Frederic Nguyen

Van Dau

Vincent Cros

Maxen Cosset-Cheneau

Paul Nöel

Laurent Vila

Julien Rault

Patrick Lefèvre

François Bertran

Raphaël Salazar

Keywords: Quantum oxide heterostructures Oxide heterostructures, spin-charge interconversion, spinorbitronics

Over the past few decades, the increasing My main concern at the moment is not having enough space to thank each and every one of the details that, in one way or another, have facilitated the realization of this thesis. If I did, I could write 200 more pages and, even then, I am sure I would leave something unmentioned. Good details abound, as good people have abounded around me during this stage of my life.

This path was initiated on the basis of trust, from my professor Carlos León, as well as from my supervisors Agnès Barthélémy and Manuel Bibes. To you Carlos, I thank you for believing in

demand for electronic devices has prompted the development of new technologies and the miniaturization of devices. In this context, a new field called spintronics has emerged. It exploits the spin of electrons to encode and process data, increasing the performance of devices in terms of capacity, speed and efficiency. However, in this field, it is essential to implement platforms that allow interconversion between charge and spin currents in order to integrate them into real devices. Among the many possibilities, two-dimensional electron gases (2DEGs) are good candidates to achieve efficient spincharge interconversion by means of direct/inverse Edelstein effects.

Thus, this PhD thesis focuses on the spin-charge interconversion properties of 2DEGs formed after the deposition of metals on transition metal oxides. In particular, metals with different oxygen affinity (aluminum, tantalum or yttrium) were deposited on strontium titanate (STO) and potassium tantalate (KTO). These systems were synthesized by magnetron sputtering, a technique that has wide industrial applicability. This study was carried out as a function of the thickness of the deposited metal. The results obtained include characterization by X-ray photoelectron spectroscopy (XPS), surface characterization by atomic force microscopy (AFM) and basic characterization of the magnetotransport properties of the resulting 2DEGs. In addition, angle-resolved photoemission spectroscopy (ARPES) experiments were performed to highlight the role of the complex band structure of the KTO on the spin/charge interconversion efficiency.

After this characterization, the applicability of the different systems for spin/charge interconversion platforms was determined. For this purpose, we have performed spinpumping ferromagnetic resonance (SP-FMR) experiments and anisotropic magnetoresistance (AMR) measurements.

The final chapter of the thesis focuses on the ability of the different systems to exert spin-orbit torques (SOT) on an adjacent ferromagnetic film. First, details of the optimization of the heterostructures in terms of thickness and magnetic properties will be given, followed by the quantification of the SOT by magnetotransport measurements. Finally, preliminary results will be presented on the observation of magnetic textures that probably present a skyrmionic character and thus, could be manipulated by an electric current exploiting the direct/inverse Edelstein effects. The visualization of these skyrmionic spin textures has been performed by magnetooptical Kerr effect (MOKE) microscopy, magnetic force microscopy (MFM) and X-ray photoemission electron microscopy (X-PEEM).

To Lucia, for being not only light but love.

To my family, for being my most precious fortune.

To my friends, for crossing my path.

As for my research group, I would like to thank Diogo Castro Vaz for giving me the encouragement and knowledge I needed to start on the right foot. To Felix Trier, sincere thanks for his immeasurable efforts to help me during my first years. To Jin Hong Lee for his friendship and for the many absurd conversations. To Victor Haspot, for always being kind and appreciating my work. Also, to Raphaël Aeschlimann and Johanna Fischer for sharing their passion for materials science. Thanks to Julien Brehin for being a wonderful person and sharing much of this journey with me, certainly one of the best partners you may ever have. Also, to Sara Varotto for all the enthusiasm during the long hours of work and, above all, for the good vibes she brings with her.

To the wise Colonel Srijani Mallik, for giving me hope in the most difficult moments of the thesis, and keeping it up when they were over. To Fernando Gallego, for being a wonderful person and the living proof that you can survive perfectly well without eating a single vegetable. To Hugo Witt, for being a good apprentice and staying longer with us.

I would like to acknowledge the invaluable help from Sachin Krishnia regarding the measurements and analysis of the SOT results, as well as all his efforts to have them included in this thesis. Also, to Sougata Mallick, for his fruitful discussions on skyrmions and many other moments. To Fernando Ajejas for bearing with me (although I want to believe that this led him to quit smoking), to Víctor Rouco for all those details to make my integration easier and his funny accent, and to Carolina de Dios, David Sánchez and Santiago Carreira who I am not very sure what they have done apart from being such great people (if I do not mention them, they will get mad).

I thank my ex-colleagues at the Instituto de Cerámica y Vidrio, who accompanied me during the first steps of my scientific career. Among others, I would like to make a special mention to the group of José Francisco Fernández, and thank him for all the knowledge I relied on during the course of this thesis. I would like to thank my friends, both those from before starting this path and those I have made along the way, for the great support they have given me during all this time. As well as the members of the Moy Yat Ving Tsun Martial Intelligence who have shared with me an invaluable experience that is difficult not to profit from.

IX

Debo agradecer a mi familia todo el cariño y apoyo que me han dado desde la distancia durante todo este tiempo, por perdonarme mil despistes y por acogerme siempre con los brazos abiertos.

A ellos, y especialmente a mis padres y hermanas, quiero dedicar esta tesis con todo mi cariño.

Gracias por ser como sois. THANK YOU, Lucia, because anything I write in these lines would be unable to describe everything you have done for me. You proposed to make me smile every day and you did it, you proposed to make me fall in love and you did it, you proposed to make me finish my thesis and here we are.

You are the best person I have ever met and no matter what happens, it is clear to me that with you I have already won.

Finally, I would like to warmly thank my jury for their patience and the time spent reading this thesis, which I hope will be to their liking.

XI

Résumé

Dans cette thèse, nous étudions le potentiel des 2DEGs métal/oxyde à convertir les courants de charge en courants de spin, ou vice versa, ainsi qu'à agir sur la magnétisation d'un matériau magnétique adjacent.

Le premier chapitre de cette thèse fournit un contexte théorique pour faciliter la compréhension, et est divisé en deux parties. La première partie traite du concept des courants de spin et de charge basé sur le modèle à deux courants, c'est-à-dire une conduction parallèle à travers deux canaux de résistivité différente pour des projections de spin opposées. Ensuite, les principes physiques fondamentaux de l'interaction spin-orbite (SOI) par laquelle le spin de l'électron se couple à son mouvement autour du noyau atomique sont introduits, ainsi que les mécanismes de relaxation du spin par lesquels l'information associée à l'état de spin résultant de ce couplage peut être perdue.

Le couplage spin-orbite (SOC) permet de convertir les courants de charge en courants de spin via l'effet Hall de spin (SHE) ou l'effet Edelstein direct (DEE). Ces deux mécanismes sont expliqués en détail, ainsi que les mécanismes réciproques de l'effet, tels que l'effet Hall de spin inverse (ISHE) et l'effet Edelstein inverse (IEE), qui permettent de convertir les courants de spin en courants de charge. Nous expliquons les fondements théoriques des techniques utilisées pour pomper des courants de spin purs dans les 2DEGs métal/oxyde au moyen d'expériences de pompage par résonance ferromagnétique (SP-FMR) et caractérisons le potentiel de ces systèmes pour la conversion des courants de spin en courants de charge par IEE. D'autre part, la base théorique des mesures de magnétorésistance bilinéaire (BMR) est également introduite, ce qui permet de présenter le potentiel des 2DEG Al/KTO pour convertir les courants de charge en courants de spin par DEE.

La capacité de convertir les courants de charge en courants de spin permet à ces systèmes d'exercer un couple orbital de spin (SOT) sur l'aimantation d'un matériau ferromagnétique adjacent. Ainsi, ce chapitre aborde également les fondements théoriques de SOT, ainsi qu'une brève introduction aux configurations magnétiques chirales que nous tenterons de combiner avec ces systèmes.

La deuxième partie du premier chapitre se concentre sur des principes fondamentaux plus pratiques. Tout d'abord, une brève introduction aux oxydes de métaux de transition est donnée, soulignant leur polyvalence en termes de propriétés, suivie d'une description détaillée des propriétés des oxydes utilisés dans la thèse, le titanate de strontium (STO) et le tantalate de potassium (KTO). Les propriétés des 2DEG sont étroitement liées à la nature des oxydes qu'ils contiennent. Par conséquent, en prenant le STO comme exemple, ce chapitre se termine par la présentation des facteurs qui régissent le processus de formation de 2DEG par dépôt de métal, tels que la maniabilité du métal déposé et la chaleur de formation de l'oxyde le plus stable, ainsi XII que les propriétés électroniques particulières en termes de structure de bande, de comportement de tension de grille et de propriétés de magnétotransport.

La section sur les techniques expérimentales présente les principes de base et les détails pratiques des techniques utilisées dans la thèse. Tout d'abord, la pulvérisation magnétron est présentée comme la principale technique de synthèse pour la croissance des échantillons, en expliquant son fonctionnement, en soulignant sa grande polyvalence et son applicabilité industrielle.

Dans ce qui suit, l'effet photoélectrique est présenté comme la base de la spectroscopie photoélectronique à rayons X (XPS) et de la spectroscopie de photoémission résolue en angle (ARPES), et les particularités de ces deux techniques sont expliquées en se référant aux principes physiques fondamentaux, aux informations accessibles grâce à elles, et à des informations plus spécifiques sur les équipements sur lesquels ces expériences ont été réalisées.

Les méthodes utilisées pour caractériser les propriétés de magnétotransport des 2DEGs métal/oxyde, telles que la résistivité, la magnétorésistance et les mesures de l'effet Hall, sont présentées. Les différentes configurations de mesure sont introduites et la dérivation mathématique de la densité de porteurs et des mobilités électroniques caractéristiques de les mesures de base du magnétotransport (résistivité, magnétorésistance et effet Hall) et la caractérisation de la surface par microscopie à force atomique (AFM) sont présentées. Cette caractérisation a été réalisée selon une procédure très systématique en fonction de l'épaisseur déposée et en utilisant des substrats très similaires. Cette étude nous a permis de déterminer qu'il existe une épaisseur de métal en dessous de laquelle le 2DEG n'est pas protégé contre la réoxydation, et au-dessus de laquelle il existe un canal de conduction supplémentaire pour le transport des électrons, c'est-à-dire la couche métallique de surcroissance.

La caractérisation XPS in situ après dépôt d'Al, Ta ou Y sur STO a confirmé que la réduction du substrat est différente selon le métal déposé, ainsi que l'épaisseur du métal oxydé par contact direct avec le substrat. D'autre part, à partir de la caractérisation XPS après exposition des échantillons à l'air, nous avons constaté que l'épaisseur de métal à déposer pour protéger le 2DEG de la réoxydation est également différente selon le métal déposé, ainsi que l'épaisseur à laquelle la phase métallique commence à apparaître. Nous constatons que la réduction du substrat et Dans une deuxième section, nous présentons les résultats obtenus à partir de la caractérisation de la structure de bande des 2DEGs Al/KTO par spectroscopie de photoémission résolue en angle (ARPES). A partir de ces résultats, nous observons une structure de bande complexe ainsi qu'une grande séparation de type Rashba qui confirme la grande attractivité de ce système pour l'interconversion spin-charge.

La troisième section comprend les résultats obtenus sur la capacité de ces métaux/oxydes à réaliser le processus d'interconversion spin-charge. Nous abordons ici les courants de charge générés par l'effet Edelstein inverse (IEE) dans les 2DEGs métal/STO en réalisant des expériences de pompage de spin par résonance ferromagnétique (SP-FMR). À partir de ces résultats, nous constatons que tous ces systèmes présentent une efficacité de conversion spin/charge élevée, ainsi que certaines similitudes et différences dans la dépendance à la tension de grille appliquée.

Ces similitudes et ces différences sont discutées en termes de similitudes et de différences dans la structure de bande, ainsi qu'en termes de confinement des 2DEG et de transparence de la barrière d'oxyde au tunnelage des électrons. Deuxièmement, des expériences ont également été réalisées avec des 2DEGs Al/KTO, dans lesquelles une tendance avec la tension de grille très différente de celle observée pour le STO a été observée, comme prévu à partir d'une structure de bande complètement différente. Dans ce cas, l'efficacité de conversion est inférieure à celle obtenue pour les 2DEGs Al/STO et ne montre aucun changement de signe sur la gamme de tensions étudiées. D'autre part, dans cette section nous incluons les résultats obtenus sur le processus de conversion des courants de charge en courants de spin par l'effet Edelstein direct dans les 2DEGs Al/KTO. La capacité de ces systèmes à réaliser le processus de conversion chargespin a été effectuée au moyen de mesures de magnétorésistance bilinéaire. Ces résultats nous ont permis d'estimer une gamme de valeurs de coefficient de Rashba pour ce système parmi les plus élevées rapportées à ce jour, réaffirmant le potentiel de ce système pour les processus d'interconversion.

La dernière section de résultats se concentre sur l'optimisation des hétérostructures Pt/Co/AlOX(TaOX)/STO pour démontrer le potentiel de ces 2DEGs en termes de manipulation de l'aimantation d'un matériau magnétique adjacent et la possibilité de les combiner avec des textures magnétiques chirales. À cette fin, le couple exercé par le 2DEG à deux tensions de grille très différentes a été caractérisé dans des échantillons dans lesquels l'épaisseur du revêtement a été minimisée tout en préservant l'anisotropie magnétique perpendiculaire (PMA). De l'analyse, il est obtenu que le couple est très similaire aux deux valeurs de tension, où la contribution de 2DEG et Pt au couple est très différente. Ceci suggère a priori la contribution du 2DEG au couple de magnétisation, bien que la confirmation finale nécessite des expériences supplémentaires.

Enfin, la dernière section présente les résultats obtenus dans les premières étapes vers la combinaison de ces systèmes avec des textures magnétiques chirales, montrant des résultats très prometteurs dans ces hétérostructures.

Introduction

The increasing worldwide demand for higher performance electronic devices has become a major challenge for our society as we approach the physical limits of the current technology, i.e., complementary metal oxide semiconductor (CMOS) technology. Although breakthroughs in production and design techniques have made it possible to miniaturize and improve microprocessors according to Moore's law, the dimensions of CMOS-based circuits will no longer be miniaturizable since quantum effects and power dissipation become prominent at the nanometer scale. Moreover, the power consumption of microelectronic chips is a major issue and, if this sector continues to grow at its recent rate, information and communication technology will consume more than 20% of the world's electricity by 2030.

In recent years, new lines of research have been developed with the aim of finding a technology capable of overcoming these limitations. In particular, the field of spinorbitronics aims to benefit from the coupling of the electron spin to its motion within the atomic lattice for the development of beyond-CMOS devices.

Just as early spintronic devices led to a revolution in data storage, such as the giantmagnetoresistance read heads of hard drives, new paradigms have been proposed to revolutionize computing. Among these new paradigms is Intel's magnetoelectric spin-orbit (MESO) transistor, in which the magnetization of a ferromagnetic element is written by applying a voltage to a multiferroic magnetoelectrically coupled with it, and read out by a material capable of converting the spin current generated from the ferromagnet into a charge current. The development of MESO and other spin-based beyond-CMOS logic devices involves novel physical phenomena, as in this case is magnetoelectric coupling and spin-charge conversion, but also requires recourse to quantum materials much more exotic than those currently used in CMOS circuits.

In this respect, oxide interfaces are really appealing. They exhibit a wide range of unusual properties such as superconductivity, Rashba-type spin-orbit coupling (RSOC), and high tunability by electric fields. Before I joined the Unité Mixte de Physique CNRS/Thales, scientists from this laboratory, in collaboration with researchers from Spintec, demonstrated that the RSOC of SrTiO3based interfaces could convert spin currents into charge currents with very high efficiency. This not only triggered interest from research areas to understand the large effect and its unusual gate dependence, but also the interest from industry. In particular, Intel collaborated with our lab to explore the potential of STO interfaces as the readout element of MESO transistors.

XVII

Aim of this thesis

The aim of this thesis is to further study the potential of STO interfaces for spin-charge interconversion. On the one hand, different metal/STO systems will be investigated to clarify the role of the metal of choice in the 2DEG formation process and the resulting interconversion properties. On the other hand, the comparison between Al/STO and Al/KTO 2DEGs gives us the opportunity to access very different playgrounds and may be useful to also unravel the role of the oxide and the underlying physics of the spin-charge interconversion process, which becomes essential in order to achieve optimal efficiency. Subsequently, we intend to study whether these systems are capable of exerting torque on a ferromagnetic film, as well as combining with chiral magnetic textures for further manipulation.

Organization of this thesis

The thesis is organized in four chapters: State of the art, Experimental Techniques, Results, and

Summary and Perspectives.

The first chapter, State of the art, is organized in two parts. Part I deals with the theoretical background and introduces the concept of spin currents on the basis of the two-current model, as well as the fundamentals of spin-orbit interaction (SOI) and spin relaxation processes.

Subsequently, the mechanisms of spin-charge interconversion by the spin Hall effect (SHE) as well as by the Rashba-Edelstein effect (REE) are presented, together with the underlying physics of the techniques used to characterize the spin-charge interconversion efficiency of metal/oxide 2DEGs, namely spin-pumped ferromagnetic resonance (SP-FMR) experiments and bilinear magnetoresistance (BMR) measurements. Finally, we provide the theoretical basis of spin-orbit torque (SOT), and make a brief introduction to antisymmetric exchange interaction (DMI) and chiral magnetic textures, such as skyrmions. On the other hand, Part II focuses on the synthesis and properties of metal/STO 2DEGs. Firstly, the factors that govern the 2DEG formation process by metal deposition are presented. Secondly, we present the particularities of these systems in terms of band structure, magnetotransport properties and behavior under an applied gate voltage.

The second chapter, Experimental Techniques, focuses on the theoretical principles and provides some practical details on the techniques employed during this thesis. We explain magnetron sputtering, which is the technique of choice for the synthesis of metal/oxide 2DEGs, as well as the basis of X-ray photoemission spectroscopy (XPS) and angle-resolved electron photoemission XVIII spectroscopy (ARPES). In addition, this chapter introduces the methods used to characterize the magnetotransport properties of metal/oxide 2DEGs, as well as to determine the ability of these systems for spin-charge interconversion and to exert a torque on the magnetization of a ferromagnetic thin film. Finally, the second chapter concludes by presenting the microscopy techniques used to image magnetic textures.

