISHE), where an injected charge current I c in a high spin-orbit coupling material (Pt) induces a spin current I s in an adjacent layer (Cu). (d) Normalized voltage as a function of H due to induced spin accumulation in a Pt wire.Note that the variation of the extracted resistance for positive and negative applied field, ∆R c and ∆R s , is the same in both SHE and ISHE experiments, seemingly confirming their Onsager reciprocity. However, due to the intrinsic differences between both geometries, this reciprocity may need a more careful investigation.

Figure 1 . 12 .

 112 Figure 1.12. Spin relaxation processes in spin-to-charge current interconversion phenomena. (a) Inverse Edelstein effect. The spin-to-charge current conversion efficiency λ IEE depends on the relaxation time τ s of an out-of-equilibrium spin distribution in the 2DEG. Additional contribution may arise due to the efficiency of spin current transmission across the interface, as well as electronic exchange between the TI/2DEG and the FM, j back s . (b) Direct Edelstein effect. The charge-to-spin current conversion efficiency q DEE depends independently on the relaxation time τ s within the 2DEG/TI and a second spin relaxation time τ b outside the 2DEG/TI where carriers propagate through the barrier towards the FM. Inspired by [109] and a private communication with professor YoshiChika Otani.

Figure 2 . 1 .

 21 Figure 2.1. Structural and electronic properties of SrTiO 3 . (a) Crystal structure of SrTiO 3 with alternating neutrally charged (SrO) and (TiO 2 ) planes [in the (001) direction]. (b) Energy levels of the Ti 3d orbitals for an isolated Ti atom in spherical symmetry (on the left) and for a Ti atom in a cubic SrTiO 3 crystal (on the right). In the latter, a crystal field splitting of about 2 eV separates degenerate e g states from degenerate t 2g states, composed of d xy and d yz,xz orbitals. Adapted from [124] (c) Calculated band structure of cubic SrTiO 3 , with the valence band maximum composed of O 2p orbitals and the conduction band minimum of Ti 2p t 2g orbitals (colored boxes). The Fermi level position, represented by the dashed line, lies just above the valence band maximum. On the right, the corresponding density of states N (E).Adapted from[START_REF] Tilley | [END_REF].

Figure 2 . 2 .

 22 Figure 2.2. Oxygen vacancies in STO. (a) Representation of the structural effect of an oxygen vacancy. The absence of an oxygen atom in the lattice, i.e. formation of a positively charged oxygen vacancy V +/++ O provokes outward displacement of the neighboring Sr and Ti cations. (b) Energy position of the defect levels of neutral V O , ionized V + O and double-ionized V ++

Figure 2 . 3 .

 23 Figure 2.3. Structural properties and defect states in LaAlO 3 . (a) Crystal structure of LaAlO 3 with alternating charged (LaO) + and (AlO 2 ) -planes [in the (001) direction]. (b) Energy position of the defect levels of neutral V O , ionized V + O and double-ionized V ++ O oxygen vacancies in LaAlO 3 within the band gap. (c) Formation energy of an oxygen vacancy with different charged states in LaAlO 3 . Below 3.6 eV, V ++ O are the most stable and favorably formed defects. Adapted from [138]. (d) Representation of the structural effect of an oxygen vacancy in LaAlO 3 . The formation of a positively charged oxygen vacancy V +/++ O

Figure 2 . 4 .

 24 Figure 2.4. Discovery of the high-mobility electron gas between insulating LAO and STO. (a) Reflection high-energy electron diffraction intensity oscillations of the specular reflected beam for the growth of 16 unit cells of LAO on TiO 2 -terminated SrTiO 3 . (b,c,d) Temperature dependence of the longitudinal resistance R xx , Hall coefficient R H and carrier mobility µ Hfor samples grown between 10 -4 and 10 -6 mbar of oxygen partial pressure. The dashed line represent a sample grown at 10 -6 mbar that was additionally post-annealed for 2 h at 400 • C under 1 atm of oxygen. Adapted from[START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF].

Figure 2 . 5 .

 25 Figure 2.5. Critical thickness for conduction in LAO//STO interfaces.For LAO thicknesses between 0 and 3 unit cells, the heterostructure is found to be insulating. At a critical thickness t c of 4 uc, finite conductivity σ s is detected[START_REF] Thiel | Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures[END_REF].

Figure 2 . 6 .

 26 Figure 2.6. Resistance mapping around the interface of LAO//STO samples through conductive-tip atomic force microscopy. (a) After the high temperature growth of LAO, oxygen vacancies are created within STO, rendering its bulk conducting (blue area). (b) After a post-annealing step under high oxygen pressures, the vacancies are filled, so that only the quasi-2D electron gas with a thickness of about 7 nm is observed. The pink area signals the insulating part. Adapted from [144].

Figure 2 . 7 .

 27 Figure 2.7. (a) Field-effect modulation of the sheet resistance R sheet as a function of temperature for LAO//STO samples. The superconducting transition observed at around 250 mK is suppressed for negative gate voltages. Adapted from [147]. (b) SQUID magnetometry image mapping the magnetic dipoles in LAO/STO samples at 20 mK. Adapted from [152].

  5 e -per uc are transferred from the surface of the LAO (O 2p valence bands) towards the STO surface (empty

Figure 2 . 8 .

 28 Figure 2.8. Schematic representation of the polar discontinuity at LAO//STO(001) heterointerfaces. (a) On the left side, the unreconstructed n-type LaO/TiO 2 interface.Along the (001) direction STO shows neutrally charged planes (Q=0) while LAO planes have an associated alternated charge of Q=1 and Q=-1. The electrostatic potential V builds up from the interface and keeps increasing with LAO film thickness. On the right side, a "polar catastrophe" is avoided through the transfer of half an electron to the interface. The potential remains finite since the electric field oscillates around E = 0. (b) Energy band diagram of the LAO/STO interface. The increasing thickness raises the internal potential allowing the LAO valence band (VB) to tilt until it reaches the STO conduction band (CB). At a given critical thickness t c , Zener breakdown occurs and electrons are able to be transferred from the LAO surface towards Ti 3d states at the interface, where a q2DEG appears. Adapted from[START_REF] Vaz | Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures[END_REF].

Figure 2 . 9 .

 29 Figure 2.9. Experiments confirming the validity of the polar catastrophe scenario. (a)Schematic of the potential build-up as a function of the thickness t for a pure LAO film (light blue) and a LASTO:0.5, a LAO layer diluted with 50% of STO (dark blue). Altering the composition of the LAO film translates in a modulation of its formal polarization, so that the critical thickness for conduction can be increased. Adapted from[START_REF] Reinle-Schmitt | Tunable conductivity threshold at polar oxide interfaces[END_REF]. (b) Quantitative spectroscopic construction of the evolution of band alignment across the LAO/STO interface, confirming the existence of a built-in electric field E in the LAO layer. Adapted from[START_REF] Huang | Mapping Band Alignment across Complex Oxide Heterointerfaces[END_REF]. (c) Expansion of the LAO c-axis parameter with increasing film thickness, supporting the idea of an increasing internal potential within LAO. The dashed horizontal line indicates the pseudocubic LAO bulk lattice constant. Adapted from[START_REF] Cancellieri | Electrostriction at the LaAlO 3 /SrTiO 3 Interface[END_REF].

Figure 2 .

 2 Figure 2.10. (a) Expected layer occupancy of O, La, Sr, Al and Ti atoms as a function of their position within an LAO//STO heterostructure, emphasizing the interdiffusion between LAO and STO. Adapted from [179]. (b) STEM and EELS of conducting LAO//STO samples grown by MBE. On the left, the high-angle annular dark-field STEM image reveals the crystalline epitaxial growth. On the right, the concentration map of La and Ti shows small amount of intediffusion at the interface. Modified from [180].

Figure 2 . 11 .

 211 Figure 2.11. Role of surface reactions in the interfacial conductivity of LAO/STO. (a)Sketch of the nanowire writing/erasing procedure in LAO(3uc)/STO samples (at the verge of conduction), using a biased tip. Adapted from[START_REF] Bi | Water-cycle mechanism for writing and erasing nanostructures at the LaAlO 3 /SrTiO 3 interface[END_REF]. (b) Ti 3+ /Ti 4+ spectral weight ratio and relative Al 2p core level shift from XPS measurements performed in LAO/STO samples in different conditions (information in the x-axis in chronological order). Adapted from[START_REF] Scheiderer | Surface-interface coupling in an oxide heterostructure: Impact of adsorbates on LaAlO 3 /SrTiO 3[END_REF]. (c) Water dissociation at AlO 2 -terminated LAO surface. Adsorption of dissociated/molecular water bonds with the surface, releasing electrons that contribute to the conduction at the LAO/STO interface. Adapted from[START_REF] Adhikari | Charge Transfer to LaAlO 3 /SrTiO 3 Interfaces Controlled by Surface Water Adsorption and Proton Hopping[END_REF].

  ], accompanied by interfacial Al-on-Ti substitutions [Al - T i (I)]. As observed in Fig.

Figure 2 . 12 .

 212 Figure 2.12. Polarity-induced defect mechanism. (a) Schematic band diagram and charge transfer at the LAO/STO interfaces. Below the critical thickness t c , all electrons are transferred from surface T i + Al (S) defects towards deep Al - T i (I), where they become trapped. (b) Formation energy ∆H of interfacial defects at thermodynamical equilibrium. ∆H < 0 means spontaneous formation. (c) Same as (a) but above t c . Here, surface oxygen vacancies V O (S) donate electrons to the interface, where some are trapped at Al - T i (I) and the rest drive the formation of a 2DEG. (d) Above t c of 4 uc, V O (S) spontaneously form at the surface of LAO. (e) With the formation of V O (S), the formation energy of Ti-on-Al defects becomes positive, hampering their formation. The low concentration of Al T i defects is therefore not sufficient to trap all electrons coming from V O (S). Modified from [165].

Figure 2 .

 2 Figure 2.13. (a) Energy levels of the splitted e g and t 2g orbitals in cubic, tetragonal and broken inversion symmetry environment. (b) Sketch of a 3D Fermi surface corresponding to bands arising from t 2g triplet in a cubic environment (in the absence of spin-orbit coupling), representative of the bulk Fermi surface of e -doped STO. (c) Hopping paths among Ti-d xy to Ti-d xy and Ti-d xz to Ti-d xz . While on the first case (left) hopping occurs equally in the x and y axis, the second case (right) illustrates vanishing hopping along the y axis.(a,c) adapted from[START_REF] Fete | Magnetotransport experiments at the LaAlO 3 /SrTiO 3 interface[END_REF] and (b) adapted from[START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF].

2 .

 2 13a, the d xz /d yz orbitals are pushed to higher energies (∼ 50 meV), so that the d xy orbitals become the lowest energy conduction band. Additionally, at around 105 K, STO undergoes a cubic-to-tetragonal transition, which slightly raises the energy of the d xy orbitals (∼ 3 meV) due to rotation of the oxygen octahedra.

  2.13c). This gives rise to an isotropic (circular) Fermi surface in the (k x , k y ) plane, leading to low effective masses in-plane and heavy effective masses in the z direction m * x/y (d xy ) < m * z (d xy ). In contrast, the d xz orbitals show particularly favorable hopping along the x and z axis, leading to a light effective mass in these two directions and heavier in the y direction m * x/z (d xz ) << m * y (d xz ). Symmetrically, a similar behavior is expected for the d yz bands.

  xz/yz bands. As sketched in Fig. 2.15, assuming an approximate triangular confining potential (due to the bending of the STO conduction band) we notice that d xy bands are located deeper in the well and thus closer to the interface. Moving away from the interface, we expect a mix of bands with d xy and d xz/yz character. These results have been predicted by several authors, using

Figure 2 . 14 .