The third chapter, Results, concerns the results obtained during this work and is organized in four sections. The first section focuses on the characterization of metal/oxide 2DEGs by XPS, and their magnetotransport properties. The second section investigates the band structure of Al/KTO 2DEGs by using ARPES. The third section focuses on the ability of metal/oxide 2DEGs to carry out spin-charge interconversion processes. The last section is devoted to the optimization of Pt/Co/AlOX(TaOX)/STO heterostructures in order to investigate the ability of the metal/oxide 2DEGs to exert a torque on the magnetization of the adjacent ferromagnetic thin layer by harmonic Hall voltage technique, and to be combined with chiral magnetic textures.

The fourth chapter, Summary and Perspectives, provides a brief summary of this thesis and discuss the implications and prospects of this work in the near future. This chapter provides the theoretical basis for a better understanding of the thesis and is organized in two parts. Part I is further divided into three sections. The first section can be considered as an introduction to spinorbitronics in which spin and charge currents are differentiated, and the physical fundamentals related to spin-orbit coupling and spin relaxation mechanisms are explained. In the next section, the spin-charge interconversion phenomena by spin Hall and Rashba Edelstein effects, as well as their reciprocal mechanisms, are discussed. This section also presents the theoretical underpinnings of the techniques used to characterize the spin-charge interconversion properties of metal/oxide 2DEGs, and investigate the ability of these systems to exert a spin-orbit pair on an adjacent ferromagnetic thin film. Finally, the third section provides a brief introduction to chiral magnetic configurations, which we will try to combine with metal/oxide 2DEGs to demonstrate their manipulation by electric currents in the near future.

Part II focuses on more applied fundamentals. First, transition metal oxides are presented as ideal platforms for the investigation of exceptional physical phenomena, describing in detail the properties of the oxides used in this thesis, strontium titanate (STO) and potassium tantalate (KTO). Finally, the particularities of STO-based 2DEGs in terms of their band structure, transport properties and response to a gate voltage are presented in a third section.

Spinorbitronics

Spinorbitronics can be considered an emerging field of research that has certain advantages over conventional spintronics, such as higher efficiency of spin-charge interconversion through Hall and Rashba-Edelstein spin effects, and reciprocal mechanisms. This can also be achieved without an additional magnetic layer in order to polarize the current and can be applied to exert a torque on the magnetization, making these systems really attractive for manipulating the magnetization of a magnetic material by means of electric currents.

To facilitate the understanding of this thesis for those less familiar with these concepts, we begin with a brief introduction in which spin currents are differentiated from charge currents. Subsequently, the theoretical basis of the spin-orbit interaction by which the electron spin is coupled in momentum space is discussed, as well as the spin relaxation mechanisms by which a spin population returns to equilibrium, leading to the loss of information linked to the spin states.

Spin and Charge Currents: The Two-Current Model

The concept that electron spin affects transport properties was introduced in 1939 by Sir Neville Mott based on experimental results obtained on transport properties in transition metals and their alloys [START_REF] Mott | The electrical conductivity of transition metals[END_REF], [START_REF] Thomson | On the electro-dynamic qualities of metals: effects of magnetization on the electric conductivity of nickel and of iron[END_REF]. In particular, transport properties were found to be closely related to the state of magnetization in ferromagnetic materials: the resistance changed abruptly during the transition from/to paramagnetic state, near the Curie temperature (𝑇 𝑐 ), and varied proportionally with the magnetization upon application of an external magnetic field. These results led Mott to suggest the two-current model, which can be understood as the parallel electron transport through two spin channels, with different resistivity for inequivalent spin orientations in a ferromagnetic material below 𝑇 𝑐 .

Thirty years later, this model was confirmed experimentally by Albert Fert and Ian Campbell on NiFe-based alloys, providing a qualitative analysis of their results [START_REF] Fert | Two-current coduction in nickel[END_REF]- [START_REF] Fert | Electrical resistivity of ferromagnetic nickel-and iron-based alloys[END_REF] and deriving an expression for the electrical resistivity of a ferromagnetic material, which reads:

𝜌 = 𝜌 ↑ 𝜌 ↓ + 𝜌 ↑↓ (𝜌 ↑ + 𝜌 ↓ ) 𝜌 ↑ + 𝜌 ↓ + 4𝜌 ↑↓ , (1.1)
where 𝜌 ↑ and 𝜌 ↓ is, respectively, the resistivity for the spin-up and spin-down conduction electrons, and 𝜌 ↑↓ the spin-mixing resistivity term. In this expression, 𝜌 ↑↓ represents the scattering processes responsible for spin-reversal, or spin-flip, events that result in current transfer between the two spin channels. In this regard, Fert et al. showed that this term could not be attributed to the collision between electrons with opposite spins, but to electron-magnon scattering [START_REF] Fert | Electrical resistivity of ferromagnetic nickel-and iron-based alloys[END_REF]- [START_REF] Yamashita | Deviations from Matthiessen's rule in electrical resistivity of nickel-based alloys[END_REF] which is significant at temperatures comparable to 𝑇 𝑐 . Thus, when 𝑇 ≪ 𝑇 𝑐 , magnon interactions freeze out preventing spin-flip events and giving rise to a term 𝜌 ↑↓ → 0. The above expression then reduces to 𝜌 -1 = 𝜌 ↑ -1 + 𝜌 ↓ -1 , which corresponds to the resistance of two parallel channels with opposite spin direction.

On the other hand, the resistance for a given spin channel 𝜌 𝜎 can be described as a function of the effective mass 𝑚 𝜎 , the electron density 𝑛 𝜎 and the spin relaxation momentum 𝜏 𝑝,𝜎 (𝜎 denotes spin) as follows:

𝜌 𝜎 = 𝑚 𝜎 𝑛 𝜎 𝑒 2 𝜏 𝜎 , (1.2)
Thus, ignoring spin-flip events, the relaxation time 𝜏 𝜎 within a spin channel for a scattering potential 𝑉 ̂𝜎 can be estimated by Fermi's golden rule. In the Born approximation:

𝜏 𝜎 -1 ~2𝜋 ħ ∑|⟨𝑘 𝑓 | 𝑉 ̂𝜎|𝑘 𝑖 ⟩| 2 ∝ 𝑁 𝜎 (𝜀 𝐹 ), (1.3) where 𝑁 𝜎 (𝜀 𝐹 ) is the density of states (DOS) at the Fermi energy, and |𝑘 𝑖 ⟩ and |𝑘 𝑓 ⟩ are the initial and final states, respectively. Therefore, from this expression, it follows that the transport properties of transition metals are an intrinsic property since since 𝑚 𝜎 , 𝑛 𝜎 ,or 𝑁 𝜎 are spindependent.

In transition metals, the main contribution to the different resistivities for the two spin channels 𝜌 ↑ and 𝜌 ↓ , is given by the difference in the density of states near the Fermi level between the split spin d-subbands, i.e., 𝑁 𝑑,𝜎 (𝜀 𝐹 ). As a first approximation, one can assume that the current is dominated by the electrons in the outermost s orbitals, which have the possibility to scatter to the d-band states. Thus, since the density of these states at Fermi energy is different for opposite spins, the probability of scattering is different and gives rise to a strong asymmetry between 𝜌 ↑ and 𝜌 ↓ . As a graphical example, Fig. 1.1.1 shows that the density of states in the fermi energy is higher for the downward spin subband than for the upward spin subband, [𝑁 𝑑,↓ > 𝑁 𝑑,↑ ], so there is higher scattering tendency and higher resistivity in the spin-down channel. Finally, it should be noted that a larger difference between 𝜌 ↑ and 𝜌 ↓ can be induced by doping or alloying the materials [START_REF] Fert | Two-current coduction in nickel[END_REF], [START_REF] Campbell | Transport properties of ferromagnets[END_REF].

Thus, the charge carried can be different through both channels and the total charge current (𝑗 𝑐 ) is defined by the sum of both, while the spin current (𝑗 𝑠 ) is defined as the difference of the currents flowing through both channels, which is nonzero as soon both currents are inequivalent. energy (𝜀 𝐹 ) is higher for spin-down than for spin-up electrons. This leads to higher scattering into these levels and consequently to higher resistivity for the spin-down channel, as depicted by the two-current mode in panel (c).

𝑗 𝑐 = 𝑗 ↑ + 𝑗 ↓ (1.4a) 𝑗 𝑠 = 𝑗 ↑ -𝑗 ↓ (1.4b)

Spin-Orbit Coupling and Spin Relaxation Phenomena

The charge and spin currents are intimately related by the spin-orbit interaction (SOI). On the one hand, SOI couples the spin of electrons to their motion making spin-charge interconversion possible. On the other hand, it is also considered one of the main origins of spin relaxation, whereby information linked to the spin states is lost.

From a semiclassical point of view, the spin-orbit interaction (SOI) or spin-orbit coupling (SOC) can be considered as an electromagnetic induction field that acts on the electron when it moves with velocity 𝑣 around a nucleus. In the framework of Albert Einstein's relativity, the magnetic induction on the electron is given by:

𝐵 = 1 𝑐 2 𝐸 × 𝑣, (1.5)
where 𝑐 is the speed of light and 𝐸 is the electric field due to the nearby nucleus. As the magnetic field 𝐵 is perpendicular to 𝑣 and 𝐸, it is parallel to the angular momentum 𝐿, as depicted in panel (a) of Fig. 1.1.2, acting on the total spin magnetic moment 𝜇 which is antiparallel to 𝑆. Thus, the interaction of the magnetic moment of the electron 𝜇 interacts with the induction field 𝐵, adding an additional spin-orbit (SO) term to the Hamiltonian, which reads:

𝐻 ̂𝑆𝑂 = - 1 2 𝜇 • 𝐵, (1.6)
where

1 2
is the relativistic Thomas-Wigner factor [START_REF] Thomas | The motion of the spinning electron[END_REF], [START_REF] Wigner | On unitary representations of the inhomogeneous Lorentz group[END_REF]. Now, considering that the spin magnetic moment is defined as:

𝜇̂= -𝛾𝑆 ̂= - 𝑔 𝑒 𝑒 2𝑚 𝑒 𝑆 ̂, (1.7)
where 𝛾 is the gyromagnetic ratio, 𝑒 is the elementary charge, 𝑚 𝑒 the electron mass, and 𝑔 𝑒 the g-factor, respectively. This additional term added to the Hamiltonian can also be rewritten as:

𝐻 ̂𝑆𝑂 = - 𝑔 𝑒 𝑒 4𝑚 𝑒 2 𝑐 2 1 𝑟 𝑑𝑉(𝑟) 𝑑𝑟 𝑆 ̂• 𝐿 ̂, (1.8)
where the angular momentum is 𝐿 = 𝑟 × 𝑝, 𝑉(𝑟) the potential at a point 𝑟, and 𝑝 the electron momentum. Equation (1.8) already reveals the coupling between the spin (𝑆) and the orbital (𝐿) momentum. However, this expression requires an approximate value for 𝑉(𝑟) and calculating the coupling term 𝑆 ̂• 𝐿 ̂. In contrast, solid-state physics considers the Hamiltonian arising from the SO interaction, which can be expressed as follows:

𝐻 ̂𝑆𝑂 = ħ𝑔 𝑒 𝑒 8𝑚 𝑒 2 𝑐 2 (∇𝑉 × 𝑝) • 𝜎 ̂, (1.9a) 𝐻 ̂𝑆𝑂 = ħ 2 𝑔 𝑒 𝑒 8𝑚 𝑒 2 𝑐 2 (E × 𝑘 ̂) • 𝜎 ̂, (1.9b)
where 𝑝̂= ħ𝑘 ̂≡ -𝑖ħ∇ is the linear momentum operator, and 𝜎 ̂ are the Pauli matrices, so that 𝑆 ̂= ħ 2 𝜎 ̂. The total potential 𝑉 can be defined as a periodic potential corresponding to the lattice and an aperiodic part that represents the contribution from impurities, external electric fields, confinement and boundaries. Thus, the electron spin 𝜎 is coupled to the momentum 𝑘 by the SOI, causing it to precess about the induction field direction, while the motion of the electron around the nucleus causes this precession to fluctuate in both magnitude and orientation. This phenomenon implies that spin is not conserved, which is one of the main challenges of spin transport. Specifically, the process by which a spin population returns to equilibrium is called spin relaxation, and can occur by different mechanisms arising from the SOI itself or from hyperfine interactions. In the following, spin relaxation mechanisms are introduced considering the motion of an electron in the presence of a fluctuating magnetic field. Subsequently, the two main mechanisms for spin relaxation arising from SOI, the Elliot-Yafet and the D'yakonov-Perel' mechanisms, are presented. Finally, the spin relaxation mechanism emerging from hyperfine interactions between the electron spin and the nucleus spin are briefly introduced.

Electron spin in a fluctuating magnetic field

The spin relaxation and dephasing times, respectively 𝑇 1 and 𝑇 2 , can be defined with the Bloch-Torrey equations for magnetization dynamics, as well as derived by means of a 'toy model', in which the electron spin in a fluctuating magnetic field is considered, i.e., following the approach of Fabian and Wu [START_REF] Fabian | Spin relaxation and spin dynamics in semiconductors[END_REF].

The dynamics of a single electron with spin 𝑆 in the presence of an external magnetic field along 𝑧, defined by a longitudinal static component 𝐵 0 and a transverse component fluctuating around zero 𝐵 ⊥ , is determined by the Bloch equations [START_REF] Fabian | Spin relaxation and spin dynamics in semiconductors[END_REF], [START_REF] Bloch | Nuclear induction[END_REF]:

𝜕𝑆 𝑦 𝜕𝑡 = -𝜔 0 𝑆 𝑥 - 𝑆 𝑦 𝑇 2 , (1.10a) 𝜕𝑆 𝑦 𝜕𝑡 = -𝜔 0 𝑆 𝑥 - 𝑆 𝑦 𝑇 2 , (1.10b) 𝜕𝑆 𝑧 𝜕𝑡 = - 𝑆 𝑧 -𝑆 𝑧 0 𝑇 1 , (1.10c)
where 𝑆 𝑧 0 is the value of the spin at equilibrium in the presence of a static magnetic field 𝐵 0 given by the Larmor frequency, 𝜔 0 = with 𝜏 𝑐 being the time it takes for the phase of the effective magnetic field to be lost. In systems in which conduction is mediated by electron transport, 𝜏 𝑐 is defined by the momentum relaxation time 𝜏 𝑝 . Typically, these times correspond to magnitudes below picoseconds and, therefore, 𝑇 1 = 𝑇 2 is satisfied for magnetic fields up to several tesla.

Qualitatively, spins oriented along a magnetic field can precess a full period with the same phase shift in terms of the transverse component. On the other hand, if the external field |𝐵 0 | increases, the variation of the longitudinal component (𝑆 𝑧 ) is reduced, inhibiting the phase shift. For a weak magnetic field (𝜔 0 𝜏 𝑐 ≪ 1), this "toy model" gives rise to a general expression which takes the form:

1 𝑇 1 = 1 𝑇 2 = 𝜔 2 ̅̅̅̅ 𝜏 𝑐 , (1.11)
where the overline denotes the average for random occurrences of 𝐵(𝑡). Surprisingly, from equation (1.11), we find that the spin relaxation time is inversely proportional to the correlation time 𝜏 𝑐 and, therefore, the more random the magnetic field the less the electron spin decays.

This can be explained by the well-known motional narrowing phenomenon whereby the phase shift is inhibited by random fluctuations of the magnetic field [START_REF] Zutic | Spintronics: fundamentals and applications[END_REF]. In the following, we will present the main mechanisms of spin relaxation that lead to a loss of spin information.

Elliot-Yafet spin relaxation mechanism

In this mechanism [START_REF] Elliot | Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors[END_REF], the spin relaxation process is attributed to momentum dispersion, either by phonons at high temperature or by impurities at low temperature. This process thus requires coupling of the electron spin wave function to the ion lattice, i.e., it requires SOI. In this context, Elliot considered the case of elementary metals with inversion symmetry and showed that the Bloch wave functions in the presence of SOI under the form of equation (1.9a) are not eigenstates of 𝜎 ̂𝑧, but a mixture of spin-up |↑⟩ and spin-down |↓⟩ states, the Pauli spinors. Furthermore, a spin-dependent scalar and periodic ion potential is considered in this model, as well as spin relaxation for conduction electrons is attributed to spin-flip events, which occur approximately every 100 scattering events in metals [START_REF] Beuneu | The Elliot relation in pure metals[END_REF]. On this way, Elliot managed to relate the spin relaxation time 𝑇 1 to the deviation of the g-factor from the value corresponding to a free electron 𝑔 0 =2.0023, by means of [START_REF] Elliot | Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors[END_REF]:

1 𝑇 1 = 𝜉 (𝛿𝑔) 2 𝜏 𝑝 , (1.12)
where 𝛿𝑔 = (𝑔 -𝑔 0 ), 𝜏 𝑝 the momentum relaxation time, and 𝜉 is a numerical coefficient later introduced by Beuneu and Monod [START_REF] Beuneu | The Elliot relation in pure metals[END_REF], whose value depends on the dominant scattering mechanism (phonons, charge or neutral impurities). The experimental value of the g-factor can be measured by (conduction) electron spin resonance ((C)ESR), also known as electron paramagnetic resonance (EPR) spectroscopy. Thus, by applying this model the spin relaxation time can be estimated from the ratio 𝜏 𝑝 /𝑇 1 , which depends on the scattering mechanisms involved.

Years later, Yafet considered systems with a broken inversion symmetry in terms of the band structure and related the temperature dependence of the spin relaxation rate to that of the resistivity 𝜌 [START_REF] Khaetskii | Spin relaxation in semiconductor quantum dots[END_REF] as follows:

1 𝑇 1 (𝑇) ~ ρ(T), (1.13)
Thus, assuming that no Umklapp processes contribute to the resistivity and knowing that 𝜏 𝑝 -1 ~ ρ(T), Yafet showed that, for centrosymmetric conductors in the presence of electron and phonon scattering processes at low temperature, the dependence of the spin relaxation time on temperature was similar to the Bloch-Grüneisen law for the resistivity of metals [START_REF] Ashcroft | Solid State Physics[END_REF], i.e., 𝑇 1 (𝑇)~ 𝑇 -5 .

Within this model, both spin events and spin relaxation are attributed to electron-phonon interactions. These two processes are usually of the same magnitude and should be considered simultaneously to not overestimate the spin relaxation rate, since the interaction is destructive.

Although this model may not be valid in all the cases, as for Si, where 𝑇 1 (𝑇)~𝑇 -3 [START_REF] Cheng | Theory of the spin relaxation of conduction electrons in silicon[END_REF], its validity for elementary metals has been tested by Beauneu and Monod [START_REF] Beuneu | The Elliot relation in pure metals[END_REF], [START_REF] Monod | Conduction-electron spin flip by phonons in metals: analysis of experimental data[END_REF].

The Elliot-Yafet spin relaxation mechanism is determined from the dependence of the relaxation time on temperature such that 𝜏 𝑠𝑓 ≡ 𝑇 1 , which is expected to vary with momentum relaxation time, as depicted in Fig. 1.1.3 (a), according to [START_REF] Pikus | Spin Relaxation under Optical Orientation in Semiconductors[END_REF]:

1 𝜏 𝑠𝑓 𝐸𝑌 (𝜀 𝑘 ) = 𝜉 (𝜆 𝑆𝑂 ) 2 (∆𝜀) 3 𝜀 𝑘 𝜏 𝑝 (𝜀 𝑘 ) , (1.14)
where 𝜉 is the numerical prefactor introduced by Beauneu and Monod [START_REF] Beuneu | The Elliot relation in pure metals[END_REF], 𝜆 𝑆𝑂 is the atomic spin-orbit coupling constant (or energy gap between electrons with opposite spins in a given band), and ∆𝜀 is the gap energy from the conduction band to the nearest valence band (i.e., the band gap energy in a semiconductor) to which it is coupled by the SOI. According to expression (1.14), the lower the gap energy and the larger the induced spin orbital in centrosymmetric conductors, the shorter the Elliot-Yafet spin relaxation time 𝜏 𝑠𝑓 𝐸𝑌 , i.e., the faster the electron spin decays and the faster the spin information is lost.

D'yakonov-Perel' spin relaxation mechanism

Dyaknonov and Perel' [START_REF] Dyakonov | Current-induced espin orientation of electrons in semiconductors[END_REF], [START_REF] Marushchak | The effect of strain on the spin relaxation of conduction electrons in Ill-V semiconductors[END_REF] also proposed a SOC-based spin relaxation mechanism for systems with lack of inversion symmetry either of the same crystal structure (e.g., zinc-blende),

or by the presence of a heterointerface (such as surfaces or interfaces).

For crystal structures without inversion symmetry, spin-orbit coupling lifts the spin degeneracy in the band structure, 𝜀 𝑘,↑ ≠ 𝜀 𝑘,↓ , preserving the Kramers degeneracy due to time-reversal symmetry, 𝜀 𝑘,↑ = 𝜀 -𝑘,↓ . That is, considering that momentum 𝑘 represents the position of the electron in reciprocal space, electrons with opposite spin polarizations do not have the same energy at the same 𝑘 position, but they do have the same energy when placed in inverse positions, i.e., 𝑘 and -𝑘. The spin-orbit coupling is described by a spin-orbit effective field 𝐵 𝑆𝑂 (𝑘), which emerges from the band structure, and introduces a Zeeman-type term in the Hamiltonian of the form: where 𝛺 𝑘 = 𝑒𝑔 𝑒 2𝑚 𝑒 𝐵 𝑆𝑂 (𝑘) is analogous to the spin precession frequency around 𝐵 𝑆𝑂 , also known as the Larmor frequency, and which we will conveniently refer to as the effective SO field. The time symmetry requires that 𝛺 𝑘 be an odd function of momentum, 𝛺 𝑘 = -𝛺 -𝑘 , which makes the electron wave functions not a pure Zeeman state, but a mixture of up and down spin states.

𝐻 ̂𝑆𝑂 𝐷𝑃 = ħ𝑒𝑔 𝑒 4𝑚 𝑒 𝐵 𝑆𝑂 (𝑘) • 𝜎 ̂= ħ 2 𝛺 𝑘 • 𝜎 ̂, (1.15)
Within the D'yakonov-Perel' relaxation mechanism, the spin of electrons, which obey 𝛿𝑆 𝛿𝑡 = 𝛺 𝑘 × 𝑆, experience a fluctuating effective field as 𝛺 𝑘 𝜏 𝑝 ≤ 1. Thus, the spin phase traverses a random path in a time interval determined by the momentum dispersion 𝜏 𝑝 , which plays the role of correlation time 𝜏 𝑐 . Thus, after an average time 𝜏 𝑝 , the spin of an individual electron scatters from 𝑘 to 𝑘' and the effective field 𝛺 𝑘 becomes distinct. The D'yakonov-Perel' relation, valid for 𝛺 ̅ 𝑘 𝜏 𝑝 ≤ 1, is given by:

1 𝜏 𝑠 𝐷𝑃 (𝜀 𝑘 ) = 𝜉𝛺 ̅ 𝑘 𝜏 𝑝 (𝜀 𝑘 ), (1.16)
where 𝜉 is again the numerical coefficient that depends on the specific momentum relaxation mechanism. The effective SO field 𝛺 ̅ 𝑘 emerging from the band structure exhibits two terms: one due to a lack of inversion symmetry of the crystal structure (bulk inversion symmetry (BIA), or

Dresselhaus) [START_REF] Dresselhaus | Spin-orbit coupling effects in zinc blende structures[END_REF], and one related to the presence of heterointerfaces (structure inversion symmetry (SIA), or Bychkov-Rashba) [START_REF] Rashba | Spin-orbit coupling in condensed matter physics[END_REF]- [START_REF] Bychkov | YuBychkov_Rashba_JournalofExperimentalTheoretical_Phys_Lett_1984[END_REF].

On the one hand, Dresselhaus previously demonstrated that the spin splitting induced in crystals with zinc-blende crystal structure is proportional to the cube of the lattice momentum [START_REF] Dresselhaus | Spin-orbit coupling effects in zinc blende structures[END_REF]. In this context, D'yakonov and Perel' showed that the effective SO field arising from the BIA can also be written as [START_REF] Marushchak | The effect of strain on the spin relaxation of conduction electrons in Ill-V semiconductors[END_REF]:

𝛺 𝑘 𝐵𝐼𝐴 = ħ 2 𝛽 𝐷 √2𝑚 𝑐 3 𝜀 𝑔 𝜅(𝑘), (1.17)
where 𝛽 𝐷 is a dimensionless parameter representing the Dresselhaus SOI strength, 𝑚 𝑐 is the effective mass of the electron in the conduction band, 𝜀 𝑔 is the bandgap energy, and

𝜅(𝑘) = [𝑘 𝑥 (𝑘 𝑦 -𝑘 𝑧 ) 2 , 𝑘 𝑦 (𝑘 𝑧 -𝑘 𝑥 ) 2 , 𝑘 𝑧 (𝑘 𝑥 -𝑘 𝑦 ) 2 ]
, where 𝑘 𝑖 is the lattice wave vector components.

On the other hand, Bychkov and Rashba considered spin-splitting induced by an asymmetric confining potential normal to the interface, as is the case for heterostructures and quantum wells (QWs). Considering the Hamiltonian in equation (1.15), the effective SO field due to the SIA was defined as [START_REF] Bychkov | Oscillatory effects and the magnetic susceptibility of carriers in inversion layers[END_REF], [START_REF] Bychkov | YuBychkov_Rashba_JournalofExperimentalTheoretical_Phys_Lett_1984[END_REF]:

𝛺 𝑘 𝑆𝐼𝐴 = 2𝛼 𝑅 ħ (𝑘 × 𝑧), (1.18)
where 𝑧 is the unit vector normal to the interface and 𝛼 𝐵𝑅 is the Bychkov-Rashba SOI strength (in units of eV•m). It should be noted that when 𝛺 𝑘 𝑆𝐼𝐴 and 𝛺 𝑘 𝐵𝐼𝐴 are of the same order of magnitude, this gives rise to in-plane anisotropic phase shift velocities, as shown in [001] QWs [START_REF] Kainz | Anisotropic spin-splitting and spin-relaxation in asymmetric zinc blende semiconductor quantum structures[END_REF], [START_REF] Averkiev | Giant spin relaxation anisotropy in zinc-blende heterostructures[END_REF].

The most striking difference between the Elliot-Yafet and D'yakonov-Perel' relaxation mechanisms is their opposite dependence on the momentum relaxation time 𝜏 𝑝 , as depicted in Fig. Finally, it should be noted that, in systems with absence of inversion symmetry, both relaxation mechanisms compete, and the dominance of one or the other depends on the material under consideration, as well as its crystal structure, orientation, and conditions such as temperature or doping.

Mechanism of spin relaxation by hyperfine interactions

The hyperfine interaction corresponds to the exchange interaction between electron spin and nuclear spin, which provides an important mechanism for concerted spin dephasing [START_REF] Perel | Optical orientation in a system of electrons and lattice nuclei in semiconductors. Theory[END_REF], as well as for individual spin decoherence at donor sites [START_REF] Khaetskii | Spin relaxation in semiconductor quantum dots[END_REF], [START_REF] Paget | Low field electron-nuclear spin coupling in gallium arsenide under optical pumping conditions[END_REF] or quantum dots. In the context of spintronics, hyperfine interaction may play an important role in spin depolarization during electrically driven spin current injection experiments [START_REF] Chan | Hyperfine interactions and spin transport in ferromagnet-semiconductor heterostructures[END_REF].

The static hyperfine interaction between the electron spin 𝑆 at position 𝑟 and a nuclear spin 𝐼 𝑗 at position 𝑅 𝑗 , where j denotes the j-th nucleus, is described by the Fermi contact Hamiltonian [START_REF] Perel | Optical orientation in a system of electrons and lattice nuclei in semiconductors. Theory[END_REF], [START_REF] Paget | Optical Orientation[END_REF]:

𝐻 ̂= 8𝜋 3 𝜇 0 4𝜋 𝑔 0 ħ𝜇 𝐵 𝛾 𝑛 𝑆 ̂• 𝐼 ̂𝑗𝛿(𝑟 -𝑅 𝑗 ), (1.19)
where 𝜇 0 is the vacuum permeability, 𝑔 0 =2.0023 is the free electron g-factor, 𝜇 𝐵 is the Bohr magneton, 𝛾 𝑛 is the nuclear gyromagnetic ratio. Therefore, localized electrons experience the combination of moments of a large number of nuclei (typically 10 4 -10 6 lattice sites) and an effective magnetic field 𝐵 𝑛 given by [START_REF] Paget | Optical Orientation[END_REF]:

𝐵 𝑛 = 2 3 𝜇 0 𝑔 0 𝑔 ħ𝛾 𝑛 〈𝐼〉|𝜓 𝑘 (𝑅 𝑗 )| 2 , (1.20)
where 𝜓 𝑘 (𝑅 𝑗 ) is the enveloping wave function at the nucleus site. In particular, equation (1.20) corresponds to the case of a uniformly polarized nucleus with a nuclear spin 〈𝐼〉 throughout the probed interaction volume. When two of the nuclear spins are aligned, |𝐵 𝑛 | can reach values up to tesla. However, the interaction with the nuclear spins causes the electron spin phase to experience a random walk, and a strongly reduced effective field.

In metals and semiconductors, these hyperfine interaction mechanisms are negligible in terms of effective spin relaxation when compared to SO-induced mechanisms (i.e., Elliot-Yafet and D'yakonov-Perel' mechanisms). Due to their delocalized nature, conduction electrons are weakly coupled to the nucleus and spin relaxation induced by hyperfine interactions is strongly inhibited [START_REF] Overhauser | Paramagnetic Relaxation in Metals[END_REF]. In contrast, hyperfine interactions play an important role in relaxing the spin of electrons localized in a confined volume, such as at dangling boundaries, donor sites, and quantum dots.

Spin-Charge Interconversion and Spin-Orbit Torque

Once the theoretical basis of spin-orbit coupling and spin relaxation mechanisms have been presented, in this section we address SOC-derived effects, with high applicability in spintronics.

In particular, SOC allows spin-charge interconversion and the possibility of exerting a torque on the magnetization of a magnetic material. The different mechanisms by which spin-charge interconversion can take place, such as the spin Hall effect and the Rashba Edelstein effect, as well as their reciprocal effects, are introduced. This section also discusses the fundamentals of the techniques used for the characterization of the conversion properties of metal/oxide 2DEGs, and introduces the theoretical foundations of the spin-orbit pair.

Spin Hall Effect

The spin Hall effect (SHE) is a phenomenon by which a charge current is partially converted into a spin current transverse to the current direction in non-magnetic materials, which originates from the SOI [START_REF] Dyakonov | Current-induced espin orientation of electrons in semiconductors[END_REF]. On the other hand, the inverse spin Hall effect (ISHE) is the reciprocal phenomenon whereby a spin current is partially converted into a transverse charge current [START_REF] Averkiev | Giant spin relaxation anisotropy in zinc-blende heterostructures[END_REF]. The spin and charge currents for SHE and ISHE are related by:

𝑗 𝑠 𝑆𝐻𝐸 = - ħ 2𝑒 𝜃 𝑆𝐻𝐸 (𝑗 𝑐 × 𝑠), (1.21a) 𝑗 𝑐 𝐼𝑆𝐻𝐸 = - 2𝑒 ħ 𝜃 𝑆𝐻𝐸 (𝑗 𝑠 × 𝑠), (1.21b)
where 𝑠 is the spin polarization, and 𝜃 𝑆𝐻𝐸 = 𝜎 𝑥𝑦 𝑆𝐻𝐸 /𝜎 𝑥𝑥 , the so-called spin Hall angle, represents the conversion efficiency of charge currents into spin currents by the SHE, or vice versa by the ISHE. In the following, we will discuss the three main mechanisms identified from semiclassical transport theory, which are classified as extrinsic, if due to impurities giving rise to spindependent scattering times (skew jump and side-jump mechanisms), or intrinsic, if attributed to the band structure of the material.

Extrinsic mechanisms

Mott was the first to show that SOI gives rise to asymmetric scattering of spin-carrying particles [START_REF] Mott | The scattering of fast electrons by atomic nuclei[END_REF]. From a semiclassical point of view, electron scattering by charged impurities generates a transverse force acting on the electron proportional to the Zeeman energy, 𝑔 𝑒 𝜇 𝐵 𝐵 • 𝑆.

Since the direction of the force depends on the spin orientation, the spin-up and spin-down are deflected in opposite directions (see panel (a) of Fig. ). This mechanism known as Mott-skew scattering was proposed to explain, among other phenomena, the anomalous Hall effect (AHE) [START_REF] Smit | Magnetoresistance of ferromagnetic metals and alloys at low temperatures[END_REF], [START_REF] Smit | The spontaneous Hall effect in ferromagnetics I[END_REF]. In addition, this mechanism was adopted by D'yakonov and Perel' to predict a non-equilibrium spin accumulation on the sides of a current-carrying non-magnetic conductor, with opposite spin directions on opposite sides [START_REF] Dyakonov | Current-induced espin orientation of electrons in semiconductors[END_REF]. This effect was theoretically rediscovered 28 years later by Hirsch, who coined it the spin Hall effect [START_REF] Hirsch | Spin Hall effect[END_REF].

On the other hand, the side-jump mechanism proposed by Berger [START_REF] Berger | Comment on side-jump and side-slide mechanisms for ferromagnetic Hall effect: a Reply[END_REF], [START_REF] Berger | Side-jump mechanism for the Hall effect of ferromagnets[END_REF] to explain the anomalous Hall effect (AHE) in magnetic materials is described as a lateral displacement of the wave vector at each scattering event, which also depends on the spin and contributes to the spin Hall conductivity (𝜎 𝑥𝑦 𝑠-𝑗 ) (Fig. 1.2.2. (b)). Finally, the understanding of side-jump scattering falls within the field of quantum, and its importance with respect to skew scattering is still under debate [START_REF] Sinova | Spin Hall effect[END_REF]- [START_REF] Nagaosa | Anomalous Hall effect[END_REF].

Intrinsic mechanisms

In turn, Karplus and Luttinger proposed an intrinsic mechanism to explain the AHE. Thus, this mechanism did not depend on spin-dependent scattering, but was due to spin splitting bands near the Fermi level in the presence of SOI. In this sense, the semiclassical Boltzmann approximation leads to the following expression for the carrier velocity:

𝑣 𝑘 = 1 ħ 𝛿𝜀 𝑘 𝛿𝑘 + 𝑒𝐸 × 𝛺 𝑘 , (1.22)
where the first term is the normal velocity, and the second is the abnormal velocity related to the Berry curvature 𝛺 𝑘 of the Bloch band. For quasiparticles, 𝛺 𝑘 acts as an effective magnetic field in reciprocal space, emerging from the SOI induced at inter-band crossing points. Remarkably, 𝛺 𝑘 is nonzero for systems with broken-time-reversal symmetry, or broken inversion symmetry. In turn, Berry's phase leads to a component of the Hall conductivity (𝜎 𝑥𝑦 𝑖𝑛𝑡 ), and is the origin of the AHE and (I)SHE. The intrinsic mechanism can be very large in heavy metals with a strong SOC (SOC ∝ Z 4 ), such as Pt, which has become the most common system for ISHE study.

Rashba Effect, Edelstein Effect, and Inverse Edelstein Effect

Edelstein effects are an alternative means for spin-charge interconversion in systems with lack of structure inversion symmetry (SIA), such as two-dimensional electron gases (2DEG). On the one hand, the inverse Edelstein effect (IEE) allows the conversion of pure spin currents into charge currents and is, therefore, the analogue of ISHE. On the other hand, the reciprocal Onsager effect, called the direct Edelstein effect (DEE), allows the conversion of charge currents into spin currents as the SHE. However, before introducing the Edelstein effects, it is necessary to introduce the two-dimensional Bychkov and Rashba Hamiltonian for systems with broken inversion symmetry.