 214 Figure 2.14. Schematic representation of the STO(001) surface 2DEG subbands, with three light d xy and two heavy d xz and d yz bands, as a function of (a) the Fermi level E F position and (c) in momentum space and constant energy. (b,d) Experimental observation of the previous schematics using ARPES. Modified from[START_REF] Walker | Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy[END_REF]. (e) Realistic orbitally resolved electronic structure of the 2DEG in STO(001). The magnified panels reveal a weak Rashba-type spin splitting at the band bottom, which becomes heavily enhanced (by one order of magnitude) at the avoided crossings between light (blue) and heavy (red) subbands, where orbital character becomes strongly mixed. (f ) Calculated Fermi surface emphasizing how orbital mixing and large spin splittings occurs at the crossings of circular d xy and elliptical d xz,yz bands. Adapted from[START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF].

Figure 2 . 15 .

 215 Figure 2.15. Top -Schematic band profile of the STO conduction band at the interface with LAO. Bottom -Carrier density distribution n for both light (dark area) and heavy (ligh area) bands. Adapted from [40].

Figure 2 . 16 .

 216 Figure 2.16. Experimental setup combining two pulsed laser deposition (PLD) chambers, XPS and magnetron sputtering. All individual setups are connected in-vacuo (10 -9 mbar range) through the cluster at the center. Samples are introduced in the system using the loadlock. Adapted from [210].

Figure 2 . 17 .

 217 Figure 2.17. Materials used for STO substrate termination. (a) PTFE beaker for buffered-HF solution and borosilicate glass beaker for deionized water. (b) PVDF dipper. (c) Tube furnace for substrate annealing. Three thermostats control the temperature in three different positions of the furnace. Adapted from [210].

Figure 2 . 18 .

 218 Figure 2.18. AFM on (a) STO untreated surface exhibiting rather flat surface and small corrugations with a height of about 0.70 nm, (b) STO after HF-based termination procedure showing TiO 2 -termination and steps with a height of about 0.48 nm, (c) LAO(2uc)//STO heterostructure right after LAO growth, showing the preservation of the step-and-terrace like surface structure. (d) NiFe(2.5nm)/LAO//STO right after sputtering deposition, exhibiting increased roughness due to oxidation of the metallic capping.

Figure 2 . 19 .

 219 Figure 2.19. Pulsed laser deposition basics. (a) Schematic of the PLD process, with a short laser pulse ablating a small portion of the target which gets transferred to the substrate. Modified from [221]. (b) Different RHEED patterns for a flat crystalline surface, a stepped surface and 3D islands. Modified from [222]. (c) Monitoring the formation of a single monolayer through RHEED. The fractional layer coverage θ is shown along with the corresponding RHEED oscillation signal. Adapted from [223].

Figure 2 . 20 .Figure 2 . 21 .

 220221 Figure 2.20. Pulsed laser deposition system. (a) Exterior of the PLD chamber. Although not visible, the phosphor screen and camera used to monitor the RHEED diffracted electrons are behind the chamber, aligned with the RHEED gun. (b) Schematic of the PLD setup.Adapted from[START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF]. (c) Interior of the PLD chamber. The target carousel allows the storage of 5 different targets inside the chamber at the same time, with a mechanical system that allows rotation between targets, as well as the rotation of individual target. Adapted from[START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF].

Figure 2 . 22 .

 222 Figure 2.22. Growth of LAO ultra-thin films. (a) Interior of the PLD chamber and substrate holder. An infrared laser is used to locally heat the back-side of the sample holder. x and y positioning are controlled through knobs on the outside of the chamber. (b) Typical RHEED oscillations and diffraction spots. For consistency, monitoring is always performed on the (0-1) diffraction spot. (c) Characteristic plume formed after ablating the LAO target with a single beam pulse, at 2 × 10 -4 mbar of oxygen. Modified from [210].

Figure 2 . 23 .

 223 Figure 2.23. A typical PLD growth procedure of LAO, showing the substrate temperature T , partial oxygen pressure P O2 inside the chamber and laser energy ( before being attenuated) as a function of time. The green area represents the ablation period.

Figure 2 .

 2 Figure 2.24. (a) Basics of physical sputtering process. Adapted from [228]. (b) 3D representation of magnetron sputtering. Adapted from [229]. (c) Exterior of the sputtering chamber.(d) Interior of the sputtering chamber. Ar atoms are accelerated towards the metal target, located inside the cylinder and mounted on a dc magnetron source, hence generating a plasma. Adapted from[START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF].

Figure 2 . 25 .

 225 Photoelectron

Figure 2 . 26 .

 226 Photoelectrons Photoelectrons

Figure 2 . 27 .

 227 Figure2.27. Experimental XPS system. (a) Exterior of the XPS chamber. Emitted electrons enter the transfer lens of the analyzer. There, they are retarded/accelerated to match the analyzer pass energy before entering the analyzer itself and being finally collected by the electron detector. A preamplified signal is then sent to the optical receiver before reaching the amplifier and computer. (b) Interior of the XPS chamber. The X-ray gun can be retracted to allow positioning of the sample holder. (c) Typical survey scan performed on a bare STO substrate. Modified from[START_REF] Vaz | Growth and Electrostatic/chemical Properties of Metal/LaAlO 3 /SrTiO 3 Heterostructures[END_REF].

Figure 2 . 28 .

 228 Figure 2.28. Schematic of transport configurations. (a) Four contacts are placed at the corners of the sample in (b) Van der Pauw configuration and (c) Hall configuration. On the right, illustration of the electron deflection under application of an out-of-plane magnetic field B. Modified from[START_REF] Lesne | Non-Equilibrium Spin Accumulation Phenomena at the LaAlO 3 /SrTiO 3 (001) Quasi-Two-Dimensional Electron System[END_REF] and[START_REF] Vaz | Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures[END_REF].

Figure 2 . 29 .

 229 Figure 2.29. Transport experiments. (a) Wire bonding of a sample in a (b) 8-wire geometry (4-wire for Hall resistance and 4-wire for longitudinal resistance) sketch. This geometry allows the collection of both Hall and magnetoresistance, sequentially sourcing between the two channels, yet in a single measurement run. Adapted from [210].

Figure 2 . 30 .

 230 Figure 2.30. XPS experiments on LAO//STO heterostructures. (a) Ratio of the Ti 3+ intensity, extracted from the Ti 2p core-level spectra (inset), as a function of the LAO thickness.Modified from[START_REF] Takizawa | Electronic charges and electric potential at LaAlO 3 /SrTiO 3 interfaces studied by core-level photoemission spectroscopy[END_REF]. (b) Ti 2p core-level spectra collected for a LAO(5uc)//STO sample. Angle-dependent experiments reveal an increasing Ti 3+ feature (inset), which can be used to estimate the thickness d of the 2DEG. Modified from[START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF].

Figure 2 . 32 .

 232 Figure 2.32. Transport properties of a LAO(5uc)//STO sample. (a) Sheet resistance R s as a function of temperature T . (b) Transverse resistance R xy (Hall) collected at 2 K for an external out-of-plane magnetic field H between 9 and -9 T. (c) Sheet carrier concentration n s as a function of T , taken from the high field regime slope of Hall experiments (from 2 to 300 K). Although the uncertainties are not shown they are less than 1% (error associated with the linear fitting at high fields). (d) Carrier mobilities µ as a function of T . Modified from [166].

Figure 2

 2 Figure 2.33. Layer-resolved density of states of (a) LAO(1uc)//STO and (b) Co(1ML)/LAO(1uc)//STO. (c) Antisymmetrized Hall resistance R xy as a function of an out-of-plane magnetic field H for uncapped LAO(5uc)//STO sample (black curve) and Co/LAO(n)//STO samples with n = 1, 2 and 4 uc (colored curves). In the inset, the Hall effect collected from a reference Co//STO sample. All data was collected at T = 1.4 K. Modified from [121].

  2.33c). Note, in the inset, that experiments on a Co reference sample only show the anomalous Hall effect characteristic of a ferromagnetic conductor, proving that the Hall trace observed is indeed occurring due to the conducting LAO//STO interface.

Figure 2 . 34 .

 234 Figure 2.34. Transport properties of in situ grown M/LAO(2uc)//STO samples, with M = Co, Ti, Ta, Nb and NiFe. (a) Sheet resistance R s as a function of temperature. In the inset, a schematic of the parallel conduction in metal-capped LAO//STO samples. (b) Magnetoresistance M R and (c) Hall effect as a function an applied out-of-plane magnetic field H collected at 10 K. In the inset, the schematic Hall configuration. (d) Temperature dependence of the Hall effect collected for a Co/LAO(2uc)//STO sample. While at low temperatures the Hall trace is large and non-linear (signaling the presence of a 2DEG), at room temperature conduction is dominated by the magnetic Co layer, which displays anomalous Hall effect (see Section 1.5.1). Partially modified from [6].

Figure 2 .

 2 Figure 2.35. 2-channel model and metal/q2DEG transport contributions disentanglement. (a) In longitudinal configuration, the metal and q2DEG layer can be viewed as two resistances in parallel, separated by a thin LAO layer. (b) In Hall configuration, additional (Hall) voltages are generated in each layer.(c,d) Extraction of the q2DES contribution (red curve) based on the magnetotransport and Hall data of both reference metal (gray curve) and metal + q2DES (black curve) for a Ta/LAO(2uc)//STO sample. The obtained longitudinal resistance R xx and Hall data R xy are fitted simultaneously with a two-band model (light orange curve). In the inset, the zoomed Hall data for a reference Ta metallic layer. Adapted from[START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

Figure 2 . 36 .

 236 Figure 2.36. q2DEG isolated transport properties. (a) Transverse (Hall) resistance R xy and (b) longitudinal magnetoresistance M R of the q2DES formed at LAO(2 uc)//STO samples capped with different reactive metals. Adapted from [6].

Figure 2 . 37 .

 237 Figure 2.37. Normalized Ti 2p core-level spectra of LAO(1uc)//STO samples capped by 3 Å of (a) Co and (b) Ta.For each sample, three stages are shown: STO bare substrate before deposition (black curve), after LAO growth (grey curve), and after metal deposition (colored curve). The difference between the grey and colored curves, shown below the spectra, highlights the presence of Ti 3+ after Co and Ta deposition. In the insets, angle dependence of the spectral weight in the Ti 3+ region before and after metal deposition. (c,d) Expanded view of the Ti 2p 3/2 core-level spectra (dots) fitted with both Ti 4+ (grey area) and Ti 3+ contributions (colored area). All data was collected in-situ. Adapted from[START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

Figure 2 .

 2 Figure 2.38. (a) Co 2p core-level spectra of a Co(3Å)/LAO(1uc)//STO sample (green), compared with a fully metallic (black) and a fully oxidized (light green) Co reference sample, revealing a partially oxidized Co capping. (b)Fitted Ta 4f core-level spectrum of a Ta(3Å)/LAO(1uc)//STO sample with multiple Ta oxide peaks, following Ref.[START_REF] Moo | An XPS depth-profile study on electrochemically deposited TaO x[END_REF]. No Ta metal peak is discernable (usually located 5 eV away from the oxide peak) which indicates that the Ta capping is nearly fully oxidized. Adapted from[START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

2. 5 . 3

 53 Noble metals on LaAlO 3 (<4uc)/SrTiO 3 Here, we perform similar experiments as the ones described in the last section, but using a different set of materials: noble metals. The Hall effect and MR measurements (under an applied magnetic field of ± 4 T) for Au-, Pd-and Pt-capped LAO(2uc)//STO samples is shown in Fig.2.39. The thickness of the metallic layer ranged between 3-4 nm (slighlty larger than previous experiments to ensure an homogeneous film). We readily notice striking differences when compared to LAO//STO samples capped with reactive metals. The Hall trace is perfectly linear and the Hall resistance only changes by a few tens of mΩ over a field of 4 T. The carrier densities associated with these small slopes are in the 10 22 cm -3 range, indicating that only the metal is contributing to transport in these samples. Similarly, the MR, displayed in the inset, shows values in the range of 0.001, characteristic of a metallic layer. At first, these experiments suggest that no q2DEG is formed for this set of metals, with conduction occurring only in the metallic capping layer.