Rashba spin-orbit interaction

The Rashba effect appears as a manifestation of SOI in solids, where spin degeneracy arises due to SIA. This 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] Rashba | Spin-orbit coupling in condensed matter physics[END_REF] in two-dimensional quantum wells and electron gases, where a potential gradient in the normal direction 𝐸 = 𝐸 𝑧 𝑧 leads to inversion symmetry breaking. Thus, the Bychkov-Rashba spin-orbit Hamiltonian is defined by:

𝐻 𝑅 (𝑘) = ħ 2 𝑘 2 2𝑚 + 𝛼 𝑅 (𝑘 × 𝑧) • 𝜎, (1.23)
where the first term represents the free-electron dispersion relation and the second term is the spin-orbit Hamiltonian, with 𝛼 𝑅 being the Rashba coefficient, 𝑘 the wave vector in the 2DES plane, 𝑧 the unit vector normal to the 2DES plane, and 𝜎 the unitary Pauli spin matrices (𝜎 = (2/ħ)𝑠).

The solutions to the Schrödinger equation with the Rashba Hamiltonian are given by: On the other hand, SIA gives rise to an effective magnetic field 𝛺 𝑘 𝑆𝐼𝐴 that acts on non-equilibrium spins and induces spin relaxation in the D'yakonov-Perel' frame. This magnetic field depends on the momentum as follows:

𝜀 ± (𝑘) = ħ 2 𝑘 2 2𝑚 ± 𝛼 𝑅 𝑘, ( 1
𝛺 𝑘 𝑆𝐼𝐴 = 2𝛼 𝑅 ħ (𝑘 × 𝑧), (1.25)

Direct and Inverse Edelstein effects

On this basis, we can derive the relationship between the charge current and the non-equilibrium spin density following the approach of Rojas Sanchez et al. [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF], who was the first to successfully demonstrate the inverse Edelstein effect (IEE) at Ag/Bi(111) interfaces.

In the presence of a two-dimensional charge density, 𝑗 𝑐 , along -𝑥, the two Fermi contours shift in the same direction by the same amount of ∆𝑘 𝑥 , yielding two excess spin densities δ𝑠 + and δ𝑠 - with opposite polarization along 𝑦, as shown in Fig. (𝑘 𝐹 + ∆𝑘𝑥), are not equivalent. In the free-electron model, the relation between the twodimensional charge current density 𝑗 𝑐 ± carried by the two Fermi contours and the corresponding spin densities δs ± can be written as [START_REF] Gambardella | Current-induced spin-orbit torques[END_REF]:

δs ± = ± 𝑚 2𝑒ħ𝑘 𝐹 ± 𝑗 𝑐 ± , (1.26)
where 𝑗 𝑐 = (𝑗 𝑐+ + 𝑗 𝑐-) is the total two-dimensional charge current density. By considering the relationship between the Rashba SOI strength 𝛼 𝑅 and the difference between the two Fermi surfaces defined by:

(𝑘 𝐹+ -𝑘 𝐹-) = 2𝑘 𝑅 = 2𝑚 ħ 2 𝛼 𝑅 , (1.27)
The out-of-equilibrium spin accumulation 〈𝛿𝑠〉 = (𝛿𝑠 + + 𝛿𝑠 -) created by the DEE is determined by: ). As a result, this effect leads to uncompensated charge currents such that 𝑗 𝑐 = (𝑗 𝑐+ + 𝑗 𝑐-) ≃ 𝑒ħ/𝑚(𝑘 𝐹+ -𝑘 𝐹-)〈𝛿𝑠〉.

〈𝛿𝑠〉 = ħ 𝑒𝛼 𝑅 𝑗 𝑐 , ( 1
Furthermore, using the latter expression in combination with the relation given in (1.27), we arrive at equation (1.28), allowing us to reciprocally relate the charge currents and the out-ofequilibrium averaged spin density generated by both Edelstein effects.

Finally, it is convenient to relate the average spin accumulation 〈𝛿𝑠〉, spin currents 𝑗 𝑠 and charge currents 𝑗 𝑐 for both DEE and IEE. Assuming that the origin of a spin accumulation 〈𝛿𝑠〉 along 𝑦 is a spin current directed along -𝑧 [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] as well as that the momentum transmission/reflection from the source of the spin density to the drain is isotropic, the relation between 𝑗 𝑠 and 〈𝛿𝑠〉 is given by:

𝑗 𝑠 𝑒 = 〈𝛿𝑠〉 𝜏 𝑠 * , (1.29)
where 𝜏 𝑠 * is the effective spin-momentum relaxation time expressing the balance between spin injection and spin density, under the assumption that spin and momentum are completely locked in a pure SOI Rashba regime. Within the "microscopic theory of the inverse Edelstein effect", Shen, Vignale, and Raimondi [START_REF] Shen | Microscopic theory of the inverse Edelstein effect[END_REF] provided an expression for 𝜏 𝑠 * in terms of the momentum relaxation time, the Elliot-Yafet (EY) and D'yakonov-Perel' spin relaxation times, which translates to: where 𝜆 𝐼𝐸𝐸 represents the spin-to-charge conversion efficiency by the IEE and thus has a similar role to that of the spin Hall angle 𝛳 𝑆𝐻𝐸 in the ISHE. Unlike the (I)SHE, where the charge current and spin current are both three-dimensional, resulting in a dimensionless ratio that defines the 𝛳 𝑆𝐻𝐸 , the charge current in the Edelstein effects is, by definition, two-dimensional. This makes the efficiency factor not dimensionless, but measured in units of length [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF].

𝜏 𝑠 * = 1 𝜏 𝐸𝑌 -1 + 𝜏 𝐷𝑃 -1 , ( 1
During this thesis, we will investigate the spin-charge interconversion efficiency of twodimensional electron gases (2DEGs), for which we need to be able to create spin currents and detect the generated charge currents, or vice versa. In the next two sections, we will give a brief introduction to the background and fundamentals of the two techniques used to determine conversion efficiencies. On the one hand, spin pumping ferromagnetic resonance (SP-FMR)

experiments will be performed to determine the spin-to-charge conversion efficiency, as well as bilinear magnetoresistance (BMR) measurements will be performed to determine the charge-tospin conversion efficiency. Technical details regarding the practical measurements will be discussed in Sec. 2.3.3 and 2.3.2, respectively.

Spin-Pumping Ferromagnetic Resonance

Ferromagnetic resonance

In a ferromagnetic material, strong exchange interactions tend to align the magnetic moments in the same direction, allowing the description of the spin ensemble as a macrospin with magnetization 𝑀 ⃗⃗ . As such, the first theoretical description of the precession of the magnetization in a ferromagnetic was proposed by Lev Davidovitch Landau and Evgeny Mikhailovich Lifshitz in 1935 [START_REF] Landau | On the theory of dispersion of the magnetic permeability bodies[END_REF]. Their equation, coined as Landau-Lifschitz equation, describes the motion of magnetization around an effective magnetic field (𝐻 ⃗ ⃗ 𝑒𝑓𝑓 ):

𝑑𝑀 ⃗⃗ 𝑑𝑡 = -𝛾𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 , (1.33)
where 𝛾 is the gyromagnetic ratio defined as 𝛾 = 𝑔𝜇 𝐵 ℏ , 𝑔 is the electron g-factor (being 2 < g < 2.2 in a ferromagnetic material), 𝜇 𝐵 is the Bohr magneton and ℏ is the reduced Planck constant. Here, 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 is the effective magnetic field, which accounts for all external and internal sources of magnetic fields, including the external magnetic field 𝐻 ⃗ ⃗ 0 , the demagnetizing field 𝐻 ⃗ ⃗ 𝐷 , and the anisotropy field 𝐻 ⃗ ⃗ 𝑘 , as follows:

𝐻 ⃗ ⃗ 𝑒𝑓𝑓 = 𝐻 ⃗ ⃗ 0 + 𝐻 ⃗ ⃗ 𝐷 + 𝐻 ⃗ ⃗ 𝑘 , (1.34)
According to Landau-Lifschitz equation, the magnetization will describe a perpetual precession around the effective field axis, as depicted in Fig. 1.2.4 (a). However, this situation does not represent a real system, in which several processes such as electron-phonon, electron-magnon or magnon-phonon scattering result in a loss of angular momentum. In order to describe the magnetization dynamics by considering the losses and the consequent relaxation of the magnetization towards its equilibrium, Gilbert added a new damping term to equation 1.33. Thus, the Landau-Lifshitz-Gilbert (LLG) takes the form [START_REF] Gilbert | A phenomenological theory of damping in ferromagnetic materials[END_REF]:

𝑑𝑀 ⃗⃗ 𝑑𝑡 = - 𝑔𝜇 𝐵 ℏ 𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 + 𝛼 𝑀 𝑠 𝑀 ⃗⃗ × 𝑑𝑀 ⃗⃗ 𝑑𝑡 , (1.35)
where 𝛼 is the dimensionless Gilbert damping constant and 𝑀 𝑠 is the saturation magnetization.

In the presence of damping, the magnetization 𝑀 ⃗⃗ precesses around the direction imposed by the magnetic field until they align, as illustrated in Fig. 1.2.4 (b). The Gilbert damping then describes how fast the magnetization aligns with 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 , which occurs within a time scale of ℏ 𝛼𝑔𝜇 𝐵 𝐻 𝑒𝑓𝑓 ⁄ .

A magnetized material is then a damped harmonic oscillator characterized by its own resonance frequency. If an external magnetic field (𝐻 0 ⃗⃗⃗⃗ ) oscillates at the resonance frequency, the precession motion is strongly amplified and can even be maintained. This is precisely the ferromagnetic resonance (FMR) condition which is obtained by solving the LGG equation. This effect was first observed by J. H. E. Griffiths in ferromagnetic metals in 1946 [START_REF] Griffiths | Anomalous high-frequency resistance of ferromagnetic metals[END_REF]. In order to avoid unnecessary long calculations, we will not derive the resolution of LGG equation, but it can be easily found for instance in ref. [START_REF] Farle | Ferromagnetic resonance of ultrathin metallic layers[END_REF].

In practice, the resonance condition is sought by applying a static (DC) magnetic field to establish the single domain configuration, as well as a small radiofrequency (RF) magnetic field, which acts as a periodic excitation (see section 2.3.3 for experimental details). Thus, the DC magnetic field creates an energy splitting of the eigenstates, the so-called Zeeman splitting, whose energy increases as a function of the applied magnetic field and is given by 𝐸 = 𝑔𝜇 𝐵 𝐻. In this way, the microwave RF field can excite magnetic dipole transitions between the unfolded levels if a suitable energy 𝐸 = ℏ𝜔 is provided, as depicted in Fig. 1.2.4 (c). The resonance condition is usually achieved by adjusting the DC magnetic field, since the variation of the microwave frequency over large ranges is more complicated, when the following expression is satisfied:

𝜔 𝑟𝑒𝑠 = 𝛾𝐻 ⃗ ⃗ 𝑒𝑓𝑓 , (1.36)
This equation is different from the well-known Kittel relation, since it is not considering the link between 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 and the magnetic field via the demagnetizing field. The resonance condition taking into account the Kittel relation would take the form:

𝜔 𝑟𝑒𝑠 = 𝛾 √ (𝑀 𝑆 + 𝐻 ⃗ ⃗ 0 + 𝐻 ⃗ ⃗ 𝑘 )(𝐻 ⃗ ⃗ 0 + 𝐻 ⃗ ⃗ 𝑘 ), (1.37)

Spin-pumping at resonance

Spin pumping by ferromagnetic resonance (SP-FMR) is one of the most popular techniques to investigate spin-to-charge conversion mechanisms such as ISHE or IEE. The first to demonstrate injection of a spin current by ferromagnetic resonance were the pioneers Silsbee and Johnson [START_REF] Johnson | Coupling of electronic charge and spin at a ferromagneticparamagnetic metal interface[END_REF] in the 1980s. Later, Tserkovniak, Brataas, Mizukami et al. [START_REF] Mizukami | Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films[END_REF], [START_REF] Tserkovnyak | Enhanced gilbert damping in thin ferromagnetic films[END_REF] developed the theory of spin pumping, although it was not until 2006 when Saitoh and Costache et al. [START_REF] Saitoh | Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect[END_REF], [START_REF] Costache | Electrical detection of spin pumping due to the precessing magnetization of a single ferromagnet[END_REF] showed the possibility of injecting a spin current into Pt and detecting the charge current generated by ISHE.

Spin injection by spin pumping in ferromagnetic resonance is considered the reciprocal effect of spin torque. If a spin current is injected into a ferromagnetic (FM) material from an adjacent nonmagnetic (NM) layer, a torque (𝜏) will be exerted on the magnetization of the ferromagnetic through the s-d exchange (Fig. 1.2.5 (a)). Consequently, the magnetization will precess upon being pulled out of equilibrium, adding an extra term (Δ𝛼 𝑆𝑃 ) to the Gilbert damping to describe the dynamics, which modifies the LGG equation as follows:

𝑑𝑀 ⃗⃗ 𝑑𝑡 = - 𝑔𝜇 𝐵 ℏ 𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 + 𝛼 𝑀 𝑠 𝑀 ⃗⃗ × 𝑑𝑀 ⃗⃗ 𝑑𝑡 + Δ𝛼 𝑆𝑃 𝑀 𝑠 𝑀 ⃗⃗ × 𝑑𝑀 ⃗⃗ 𝑑𝑡 , (1.38)
Note that, if the magnetization of the FM layer precesses, angular momentum is transferred to the adjacent layer and the torque is damped by the emission of a spin current from the FM layer to the NM layer. Therefore, Δ𝛼 𝑆𝑃 describes such an additional relaxation mechanism, which can be determined by measuring two samples with and without the NM layer.

The spin injection efficiency is related to the coupling between the FM and the NM materials: the larger the angular momentum loss (i.e., larger damping), the higher the spin current injection efficiency by spin pumping. The polarized spin current generated by a precessing FM and injected into the adjacent NM layer, will depend on the magnetization precession according to Tserkovnyak, Brataas et al. [START_REF] Tserkovnyak | Spin pumping and magnetization dynamics in metallic multilayers[END_REF], [START_REF] Brataas | Spin battery operated by ferromagnetic resonance[END_REF] model:

𝑗 𝑠 𝑝𝑢𝑚𝑝 = ℏ 4𝜋 𝑅𝑒(𝑔 ↑↓ ) 𝑀 𝑠 2 𝑀 ⃗⃗ × 𝑑𝑀 ⃗⃗ 𝑑𝑡 ( 2𝑒 ℏ ), (1.39)
Note that the instantaneous spin current injection is perpendicular to the magnetization and the magnetization derivative. Thus, the spin current generated at the interface leads to spin accumulation at the interface with the NM material. The quantity 𝑔 ↑↓ is the spin-mixing conductance per unit area that controls the spin transport across the NM/FM, i.e., the interface transparency. This magnitude encodes the efficiency of spin injection; thus, it depends on the additional damping Δ𝛼 𝑆𝑃 and the thickness of the FM layer (𝑡 𝐹𝑀 ). If one assumes that the NM layer is not reflecting back the spins into the FM, meaning that its thickness is much larger than the spin diffusion length, the link between 𝑔 ↑↓ and Δ𝛼 𝑆𝑃 can be derived:

Δ𝛼 𝑆𝑃 = 𝑔𝜇 𝐵 4𝜋𝑀 𝑠 𝑡 𝐹𝑀 𝑅𝑒(𝑔 ↑↓ ), (1.40)
The polarized spin current can be obtained by integrating 𝑗 𝑠 𝑝𝑢𝑚𝑝 over the period of the RF wave (0 → 2𝜋/𝜔) [START_REF] Costache | Electrical detection of spin pumping due to the precessing magnetization of a single ferromagnet[END_REF] and its estimation is crucial for the extraction of the spin-to-charge conversion efficiency.

Bilinear Magnetoresistance

In the present section we will discuss the model underlying the technique used in this work to explore the charge-spin conversion. It is a fairly recent model developed by Vaz et al. [START_REF] Vaz | Determining the Rashba parameter from the bilinear magnetoresistance response in a two-dimensional electron gas[END_REF] applicable to 2DEGs and based on the one previously proposed by Guillet et al. [START_REF] Guillet | Observation of large unidirectional Rashba magnetoresistance in Ge(111)[END_REF]. Bilinear magnetoresistance (BMR) is attributed to the interplay between current-induced spin polarization and scattering processes due to inhomogeneities or spin-momentum locking [START_REF] Dyrdał | Spin-momentum-locking inhomogeneities as a source of bilinear magnetoresistance in topological insulators[END_REF].

Moreover, unlike other unidirectional effects, such as spin Hall magnetoresistance, it manifests itself in individual materials. It has recently been reported in topological insulators such as individual Bi2Se3 layers [START_REF] He | Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states[END_REF], and in Rashba 2DEGs [START_REF] Guillet | Observation of large unidirectional Rashba magnetoresistance in Ge(111)[END_REF] such as the LaAlO3/SrTiO3 interface [START_REF] Narayanapillai | Current-driven spin orbit field in LaAlO3/SrTiO3 heterostructures[END_REF].