Figure 2 . 39 .

 239 Figure 2.39. Antisymmetrized Hall resistance R xy as a function of an applied out-of-plane magnetic field H for LAO(2uc)//STO samples capped in situ with noble metals (Pt, Au, or Pd). In the inset, the magnetoresistance M R for the same samples. Adapted from [6].

Figure 2 .

 2 Figure 2.40. (a) Normalized Ti 2p core-level spectra of LAO(1uc)//STO samples capped by approximately 3 Å of Au (see also Fig. 2.37). (b) Zoomed Ti 2p peak, with no sign of a Ti 3+ component. (c) Au 4f core-level spectrum of an Au(3Å)/LAO(1uc)//STO. The overlap with the Au metallic reference hints to a fully metallic Au capping. Adapted from [6].

Figure 2 .

 2 Figure 2.41. (a) Energy band diagram of a metal/n-type semiconductor interface at the Schottky limit. Upon contact, band bending occurs at the semiconductor side, so that both E F align. (b) Sketch of the formation of a charged depletion region in a bulk semiconductor upon contact with a single metal cluster, due to the band bending shown in panel (a). Adapted from [140].

2. 5 . 4 . 2

 542 Chemical interactions: mass transportChemical interactions between metals and oxides involve both surface reactions and mass transport driven by gradients in the electrochemical potential (over more than one lattice distance). Generally, these interactions can be classified in four different categories (following the notation in Ref.[START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF]:1. Redox reactions. At a metal/oxide interface (M e I M e II O x ), a redox reaction induces oxidation of the metallic layer and reduction of the oxide substrate, so that:M e I M e II O x → M e I O y M e II O x-y (2.16)Of all types of possible reactions, these are the most common, especially for reactive metals on oxides. As an example, high resolution transmission electron microscopy (HRTEM) and electron energy loss spectroscopy (EELS) revealed that at the interface of Nb/TiO 2 (110), the first two monolayers of Nb were oxidized, accompanied with partial reduction of a ∼2 nm layer within the TiO 2[START_REF] Marien | Nb on (110) TiO 2 (rutile): growth, structure, and chemical composition of the interface[END_REF].

Fig. 2 . 42 .Figure 2 . 42 .Figure 2 . 43 .

 242242243 Fig. 2.42.The Cabrera-Mott theory can be extended to interactions at metal/oxide interfaces, where

Figure 2 . 44 .

 244 Figure 2.44. Relation between the enthalpy of oxide formation ∆H O f per mol of oxygen and work functions φ M of different metals. Data extracted from Ref. [260].

Figure 2 . 45 .

 245 Figure 2.45. Sheet carrier density n s , Ti 3+ /Ti 4+ spectral area ratio, and relative metal oxide quantity M OX for the q2DES formed at M/LAO//STO heterostructures as a function of (a) the enthalpy of oxide formation ∆H O f per mol of oxygen and (b) the work function φ M of the metal used as capping layer. Dotted lines serve as a guide to the eye. Partially adapted from [6].

Figure 2 . 46 .

 246 Figure 2.46. Schematic energy band diagram for (a) Co/LAO(1-2uc)//STO and (b) Ta/LAO(1-2uc)//STO before (grey lines) and after (black lines) band alignment between the metal and the LAO//STO heterostructure. Due to the initial difference between the position of E M F and E ST O F

Figure 2 .

 2 Figure2.47. Ti 2p core-level spectra collected for an LAO(1uc)//STO (black curve) and Ta(3Å)/LAO(1uc)//STO sample (colored curve). The Ti 3+ feature observed in-situ and appearing after Ta deposition is suppressed when the sample is taken out of the chamber for a few minutes and then re-measured, signaling oxygen refilling by simple exposure to air.

Figure 2 .

 2 Figure 2.48. (a) Transverse (Hall) resistance R xy , (b) MR, and (c) normalized sheet resistance R s as a function temperature T for Pt(3nm)/LAO(x)//STO samples, with x = 2, 5, 7, 9, and 10 uc. (d) Schematic energy band diagram of Pt/LAO(5uc)//STO before (grey lines)and after (black lines) Pt/LAO interface formation, where E SC represents the space charge electric field generated by the electron transfer towards the Pt layer. Adapted from[START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

  Very recently, several other works regarding the use of capping layers to create/manipulate the properties of the 2DEG in STO have surfaced. Among them, Zhou et al. used thin metallic capping layers of Al, Ti, Co, Au and Pt to tuned the carrier density at the LAO//STO interface [265]; Posadas et al. studied through spectroscopy methods the 2DEG formed in M//STO heterostructures, where M = Ti, Al, Nb, Pt, Eu and Sr [266]; Kormondy et al.

1

 1 Searching for 2D systems with large Rashba coefficients

Figure 3 . 1 .

 31 Figure 3.1. Transport properties of semiconductor quantum wells (QW). (a) Calculated band diagram, electron distribution (dotted line) and (b) Schubnikov-de Haas oscillations as a function of gate voltage V g for a QW in In 0.53 Ga 0.47 As/In 0.52 Al 0.48 As heterostructures. Adapted from [276]. (c) Magnetoresistance for QW in InAlAs/InGaAs/InAlAs with different impurity concentrations, showing a transition between weak localization and weak antilocalization transport regimes. (d) Gate voltage dependence of the Rashba coefficient α (and spin splitting ∆ 0 , in the inset) as a function of the impurity concentration. Adapted from [272].

Figure 3 . 2 .

 32 Figure 3.2. Experimental observations of Rashba-split bands at the metallic surfaces of (a) Au(111) [284], (b) Ag(111) [282], (c) Cu(111) [283], and (d) Bi/Ag(111) [285].

111 ) 112 9Figure 3 . 3 .

 11111233 Figure 3.3. Spin-to-charge current conversion in all-metallic Ag/Bi Rashba interface. (a)Schematic of the NiFe/Ag/Bi heterostructure. By applying a radio frequency (rf) field along y and a dc magnetic field H along x (aligning the magnetization M in this direction), a spin current J s is generated in -z towards the Rashba interface. There, it gets converted in a charge current J c (along -y), which is detected by two voltage V probes. (b) Spin pumping results for two reference samples, NiFe/Ag and NiFe/Bi, and the Rashba system NiFe/Ag/Bi. The top panels represent the ferromagnetic resonance spectra. At resonance, the injected spin current drives a current peak I, which is presented in the bottom panels. Modified from[START_REF] Rojas-Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF].

  1.9), the band structure of topological surface states are characterized by a single helical Dirac cone connecting the bulk valence and conduction bands, as represented in Fig.3.4a and shown through ARPES in Fig.3.4b. Depending on the properties of the material, the spin texture helicity takes a positive/negative value, with a sign change when crossing the Dirac point. The spin configuration of the Fermi contour may therefore be manipulated by shifting the E F above or below this point, allowing a certain degree of tunability.

Figure 3 . 4 .

 34 Figure 3.4. Topological insulators and their use for spin-to-charge current interconversion. (a) Schematic spin-polarized band structure at the surface of a topological insulator. One of two types of spin-momentum locked Fermi contours (with opposite spin chiralities) can be obtained above or below the Dirac point. (b) ARPES measurements of the band structure at the surface of topological insulator Bi 2-x Ca x Se 3 . Adapted from [298]. (c) Illustration of charge-to-spin current conversion in a topological insulator, in the framework of the direct Edelstein effect (DEE). See Section 1.6.3.1 for more details. (d) Charge-to-spin current conversion detection through spin-torque ferromagnetic resonance, in a NiFe/Cu/(Bi 1-x Sb x ) 2 Te 3 heterostructure.The plot shows the conversion efficiency q ICS (equivalent to what we previously called q DEE ) as a function of the Sb doping level, which modulates the position of the E F above/below the Dirac point. Adapted from[START_REF] Soumyanarayanan | Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces[END_REF][START_REF] Kondou | Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators[END_REF]. (e) Spin-to-charge current conversion in Fe/Ag/α-Sn heterostructures. The plot shows the detected charge current (at FMR resonance). Note that when Fe is in direct contact with α-Sn, the topological surface states are destroyed, suppressing any spin-to-charge current conversion effects. Adapted from[START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF].

Figure 3 . 5 .

 35 Figure 3.5. Spin-to-charge interconversion in oxide-based 2DEGs. (a) Schematic of the experimental demonstration of spin-to-charge current conversion in LAO//STO heterostructures.Applying an rf field h rf along x and a dc magnetic field H along y (aligning the magnetization M in this direction), a spin current J s is generated in -z towards the Rashba 2DEG. There, it gets converted in a charge current J c (along x), which is detected by two voltage V probes. A back-gate voltage contact V g allows modulation of the electrostatic and Rashba properties of the 2DEG. (b) Spin-to-charge conversion efficiency λ IEE as a function of the V g . A maximum of 6.4 nm obtained at V g = 125 V is attributed the region in the band structure were light and heavy bands cross each other (inset). Modified from[START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]. (c) Charge-to-spin current conversion in LAO//STO, detected through ST-FMR. An rf current I r f sourced in the Rashba 2DEG along x is converted in a spin current along z, which drives changes in the magnetization dynamics of the CoFeB layer. (d) ST-FMR signal collected at room temperature and corresponding symmetric and antisymmetric components (see next sections). Adapted from[START_REF] Wang | Room-Temperature Giant Charge-to-Spin Conversion at the SrTiO 3 /LaAlO 3 Oxide Interface[END_REF]. (e) Non-local 2D spin Hall effect in LAO//STO interfaces. A charge current j c source between contacts I S and I D is converted in a spin current j s (polarized out-of-plane), that propagates to the second Hall-bar branch, where it gets reconverted in a charge current. (f ) Hanle experiments, where an applied in-plane magnetic field B destroys the spin polarization of the converted spin current, leading to the detection of a smaller V . The spin diffusion length of the 2DEG can be derived by altering the length of the channel L. For larger lengths, the spin current is eventually lost (inset). Adapted from[START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF].

Figure 3 . 6 .

 36 Figure 3.6. Scattering times and Rashba coefficients for various 2D systems. The diagonal colored lines represent the expected spin-to-charge current conversion efficiency λ IEE . Adapted from [309].

Figure 3 . 7 .

 37 Figure 3.7. Basics of FMR. (a) While increasing an applied magnetic field H, the Zeeman splitting of two energy eigenstates is increased. If the resonance condition is established, a radio frequency field with energy ω 0 can induce transitions between them. (b) At resonance, a peak is observed for the imaginary part of the dynamic magnetic susceptibility χ displaying a Lorentzian lineshape. (c) The field-derivative of χ translates in what is normally called the FMR signal, ultimately indicating energy absorption by the ferromagnetic layer. Modified from[START_REF]Ferromagnetic Resonance -Theory and Applications[END_REF]. (d) Illustration of the magnetization relaxation process after the rf field in turned off. Notice how a damping-like effect aligns m with H ef f . Adapted from[START_REF] Czeschka | Spin Currents in Metallic Nanostructures[END_REF].

Figure 3 . 8 .

 38 Figure 3.8. Schematic of a FMR-operated spin battery. At resonance, the applied magnetic field H ef f and rf microwave h rf maintain a precessional motion (with angle Θ) of the magnetization m in the ferromagnet (FM). A spin current I pump s

Figure 3 . 9 .

 39 Figure 3.9. (a) Schematic of the experimental cavity setup used for FMR-driven spin pumping. The electromagnets on both sides produce a dc magnetic field H dc . The sample is glued to a holder (shown in blue) which allows the connection of three electrical contacts (usually two for voltage detection and one for gate voltage). Adapted from [40]. (b) Schematic setup of FMR-driven spin-to-charge current conversion experiments in FM/LAO//STO heterostructures. Geometrical considerations given in Fig. 3.5a.

Figure 3 . 10 .