Later on, the effect was clearly observed in the Rashba states of the Ge [START_REF] Blount | Soft phonon modes and the 110 K phase transition in SrTiO3[END_REF] surface [START_REF] Guillet | Observation of large unidirectional Rashba magnetoresistance in Ge(111)[END_REF], and interpreted on the basis of spin-momentum locking in a Rashba 2DEG. For this purpose, they considered the magnetotransport within the unfolded spin subsurface of a 2DEG Rashba using the following Hamiltonian:

ℋ = ℏ 2 𝑘 2 2𝑚 * + 𝛼(Δ𝑘 × 𝜎) • 𝑧̂+ 𝑔𝜇 𝐵 𝜎 • 𝐵, (1.41)
where ℏ is the reduced Planck constant, 𝑘 is the momentum, 𝑚 * is the effective mass of electrons, 𝛼 is the Rashba spin-orbit interaction, 𝜎 the vector of Pauli matrices, 𝑔 is the Landé factor or the so-called g-factor, and 𝜇 𝐵 is the Bohr magnetron. Thus, when a current 𝑗 flows through a Rashba 2DEG system, it is produced a shift Δ𝑘 of the Fermi contour, which results in a current-induced out-of-equilibrium energy term equal to 𝛼(Δ𝑘 × 𝜎) • 𝑧. Further, because Δ𝑘 will be proportional to the electric field, we can describe the non-equilibrium energy by the introduction of a pseudomagnetic field 𝐵 𝑗 acting on the spins. The current-induced magnetic field 𝐵 𝑗 is oriented along 𝑦 ̂ if the current is directed along 𝑥 ̂, as well as it is proportional to the current density. Moreover, if an external magnetic field (𝐵 𝑒𝑥𝑡 ) is applied, 𝐵 𝑗 will be added (or subtracted)

to the 𝑦 ̂ component depending on the current-induced spin polarization, as depicted in panels orientation between the magnetic field and the current direction. Moreover, Guillet et 2𝑚 * ± 𝛼 𝑅 𝑘. Hence, from a semiclassical point of view, for an electric field in the 𝑥 direction (𝐸 𝑥 ) and a relaxation time 𝜏, the momentum 𝑘 acquires an extra component ∆𝑘 𝑥 = 𝑒𝐸 𝑥 𝜏𝜎 𝑦 /ħ. This term is equivalent to an interaction with a magnetic field induced by the current 𝐵 𝑗𝑦 along the y-axis, as shown in the figure, with 𝑔𝜇 𝐵 𝐵 𝑗𝑦 = 𝑏 𝑗𝑦 = -𝛼 𝑅 𝑒𝜏𝐸 𝑥 /ħ (more generically 𝑔𝜇 𝐵 𝐵 𝑗𝑦 = 𝑏 𝑗𝑦 = -𝛼 𝑅 𝑒𝜏(𝑧 𝑥 𝐸)/ħ)). Here, 𝑏 = 𝑔𝜇 𝐵 𝐵 is given in units of energy.

On the other hand, from a microscopic point of view, this work relied on the approximation proposed by Dyrdal et al. to calculate the BMR component [START_REF] Dyrdał | Spin-momentum-locking inhomogeneities as a source of bilinear magnetoresistance in topological insulators[END_REF]. Accordingly, they assume that the total Hamiltonian in the presence of an external electric field is expressed as:

𝐻 ̂𝑘𝑘´= [𝐻 ̂𝑘 0 + 𝐻 ̂𝑘 𝐴 ]𝛿 𝑘𝑘´+ 𝑉 ̂𝑘𝑘í 𝑚𝑝 , (1.43𝑎) 𝐻 ̂𝑘 0 = 𝐻 ̂𝑅 + 𝐻 ̂𝑏𝑒𝑓𝑓 , (1.43𝑏) 𝐻 ̂𝑏𝑒𝑓𝑓 = 𝑏 • 𝜎 + 𝑏 𝑗 • 𝜎 ≡ 𝑏 𝑒𝑓𝑓 • 𝜎, (1.43𝑐)
where 𝐻 ̂𝑘 𝐴 = -𝑒𝑣 ̂• 𝐴 describes the coupling of charge carriers with an external in-plane dynamic electric field, 𝑣 ̂ is the velocity operator, and 𝐴 denotes the electromagnetic potential vector, 𝐴(𝑡) = 𝐴 𝑤 𝑒𝑥𝑝 𝑖𝑤𝑡/ħ with 𝐴 𝑤 = ħ 𝑖𝑤 𝐸 𝑤 . The term 𝑏 • 𝜎 describes the coupling of the electron spin to the external electromagnetic field in the 𝑏 = (𝑏 𝑥 , 𝑏 𝑦 ) plane, whereas the term 𝑏 𝑗 • 𝜎 expresses the coupling of the spin with the magnetic field induced by the current described above. Subsequently, the scattering due to randomly distributed point impurities is considered, whose potential at a point 𝑟 𝑖 is given by:

𝑉(𝑟) = ∑ 𝑣(𝑟 -𝑟 𝑖 ) = ∑ 𝑣 0 𝛿(𝑟 -𝑟 𝑖 ), (1.44)

𝑖 𝑖

where 𝑣 0 is the potential from a single impurity and 𝑤 = 𝑛 𝑖 𝑣 0 2 . Hence, 𝑉 ̂𝑘𝑘í 𝑚𝑝 = 𝑉 𝑘𝑘´𝜎0 .

Finally, they calculated the relaxation times and conductivity according to Green's theorem and used the Born's self-consistent approximation to find the relaxation times. The relaxation time depends on both the external magnetic field and the spin density, and that this simple scalar scattering potential is sufficient to give rise to a bilinear component proportional to 𝑗 and 𝐵, which reveals a dependence 𝑠𝑖𝑛(𝜙) with an oscillation period of 2𝜋 (being 𝜙 the angle between the magnetic field and the current as sketched in panel (c) of Fig.

Spin-Orbit Torque

The proposal to use spin-transfer torques (STTs) to manipulate magnetization, by Berger and Slonczewski in 1996 [START_REF] Slonczewski | Current-driven excitation of magnetic multilayers[END_REF], [START_REF] Berger | Emission of spin waves by a magnetic multilayer traversed by a current[END_REF], led to the conception of new devices based on a combination between STT and Giant Magnetoresistance (GMR) or Tunneling Magnetoresistance (TMR) with great potential to partially replace non-volatile magnetic information memory units [START_REF] Grollier | Switching a spin valve back and forth by current-induced domain wall motion[END_REF]. In particular, STT-MRAM allows higher densities, low power consumption and reduced cost compared to conventional devices (so-called Toggle MRAM) [START_REF] Parkin | Magnetic domain-wall racetrack memory[END_REF].

The spin-orbit torque (SOT) is generated from spin-orbit interaction, either in single materials [START_REF] Park | Spin-orbit torque switching in a single (Ga,Mn)(As,P) layer with perpendicular magnetic anisotropy[END_REF], [START_REF] Krishnia | Spin-orbit coupling in single-layer ferrimagnets: direct observation of spin-orbit torques and chiral spin textures[END_REF] or heterostructures [START_REF] Duttagupta | Spin-orbit torque switching of an antiferromagnetic metallic heterostructure[END_REF], [START_REF] Amin | Interfacial spin-orbit torques[END_REF]. Although SOT and STT allow manipulating the magnetization [START_REF] Demidov | Spin-orbit-torque magnonics[END_REF]- [START_REF] Emori | Current-driven dynamics of chiral ferromagnetic domain walls[END_REF], SOTs are intrinsically different from the STTs, where the angular momentum of a polarized spin current is transferred to localized magnetic moments. While STT is usually generated by flowing a polarized spin current through a magnetic tunnel junction (MTJ), being the simplest case two FM layers separated by an insulating layer, SOT is generated by applying an in-plane current through a non-magnetic/magnetic bilayer (typically Pt, Ta or W are used as NM materials). (b) Interfacial Edelstein effect: a current flowing through an HM builds an internal electric field (Rashba field) perpendicular to the film surface, which polarizes electrons and generates spin accumulation at the interface. Reproduced with permission from [START_REF] Han | Spin-orbit torques: materials, physics, and devices[END_REF].

The SOT concept was initially developed to tune the magnetization dynamics in Ni81Fe19/Pt bilayers [START_REF] Ando | Electric manipulation of spin relaxation using the spin hall effect[END_REF] and in dilute magnetic (Ga,Mn)As semiconductors [START_REF] Chernyshov | Evidence for reversible control of magnetization in a ferromagnetic material by means of spin-orbit magnetic field[END_REF]. Subsequently, a relevant area of research was developed when current-induced switching was observed in Pt/Co/AlOX [START_REF] Miron | Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer[END_REF] and CoFeB/Ta heterostructures, i.e., with prototypical materials in the information storage industry.

SOT generation is mainly due to two phenomena: the spin Hall effect (SHE) in heavy metals (FM)

and the direct Edelstein effect (DEE) at surfaces or interfaces lacking structural inversion symmetry (SIA). In the presence of electric current, both phenomena promote an out-ofequilibrium spin accumulation at the interface between the SOC material (e.g., a two-dimensional electronic system or a heavy metal) and the FM material. Subsequently, this spin accumulation or spin current diffuses into the FM layer, transferring angular momentum and thus exerting a torque on the magnetization that allows its manipulation. Unlike the STT counterpart, where the current must pass through a ferromagnetic layer, the typical SOT configuration involves the flow of a lateral current through the heavy-metals or interfaces and offers higher performance and flexibility in terms of structure design, as well as faster spin dynamics. This makes SOT key in the development of next-generation spintronics-based MRAM devices and has driven intense research by the scientific community over the past 10 years [START_REF] Han | Spin-orbit torques: materials, physics, and devices[END_REF].

The effective magnetic field exerted by SOTs can be decomposed into two components, the damping-like torque (𝐻 𝐷𝐿 ), directed along the current direction, [START_REF] Miron | Perpendicular switching of a single ferromagnetic layer induced by inplane current injection[END_REF], [START_REF] Nguyen | Spin torque study of the spin Hall conductivity and spin diffusion length in platinum thin films with varying resistivity[END_REF] and the field-like torque (𝐻 𝐹𝐿 ) [START_REF] Avci | Fieldlike and antidamping spin-orbit torques in as-grown and annealed Ta/CoFeB/MgO layers[END_REF]. These two terms are defined as:

𝐻 𝐷𝐿 = 𝜎 × 𝑚, (1.49𝑎) 𝐻 𝐹𝐿 = 𝜎, (1.49𝑏)
where 𝑚 and 𝜎 represent the directions of the magnetization and spin polarization, respectively.

Therefore, 𝐻 𝐷𝐿 depends on the magnetization while 𝐻 𝐹𝐿 does not, enabling us to identify whether the effective field is damping or field-like by measuring its dependence on the direction of the magnetization. Further, the damping-like torque dominates the magnetization switching and its sign determines the switching direction. On the other, the field torque determines the critical current for switching and the speed of the process. The SOT efficiency is determined by the charge-spin conversion efficiency, which is characterized by the spin Hall angle 𝜃 𝑆𝐻𝐸 in HM, and by 𝜆 𝐼𝐸𝐸 at Rashba interfaces.

In recent years, the importance of both components has been investigated in HM such as Pt [START_REF] Nguyen | Spin torque study of the spin Hall conductivity and spin diffusion length in platinum thin films with varying resistivity[END_REF] or Ta [START_REF] Emori | Current-driven dynamics of chiral ferromagnetic domain walls[END_REF], in Weyl semimetals such as MoTe2 [START_REF] Stiehl | Layer-dependent spin-orbit torques generated by the centrosymmetric transition metal dichalcogenide β-MoTe2[END_REF] or WTe2 [START_REF] Shi | All-electric magnetization switching and Dzyaloshinskii-Moriya interaction in WTe2/ferromagnet heterostructures[END_REF], and in topological materials such as BixSe1-x [START_REF] Dc | Room-temperature high spin-orbit torque due to quantum confinement in sputtered BixSe(1-x) films[END_REF]. The characterization of current-induced torques has been approached using several methods, including the second harmonic Hall voltage technique (see Section 2.3.4 for details), spin-torque ferromagnetic resonance [START_REF] Liu | Spin-torque ferromagnetic resonance induced by the spin Hall effect[END_REF], and optical methods [START_REF] Fan | Quantifying interface and bulk contributions to spin-orbit torque in magnetic bilayers[END_REF].

Finally, it is worth noting that Rashba 2DEGs are attracting the attention of researchers due to remarkable charge spin interconversion efficiencies, which makes them excellent candidates for exerting SOTs. Very recently, Lee et al. [START_REF] Lee | Direct observation of spin accumulation and spin-orbit torque driven by Rashba-Edelstein effect in an InAs quantum-well layer[END_REF] reported the induction of a sizeable field-like torque at room temperature from InAs quantum wells, as well as that the DEE-driven spin accumulation is 14 times larger than the SHE counterpart. On the other hand, using the ST-FMR technique, Wang et al. [START_REF] Wang | Room-temperature giant charge-to-spin conversion at the SrTiO3-LaAlO3 oxide interface[END_REF] reported very high SOT efficiency for STO/LAO/CoFeB heterostructures (⁓6.3), two orders of magnitude higher than those found in HM, such as Pt and Ta. These results therefore confirm that Rashba 2DEGs are really promising for the development of SOT-based devices.

Chiral Magnetism

The antisymmetric exchange interaction, coined as Dzyaloshinskii-Moriya interaction (DMI), was discovered in the early 20th century after the observation of weak ferromagnetism in typically antiferromagnetic α-Fe2O3 crystals. In 1958, Dzyalonshinskii [START_REF] Dzyaloshinsky | A thermodynamic theory of 'weak' ferromagnetism of antiferromagnetics[END_REF] showed that the interaction was due to relativistic spin lattice and magnetic dipole interactions, and two years later, Moriya [START_REF] Moriya | Anisotropic superexchange interaction and weak ferromagnetism[END_REF] finally identified SOC as the underlying mechanism of such interaction. DMI consists of a superexchange interaction between two neighboring magnetic spins, which is mediated by a nonmagnetic atom. Thus, the DMI between two atomic spins 𝑆 𝑖 and 𝑆 𝑗 is defined as:

𝐻 𝑖,𝑗 𝐷𝑀 = 𝐷 𝑖𝑗 • (𝑆 𝑖 × 𝑆 𝑗 ), (1.50) where 𝑟 𝑖𝑗 is the direction connecting both spins and 𝐷 𝑖𝑗 is a constant vector whose value will depend on the crystal symmetry and, therefore, is proportional to 𝑟 𝑖𝑗 . Thus, DMI favors the tilt of 𝑆 𝑛 (𝑛 =1,2,3,4) are the spins of the magnetic atoms, while 𝑑 12 and 𝑑 34 are the corresponding DMI vectors (b). Reproduced with permission from [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF].

neighboring spins around the vector 𝐷 𝑖𝑗 , introducing a specific chirality into the magnetic configuration, promoting the stabilization of spirals, cycloids, or topological spin configurations such as magnetic skyrmions. Symmetry requirements dictate that this chiral interaction can only exist in magnetic materials lacking inversion symmetry [START_REF] Yang | Anatomy of Dzyaloshinskii-Moriya interaction at Co/Pt interfaces[END_REF]. Consequently, DMI can arise both in the bulk in materials lacking inversion symmetry (BIA) [START_REF] Mühlbauer | Skyrmion lattice in a chiral magnet[END_REF] and at surfaces or interfaces (SIA).

Thus, it has been shown that the interaction between two magnetic sites at the interface with a non-magnetic material with SOC, such as a heavy metal, has a considerable chiral contribution in magnetic thin films [START_REF] Bode | Chiral magnetic order at surfaces driven by inversion asymmetry[END_REF], as depicted in panel (a) in Fig. 1.3.1. For example, Heinze et al. [START_REF] Heinze | Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions[END_REF] reported the presence of nanoskyrmions lattices (extended only a few lattice parameters) in Fe monolayers grown on Ir [START_REF] Blount | Soft phonon modes and the 110 K phase transition in SrTiO3[END_REF] without the need for a magnetic field to stabilize them. Also, Tokura et al. [START_REF] Yu | Real-space observation of a two-dimensional skyrmion crystal[END_REF] have imaged two-dimensional skyrmion lattices in Fe0.5Co0.5Si thin films using Lorentz transmission electron microscopy.

In low-dimensional systems, strong interfacial DMI (iDMI) can also arise at HM/FM interfaces due to spatial inversion symmetry breaking, which determines its sign and direction while the magnitude depends on the SOC strength [START_REF] Yang | Anatomy of Dzyaloshinskii-Moriya interaction at Co/Pt interfaces[END_REF]. In this sense, different combinations of HM/FM and multilayer interfaces, such as Co/Pt, Pt/Co/AlOX, Pt/CoFeB/AlOX or (Ir/Co/Pt)x10, are currently being investigated in order to obtain additive contributions that increase the effective DMI [START_REF] Cho | Thickness dependence of the interfacial Dzyaloshinskii-Moriya interaction in inversion symmetry broken systems[END_REF]- [START_REF] Chauleau | Chirality in magnetic multilayers probed by the symmetry and the amplitude of dichroism in x-ray resonant magnetic scattering[END_REF], as depicted in panel (b) of Fig. 1.3.1 Although isolated skyrmions have recently been observed at room temperature in such heterostructures, their nucleation and stabilization usually require an external force. However, not many experimental studies have reported the observation of skyrmions at high temperatures and without external current/magnetic field [START_REF] Brandão | Observation of magnetic skyrmions in unpatterned symmetric multilayers at room temperature and zero magnetic field[END_REF].

So far, this could be achieved by using lithographically fabricated structures to confine single or multiple skyrmions depending on the features of the patterned samples [START_REF] Ho | Geometrically tailored skyrmions at zero magnetic field in multilayered nanostructures[END_REF].

Chiral spin textures: magnetic bubbles and skyrmions

Thanks to DMI, skyrmions can be stabilized in non-centrosymmetric systems, but they can also form in centrosymmetric ones from the competition between dipole-dipole interaction (DDI) and magnetic anisotropy. Skyrmions formed under DDI are traditionally called magnetic bubbles or skyrmions bubbles.

An obvious difference between magnetic bubbles and skyrmions is size: the diameter of skyrmions formed under DMI typically ranges from 3 to 200 nm, whereas magnetic bubbles sustained under DDI are larger, from 100 nm to several micrometers [START_REF] Wiesendanger | Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics[END_REF]. On the other hand, DMI-stabilized skyrmions are composed of spins oriented in whirls, i.e., the spins are swirled so that in the center they point in the opposite direction to that of the periphery. This type of configuration provides them with topological protection against disorder and thermal fluctuations. Thus, DMI skyrmions exhibit collective chirality and polarity due to their intrinsic DMI, whereas DDI-stabilized magnetic bubbles exhibit individual features and deform randomly due to the weaker DDI, making them difficult to stabilize and control. Therefore, DMI skyrmions are the favorite candidate for spintronics applications despite the difficulties in reversing the polarity of the whole swirl due to intrinsic DMI.

Depending on the different symmetries and interactions (in the crystal lattice or at the interface), there are two types of magnetic skyrmions: Néel-type skyrmions and Bloch-type skyrmions. In Néel-type skyrmions, the spins rotate in the direction perpendicular to the plane of the system, while in Bloch-type skyrmions they rotate in the plane, as can be seen in Fig. 1.3.2 (a) and (b), respectively. Due to their geometry, Néel-type skyrmions are typically found in 2D interfaces or materials, whereas Bloch-type skyrmions are mostly formed in bulk [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF].