 310 Figure 3.10. Spin rectification effects. (a) Illustration of the rf lines within the loop gap cavity ideally aligned with the sample. (b) In a realistic case, a small misalignment generates a rf current j rf driving additional voltage components to the overall signal. (c) The total voltage signal extracted from spin pumping experiments is, in the geometry previously described, composed of contributions arising from the inverse Edelstein effect (IEE), spin Seebeck effect (SSE), anisotropic magnetoresistance (AMR), planar Hall effect (PHE) and anomalous Hall effect (AHE). While the symmetric voltage component contains all of them, the last three can be specifically identified through the antisymmetric component. Modified from [318].

Figure 3 . 11 .

 311 Figure 3.11. Characterization of NiFe/LAO//STO heterostructures. (a) RHEED oscillations during the growth of 2 uc of LAO on a STO(001) substrate. The inset shows the diffraction patterns before (left) and after (right) the film's growth. (b) AFM image of the NiFe/LAO//STO surface. The step-and-terrace topography is confirmed in the bottom plot. (c) Scanning TEM cross-section. Modified from [303].

Figure 3 . 12 .

 312 Figure 3.12. Electrical transport properties of NiFe/LAO(2uc)//STO samples. (a) Temperature dependence of the sheet resistance R s of the NiFe/LAO//STO sample (blue curve), a reference NiFe//STO (beige curve) and the extracted isolated contribution of the q2DEG (light blue curve). For comparison, the standard behavior of an uncapped LAO(5uc)//STO is shown in the inset. (b) Longitudinal magnetotransport and (c) Hall effect at T = 2 K for a NiFe/LAO(2uc//STO sample (blue curve), a reference NiFe//STO (beige curve) and the extracted q2DEG contribution (light blue curve). Both q2DEG curves are simultaneously fitted with a 2-band model (red curve) introduced in Eq. 2.12. Modified from [303].

Figure 3 . 13 .

 313 Figure 3.13. Ferromagnetic resonance in NiFe/LAO//STO. (a) FMR signal collected at room temperature for microwave frequencies ranging from 4 to 24 GHz (in steps of 2 Ghz).The black liens show the fits using Eq. 3.10. (b) External magnetic field H dependence of the resonance frequency f for a NiFe/LAO//STO and a reference NiFe//LAO sample. The black lines represent the fits using Eq. 3.3 used to extract the effective magnetization M ef f . (c) Resonance frequency f dependence of the peak-to-peak linewidth for the same two samples. The black lines represent the fits (using Eq. 3.4) which allow the extraction of the damping constant α G . Adapted from[START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

  of a NiFe film on LAO(2uc)//STO and on an LAO substrate (reference sample). Here, the enhanced damping, from α N iF e ef f = 6.45 × 10 -3 to α N iF e/2DEG ef f = 7.77 × 10 -3 , hints for the existence of an extra spin relaxation channel given by the 2DEG, even though its resistance is several kΩ at room temperature.

Figure 3 . 14 .

 314 Figure 3.14. Spin-to-charge current conversion in LAO//STO 2DEGs. (a) Schematic of spin pumping experimental configuration. Measurements were performed in loop gap cavity at T = 7 K. More details regarding geometrical considerations in Fig. 3.5a. (b) FMR signal at positive (red) and negative (blue) dc magnetic fields H dc , at T = 7 K and applying a back-gate voltage of V g = 125 V. (c) Detected voltage (normalized to the square of the rf field)for positive (red) and negative (blue) H dc . Each curve is disentangled in a symmetric (dotted line) and antisymmetric (thin line) component using Eq. 3.9. The inset shows similar data collected at room temperature. (d,e,f ) Same as the previous panels but for a reference NiFe//LAO sample. Partially adapted from[START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF].

Figure 3 . 15 .

 315 Figure 3.15. Out-of-plane angular dependence θ H for a NiFe/LAO//STO sample at T = 7 K and under V g = 100 V. (a) Resonance field and numerical fit (red curve) allowing the extraction of M ef f and the effective g-factor g * e .(b) Peak-to-peak linewidth ∆H pp and contributions due to the Gilbert damping ∆H G and perpendicular anisotropy dispersion due to inhomogeneities in the FM layer ∆H θ , extracted from the fit (red curve) described by Eq. 3.5. In the inset, the equilibrium angle of magnetization θ 0M as a function of the angle of the applied magnetic field θ H . (c) Normalized symmetric voltage and fit (red curve) using a numerical function proportional to sin(θ 0M ). Adapted from[START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF] (supplementary).

Figure 3 . 16 .

 316 Figure 3.16. Detected voltage in spin pumping experiments as a function of the applied back-gate voltage V g for (a) reference NiFe//LAO (at T = 7 K) and (b) NiFe/LAO//STO (at room temperature). (c) Normalized detected voltage for NiFe/LAO//STO sample at T = 7 K. Modified from [40].

Figure 3 . 17 .

 317 Figure 3.17. Back-gate voltage dependence of IEE in the LAO//STO q2DEG. (a) Calculated charge current generated from the symmetric voltage peak in spin pumping experiments (see Eq. 3.11) performed at T = 7 K. (b) Same as panel (a) but plotting the peak maxima for both positive (red) and negative (blue) external magnetic field H dc . (c) Estimation of the spin-to-charge current conversion efficiency λ IEE as a function of V g . Modified from [303].

Figure 3 . 18 .

 318 Figure 3.18. Electrostatic doping of the q2DEG in LAO//STO. (a) Schematic of an LAO//STO sample with a metallic back-gate contact. (b,c,d) Illustration of the quantum well for different gate voltages.Starting from an as-grown sample and at V g = 0 V (state I), applying a positive V g fills the quantum well up until electrons start to spill out, i.e. irreversibly escaping from it (state II). Applying a negative V g depletes the quantum well (state III). The process of filling/depletion is considered reversible, as long as the V g applied is below the (previous) maximum V g . (e) Sheet resistance of an LTO//STO sample (comparable to LAO//STO) measured for several positive ∆V G > 0 and negative ∆V G < 0 sweeps. The equivalent regions for states I, II and III (from the previous panels) are also identified. Modified from[START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO 3 (X = Al, Ti)/SrTiO 3[END_REF].

STARTFigure 3 . 19 .

 319 Figure 3.19. Transport properties of NiFe/LAO(2uc//STO samples as a function of the back-gate voltage V g at T = 5 K. (a) Longitudinal resistance R xx as a function of V g . Data in blue and green represent a sweep towards positive and negative direction, respectively. Below V g = 0 V, the transport properties are dominated by the metallic NiFe layer. (b) Magnetoresistance and (c) Hall effect as a function of V g . (d) Extracted isolated q2DEG contribution (red curve) and corresponding 2-band fitting (green curve) for V g = 200 V.

Figure 3 . 20 .

 320 Figure 3.20. Origin of the spin-to-charge current conversion efficiency maximum. (a) Schematic band structure of the 2DEG at the LAO//STO interface. At around 1.68 × 10 13cm -2 (Lifshitz transition[START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]) the heavy d xz,yz bands start to be occupied. Above that, at the region where the heavy and light bands cross each other, large spin-orbit effects are predicted[START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF]. The highlighted area represents the expected gate voltage region swept. (b) In this range, the λ IEE sign change (at V g ∼ 0 V) is attributed to the onset of occupation of heavy bands, which contribute with an opposite sign to the overall "effective" Rashba coefficient. The maximum observed at V g = 125 V is linked to the avoided band crossing region. (c) Calculated band structure including atomic spin-orbit coupling, which induces band splitting at the Γ point. On the right, calculated spin-orbit strength (L.S product) as a function of energy. Modified from[START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO 3 /SrTiO 3 interface[END_REF]. (d) Spin splitting ∆ and k-cubic Rashba coefficient α 3 as a function of the 2DEG carrier density. A maximum is found for n 3 × 10 13 cm -2 (slighly above the expected Lifshitz transition) matching the avoided band crossings region. Modified from[START_REF] Liang | Nonmonotonically tunable Rashba spin-orbit coupling by multiple-band filling control in SrTiO 3 -based interfacial d-electron gases[END_REF].

Figure 3 . 21 .Figure 3 . 22 .

 321322 Figure 3.21. Influence of the LAO thickness in the properties of NiFe/LAO//STO heterostructures. (a) Normalized (to R at 300 K) resistance as a function of temperature for an LAO thickness of 0, 1 and 2 uc. (b) Hall effect and (c) magnetoresistance experiments. (d) Schematic of spin-to-charge current conversion experiments on a NiFe//STO sample (additional considerations in Fig. 3.5a). (e) Normalized (detected) voltage from spin pumping experiments as a function of the back-gate voltage V g at T = 7 K.

Figure 3 . 23 .

 323 Figure 3.23. In situ XPS study of a NiFe(6Å) layer deposited on STO(001). (a) Ni 2p core level spectra for a fully metallic NiFe reference sample (left panel), for NiFe//STO (middle panel) and for an oxidized NiFe reference sample (right panel). (b) Same as (a) but for the Fe 2p core level spectra.

Figure 3 . 24 .

 324 Figure3.24. Schematic of the expected interactions at the NiFe//STO interface. Due to the higher concentration of Ni in comparison with Fe (80% and 20%, respectively), and the strong tendency for Fe to oxidize, conducting puddles may be induced at the surface of STO. When spin pumping is performed in NiFe//STO heterostructres, conversion may occur locally on these puddles, which generates a charge current that flows through the NiFe layer and is detected by the two voltage probes. From an electrical transport perspective, the inhomogeneous 2DEG cannot be detected.

Figure 3 .

 3 Figure 3.25. In situ XPS study of metal//STO heterostructures. (a) Ti 2p core level spectra of a Ta(3Å)//STO sample, before (black) and after (red) Ta deposition. The grey and orange curves represent data collected at a take-off angle of 50°. The Ti 4+ and Ti 3+ components are indicated for both spin-split Ti 2p peaks. (b) Ta 4f core level spectra for a Ta(3Å)//STO sample. The spectra resembles the one collected in Fig.2.38 for Ta(3Å)/LAO//STO heterostructures, where the Ta layer was found to be fully oxidized[START_REF] Vaz | Tuning Up or Down the Critical Thickness in LaAlO 3 /SrTiO 3 through In Situ Deposition of Metal Overlayers[END_REF]. (c) Same as panel (a) but for an Al(3Å)//STO sample. (d) Al 2p core level spectra for a Al(3Å)//STO sample. Due to severe charging effects and ambiguity regarding the nature of the Al peak observed (metallic or fully oxidized), the magnitude of the binding energy shift for Sr 4s and Sr 4p peaks is investigates (see inset). Shifting the Al peak by the same amount (∼ -12 eV), we find its effective binding energy to be 74.5 eV, which correspods to the position attributed for oxidized Al[START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF].

Figure 3 .

 3 Figure 3.26. (a,d,g,j) Sheet resistance R s as a function of temperature, (b,e,h,k) longitudinal sheet resistance R xx and(c,f,i,l) transverse resistance R xy (Hall effect) as a function of applied out-of-plane magnetic field H for AlOx/NiFe/M//STO samples, where M = Al(0.3nm), Al(0.9nm), Ta(0.3nm) and Ta(0.9nm). On the middle and right panels, the transport properties for the total stack (black), the metallic reference (red), the extracted isolated q2DEG contribution (blue) and the simultaneous 2-band fitting (green) are shown, following the procedure described in Section 2.5.2.1.

1 )Figure 3 . 27 .

 1327 Figure 3.26. (a,d,g,j) Sheet resistance R s as a function of temperature, (b,e,h,k) longitudinal sheet resistance R xx and(c,f,i,l) transverse resistance R xy (Hall effect) as a function of applied out-of-plane magnetic field H for AlOx/NiFe/M//STO samples, where M = Al(0.3nm), Al(0.9nm), Ta(0.3nm) and Ta(0.9nm). On the middle and right panels, the transport properties for the total stack (black), the metallic reference (red), the extracted isolated q2DEG contribution (blue) and the simultaneous 2-band fitting (green) are shown, following the procedure described in Section 2.5.2.1.