Chiral spin textures, especially skyrmions, are of special interest for the next generation of spintronic devices, as there is the possibility to nucleate, manipulate, detect, or annihilate these nano-objects which can be used as magnetic bits for data storage [START_REF] Parkin | Magnetic domain-wall racetrack memory[END_REF]. These spin textures are even more attractive considering the extremely low spin bias currents needed to move them and their high stability due to their topological nature [START_REF] Jonietz | Spin transfer torques in MnSi at ultralow current densities[END_REF], [START_REF] Fert | Skyrmions on the track[END_REF]. Therefore, for skyrmions to be real candidates for next-generation spintronics devices, the research community must address three major challenges in the coming years: stability at room temperature, deterministic nucleation, and efficient skyrmion motion. reproduced with permission from [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF].

Part II

Since this thesis focuses on the synthesis and full characterization of 2DEGs appearing at the interface between perovskite oxides and metals, this section provides a brief introduction to the broad field of transition metal oxides, highlighting their great potential in terms of properties and as platforms to study new physical phenomena. Subsequently, the properties of the transition metal oxides used during this thesis to host 2DEGs, i.e., SrTiO3 and KTaO3, will be discussed in detail. In addition, we will present the factors governing the synthesis process of metal/oxide 2DEGs and finally, we will describe the state of the art regarding the electronic properties of STObased 2DEGs in terms of band structure, response to a back-gate voltage, and magnetotransport properties.

Transition Metal Oxides

Transition metal oxides (TMOs) combine a two or three-dimensional close packing of oxygen ions with transition metal cations, i.e., d or f groups of the periodic table. TMOs are stable into a great variety of crystalline structures (e.g., rock salt, corundum, spinel, fluorite, rutile, perovskite) depending on the stacking of oxygen (hexagonal or cubic) and cation occupation. They exhibit a broad range of properties resulting from the complex interplay between charge, spin, orbital and lattice degrees of freedom (see Fig. 1.4.1) such as electrical conductivity, magnetism, ferroelectricity, multiferroicity, high temperature superconductivity, colossal magnetoresistance, and metal-to-insulator transitions [START_REF] Tokura | Correlated-electron physics in transition-metal oxides[END_REF].

Regarding the electronic band structure, it is typically formed by a valence band built by overlapping 2p orbitals of oxygen ions and a conduction band composed of 'd' (or 'f') orbitals of transition metal cations. Further, the degeneracy of 'd' orbitals is lifted by the interaction of delectrons with the surrounding oxygen polyhedral, the so-called crystal field splitting.

The overlapping of 'd' orbitals with 'p' orbitals dictates the balance between localization/delocalization of electrons. A poor overlapping of 'd' with 'p' orbitals leads to very narrow electronic bands (1-2 eV) and tends to localize electrons at atomic sites. On the other hand, a larger overlapping favors electron delocalization by favoring the hopping between neighboring orbitals. As a result of this subtle balance, the electrons arrange into the lattice in order to minimize on-site repulsion Coulomb energy i.e., mediated by electron-electron interactions. This phenomenon is called electronic correlation and leads to the complex spin, charge and orbit long range order characteristic of TMOs. Consequently, the new electronic phases arising from these electronic correlations are extremely sensitive to modifications in the overlapping of 'd' and 'p' orbitals, and TMOs properties are drastically altered by modifying elemental composition or by application of external stimuli (temperature, pressure, light, electric and magnetic fields, etc.) [START_REF] Khomskii | Transition metal compounds[END_REF], [START_REF] Imada | Metal-insulator transitions[END_REF].

Particularly appealing within TMOs are the perovskites, with general formula ABO3, which present

a

SrTiO3

Strontium titanate (STO), with chemical formula SrTiO3, is a non-toxic ceramic material with high commercial availability. It can be synthesized as single crystals (e.g., by the Verneuil process [109],

[110] and it is well-known to be widely employed substrate for the epitaxial growth of thin films since 1980s. This was initially boosted by the coincidence of its lattice parameter with that of the other oxides (e.g., high-Tc superconductors), and later backed up by its remarkably array of properties, either in its pristine form or slightly modified by doping, strain, etc (e.g., high dielectric constant, ferroelectricity, insulator-to-metal transition, superconductivity, etc.).

Most of the properties of STO arise from its crystal symmetry, and its mixed ionic-covalent character, i.e., an ionic bonding between Sr 2+ and O 2-ions and a covalent one between Ti 4+ and O 2-. Consequently, some of them (e.g., dielectric behavior, insulator-to-metal transition) can be qualitatively well understood by considering both their crystal and electronic structures.

At room temperature, STO has a perovskite crystal structure (space group Pm-3m) with a lattice parameter of 3.905 Å. It is cubic, centrosymmetric, and thus, paraelectric, with the titanium atom lying at the centre of both the cube and the surrounding oxygen octahedron.

STO remains paraelectric even below its ferroelastic transition at T~105K [START_REF] Blount | Soft phonon modes and the 110 K phase transition in SrTiO3[END_REF]. At this temperature, bulk STO becomes tetragonal (a = b ≠ c; space group I4/mcm) by rotating neighbouring oxygen octahedra in opposite directions along the out-of-plane c-axis (antiferrodistortive transition (AFD), Glazer classification [START_REF] Glazer | The classification of tilted octahedra in perovskites[END_REF]: a 0 a 0 c -). This transition "doubles" the unit cell parameter, and naturally leads to the formation of ferroelastic domains with different orthogonal orientations. Such transition can also be triggered by stress and pressure, and is affected by both defects [START_REF] Hünnefeld | Influence of defects on the critical behavior at the 105 K structural phase transition of SrTiO3: on the origin of the two length scale critical fluctuations[END_REF] and doping.

It has been argued that lowering of the temperature may lead to orthorhombic (55 -35 K) and triclinic structures, although the magnitude of these additional perturbations is significantly smaller than the transition to tetragonal structure. At even lower temperatures T~4K, the unit cell elongates and a double-well potential develops for the titanium atom, with minima situated near opposite ends of the long axis of the oxygen octahedron [START_REF] Lytle | X-ray diffractometry of low-temperature phase transformations in strontium titanate[END_REF]. Yet, the quantum fluctuations of the titanium atom between these two minima suppress ferroelectric ordering even at T~0 K, which makes of STO quantum paraelectric (also called incipient ferroelectric) at very low temperatures [START_REF] Müller | SrTiO3: an intrinsic quantum paraelectric below 4 K[END_REF].

Thus, ferroelectricity cannot be achieved in stoichiometric bulk STO just by decreasing temperature. However, it can be easily induced either by applying an electric field or stress (mechanical strain, pressure, …) [START_REF] Burke | Stress induced ferroelectricity in SrTiO3[END_REF], [START_REF] Guennou | Pressure-temperature phase diagram of SrTiO3 up to 53 GPa[END_REF] as well as by cation or isotope substitution [START_REF] Bednorz | Sr1-xCaxTiO3. An XY quantum ferroelectric with transition to randomness[END_REF], [START_REF] Mitsui | Dielectric and x-ray studies of CaxBa1-xTiO3 and CaxSr1-xTiO3[END_REF].

Stoichiometric STO is a wide bandgap semiconductor that easily becomes conducting. This insulator-to-metal transition occurs at very low carrier concentrations ~10 14 cm -3 , which can be obtained by both electron donors (e.g., La 3+ (Nb 5+ ) on Sr 2+ (Ti 4+ ) sites) and electron acceptors dopants (e.g., Na 1+ (Fe 3+ ) on Sr 2+ (Ti 4+ ) sites), or defects (e.g., oxygen vacancies [START_REF] Frederikse | Electronic transport in strontium titanate[END_REF], [START_REF] Lee | Phase transitions via selective elemental vacancy engineering in complex oxide thin films[END_REF]). The resulting conductivity is either n-type (donors, oxygen vacancies) or p-type (acceptors) depending on whether the new electronic states introduced by the impurities/defects are located near the conduction band or the valence band edge, respectively. Further, the doping has a strong influence in the resistivity and mobility at low temperature as can be seen in panels (a) and (b) in Fig. 1.4.2 [122]. This, together with the high dielectric constant [START_REF] Neville | Permittivity of strontium titanate[END_REF], [START_REF] Sakudo | Dielectric properties of SrTiO3 at low temperatures[END_REF], renders STO an excellent candidate to be modulated by a gate voltage [START_REF] Trier | Electron mobility in oxide heterostructures[END_REF].

Further evidence of the rich properties of STO is that it also exhibits superconductivity when deficient in oxygen. In fact, it was the first superconducting oxide to be discovered and the starting point for the discovery of high Tc superconductors [START_REF] Koonce | Superconducting transition temperatures of semiconducting SrTiO3[END_REF]. The superconducting state, which exists at carrier concentrations as low as 10 17 cm -3 , shows a non-monotonic dependence on the carrier concentration and exhibits a maximum at Tc ~300 mK. This behavior is not in and [START_REF] Koonce | Superconducting transition temperatures of semiconducting SrTiO3[END_REF].

Since the degeneracy of Ti-3d orbitals is lifted by the crystal field, or the surrounding oxygen octahedra, the energy levels are split into a high-energy doublet (eg states) and a low-energy triplet (t2g states) (see Fig. 1.4.3). These t2g states, composed of dxy, dxz and dyz orbitals, remains near the Fermi level and couple to identical orbitals of neighbouring titanium atoms through the 2p orbitals of oxygen that lie in between. For a given orbital, the hopping is stronger along the x and y directions than along the z direction. Therefore, the effective mass along the x and y directions is smaller than that along the z direction. Consequently, the corresponding Fermi surface is cigar-shaped, elongated in the kZ direction for the dXY orbitals and in the kY and kX directions for the dXZ and dYZ orbitals, respectively. Moreover, the ferroelastic and ferroelectric distortions discussed above lift the degeneracy of the three t2g orbital, as do spin-orbit interactions and the breaking of inversion symmetry near a surface or an interface.

Interestingly for our purposes, STO is a material well known to host 2DEGs at the interface with other oxides such as the aforementioned LAO/STO case, but also at its surface. Indeed, for instance, Santander-Syro et al. [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF] reported the emergence of a 2DEG at the surface of in situ cleaved STO single crystals through Angle-Resolved Photoemission Spectroscopy (ARPES). This suggested the possible critical role of oxygen vacancies, which are extremely easy to form under oxygen-reduced atmosphere, in these kinds of systems.

KTaO3

Potassium tantalate (KTaO3, KTO) is an insulating material with a cubic perovskite structure (space group Pm-3m) with a lattice constant of 3.989Å, a bandgap of 3.6 eV and a dielectric constant that reaches values > 4500 upon cooling to low temperatures. It is a material very similar to STO in terms of structure, dielectric permittivity, transport properties and drastic response under external stimuli.

Like STO, KTO remains at the edge of a ferroelectric transition at low temperatures, which is prevented by quantum fluctuations [START_REF] Liu | Discovery of two-dimensional anisotropic superconductivity at KTaO3 (111) interfaces[END_REF]. The large static dielectric constant of KTO is expected to affect its transport properties, especially at low temperatures, due to polarization shielding of charged impurities or ionized donor scattering centers [START_REF] Wemple | Some transport properties of oxygen-deficient single-crystal potassium tantalate (KTaO3)[END_REF]. Ferroelectricity can be triggered by stresses [START_REF] Uwe | Raman-scattering study of stress-induced ferroelectricity in KTaO3[END_REF], [START_REF] Uwe | Stress induced ferroelectricity in KTaO3[END_REF]or by substituting with Li or Nb [START_REF] Andrews | X-ray scattering study of the random electric dipole system KTaO2: Li[END_REF], as well as induced by defects [START_REF] Aktas | Polar correlations and defectinduced ferroelectricity in cryogenic KTaO3[END_REF]. Coexistence of dipolar glassy states and ferroelectricity occurs as a function of dopant concentration, and KTO becomes highly conductive when n-type doped [START_REF] Wemple | Some transport properties of oxygen-deficient single-crystal potassium tantalate (KTaO3)[END_REF]. Electron conduction in oxygen-deficient KTO has several features of interest that differentiate it from STO, e.g., estimated effective masses are lower and mobilities are higher (see Fig. In particular, mobilities and conductivities are remarkably large for a d-band oxide semiconductor reaching values of 23000 cm 2 /V•s and 8x10 3 ohm/cm at 4.2 K. The larger mobility (and lower effective mass) in KTO than in STO is consistent with the expected larger overlap of 5d orbitals compared with 3d. The effect of 5d overlap apparently compensates the somewhat larger lattice constant.

It should be noted that the large mobility at low temperature in KTO appears to be a consequence of the shielding of the charged scattering centers (by the large static dielectric constant). In the lattice scattering region above 100 K, where the Hall mobility is almost independent of carrier concentration, both KTO and STO exhibit Hall mobilities that follows a power-law dependence of the form μH proportional to T -3 , suggesting strong similarities in scattering. Lattice scattering clearly dominates at these temperatures. Below 100K, the Hall mobilities dependence with carrier concentration arises from impurity or ionized F donor scattering centers. An important consideration regarding these low temperature data is the question of degeneracy. Free-carrier absorption results are quite different, however only the KTO data being indicative of polar-mode lattice scattering [START_REF] Wemple | Some transport properties of oxygen-deficient single-crystal potassium tantalate (KTaO3)[END_REF].

The electronic states near the Fermi level in electron doped KTO are derived from Ta 5d states.

In particular dXY, dXZ and dYZ orbitals in t2g manifold. The large spin-orbit coupling in these states lift the degeneracy of the t2g manifold and splits the J =1/2 states to an energy ~0.4eV higher than the J =3/2 states. The two J=3/2 states are degenerate near the Γ-point and disperse as 'light' with permission from [START_REF] Wemple | Some transport properties of oxygen-deficient single-crystal potassium tantalate (KTaO3)[END_REF], and panel (c) from [START_REF] Liu | Discovery of two-dimensional anisotropic superconductivity at KTaO3 (111) interfaces[END_REF].

and 'heavy' electron states at finite momenta. Unlike in STO, there is no symmetry lowering lattice distortion at lower temperatures to lift this degeneracy at the 𝛤-point, though confinement can also lift degeneracies [START_REF] Liu | Discovery of two-dimensional anisotropic superconductivity at KTaO3 (111) interfaces[END_REF].

Unlike STO, superconductivity has never been reported in doped KTO. It was only reported that ionic liquid gating could be used to tune the surface of KTO 001 into a weak superconducting state with Tc= 47 mK [START_REF] Ueno | Discovery of superconductivity in KTaO3 by electrostatic carrier doping[END_REF].

Further, in analogy with the STO-based interfaces, it has been demonstrated that KTO can also host a 2DEG at its surface [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF] or when forming an interface with other oxides [START_REF] Zhang | Highly mobile two-dimensional electron gases with a strong gating effect at the amorphous LaAlO3/KTaO3 interface[END_REF], [START_REF] Zou | LaTiO3/KTaO3 interfaces: a new two-dimensional electron gas system[END_REF],

exhibiting signatures of spin-orbit coupling in low-temperature magnetoresistance [START_REF] Wadehra | Planar Hall effect and anisotropic magnetoresistance in polar-polar interface of LaVO3-KTaO3 with strong spin-orbit coupling[END_REF]. Since

Ta is much heavier than Ti, spin-orbit effects are expected to be more intense in KTO. Also, last year Liu et al. [START_REF] Liu | Discovery of two-dimensional anisotropic superconductivity at KTaO3 (111) interfaces[END_REF] showed a superconducting 2DEG at ≈2K forming by the deposition of Eu on top of ( 111)-oriented KTO (see Fig. KTO 2DEG with a critical temperature of about 1 K [START_REF] Chen | Two-Dimensional Superconductivity at the LaAlO3/KTaO3 (110) Heterointerface[END_REF]. Thus, superconductivity in KTO 2DEGs appears at higher temperature compared to STO (typically in the order of few hundreds of mK).

Synthesis of 2DEGs by Metal Deposition on Oxides

The deposition of metals on oxides gives rise to electronic and chemical interactions that determine the final properties of the interlayer. On one hand, electronic interactions are carried out by the principle of energy minimization and a continuous electric potential at the heterointerface. In the case of electronic transfer, the difference between the work functions of the materials involved determines how much charge and in which direction it is transferred. On the other hand, chemical interactions involve interdiffusion over length scales larger than a monolayer or the formation of new phases [START_REF] Perel | Optical orientation in a system of electrons and lattice nuclei in semiconductors. Theory[END_REF], which requires the transport of mass and charge over distances larger than the lattice parameter. For this second case, the driving force is the electrochemical gradient, which consists of the electric potential and/or the chemical potential gradient.

It is worth mentioning that electronic and chemical interactions are strongly interrelated. On one hand, charge transfer, dipole formation, and Schottky barriers are strongly affected by chemical reactions and atomic diffusion at the interface. On the other hand, the same charge transfer process not only has an effect on the properties, but can severely affect the diffusion dynamics [START_REF] Brillson | The structure and properties of metal-semiconductor interfaces[END_REF]. As for the possible interactions, these can be classified into four major groups: redox reactions, interdiffusion, encapsulation and alloy formation.