Figure 3 . 28 .

 328 Figure 3.28. Schematic of spin-to-charge current conversion experiments on NiFe/Ta//STO and NiFe/Al//STO heterostructures. The thickness of the metallic insertion used was either 0.3 or 0.9 nm. Additional geometrical considerations in Fig. 3.5a.

3. 28 .Figure 3 . 29 .

 28329 Figure 3.29. Normalized voltage and currents detected at T = 7 K from spin-to-charge current conversion experiments in AlOx/NiFe/Ta(x)//STO heterostructures, where x = 0.3 nm (top panels) and 0.9 nm (bottom panels), as a function of the back-gate voltage V g . On the left, the raw voltage peaks (dashed lines) and symmetric (thick lines)/antisymmetric (thin lines) at FMR resonance are shown for a positive applied dc magnetic field H dc . On the right, the peak charge current produced as a function of V g for positive H dc (red circles). Additionally, the antisymmetric part (light grey circles) is shown. Even though this contribution comes from the NiFe (which is practically not affected by V g ), its change can be possibly related with the changes in the rf field lines due to the large modulation of the dielectric constant in STO with applied V g , which destabilizes the cavity.

Figure 3 . 30 .

 330 Figure 3.30. Normalized voltage and currents detected at T = 7 K from spin-to-charge current conversion experiments in AlOx/NiFe/Al(x)//STO heterostructures, where x = 0.3 nm (top panels) and 0.9 nm (bottom panels), as a function of the back-gate voltage V g . Similar to Fig. 3.29.

3. 4 . 3 3 3. 4 . 3 . 1

 433431 Giant inverse Edelstein effect in NiFe/Al//SrTiO Chemical and structural characterization We started by annealing a TiO 2 -terminated STO substrate at 730 • C under a rich oxygen pressure, to clean the surface and remove any existing oxygen vacancies. Then, we transfer the prepared STO in-vacuo to the sputtering chamber, where we deposit a 0.9±0.1 nm of

Figure 3 . 31 .

 331 Figure 3.31. XPS characterization of Al(9Å)//STO heterostructures. (a) Ti 2p core level spectra for an STO substrate before (black) and after (dark red) deposition of 9 Å of Al. As shown in yellow, the spectra is fitted with three components, Ti 4+ , Ti 3+ and Ti 2+ , using the relative areas and peak distance constrains from XPS bibliography[START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF]. In the inset, the Al 2p core level spectra revealing a metallic (25%) and oxidized (75%) Al components within the capping layer. (b) Ratio between the sum of the peak areas from Ti 3+ and Ti 2+ and the peak area from Ti 4+ for different take-off angles. The error bars come from the fitting process in the software CasaXPS, using a Monte Carlo procedure[START_REF]Uncertainty Estimates in XPS[END_REF]. The green dashed line represents the best fit using the model from Sing. et al[START_REF] Sing | Profiling the Interface Electron Gas of LaAlO 3 /SrTiO 3 Heterostructures with Hard X-Ray Photoelectron Spectroscopy[END_REF], shown in Eq. 3.17. The experimental Ti 2p core level spectra as a function of the take-off angle are shown in the inset.

Figure 3 . 32 .

 332 Figure 3.32. Scanning transmission electron microscopy (STEM) experiments of NiFe/Al(0.9nm)//STO samples. (a) High-angle annular dark field (HAADF) analysis and (b) a zoomed area at the interface. (c-f ) Elemental dispersive X-ray spectroscopy (EDX) analysis for Ti, Sr, Al and O, respectively. The dashed white line represents the Al//STO interface position.

163

 163

Figure 3 . 33 .

 333 Figure 3.33. Electrical characterization of NiFe(2.5nm)/Al(0.9nm)//STO samples. (a) Temperature dependence of the sheet resistance R s of a NiFe/Al//STO sample (black) and a NiFe//STO reference sample (brown). The extracted contribution from the q2DEG is shown in red. (b) Extracted Hall traces for the q2DEG at T = 7 K for various back-gate voltages.(c) Carrier densities n derived from fitting the extracted Hall traces with a linear model (from -175 V to 0 V, n linear ) or with a two-band model (from 25 V to 175 V, where n LM and n HM stand for the density of low-mobility and high-mobility carriers, respectively). n total is estimated from the gate voltage dependence of capacitance measurements.

  3.34a we display a sketch of the spin-to-charge current conversion experiments performed on NiFe/Al(0.9nm)//STO samples. Similarly to the previously studied NiFe/LAO//STO case, we use a FM layer to pump a spin current through the Al 2 O 3 barrier towards the q2DEG, where it gets converted into a charge current. Out-of-plane (OOP) angular dependence of the IEE ans FMR are performed, as shown in Fig.3.34b, with which we confirm the nature of the detected voltage to arise from the IEE (top panel -see a comparison to the angle dependence of a single NiFe layer in Ref.[START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF]), extract the perpendicular dispersion anisotropy ∆θ = 0.2°, the damping constant α G = 0.0066, effective saturation magnetization M ef f = 833 kA.m -1 and the effective g-factor g * e = 2.077. See Section 3.3.2 for a more detailed description. Once again, the main advantage of performing OOP experiments is the extraction of a more accurate α g (through initial extraction of g * e ) and the particular experimental advantage to perform them at low temperatures and under gate voltage (in this case T = 7 K and V g = -170 V).

Figure 3 . 34 .

 334 Figure 3.34. Spin-to-charge conversion in NiFe/Al(0.9nm)//STO samples. (a) Schematic of the spin-to-charge current conversion experiments. (b) Top panel: angular out-of-plane dependence of the amplitude of the symmetric component of the detected voltage, normalized by the square of the applied rf field. Center panel: out-of-plane angular dependence of the ferromagnetic resonance peak-to-peak linewidth ∆H pp . The fit, which takes into account the magnetic inhomogeneities of the FM layer, allows the extraction of the damping α G and the perpendicular dispersion anisotropy ∆θ. Bottom panel: out-of-plane angular dependence of the ferromagnetic resonance field H res . The fit allows extracting the effective magnetization M ef f and the effective g-factor g * e .More details on the fitting procedures in Section 3.2.1. (c) FMR curves (top) and detected voltages at FMR resonance (bottom) at different gate voltages V g , for a positive (red) and negative (blue) applied dc magnetic field H dc . The symmetric V sym and antisymmetric V asym components of the raw voltage V raw are represented using continuous thick and thin lines, respectively. (d) Spin-to-charge current conversion efficiency λ IEE as function of V g at T = 7 K.

Figure 3 . 35 .

 335 Figure 3.35. Reproducibility of the spin-to-charge current conversion experiments. The dark grey and yellow curves represent measurements performed six months apart on different samples (of the same batch).

3. 4 . 3 . 4 Figure 3 . 36 .

 434336 Figure 3.36. Electronic band structure of a q2DEG with approximately the same carrier density as the (as-grown) NiFe/Al//STO sample studied. (a) Experimental Fermi surface of the q2DEG. (b) Band dispersion along the (100) direction [purple dotted line in (a)], with overlaid bands calculated by a 8-band tight-binding model. (c) Same along the (110) direction [yellow dotted line in (a)] and (d) along ∆ direction [green line in (a)]. (e) Calculated band structure along ∆, where band inversion is observed (adapted from [332]).

Figure 3 .

 3 Figure 3.37. (a) Calculated Edelstein tensor xy as a function of energy for a 8-band model. The contributions from each pair of Rashba-split bands is displayed in different colors. The red curve shows the sum of all the contributions. (b-f ) Contribution of the k points at a given energy to xy . Positive and negative contributions are represented in blue and red, respectively. The Fermi contours are not to scale. See for example in panel (b) that the contributions over the whole Fermi contours (mostly) cancel each other out. In panel (f), the zoom shows band inversion occurring at the intersection between both heavy d xz , d yz and light d xy bands, giving rise to a region in the band structure with band inversion and topological non-trivial properties [332].

Figure 3 .Figure 3 . 39 .

 3339 Figure 3.38. (a,b) k-dependent spin-polarization around the topological avoided crossings (-14 meV), between bands 3, 4, 5 and 6. The arrows represent the spin polarization (completely in-plane) while the color code represents its absolute value. Note for example how band 3 shows a pronounced spin polarization, while band 4 (its Rashba counterpart) is weakly spin polarized, hence the large spin uncompensation driving the Edelstein effect to larger values.(c,d) Same as the previous panels, but at an energy of -34 meV. Notice that although bands 3 and 4 intersect each other, the spin polarization is completely compensated.

, Fert andFigure 4 . 1 .

 Fert41 Figure 4.1. Origin of the anisotropic magnetoresistance in ferromagnets. (a) Schematic of the density of states for s-and d-bands of ferromagnetic Ni. The electron occupation in the spin-up and spin-down bands is also shown. The arrows represent possible scattering events. Without spin-orbit coupling, no available states are present in the spin-up d-bands. Adapted from [338]. (b) Mott's two current model in the absence of spin-orbit coupling, considering s-s and s ↓ -d ↓ scattering events. (c) Fert and Campbell's model in the presence of spin-orbit coupling. Since s-d spin-flip transitions are now allowed, an additional resistivity term in the spin-up channel contributes to the overall conductivity. (d) 3d orbitals illustrating (some)possible scattering events dependending on the magnetization direction M and an applied current J . Adapted from[START_REF] O'handley | Modern Magnetic Materials: Principles and Applications[END_REF].

Figure 4 . 2 .

 42 Figure 4.2.Experimental observation of anisotropic magnetoresistance in a ferromagnetic NiFe layer with 3 nm at room temperature. The magnetic field is applied and rotated in-plane. Two resistance states are observed depending on the relative orientation between the current applied and the magnetic field direction.

Figure 4 . 3 .Figure 4 . 4 .Figure 4 . 5 .

 434445 Figure 4.3. Intrinsic origin of the AMR in Rashba 2DEGs. (a) Schematic of a 2DEG where a charge current J x and a magnetization M are parallel to the x-axis. (b) Calculated Fermi contour when M is parallel to J x , leading to a band crossing in k y . Adapted from [344].

Figure 4 . 6 .

 46 Figure 4.6. Schematic model for UMR in a Rashba 2DEG. The application of a fixed current j c along the x or -x axis, relates to a Rashba field H R (assuming that an out-of-plane confining electric field E z is present in the 2DEG) oriented in-plane along the y and -y axis, respectively.While rotating an in-plane external magnetic field H ext , the effective magnetic field H ef f seen by the 2DEG is different when the angle between j c and H ext is either 90°or 270°. This discrepancy leads to a unidirectional term in these specific orientations.

4 .

 4 7d) increasing for larger I, as well as for (negative) back-gate voltages (Fig.4.7e).

Figure 4 . 7 .

 47 Figure 4.7. Experimental observations of UMR in Rashba 2DEGs. (a,b)The different effective magnetic field H EF F acting on the LAO//STO 2DEG whether the applied magnetic field H A and the Rashba field H R are parallel or antiparallel, leads to a resistance asymmetry between θ = 0°and θ = 180°. Note that at 0°, H A and the applied current I are perpendicular. In panel (b), this asymmetry is reversed when inverting the polarity of I, consequently inverting the direction of H R . Modified from[START_REF] Narayanapillai | Current-driven spin orbit field in LaAlO 3 /SrTiO 3 heterostructures[END_REF]. (c) Similar experiments in Rashba InAs quantum wells. The unidirectional asymmetry of the resistance is observed to increase with (d) increasing current and with (e) larger (negative) gate voltages. Modified from[START_REF] Choi | Spin-polarization-induced anisotropic magnetoresistance in a twodimensional Rashba system[END_REF].

Figure 4 . 8 .

 48 Figure 4.8. Electrical characterization of patterned Hall bars in LAO(5uc)//STO heterostructures. (a) Optical microscopy image of the three Hall-bars. As indicated, the orange area is crystalline LAO(5uc) and the brown area amorphous-LAO [both on STO(001)]. (b) Longitudinal sheet resistance R s as a function of temperature T and (c) transverse resistance R xy as a function of an out-of-plane magnetic field H (Hall effect). The thin red line represent the 2-band fitting, which results in a sheet carrier density n s = 2.09 × 10 13 cm -2 .

Figure 4 . 9 .Figure 4 .

 494 Figure 4.9. (a-f ) AMR experiments on a LAO(5uc)//STO Hall-bar at T = 2 K. Each plot shows the longitudinal resistance R xx as a function of the angle θ between the applied current I c and an in-plane magnetic field H, for H ranging between 0 T and 9 T and a fixed I c = 50 µA. The black and red curves represent the data collected with I c and -I c , respectively. (g) Schematic of the Hall-bar and the respective electrical contacts.

Figure 4 .

 4 Figure 4.11. (a) Normalized unidirectional component R uni of the AMR as a function of the applied current I c at T = 2 K and with a rotating H = 3 T. (b) Evolution of the unidirectional amplitude with I c . The equivalent current density j c (for a channel width of 40 µm and an (arbitrary) q2DEG thickness of 10 nm) is shown in the upper x axis. The data be fitted with a linear function (dotted line).

  4.12c and 4.12d, the unidirectional component scales linearly with the current and magnetic field, similarly to what we saw at the Rashba LAO//STO interface. In their work, Pan He et al. link this unidirectional component to spin-momentum locked topological surface states with hexagonal warping (i.e. finite out-of-plane spin textures). By solving the Boltzmann equation for a spin-momentum locked Hamiltonian model they obtained an analytic expression for R 2ω , which indeed is found to scale linearly with both the electric field

3 Figure 4 . 12 .

 3412 Figure 4.12. AMR and UMR in the topological insulator Bi 2 Se 3 . (a) Schematic of the experimental geometry. (b) First (R ω ) and second (R 2ω ) harmonic resistances, equivalent to the dc AMR and unidirectional components (respectively), shown in Fig. 4.10a and 4.10c. Linear evolution of R 2ω with (c) applied current I and (d) applied in-plane magnetic field H.Adapted from[START_REF] He | Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states[END_REF].

Figure 4 . 14 .

 414 Figure 4.14. Unidirectional spin Hall magnetoresistance (USMR) in Co/Pt and Co/Ta bilayers. (a,b) Schematic of the USMR effect. By sourcing a current j in the bilayer, a spin current is generated through the SHE. A different resistance state is obtained depending on the relative orientation (parallel or antiparallel) between the spin polarization σ at the interface and the magnetization M of Co. Experimental measurement of R ω and R 2ω for (c) Ta/Co and (d) Pt/Co bilayer for H scans in different planes. Focusing on the blue squares (in-plane rotation), the R 2ω curve is reversed, concomitant with the different sign of the spin Hall angle for Ta and Pt, hence switching the polarization direction of interfacial (converted) spins. Adapted from [337].

Figure 4 .

 4 Figure 4.15. Schematic of the USMR theoretical model for high spin-orbit coupling metal (HM)/ferromagnet (FM) bilayers[START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF]. (a) For an external electric field E ext applied in the HM (along the x axis), the spin Hall effect drives a spin accumulation with polarization σ aligned with the -y axis. Close to the interface, the spin accumulation µ s created can be viewed as an artificial FM layer within the original FM layer. A change in longitudinal resistance arises from the spin dependence of the mobility in the FM layer, similar to the concept of current-in-plane GMR[START_REF] Fert | Historical Overview: From Electron Transport in Magnetic Materials to Spintronics[END_REF]. (b) When E ext is instead applied along -x axis, the µ s in the FM has the same orientation as its initial magnetization M , leading to small modulation of the longitudinal resistance. Adapted from[START_REF] Zhang | Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers[END_REF].

Figure 4 .

 4 Figure 4.16. (a,b) Schematic of the two resistance states unlocked by USRMR in CoFeB/topological insulator bilayers. (c) Illustration of the experiment and (d) second harmonic longitudinal resistance R 2ω as a function of a rotating in-plane magnetic field (in different planes). (e) Extraction of the USRMR R U SRM R and thermoelectric-driven R ∆T 2ω

4. 6 . 1

 61 Conceptual model for unidirectional Edelstein MR in FM/TI or FM/2DEG interfaces In this last section, we review the origin of USMR, and introduce a tentative conceptual model for a unidirectional Edelstein magnetoresistance (UEMR), which can be viewed as a USMR effect with an added constraint imposed by the spin-momentum locked Fermi contours.

4 .

 4 17d. The phenomena stemming from M parallel or antiparallel to σ leads to two different resistance states, as exemplified in Fig.4.17e. Summarizing, while in the parallel case the charge current injected is practically unaffected as it flows along the FM/NM bilayer, in the antiparallel case an increased resistance originates from additional spin-dependent scattering

Figure 4 . 17 .

 417 Figure 4.17. Conceptual model for USMR in ferromagnetic (FM)/normal metal (NM) bilayers (inspired by [363]. (a) Definition of spin current: flow of spins with opposite polarization σ in opposite directions without net charge currents involved. (b) In the presence of spin Hall effect in the NM, when the magnetization M is antiparallel to the spin polarization σ at the interface, an artificial FM layer (blue area) is formed in the FM. (c) The transfer of spins to the FM leads to an opposite spin transfer (with opposite σ) towards the NM, where, through inverse spin Hall effect, it is re-converted in a charge current j c that opposes the initially applied j c . (d) When M is parallel to σ, no artificial FM layer is formed. (e) The cases described in (b,c) and (d), lead to two resistance states. For the antiparallel case, additional resistance is introduced in the FM due to an additional spin dependent scattering channel (the artificial FM layer); in the NM due a ISHE-induced reconverted charge current j c which opposes the initial j c . In the parallel case the resistances of both FM and NM are unaltered.

4. 6 . 2

 62 Searching for UEMR in FM/LAO//STO heterostructuresIn this last section, we show preliminary results regarding the search of UEMR in FM/LAO//STO.Similarly to the experiments showed in Section 3.3 for the demonstration of inverse Edelstein effect (IEE), we use 1 mm × 4 mm slabs composed of NiFe(2.5nm)/LAO(2uc)//STO. We bond several39 contacts at the two top edges of the sample, used to apply a charge current, and two contacts at the center of the sample to detect the voltage. The geometry of the experiments,

µA 40

 40 and a rotating magnetic field with fixed intensity. The results are shown in Figs. 4.19bj, where the black and red curves represent the measured longitudinal R for positive and negative current, respectively. Here, a parallel can be made with Fig. 4.8, regarding the AMR experiments in LAO//STO heterostructures (without a FM). We start by observing a rather constant AMR amplitude up until H = 0.1 T, coming solely from the NiFe layer (classic AMR

Figure 4 . 19 . 2 Figure 4 .

 41924 Figure 4.19. AMR experiments in NiFe/LAO(2uc)//STO heterostructures. (a) Geometry of the experiments. The grey rectangle represent the sample (slab) with dimensions 1 mm × 4 mm. (b-j) Longitudinal resistance R xx as a function of the angle θ between the external in-plane magnetic field H ext and j c , at T = 2 K and with a I c = 500 µA. The magnitude of H ext ranged between 0.01 T and 9 T. The black and red curves represent the data collected for I c and -I c , respectively.

Figure 4 .

 4 Figure 4.21. (a,b) Normalized unidirectional component R uni of the AMR as a function of the magnetic field H ext at T = 2 K and I c = 500 µA. (c) Evolution of the unidirectional amplitude with H ext . The vertical dotted line delimitates the region where additional AMR features start to be observed. In the inset, a zoom of the low H ext region, where the unidirectional component disappears when NiFe dominates the parallel conduction. Note that NiFe has a "regular" ferromagnetic AMR with no unidirectional component.

Figure 4 . 22 .

 422 Figure 4.22. Temperature dependence of (a) the AMR and (b) the UMR signal in NiFe/LAO(2uc)//STO samples, for a fixed (magnitude) H = 1 T and I c = 500 µA.

  2.25b. We observe a first peak at low K.E. due to Auger electrons, and a larger peak accounting for electrons ejected form O 1s levels. At higher K.E., Si peaks are present, coming from the silicon wafer bearing a surface oxide, as well as photoelectrons from outer O 2s levels, which are the "easiest" to eject and therefore show the highest K.E.. Although K.E. is the quantity recorded during the measurement, the energy spectrum is normally constructed with the binding energy (B.E.), simply because the K.E. depends on the X-ray source, and the B.E. solely on the electronic properties of the sample. The K.E. and B.E. values are related by the Einstein's relation[START_REF] Einstein | Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen[END_REF]:

Table 1 :

 1 Extracted total sheet carrier densities n total s = n 1 + n 2 and mobilities µ 1 and µ 2 for the q2DEG formed in metal-capped LAO//STO samples. Values were obtained from the simultaneous 2-band model fitting of the Hall and MR curves in Fig.2.36.

	1 )

Table 3 :

 3 Extracted total sheet carrier densities n total s

	-1 )

  3.37b-f the Fermi contours at different energies, so that we are able to better understand the interactions between bands.For low energies (-120 meV) only the lowest d xy bands (1 + 2) are occupied. Here, the Rashba splitting gives rise to the simplest textbook case of an inner and outer Fermi contours (see Section 1.6.3.1). Due to the rather small Rashba coefficient in STO, hence small splitting, most of the Edelstein effect arising from one contour is canceled by the other contour, so

that the total xy is close to zero (zone I). At -106 meV, the second d xy pair of bands

(3 + 4)

starts to be occupied, which exhibit similar Rashba splitting with the same sign as the previous pair (1 + 2), so that the total signal increases slightly (zone II). At -62 meV we reach the band edge of the heavy d xz/yz bands (5 + 6). As discussed by other authors,

[START_REF] Shanavas | Electric Field Tuning of the Rashba Effect in the Polar Perovskite Structures[END_REF][START_REF] Seibold | Theory of the Spin Galvanic Effect at Oxide Interfaces[END_REF]

,

  d xz + d yz ) cross each other, triggering regions where band inversion with topological character is predicted [332]. 5. The additional maxima observed in the Al//STO sample (as a function of gate voltage)

	Rashba Ag/Bi bilayers (0.3 nm [294]) and at the surface of topological insulators (∼ 2
	nm [104, 302]);
	2. λ IEE can be efficiently tuned between +30 nm and -30 nm using back-gate voltage in
	the range of ± 200 V (for an STO substrate with a thickness of 0.5 mm);
	3. In the LAO//STO case we attribute the large conversion maxima (as a function of gate
	voltage) to avoided band crossings in the (100) direction, where light d xy and heavy
	d xz,yz bands cross each other [303];
	4. In the Al//STO case, ARPES experiments and a theoretical model indicate that the
	conversion maxima are observed in similar avoided crossing in the (100) direction, as
	well as in special points in the ∆ direction [parallel to (110)] where the 3 bands (d xy

this chapter, we reviewed the spin-to-charge current interconversion experiments reported in Rashba systems, such as semiconductor quantum wells and oxide-based 2DEGS, as well as in topological insulators. An introduction on the physics of ferromagnetic resonance and spin pumping was shown, which sets the foundation for the spin-to-charge current conversion experiments performed in NiFe/LAO//STO and NiFe/M//STO heterostructures, where M = Ta and Al. The main conclusions are:

1. A conversion efficiency λ IEE of 6.4 nm and ∼ 30 nm is detected at low temperatures (T = 7 K) at the q2DEG formed in LAO//STO and Al//STO structures, respectively. These values are at least one order of magnitude larger than previously achieved in all-metallic +

  First, we observe that the antisymmetric voltage component of the detected signal varies with gate voltage, sometimes becoming even larger than the symmetric part. This result is rather counterintuitive, since rectification effects (that give rise to the antisymmetric part) are expected to originate mainly from the ferromagnetic layer, which should, in principle, be practically unaffected by the gate voltage. We suspect however that the modulation observed may stem from the large dielectric constant of STO and its strong tunability with gate voltage. Depending on the dielectric constant, the rf field lines are more or less absorbed by the STO, which generally translates in unknown perturbations within the cavity for each voltage value. A possible way to disentangle this contribution, is to perform similar spin pumping experiments in a NiFe/barrier//STO sample, where the barrier blocks spin injection towards the STO, but the total rectification voltage in the NiFe layer will still suffer alterations due to modulated dielectric constant of the STO substrate. Additionally, we note that in Fig.3.34d, a drop in

	The work performed in the Al//STO system opens interesting doors for the exploration of
	more efficient charge-to-spin current conversion effects. However, considering the non-Onsager
	reciprocity discussed in Section 1.6.3.2, can a system with large spin-to-charge conversion effi-
	ciency exhibit equivalently large charge-to-spin conversion? Further experiments are required,
	possibly combining spin pumping and spin-torque ferromagnetic resonance.