For the purpose of this thesis in which we pursue the formation of 2DEG by the reduction of STO, we are particularly interested in redox reactions, which are considered to be the most important interactions at metal/oxide interfaces. These interactions involve both oxidation of the metal layer and reduction of the substrate and can be schematically described as follows:

𝑀𝑒 𝐼 ||𝑀𝑒 𝐼𝐼 𝑂 𝑥 → 𝑀𝑒 𝐼 𝑂 𝑦 ||𝑀𝑒 𝐼𝐼 𝑂 𝑥-𝑦
Good examples are the deposition of reactive metals on oxides such as TiO2 and SrTiO3 [START_REF] Diebold | The surface science of titanium dioxide[END_REF], [START_REF] Fu | Metal/oxide interfacial reactions: oxidation of metals on SrTiO3 (100) and TiO2 (110)[END_REF]. In this case, the chemical reaction can be expressed as:

𝑀𝑒 𝐼 + 𝑀𝑒 𝐼𝐼 𝑂 𝑥 → 𝑀𝑒 𝐼 𝑂 𝑦 + 𝑀𝑒 𝐼𝐼 𝑂 𝑥-𝑦
Thus, attending to thermodynamics criteria, the Gibbs free energy change associated with this reaction, 𝛥𝐺 𝑅 = ∆𝐻 𝑅 -𝑇∆𝑆 𝑅 , determines whether the reaction is favorable or not. In particular, for solid-state reactions, the entropy change ∆𝑆 𝑅 is negligible and only the enthalpy change ∆𝐻 𝑅 is considered. Thus, the heat of formation of the oxide (𝛥𝐻 𝑓 𝑜 in kJ/mol O) becomes a decisive parameter to predict whether the reaction will be spontaneous under given conditions. In fact, the variation of 𝛥𝐻 𝑓 𝑜 can be used to explain the tendencies of many metals on a specific substrate [START_REF] Diebold | The surface science of titanium dioxide[END_REF].

Thus, for the particular case of metals on STO, we can classify metals according to the value of the work function and the enthalpies of formation of their most stable oxides with respect to the STO work function and the energy required to form a single vacancy. If we tabulate the STO work function at 3.9 eV [START_REF] Robertson | Schottky barrier heights of tantalum oxide, barium strontium titanate, lead titanate, and strontium bismuth tantalate[END_REF] and the enthalpy of formation at -250 kJ/mol [START_REF] Mitra | Electronic structure of oxygen vacancies in SrTiO3 and LaAlO3[END_REF], this allows us to distinguish three major groups of metals.

The upper right corner in Fig. STO to the metal and therefore, there is no driving force for the redox reaction. This group of materials includes noble metals such as Pt, Au, Ag and Cu, as well as Co and Ni. The result of electronic transfer from the STO is a small band bending and even the ability of the metal to reoxidize the surface of reduced STO [START_REF] Pesty | Thermal stability of Pt films on TiO2(110): evidence for encapsulation[END_REF].

Further, the lower right corner includes metals that react spontaneously with STO because they have a lower enthalpy of oxide formation than that required to form a vacancy. These elements also have a similar or slightly higher work function than STO and thus, the driving force is the tendency to scavenge oxygen. However, because this process involves oxygen diffusion, this is especially impeded at low temperatures. The natural inhibition of the reaction kinetics results in confined oxygen deficient layers. The metals in this group are Al, Ti, Nb, Hf and V. Remarkably, oxides grown on STO containing metals of this group, even if amorphous, are those in which the formation of a 2DEG, with characteristics similar to the well-known LAO/STO interface, has been reported [START_REF] Rödel | Universal fabrication of 2D electron systems in functional oxides[END_REF].

Finally, the third corner of the plot (lower left) consists of metals that have both, a favourable redox reaction and a lower work function. In this case, the outward diffusion of oxygen is favoured by the electric field arising from the difference of the work function value and the reaction is more exothermic. The STO conducting layer for these systems has been reported to be less confined than those of the second group.

It should be noted that this approach does not take into account the thermodynamic factors associated with the surface and the interface, which can play a crucial role as well. The specific thermodynamic data of the reactants and products are usually not accessible, since the chemical composition of the interlayer is usually unknown, especially in the case of redox reaction on metal/oxide interfaces. An accurate determination of the thermodynamic data is complicated because the resulting phases present a thickness of only few unit cells. Therefore, calculations can only be performed assuming certain phases and conditions, which can be very inaccurate especially at low temperatures.

Electronic Properties of STO-based 2DEGs

Band structure

Both oxide surfaces and their interfaces with other materials can host exotic electronic states considerably different from those found in their bulk form. These electronic states offer new opportunities for the development of more versatile and efficient devices, which has greatly motivated their study in recent years. In this sense, an accurate characterization of the band structure of 2DEGs is a crucial step to understand the physics of these systems and fully exploit their properties in technological applications. However, these systems are intrinsically buried by nature, which makes their characterization a real challenge from a technical point of view. For example, high-resolution angle-resolved photoemission electron spectroscopy (HR-ARPES) does not provide sufficient probing depth to study 2DEGs at the prototype LAO/STO interface, even if confined to a few unit cells near the interface. This limits band structure studies by photoemission techniques to the soft or hard X-ray regime, where energy and momentum resolution is reduced.

Other spectroscopy techniques such as X-ray absorption (XAS) or inelastic X-ray scattering (RIXS) provide information on orbital symmetries and collective excitations but have no resolution in momentum space.

Meevasana et al. [START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO3 surface[END_REF] and Santander-Syro et al. [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF] were the first to report the band structure of STO-based 2DEGs using ARPES. They found that the band structure of in situ cleaved STO (001)

was very similar to that predicted theoretically by DFT simulations for the LAO/STO interface, demonstrating that the band structure and electronic properties of these 2DEGs were mainly defined by the host material.

Understanding the origin of the corresponding electric field in 2DEGs systems is an important step in controlling their charge carrier density, which is the basis of device functionality.

As mentioned in the previous section, STO and KTO are band insulators with a 𝑑 0 configuration for the transition metal, i.e., Ti 4+ in STO and Ta 5+ in KTO, which makes them easy to be electronically doped. This introduces electrons into the conduction band minimum, resulting in a three-dimensional bulk state. with permission from [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF], (d) from [START_REF] Walker | Carrier-density control of the SrTiO3 (001) surface 2D electron gas studied by ARPES[END_REF] and (e) from [START_REF] Wang | Tailoring the nature and strength of electron-phonon interactions in the SrTiO3 (001) 2D electron liquid[END_REF].

Thus, the two first publications about the 2DEG formed at the surface of (001) STO suggested that the origin of both band bending and charge carrier density could be due to the formation of oxygen vacancies. Under this scenario, two electrons are released into the STO after the formation of a vacancy, which can occupy localized electronic states or manifest as mobile electrons giving rise to the 2DEG formation. Also, supporting this oxygen vacancy scenario, the same authors observed a non-dispersive state in-gap state at approximately 1.3 eV below the Fermi level, which grows in intensity when the UV irradiation time increases. Such state was previously observed in reduced-STO, Nb-doped STO, La-doped STO [START_REF] Aiura | Photoemission study of the metallic state of lightly electron-doped SrTiO3[END_REF], [START_REF] Henrich | Surface defects and the electronic structure of SrTiO3 surfaces[END_REF]and attributed to the presence of oxygen vacancies. Further evidence was provided by DFT calculations performed in STO with oxygen deficient surfaces [START_REF] Jeschke | Localized versus itinerant states created by multiple oxygen vacancies in SrTiO3[END_REF].

Another evidence about the role of oxygen vacancies in STO-based 2DEG was provide by

McKeown et al. four years later [START_REF] Walker | Carrier-density control of the SrTiO3 (001) surface 2D electron gas studied by ARPES[END_REF]. They showed that the 2DEG at La:STO surface can be created by in situ radiating of the surface to UV light and depleted by subsequent small doses of oxygen. This explicitly demonstrated that the 2DEG emerges from the formation of oxygen vacancies due to the irradiation with photons of appropriate energy. In turn, this study also showed that the in-gap state is associated with light-induced oxygen vacancies and providing evidence that these defects at the STO surface result in both itinerant and localized electronic states.

In the following lines, we will describe qualitatively the STO-based 2DEG band structure, emphasizing the evidence about the bidimensional nature of these systems. Thus, Fig. 1.6.1 (d) shows the energy-momentum subband dispersion of the measured in-situ cleaved surface of (001) STO [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF]. ARPES data reveals five subbands, indicating a lighter effective mass for some of the carriers (corresponding to the three dispersive bands (L1-L3)), while there are two shallowest bands with lower scattering (H1-H2). From parabolic fits, it can be estimated an effective mass of 0.6 me for L1-L3 and between 9-15 me for H1 and H2 [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO3 twodimensional electron gas[END_REF].

It is clear that these states are confined at the surface of the STO crystal, so that they cannot be considered as bulk bands. This can be inferred due to the observation of several clearly nondegenerate states at the 𝛤-point, while the conduction band of STO in bulk is formed by three band barely degenerated (see Fig. 1.6.1 (a)). Both the formation of multiple subband and the high energy of the heavy bands are signatures of quantum confinement of the 2DEG close to the STO surface. Thus, the three light bands correspond with circular Fermi surface, whereas the Fermi surface of the two heavier band adopts cigar-shape [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF]. By considering the shape of the Fermi surface, the spatial anisotropy of the t2g orbitals that forms the conduction band of STO as well as the polarization dependency for such states, it can be demonstrated that lighter subbands are formed by 𝑑 𝑥𝑦 electrons, while heavier bands show a 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 character [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF]. Therefore, the cleaved surface of (001) STO exhibit the same orbital order than the one found for LAO/STO 2DEG, which is a direct consequence of the quantum confinement along the direction normal to the surface [START_REF] Van Heeringen | K•p subband structure of the LaAlO3/SrTiO3 interface[END_REF].

The absence of dispersion along 𝑘 𝑧 is direct evidence of the presence of quantum confinement since by definition the quantum wells are bidimensional. Experimentally, this can be done by varying the photon energy during the photoemission measurements with the aim of probing the perpendicular dispersion to the crystal surface. An example of such measurement in (001) STO can be seen in Fig. 1.6.1 (e). In this image one can clearly observe the Fermi wavevectors for the first two subbands (lighter ones) in the 𝑘 𝑥 𝑘 𝑧 plane along the full Brillouin zone, which are resolved over an extended range of 𝑘 𝑧 . The non-dispersive behaviour along 𝑘 𝑧 demonstrates the twodimensional character of the 𝑑 𝑥𝑦 bands [START_REF] Wang | Tailoring the nature and strength of electron-phonon interactions in the SrTiO3 (001) 2D electron liquid[END_REF]. However, the character of the 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 heavier bands is more difficult to determine and more controversial due to their lower spectral weight, which is strongly suppressed far from the bulk 𝛤-point. This makes it difficult to trace their dispersion along an extended range of 𝑘 𝑧 and therefore, to determine their dimensionality. Thus, the experimental results are contradictory: Santander-Syro et al. [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF] reported that the first heavy band H1 is bidimensional because it cannot disperse along 𝑘 𝑧 , while, on the contrary, Plumb et al. [START_REF] Plumb | Mixed dimensionality of confined conducting electrons in the surface region of SrTiO3[END_REF] claimed that the same band shows 3D-dispersions.

Santander-Syro and collaborators [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF] proposed a simple model to understand qualitatively the quantum confinement of strongly anisotropic bands with 𝑡 2𝑔 orbital character. Thus, each 𝑡 2𝑔 orbital is associated with electron motion with a light effective mass along two crystallographic axes and a heavy mass along the third direction, as is illustrated in Fig. 1.6.1 (b). Under this model, it can be inferred that the 2DEG subbands with a heavy in-plane effective mass derive from orbitals with light out-of-plane mass 𝑚 𝑧 , while in the case of light subband, these can show either a light or heavy out-of-plane mass. If these bands with such characteristics are subjected to a simple wedge potential as can be seen in Fig. 1.6.1 (c) (inset), they will be shifted in energy, with a shift proportional to 𝑚 𝑧 -1/3 . The 𝑑 𝑥𝑦 band, which presents light effective mass in the surface plane and a heavy mass along the confinement direction, will experience the smallest shift relative to the bottom of the potential well and it will be sitting near the bottom of the of the wedge potential. In contrast, the band with out-of-plane 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 orbital character will be located at higher energy. This band structure can be seen in the sketch of Fig. 1.6.1 (c). This model qualitatively captures the experimental results from ARPES in (001) STO surface and from X-ray linear dichroism (XLD) of the 2DEG at LAO/STO interface [START_REF] Salluzzo | Orbital reconstruction and the two-dimensional electron gas at the LaAlO3/SrTiO3 interface[END_REF], but it is too simple and unable to accurately predict the relative subband energies from ARPES experiments. A more realistic quantum well can be obtained from DFT calculations of bulk cubic STO by including SOC [START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO3 surface[END_REF].

In Rashba SOC systems, inversion symmetry breaking lifts spin degeneracy (Fig. 1.6.2). The magnitude of spin splitting in a Rashba system is proportionally linear to the "Rashba" electric field. This behavior is typically observed in conventional semiconductor-based 2DEGs and is a prerequisite for many applications in spintronics. Furthermore, the Rashba splitting is expected to scale with the magnitude of the SOC. Considering the light atomic masses of STO and the consequent small SOC, a small Rashba effect is to be expected in STO-based 2DEGs.However, a tunable spin splitting of 2-10 meV has been reported from transport experiments under the application of a suitable gate voltage for 2DEGs at the LAO/STO interface [START_REF] Caviglia | Tunable Rashba spin-orbit interaction at oxide interfaces[END_REF] and STO [START_REF] Nakamura | Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide[END_REF].

Such a splitting showed a nonlinear dependence on gate voltage and weak antilocalization measurements suggest that it is proportional to 𝑘 3 rather than scaling linearly with 𝑘, as would be expected from the simplest Rashba model.

Zhong et al. [START_REF] Zhong | Theory of spin-orbit coupling at LaAlO3/SrTiO3 interfaces and SrTiO3 surfaces[END_REF] reported that these behaviours can be understood as the signature of a nonconventional Rashba spin-splitting emerging from the multi-orbital nature of the STO-based 2DEGs. In the region of the crossing points between lighter and heavier bands, the spin-splitting increases and it deviates from the 𝑘-linear form. The authors of [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO3 twodimensional electron gas[END_REF]related such an increase to the orbital angular momentum at the avoided crossing points between the different bands, which further enhances spin-orbit interaction. Therefore, the gate voltage can be used in transport measurements to modulate the Rashba coefficient by controlling the filling of the band structure.

The electrostatic effect can be very important in STO-based 2DEG, where the spin splitting increases by about one order of magnitude at the avoided crossing of the 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 and 𝑑 𝑥𝑦 bands.

However, this spin splitting never exceeds 10 meV and remains below the resolution of highresolution ARPES measurements.

Electrostatic gating

As mentioned above, STO possesses a large dielectric constant and is therefore a good candidate for the development of field-effect based devices. In particular, the application of a gate voltage allows modulating the properties of STO-based 2DEGs giving rise to very versatile properties.

Thiel et al. [START_REF] Thiel | Tunable quasi-twodimensional electron gases in oxide heterostructures[END_REF] demonstrated that it was possible to modulate the carrier density in STO-based 2DEGs by applying a back-gate voltage, which facilitates the characterization of these systems since the experiments do not require any additional processing in the vicinity of the 2DEG. The key to the electrostatic doping of the 2DEG is based on the high dielectric constant of the STO.

Thus, for an infinite parallel plate capacitor (𝑆 ≫ 𝐿 2 ), the capacitance is given by.

𝐶(𝑉) = 𝜀 0 𝜀(𝑉) 𝑆 𝐿 , (1.51)
where 𝑉 is the voltage measured across the dielectric medium, 𝜀 0 =8.854 x 10 -12 F•m -1 is the vacuum permittivity, 𝑆 is the surface of the plates and 𝐿 represents the separation between them.

When a gate voltage, 𝑉 𝑔 , is applied, the resulting charge can be calculated as:

∆𝑄 = ∫ 𝐶(𝑉)𝑑𝑉, (1.
𝑉 𝑔 0 52)

Therefore, the carrier density per unit area that can accumulate on the surface of the plates is given by:

∆𝑛 𝑠 = 1 𝑒𝑆 ∆𝑄 = 𝜀 0 𝑒𝐿 ∫ 𝜀(𝑉)𝑑𝑉, (1.53)
𝑉 𝑔 0

For the back-gate configuration, the voltage is applied between the conductive interface (in our case the 2DEG) and the bottom of the STO substrate, which acts as the dielectric medium.

Commercial STO substrates typically have a thickness of 0.5 mm (L), which corresponds to a dielectric breakdown voltage around 1000 V. However, at low temperature, the voltage is limited to about ±250 V due to the dielectric breakdown of liquid He. If we applied 250 V, this give rise to an electric field, 𝐸, of 0.5 MV.m -1 (taking L = 0.5 mm). Further, it is well-known that the dielectric constant of STO depends a lot on temperature and is also electric field dependent at low temperatures. Thus, one can infer that taking 𝜀STO≃18.000 (E = 0.5 MV.m -1 ) at about 4 K, leads to Δ𝑛 𝑠 ≃2x10 13 cm -2 (T < 10 K). Note that the charge carrier densities of the STO-based 2DEGs are typically in the range of few 10 12 -10 13 cm -2 , so that electrostatic field-effect across the STO substrate represents an efficient way to modulate the electron carrier density at low temperatures. However, at room temperature, 𝜀 𝑆𝑇𝑂 ≃300, implying a drop of two orders of magnitude of the charge carrier density. Therefore, at RT, the back-gating loses its effect on the 2DEG carrier density.

In this regard, the charge carrier dependence of the electron mobilities must be considered as well. For instance, Bell et al. [START_REF] Bell | Dominant mobility modulation by the electric field effect at the LaAlO3/SrTiO3 interface[END_REF] reported that the electron mobility dropped one order of magnitude (from 10 3 to 10 2 cm 2 V -1 s -1 ) when the carrier density was reduced. This prevents the realization of a low carrier density state (down to few 10 12 cm -2 ) preserving high electron mobilities, at least if one uses a back-gating configuration.

Another appealing possibility is the use of a top-gate configuration, which would enable the perspectives of 2DEGs for technological application since it will offer the opportunity to design devices for lateral charge (and of course, spin) transport with on-demand gates geometries.

Several groups [START_REF] Förg | Field-effect devices utilizing LaAlO3-SrTiO3 interfaces[END_REF], [START_REF] Eerkes | Modulation of conductance and superconductivity by top-gating in LaAlO3/SrTiO3 2-dimensional electron systems[END_REF] have already reported an efficient electrostatic field-effect using a top-gate configuration in the 2DEG of LAO/STO interface, showing similar results in terms of charge carrier modulation to those reported using back-gate geometries.

Achieving an efficient field-effect modulation of the STO-based 2DEGs is a crucial step in understanding the fundamental properties of these systems with respect to, for instance, its electron doping level.