λ IEE occurs. Although the origin of this is still unknown, it may once again be connected to the gate voltage dependence of the dielectric constant in STO, which drives a different carrier density modulation depending on the gate voltage applied. Interestingly, we add that this drop is suppressed above T = 15 K.

Even though the conversion efficiency found in the Al//STO systems starts to reach values that may be interesting for device applications, they still require low temperature. From preliminary results on the temperature dependence of λ IEE , we find values around 1 nm at 300 K. Note also that at room temperature, the dielectric constant of STO drops significantly, hampering any efficient back-gate voltage modulation. This may ultimately require the use of a top-gate voltage geometry.

  4.1a. In its ferromagnetic phase, the spin-dependent asymmetry dictates that, at the Fermi level E F , the spin-down Fermi surface is composed of conduction s ↓ and d ↓ states, while the spin-up surface is only composed of conduction s ↑ -electrons. This means that while s ↓ -s ↓ and s ↓ -d ↓ scattering transitions are allowed for spin-down electrons, spin-up electrons can only undergo s ↑ -s ↑ transitions (since there are no d ↑ states available at the E F ). As shown in Fig.4.1b, according to the two-current model developed by Mott[START_REF] Mott | Electrons in transition metals[END_REF] (and introduced in Section 1.2), a parallel resistance model taking into account these transitions can be considered (at low temperatures and in the absence of spin-orbit coupling). Within this model, the resistivity of the two spin channels is different, so that ρ ↓ = ρ ↑ 38 . This difference was experimentally confirmed and measured by Fert and Campbell for Ni alloys containing Co, Mn, Cr, or Ti as dilute impurities[START_REF] Fert | Two-Current Conduction in Nickel[END_REF].When spin-orbit coupling is considered, scattering with spin flipping is now possible, and a certain amount of d ↑ states become mixed into the d ↓ band, and vice-versa. In this scenario,d↑ states become available at the E F . s ↑ electrons can now scatter to both d ↑ and (majority) d ↓ states, which adds a new element to the Mott's model (see Fig. 4.1c). The crucial feature in this mechanism is that d ↑ -d ↓ mixing is not isotropic, and s electrons can only scatter into a d hole state if the conduction electron momentum k is in the same plane as the orbit of the empty d state, which can essentially be controlled by the magnetization direction M .

  205 • (2016) Japanese/French Oxide Spintronics Joint Workshop, Metal-induced conductivity at LaAlO 3 /SrTiO 3 interfaces. Paris, France Posters • (2017) 18e Colloque Louis Néel 17, The potential of LaAlO 3 /SrTiO 3 interface for spintronics. Paris, France • (2016) GdR OXYFUN 2016, Metal-Induced Interfacial Conductivity between Band Insulators. Autrans, France • (2015) WOE22, Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures. Paris, France • (2015) International School of Oxide Electronics 2015, Magnetotransport properties of metal/LaAlO 3 /SrTiO 3 heterostructures. Cargèse, France

Even though the classical and quantum mechanical notion of angular momentum share the same relation L = r × k, an electron is not actually rotating around the nucleus (or around itself). The classical idea of orbits does not work for electrons since they have no definite position, as stated in Heisenberg's uncertainty principle[START_REF] Heisenberg | Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[END_REF]. As an intuitive example, solving Schrödinger's equation one notices that for an s-electron L = 0, when classically speaking it should be rotating around the nucleus with finite angular momentum.

By sending a beam of silver atoms through an inhomogeneuos magnetic field, Stern and Gerlach observed that the atoms would deflect in opposite directions, proving that atomic particles have an intrinsic angular momentum with quantized spatial orientation.

We note that this example is valid for elements in the same row of the periodic table. When jumping to a new row, new electronic shells are introduced, leading to a large increase of r, and subsequently a sharp decrease of the SOC.

Here, the 1/r 3 term for p orbitals dominates over the higher orbital momentum of d and f orbitals.

Two other important mechanisms can lead to spin relaxation: the hyperfine interaction[START_REF] Perel | Optical orientation in a system of electrons and lattice nuclei in semiconductors[END_REF], usually observed in semiconductors at low temperature[START_REF] Paget | Low field electron-nuclear spin coupling in gallium arsenide under optical pumping conditions[END_REF], leading to spin-exchange between the nucleus and the electron , and the Bir-Aronov-Pikus mechanism[START_REF] Bir | Spin relaxation of electrons due to scattering by holes[END_REF], most prominent in heavily p-doped semiconductors, due to exchange interaction between electron and hole spins.

If the system is anisotropic, even though there is no general relation between the two times, the inequality τ2 2τ1 holds[START_REF] Yafet | Factors and Spin-Lattice Relaxation of Conduction Electrons[END_REF].

See Section 1.6.1 for a more in depth symmetry considerations.

The other limiting case where τp Ω ≥ 1 represents the situation where the electron spin precesses at least one full cycle before being scattered to another momentum state k . In this case the spin information is lost after time τp.

In the presence of strain along the (001) direction, the k 3 -Dresselhaus term can reduce to a k-linear term[START_REF] Kachorovskii | Spin relaxation of two-dimensional electrons in noncentrosymmetric semiconductors[END_REF][START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF].

Recently, a surprising 2D hole gas was reported in STO/LAO//STO heterostructures, where electron transport was found at the bottom interface (LAO//STO) and hole transport at the top interface (STO/LAO)[START_REF] Lee | Direct observation of a two-dimensional hole gas at oxide interfaces[END_REF].

As described in the Supplementary Information of Ref.[START_REF] Yu | A polarity-induced defect mechanism for conductivity and magnetism at polar-nonpolar oxide interfaces[END_REF], the Fermi level position can be calculated self-consistently from first principles using the defect formation energies as inputs. Below the critical thickness, since all defects form deep states, the Fermi level will sit near the middle of the STO band gap. Above the critical thickness, the formation of VO shallow levels pins the Fermi level near the STO conduction band minimum.

Due to its highly corrosive and poisonous nature, we advise the use of appropriate protective gear when handling HF. Note that symptoms of poisoning after contact with a body part might start to be visible up to one day after exposure and may not cause any pain in the first few hours.

The target should be thick enough to prevent acceleareted ions from tunneling through, hampering the sputtering process. Also, for magnetic targets such as Co or Fe, we often use thinner targets, since the strong magnetic fields might interfere with the magnetron.

At this point, it is important to ensure that the plasma remains stable. If the current or Ar inflow is too low, the plasma will start to flicker and eventually be lost. If it is too high, the mean free path of ejected atoms will be heavily reduced, which lowers the deposition rate and might lead to re-deposition on the target's surface.

The photoelectron cross section is related to the probability of an electron to be ejected from a solid by a given photon energy. This quantity depends on the element, energy level and the type of source used. Values for Al-Kα and Mg-Kα are can be found from Li to U in Ref.[START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF].

Due to the insulating nature of these samples, and the fact that measurements were performed in situ, charging effects were quite severe, with peaks suffering energy shifts up to 5 eV from their reference values.

We note that in this configuration, tunneling between the two layers does not need to be considered, unlike measurements performed in current-in-plane tunneling geometry (CIPT), where the current is injected only in the top metallic layer[START_REF] Worledge | Magnetoresistance measurement of unpatterned magnetic tunnel junction wafers by current-in-plane tunneling[END_REF]

We opted for this reference for two reasons: first, small experimental errors associated with the sputtering deposition and different Ta/substrate chemical interactions may lead to small discrepancies in the effective thickness of a separate Ta reference sample; second, at room temperature, the resistance of the metal is two orders of magnitude smaller than the q2DEG, so that ∼99% of the current is flowing in the metallic layer.

The same experiment was also performed on STO substrates without any annealing step, as well as with an extra high temperature vacuum annealing, followed by the high temperature and high oxygen pressure procedure. Minimal difference was observed among samples, with the Ti 2p core level staying practically unchanged, and the O 1s core level showing an additional feature (at higher binding energy) for the nonannealed substrate, mainly due to adsorbed species[START_REF] Scheiderer | Surface-interface coupling in an oxide heterostructure: Impact of adsorbates on LaAlO 3 /SrTiO 3[END_REF].

Note that oxidation at the metal surface is excluded, since the whole process described in this section is performed in UHV.

The metallic Co spectra was collected in situ in a Co(10nm)/Au(50nm)/SiO2/Si sample. We then removed it from UHV and exposed it to air for about 1 hour. The sample was then re-measured, exhibiting a fully oxidized surface, with characteristic Co oxide peaks as reported in the literature[START_REF] Wagner | Handbook of x-ray photoelectron spectroscopy : a reference book of standard data for use in x-ray photoelectron spectroscopy[END_REF].

The asymmetry of the wavefuntion is given by how much s, p and d character a surface state shows at particular k-points. The Rashba splitting is predicted[START_REF] Bihlmayer | The Rashba-effect at metallic surfaces[END_REF] to become much lower when surface states have a predominent orbital character, reducing the asymmetry of the wavefunction.

Bi shows a Fermi surface made of two small pockets where the conduction band and valence band overlap. In this case, even if the material is conducting, the density of states at the Fermi level EF is almost zero.

A Cu layer is inserted between the NiFe and the TI in order to protect the topological surface states from degradation during the deposition of the NiFe.

These may be especially prominent when the FM layer is thin (few nm), when Ms small, or when other magnetic anisotropy effects are large.

For most systems (with the exception of ferromagnetic insulators or half-metallic ferromagnets) the imaginary part {g ↑↓ } of the spin mixing conductance in Eq. (3.6) can be disregarded[START_REF] Brataas | Spin battery operated by ferromagnetic resonance[END_REF].

We will see in the next chapter that the multi-band regime can be confirmed through AMR experiments under large magnetic fields.

DISCLAIMER: The FMR and spin pumping experiments described in the next few sections were performed in CEA Grenoble (France), through a collaboration with Paul Noël and Laurent Vila. Even though the author of this thesis spent a few weeks performing some of these experiments, the great majority of the data was collected by Paul, in the scope of his PhD thesis. We therefore conceal some of the most technical details, and focus mainly on the sample growth, characterization, and physical interpretation of the collected data, in connection with the Rashba and Edelstein effect picture.

For an absorption experiment, we expect A dis = 0. However, in practice Eq. (3.10) usually gives A dis three orders of magnitude smaller than A abs .

In a realistic case, considering the absorption of spin current by the adjacent NM metallic layer and a diffusive spin current backflow, an effective damping constant given by Eq. (3.8) is considered.

By this we mean, a choice of PLD parameters (substrate temperature, oxygen partial pressure, annealing time, etc) that leads to a quasi-2D electron gas at the LAO//STO interface.

Similar results were also obtained for Al//STO samples, which showed very similar features but much poorer imaging quality.

DISCLAIMER: All calculations were performed by Annika Johansson, Börge Göbel and Ingrid Mertig at the Max Planck Institute of Microstructure Physics (Halle). For this reason, most technical features of the calculations are omitted from this thesis, since they were not performed by the author. We therefore keep this section as simple and accessible as possible, while stressing its most important features contributing to a better understanding of the Edelstein effect.

Note that d electrons have much bigger effective mass than s electrons, and therefore contribute less to the overall conductivity.

Acknowledgements

The first step for the growth of the LAO//STO heterostructures is the surface preparation of the STO substrate. As we are dealing with a surface/interface sensitive system, the cleanness of the substrate surface is of the upmost importance. Also, as we saw in Section 2.1, the q2DEG formation depends heavily on the termination of the STO. Since the bulk crystal is composed of TiO 2 and SrO planes, the two terminations are possible. We start by focusing on the TiO 2 termination, since it is the only one that was shown to render the interface conducting [START_REF] Ohtomo | Artificial charge-modulationin atomic-scale perovskite titanate superlattices[END_REF].

The discovery of a procedure to achieve atomic flat surfaces was a major step towards the success of complex oxides as a platform for carefully engineered physical effects. The surface of commercially available single-crystal oxides, such as STO, is usually prepared by mechanochemical polishing, which results in a rather smooth and flat surface with small corrugations (less than 1 nm tall). However, epitaxial growth of oxide films required atomically flat surfaces, if possible with control over the atomic configuration at the surface. i.e. the termination. Using a controlled chemical treatment based on buffered NH 4 F-HF (hydrofluoric acid), Kawasaki et al. were able to achieve TiO 2 -terminated STO substrates with atomic flat surfaces [START_REF] Kawasaki | Atomic Control of the SrTiO 3 Crystal Surface[END_REF]. The idea was simple: HF is a powerful acid known to dissolve Sr-O bonds more efficiently than Ti-O. When STO is submerged in an HF solution, the topmost SrO sheets are removed faster, which leaves the surface rich in Ti. In the original recipe, Kawasaki submerged the samples for 10 min, proceeded with a cleaning step under pure water and ethanol. There also was special emphasis given to the pH of the acidic solution.

This landmark experiment was then improved and altered by several authors. Koster et al. suggested that hydroxylation of the topmost SrO layer (by submerging the substrate in water before the HF treatment) improved the etch-selectivity of SrO relative to TiO 2 [START_REF] Koster | Quasi-ideal strontium titanate crystal surfaces through formation of strontium hydroxide[END_REF]. Other authors analyzed in detail the chemical properties of STO surfaces after different treatments [START_REF] Kobayashi | High-resolution synchrotron-radiation photoemission characterization for atomically-controlled SrTiO 3 (001) substrate surfaces subjected to various surface treatments[END_REF], the defect-chemistry of the topmost layers [START_REF] Zhang | Depth-resolved subsurface defects in chemically etched SrTiO 3[END_REF] and potential F doping [START_REF] Chambers | Unintentional F doping of SrTiO 3 (001) etched in HF acid-structure and electronic properties[END_REF]. Controlled termination was also later achieved in the ( 110) and ( 111) crystallographic directions [START_REF] Biswas | Universal Ti-rich termination of atomically flat SrTiO 3 (001), (110), and (111) surfaces[END_REF].

Lastly, this chemical treatment was adapted to less aggressive and harmful solutions such as HCl-HNO 3 [START_REF] Kareev | Atomic control and characterization of surface defect states of TiO 2 terminated SrTiO 3 single crystals[END_REF] and even an acid-free recipe [START_REF] Connell | Preparation of atomically flat SrTiO 3 surfaces using a deionized-water leaching and thermal annealing procedure[END_REF]. We add also that most of these procedures included a high-temperature annealing step after chemical treatment, to help with structural reconstruction at the surface.

Comparably, SrO-terminated STO surfaces were also achieved experimentally. The easiest approach was based on a deposition of a single layer of SrO on a TiO 2 -terminated surface [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF]. Then, following the fact that Sr atoms tend to diffuse towards the surface through high these results seem difficult to reconcile with a simple inverse Edelstein picture. Lastly, Zhang et al. performed similar experiments on Ar+-irradiated STO and found a λ IEE of 0.23 nm [START_REF] Zhang | Spin galvanic effect at the conducting SrTiO 3 surfaces[END_REF]. The low conversion efficiency might, however, be due to the increased roughness (and reduced mobility of the 2DEG).

Regarding the reciprocal effect, experimental results on the DEE are still scarce. As shown in Fig. 3.5c and 3.5d, Wang et al. have demonstrated through ST-FMR experiments that when driving a RF charge current through the LAO//STO 2DEG, a non-equilibrium spin density is propagated perpendicularly towards the ferromagnetic top layer [START_REF] Wang | Room-Temperature Giant Charge-to-Spin Conversion at the SrTiO 3 /LaAlO 3 Oxide Interface[END_REF]. This leads to magnetization precession under the influence of the induced damping-like torque, revealed by the large symmetric contribution to the measured voltage signal. The charge-to-spin conversion efficiency was estimated to be q DEE = 0.63 nm -1 at room temperature and was found to fall markedly when temperature decreases. This decrease was attributed to a lower conduction of spin-polarized electrons through defect states in the LAO barrier. Using a Hall-bar-like geometry, Jin et al. demonstrated charge-to-spin and spin-to-charge conversion within the same device [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF]. In these experiments, a charge current injected between the source and the drain induces a perpendicular spin current (through the DEE, or 2D-SHE). The spin current propagates in the 2DEG channel, is reconverted to a charge current (through the IEE, or 2D-ISHE), and gets nonlocally detected at the adjacent contacts of the Hall-bar (Fig. 3.5e).

Since the propagating spin current has a polarization perpendicular to the plane, applying an in-plane magnetic field induces Larmor precession of the spins, so that for sufficiently large fields, the spins will become parallel to the plane. This effect can be seen in Fig. 3.5f, where Hanle experiments showed a decrease in the detected voltage with increasing magnetic field.

To close this introductory section, we show in Fig. 3.6 the scattering time τ and Rashba coefficients α R for the various two-dimensional systems discussed [START_REF] Varignon | A new spin for oxide interfaces[END_REF]. The diagonal colored lines represent the expected λ IEE calculated from Eq. 1.29, emphasizing the importance of these two quantities in spin-to-charge conversion effects.

In the following sections we shall examine in detail the spin-to-charge conversion phenomena at LAO//STO interfaces as well as a new type of systems also based on STO, where λ IEE was found to be even larger. In addition, we will introduce several technical details regarding the ferromagnetic resonance driven spin pumping technique, how to quantitatively estimate spin currents and the overall experimental setup used to perform these experiments. We also recommend the interested reader to the recent reviews of Soumyanarayanan et al. [START_REF] Soumyanarayanan | Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces[END_REF] and Han et al. [START_REF] Han | Quantum materials for spin and charge conversion[END_REF] for extended phenomena driven by spin-orbit coupling at surfaces and interfaces, as well as other promising materials and ideas for spin-to-charge current conversion. The effect is still visible when introducing a Cu barrier at the interface between YIG and Pt, but destroyed for an insulating SiO 2 layer. Adapted from [START_REF] Nakayama | Spin Hall Magnetoresistance Induced by a Nonequilibrium Proximity Effect[END_REF].

Around the same period, Nakayama et al. reported a new magnetoresistance effect, where the resistance of a Pt/YIG bilayer was observed to be altered depending on the magnetization direction of YIG [START_REF] Nakayama | Spin Hall Magnetoresistance Induced by a Nonequilibrium Proximity Effect[END_REF]. The effect was rather surprising since YIG is an electrical insulator, which meant that the resistance change was occurring in Pt, a paramagnetic metal which exhibits no AMR. The effect was termed spin Hall magnetoresistance (SMR), and set yet another landmark in the field of spintronics. We briefly explain it in the following paragraphs.

Considering a strong spin-orbit coupling material (like Pt), when a charge current j c is applied along the film plane, a spin current j s traveling orthogonality to the films plane is In the M σ case the spin current is not transferred to the FM. (f ) Similarly to the USMR, two resistance states are present depending on the relative orientations between M and σ. However, the larger spin transfer to the FM (due to higher charge-to-spin current conversion at the 2DEG) implies a larger artifical FM layer as well as larger current compensation within the 2DEG (due to spin backflow), so that, ultimately, ∆R between both states is expected to be much larger.

First off, the efficiencies expected from the DEE are much larger than for the SHE, so that the artificial FM layer (in blue) will be more easily created, and possibly extend further in the FM. Since this ejection is expected to be more efficient, a larger spin backflow will also occur towards the 2DEG (see Fig. 4.18c). Then, the initially shifted Fermi contour (by ∆k x ) will partially re-absorb an electron density with opposite spin, as shown in Fig. 4.18d. In the framework of the Edelstein effect, these electrons will necessarily have a momentum -k, which shifts the contour by -∆k x and generates a charge current j c that opposes the initially source j c . For the parallel case, similarly to USMR, the generated spin current is not able to

We then introduce a recently discovered effect, the spin Hall magnetoresistance (SMR), based on the interaction between the spin accumulation generated in a large spin-orbit coupling materials (such as Ta or Pt) and the magnetization direction of an adjacent magnetic material.

The effect was first observed in YIG/Pt bilayers [START_REF] Nakayama | Spin Hall Magnetoresistance Induced by a Nonequilibrium Proximity Effect[END_REF], but after extended to YIG/Ta [START_REF] Hahn | Comparative measurements of inverse spin Hall effects and magnetoresistance in YIG/Pt and YIG/Ta[END_REF] and CoFeB/W [START_REF] Cho | Large spin Hall magnetoresistance and its correlation to the spin-orbit torque in W/CoFeB/MgO structures[END_REF] bilayers. In essence, a larger resistance is observed when the magnetization is perpendicular to the spin polarization at the interface, where spin angular momentum is transferred to the FM. When the magnetization is parallel to the spin polarization, no change in the resistance of the bilayer is expected.

From this, a unidirectional component of the SMR was also observed in Co/Ta and Co/Pt bilayers [START_REF] Avci | Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers[END_REF]. In this case, a resistance change is observed whether the magnetization is parallel or antiparallel to the SHE-driven spin polarization. While the effect is orders of magnitude smaller than in the conventional SMR case, it bring important advantages in terms of device application. With SMR, two contacts are used to probe the resistance of the bilayer, and an additional contact is used to control the magnetization of the FM, resulting in a 3-terminal device. For USMR the magnetization can be simply switched by applying large enough currents, while the state of the magnetization can be read using the unidirectional difference in resistance, resulting in a simpler 2-terminal device.

While the effect is still rather small in the conventional FM/NM bilayers, where NM are normally high spin-orbit coupling bulk materials, new and improved alternatives may be engineered using topological insulators or Rashba 2DEG (in the same framework used to explore larger spin-to-charge current conversion efficiencies in these exotic systems). With this in mind, we developed a simple conceptual model describing a hypothetical unidirectional Edelstein magnetoresistance (UEMR). We conclude that the UEMR magnitude should, in principle, be much larger than conventional USMR, since the spin ejection (i.e. charge-to-spin conversion through Edelstein effect) is much larger than in high spin-orbit coupling bulk systems. We then performed AMR and UMR experiments on FM/LAO//STO heterostructures, while looking for traces of UEMR. First off, while the FM layer (NiFe) is conducting, it shows no unidirectional component, so that measuring the UMR in the full stack should only reveal the contribution of the 2DEG. However, the UEMR signal will still overlap with the intrinsic UMR from the 2DEG, discussed in the beginning of the chapter. Due to this, we were not able to directly detect the UEMR in this system.

In the future, it will still be desirable to replace the metallic NiFe layer with an insulating ferromagnet, such as YIG. From recent preliminary experiments, crystalline YIG with good magnetic properties could not be successfully grown on LAO//STO. We observed that by annealing the a-YIG/LAO//STO sample in extremely high temperatures (> 1000 • C) followed by a post-annealing process in a rich oxygen environment, the YIG did not become crystalline, • the other million collaborations that may result in articles at some point.

Invited Talks