From a practical case, the overdoped side is very difficult to explore due to the saturation and hysteresis process in the physical properties. From previous work, it was observed that as the gate voltage increased the resistance of the 2DEG decreased slightly to saturate rapidly and become independent of the applied voltage. This behavior is unexpected according to the laws of electrostatics, whereby more electrons should be added to the quantum well as the gate voltage is increased. This first bias curve was found to be irreversible, that is, when the voltage decreased from a maximum value (+200 V) the resistance curve deviated from the first bias curve.

This saturation regime and the hysteretic behavior can be explained by assuming that the Fermi level is very close to the top of the quantum well. Increasing the voltage adds electrons to the interface, rapidly filling the high energy subbands at the top of the well. After some time, these electrons escape into the STO substrate conduction band, causing the saturation of the carrier density and the resistance of the 2DEG. Note that this saturation is not associated with an increase in gate current, suggesting that these charges are trapped in the system. the well by applying a back gate voltage, the filling is limited by the intrinsic location of the Fermi level. Practically, after a first initialization cycle with the largest gate voltages to be used, the resistance shows a virtually non-hysteretic behaviour.

Magnetoresistance

Magnetoresistance denotes a change of resistance in materials under the application of an external magnetic field. If the field is applied normal to the sample surface, a positive magnetoresistance is usually observed, whereas if it is in the plane of the sample, a negative magnetoresistance may occur. On the other hand, at low temperatures and low magnetic fields quantum corrections such as weak localization (WL) or weak antilocalization (WAL) may also be observed [START_REF] Christensen | Stimulating oxide heterostructures: a review on controlling SrTiO3-based heterointerfaces with external stimuli[END_REF].

In the presence of a perpendicular magnetic field, ordinary magnetoresistance can be described by resorting to electron deflection due to the Lorentz force, giving rise to a positive MR. In metallic systems where transport is mediated by a single band, the ordinary magnetoresistance shows a parabolic dependence proportional to (𝜇 2 𝐵 2 ) where μ is the carrier mobility. For 2DEGs hosted at the interface of STO with other materials, it has been observed that the MR exhibits a deviate from the parabolic shape when the carrier density is above a critical value. Also, the MR is parabolic at low magnetic fields, deviating from the parabolic shape [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF]- [START_REF] Gan | Diluted oxide interfaces with tunable ground states[END_REF] above a critical value. The deviation of the MR curve from the parabolic to a bell shape, is associated with the contribution from carriers with different mobilities, i.e., it originates from the mediation of the 𝑑 𝑥𝑦 and 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 bands in transport, and can be well described by a two-band model [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF].

Disorder at the interface becomes very important at low temperature and can be caused by oxygen/cation vacancies, cation intermixing, and tetragonal domain walls. Such disorder modifies the wave behavior of electrons from extended to localized states, leading to an increase of the MR at low magnetic fields. This peak reflects the WL phenomenon, which originates from elastic scattering events that can positively interfere with the same path followed in the opposite direction [START_REF] Hikami | Spin-orbit interaction and magnetoresistance in the two dimensional random system[END_REF]. This increases the probability of localization and thus increases the resistance.

The lack of inversion symmetry at the interface can result in spin-orbit coupling and lead to negative interference characteristic of WAL, producing a decrease in resistance [START_REF] Gariglio | A spin-orbit playground: surfaces and interfaces of transition metal oxides[END_REF]. When magnetic fields are applied, both constructive and destructive interference are prevented due to the additional phase acquired by the Aharonov-Bohm effect. This results in a peak (dip) in MR around 𝐵 = 0 T for WL (WAL). WL and WAL are frequently observed in STO and STO-based heterostructures, as reported by Gariglio et al. [START_REF] Gariglio | A spin-orbit playground: surfaces and interfaces of transition metal oxides[END_REF]. WAL provides a convenient way to study spin-orbit interaction, which has been shown to be tunable by applying an electrostatic field [START_REF] Caviglia | Tunable Rashba spin-orbit interaction at oxide interfaces[END_REF], [START_REF] Niu | Giant tunability of the two-dimensional electron gas at the interface of γ-Al2O3/SrTiO3[END_REF]. Moreover, these phenomena agree with first-principles density functional theory (DFT) calculations, whereby it was predicted that the maximum spin-orbit coupling peaks at the critical point where the 𝑑 𝑥𝑦 and 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 bands cross due to band [START_REF] Zhong | Theory of spin-orbit coupling at LaAlO3/SrTiO3 interfaces and SrTiO3 surfaces[END_REF], [START_REF] Kim | Origin and transport signatures of spin-orbit interactions in one-and two-dimensional SrTiO3-based heterostructures[END_REF].

Hall effect

The Hall effect is defined as the transverse potential generated by circulating a current through a material in the presence of an out-of-plane magnetic field. In metals where the transport is mediated by a single band the dependence of this transverse voltage increases linearly with the magnitude of the magnetic field. However, in STO-based 2DEGs, the corresponding Hall curves can be both linear and nonlinear depending on the carrier density in the 2DEG [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF]. shows the total carrier density. Reprinted with permission from [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF].

Chapter 2. Experimental techniques

In this section the fundamentals and operation of the techniques employed during this thesis are presented. We will focus on magnetron sputtering, a technique currently with great applicability in the industry and which has been the mainly used technique for sample growth. Next, the electron photoemission process will be presented, as an introduction to the spectroscopy techniques used both for the compositional characterization of the samples (x-ray photoelectron spectroscopy) and for the study of the band structure of 2DEGs (angle-resolved photoemission spectroscopy). We will describe the methods used for a first characterization of the magnetotransport properties (resistivity, magnetoresistance and Hall effect measurements), and to determine the spin-charge interconversion efficiency (bilinear magnetoresistance and spinpumping ferromagnetic resonance experiments) as well as the ability of these systems to exert a torque on thin ferromagnetic films (spin-orbit torque measurements). For the latter, we use devices whose patterning procedure will be explained in detail in the corresponding subsection, referring to some of the practical singularities for these systems. Finally, we will focus on techniques related to the characterization of magnetic properties and the imaging of magnetic textures (magnetic force microscopy, magneto-optical Kerr effect microscopy, and x-ray photoemission electron microscopy).

Mask chamber

Magnetron Sputtering

Magnetron sputtering is nowadays one of the most widely used techniques for thin film deposition due to its numerous advantages. It is a vacuum coating process within the category of physical vapor deposition techniques (PVD), which basically consists of the ejection of atoms or molecules from a target material by bombardment with energetic ions, i.e., a top-down technique. The phenomenon of sputtering was first observed by Grove in 1852, but it took more than a century before it was introduced as a commercial coating process in industry [START_REF] Bräuer | Magnetron sputtering -Milestones of 30 years[END_REF].

In the mid-1970s, Chapin introduced a new variant of traditional diode sputtering, the so-called magnetron sputtering, in which the plasma density is increased as it is contained by magnetic fields. This is achieved by introducing permanent magnets behind the sputtering target (cathode), whose magnetic field constrains the charged particles, considerably increasing the efficiency of the sputtering process. This breakthrough led to its prominence in the field of vacuum coating technologies and since then, sputtering has become the most important technology for industrial thin film deposition. Thanks to its significant benefits over other vacuum coating techniques (thermal evaporation, atomic layer deposition, pulsed laser deposition, etc.), many commercial applications have been developed, ranging from microelectronics manufacturing to simple decorative coatings.

Among its many advantages, it is worth mentioning the high deposition rates and great versatility in terms of the wide variety of materials to be sputtered, such as metals, non-metals, alloys or composites. It can be easily automated and scaled up thanks to its uniformity on large-area substrates. It can be used to coat heat-sensitive substrates, such as polymers or plastics. And also, the films obtained by sputtering exhibit high purity and extremely high adhesion.

The working principle of DC magnetron sputtering is illustrated in Fig. 2.1.1 (a). First, the operational chamber is evacuated to reach high vacuum and a sputtering gas is introduced into the chamber, while pressure is regulated within the mbar range using vacuum pumps. Then, a high voltage is applied between the magnetron cathode and the anode, so the cathode becomes negatively charged and electrons are accelerated away producing collisions with other atoms of the sputtering gas. This causes an electrostatic repulsion that ionizes the gas, accelerating highenergy ions towards the target, hitting it with sufficient kinetic energy to eject atoms, molecules, or even clusters. Such sputtered material crosses the chamber and reach the surface of the substrate, thereby coating it with a thin film. Apart from the ejection of atoms from the target material, an emission of secondary electrons is produced from the target surface, which sustain the glow discharge, the so-called plasma [START_REF] Valentin Tudose | Functional Nanostructured Interfaces for Environmental and Biomedical Applications[END_REF].

The gas used for the deposition can be non-reactive (inert gas only, Ar) or reactive (mixture of inert and reactive gases, such as O2 or N with Ar). Pure metals and alloys can normally be deposited with DC sputtering, but the growth of less conducting materials such as semiconductors or oxides may require RF power. The growth of high-quality thin films requires optimizing a number of parameters such as gas flow, working pressure, power and substrate temperature.

Samples were grown using a commercial PLASSYS MP450S magnetron sputtering with a base pressure within the UHV range (about 8.5 x 10 -9 mbar). Calibration of the deposition rates has been performed by X-ray reflectometry (XRR) and atomic force microscopy (AFM), measuring the step height between deposited and non-deposited areas. The growth of all samples involved in this thesis has been carried out at room temperature under inert conditions (Ar) and a pressure of about 5.5 x 10 -4 mbar. DC current intensity, power and growth rate vary as a function of the deposited metal (see reference values in Tab. 2.1.1).

In relation to the objectives of this thesis, we will study the ability of different metals to reduce an oxide by direct contact under vacuum conditions, therefore it is paramount to perform an adequate pre-sputtering process to start from clean target materials. This pre-sputtering process has been carried out prior to each of the depositions, and to a greater extent for Al and Y, which were found to be susceptible to oxidation even under high vacuum (HV) conditions. Tab. 2.1.1: Conditions used during the growth of samples by DC magnetron sputtering, and example of the growth rates obtained by XRR and AFM measurements.

Electron Photoemission-based Spectroscopies

Today, electron photoemission-based spectroscopies play a key role in physical chemistry and materials science, allowing the chemical composition of materials, as well as many of their electronic and magnetic properties, to be determined. As the name suggests, these techniques are based on the collection of the energy spectra of photoelectrons emitted by a solid, liquid or gaseous material, and are usually classified according to the energy range of the photon beam used, which can range from a few eV (visible-ultraviolet, VUV) up to about 15 keV (hard X-rays, HX). In particular, in the case of solids, these techniques are very sensitive to the surface due to the limitation of the mean free path of the electrons.

In this work, we have used X-ray photoelectron spectroscopy (XPS) and angle-resolved photoemission spectroscopy (ARPES) in order to study the compositional changes after deposition of reactive metals on STO or KTO in Sec. 3.1, as well as the band structure of KTObased 2DEGs in Sec. 3.2, respectively. This section aims to provide the reader with the fundamentals of photoemission process and the main characteristics of these spectroscopies. It is worth mentioning that electron photoemission-based spectroscopies can also be the basis of powerful microscopes such as x-ray photoemission electron microscopy (X-PEEM), which has been used in this thesis to observe the magnetic textures after combining metal/oxide 2DEGs with Co/Pt bilayers in Sec. 3.4.

Photoemission Process

The physical basis of the above-mentioned spectroscopies is the photoelectric effect, discovered by Hertz in 1887 when he observed a relationship between light and electricity during his experiments related to the production and reception of electromagnetic waves. Subsequent research showed that classical physics could not explain this effect, and it was not until 1905 when Einstein formulated a new corpuscular theory of light to explain this phenomenon. He proposed that each photon carries an energy 𝐸 equal to ℎ𝑣, where 𝑣 is the frequency of light and ℎ is Planck's constant. Therefore, a photon could transfer its energy to an electron in the solid, which can be photoemitted if the photon energy is high enough to overcome the energy binding the electron to the solid.

Even though the photoemission of electrons should be treated as a single step, it is easier to describe it by considering the three-step model (see Fig. 2.2.1) [START_REF] Hüfner | Photoelectron Spectroscopy: principles and applications[END_REF]: i) photoexcitation, ii)

propagation to the sample surface and iii) emission in vacuum. Then, photoelectron intensity can be formulated as a product of three independent probabilities, one per each step, which will be derived in the following.

i) Photo-excitation: From first-order perturbations, one can derive the probability that a single electron is promoted from an initial state 𝜓 𝑖 with energy 𝐸 𝑖 to a final state 𝜓 𝑓 with energy 𝐸 𝑓 , due to photon absorption. For electrons in a periodic crystal, wave functions are Bloch states that depend on the wave vector 𝑘. Thus, according to Fermi's golden rule, the transmission probability per unit time (𝑊 𝑖𝑓 ) is given by:

𝑊 𝑖𝑓 = |𝑀 𝑖𝑓 | 2 𝛿(𝐸 𝑓 (𝑘 𝑓 ) -𝐸 𝑖 (𝑘 𝑖 ) -ℎ𝑣), (2.1)
where 𝛿 function determines the conservation of total energy 𝐸 𝑓 = ℎ𝑣 -𝐸 𝑖 and |𝑀 𝑖𝑓 | is the photoemission matrix element of the Hamiltonian (𝐻 ′ ), which describes the transition between the initial and final state of the electron as follows:

|𝑀 𝑖𝑓 | = 〈𝜓 𝑖 (𝑘 𝑖 )|𝐻 ′ |𝜓 𝑓 (𝑘 𝑓 )〉, (2.2)
Based on the dipole approximation, 𝐻 ′ can be expressed as the scalar product between the electromagnetic vector potential (𝐴) and the electronic momentum operator (𝑝):

𝐻 ′ ~𝑒 𝑚 𝐴 • 𝑝, (2.3)
The matrix element depends on the polarization of the photon (through 𝐴), as well as the symmetry of the initial and final states related to the orbital character of the Bloch states. Thus, the matrix element contains no direct information on the band dispersion but can provide information on electronic states, if specific measurement geometries are used.

In equation (2.1), the photon momentum with respect to the electrons in the valence bands is ignored. This is the so-called sudden approximation, which considers that the electron is instantaneously removed from the solid without any further interaction and the transition is vertical, i.e., 𝑘 𝑖 = 𝑘 𝑓 = 𝑘. Note that the above approximation is valid within the low photon energy electron from the material to the vacuum. Adapted from ref. [START_REF] Hüfner | Photoelectron Spectroscopy: principles and applications[END_REF] range up to the soft X-rays regime. Under this approximation, the integration of the transmission probability over the band structure of the system gives the internal photocurrent:

𝐼(𝐸 𝑖 , 𝜈, 𝑘) = ∑ |𝑀 𝑖𝑓 | 2 𝑖,𝑓 𝛿(𝐸 𝑓 (𝑘 𝑓 -𝐸 𝑖 (𝑘 𝑖 ) -ℎ𝜈), (2.4)
In the following, we will refer to 𝐸 𝑖 as the binding energy 𝐸 𝐵 . As for the spin information, the photon does not couple directly to the electron spin, so it is conserved during the optical transition.

ii) Propagation to the surface: Propagation of photoexcited electrons within the solid involve several elastic and inelastic scattering mechanisms with other electrons, ions, photons, and defects, that affect the energy and angular distribution of the photoemission spectrum, and reduces the intensity of the photocurrent 𝐼(𝐸 𝐵 , 𝜈, 𝑘).

The average length between two consecutive inelastic scattering events, the so-called inelastic mean free path (𝜆 𝐼𝑀𝐹𝑃 ) of electrons, depends on photon energy, following a very similar dependence for different materials that leads to the universal curve shown in Fig. 2.2.2. The "universal" expression is [START_REF] Baiqing | Angle-resolved photoemission spectroscopy and its application to topological materials[END_REF]:

𝜆 𝐼𝑀𝐹𝑃 (𝐸 𝑘𝑖𝑛 ) = 𝐴 𝐸 𝑘𝑖𝑛 2 + 𝐵√𝐸 𝑘𝑖𝑛 , (2.5)
where 𝐴 and 𝐵 are coefficients for different elements, organic or inorganic compounds. regimes (in blue and pink, respectively). Adapted from ref. [START_REF] Baiqing | Angle-resolved photoemission spectroscopy and its application to topological materials[END_REF] For elemental samples, 𝐴=143 and 𝐵=0.054, if 𝜆 𝐼𝑀𝐹𝑃 is in nm and 𝐸 𝑘𝑖𝑛 in eV. Then, the decay of the photoelectron intensity as a function of the distance traveled 𝑥 and electron energy 𝐸 is given by Lambert's exponential law:

𝐷(𝐸 𝑘𝑖𝑛 , 𝑥) = 𝑒 -( 𝑥 𝜆 𝐼𝑀𝐹𝑃 (𝐸) ) , (2. 1)
Thus, only photoelectrons emitted from a depth smaller than 𝜆 𝐼𝑀𝐹𝑃 , also called the escape depth, may be photoemitted. Note that the escape depth of electrons is of the order of 1 nm for VUV and soft-X beams and thus, smaller than the penetration distance of the photon beam (of the order of 1μm).

iii) Emission in vacuum: In the final step of the photoemission process, the photoelectron escapes into vacuum passing through the energy barrier of the surface, i.e., the work function (𝛷) of the material. The latter is defined as the energy separation between vacuum and Fermi levels, 𝛷 = 𝐸 𝑣𝑎𝑐 -𝐸 𝐹 . Therefore, the aforementioned kinetic energy of the photoemitted electrons should be corrected as follows:

𝐸 𝑘𝑖𝑛 = ℎ𝑣 -𝐸 𝐵 -𝛷, (2.7)
Then, if an electron is emitted with an in-plane wave-vector component 𝑘 ∥ forming an angle 𝜃 with respect to the sample surface and an in-plane angle 𝜑, one can write the parallel component as follows:

𝑘 ∥ = √ 2𝑚𝐸 𝑘𝑖𝑛 2 ℏ (𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜑𝑘 𝑥 + 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜑𝑘 𝑥 ), (2.8)
where the kinetic energy of the photoelectron is 𝐸 𝑘𝑖𝑛 = ħ(𝑘 ‖ + 𝑘 ⏊ )/2𝑚. Due to the symmetry breaking when the electrons pass the surface potential, only 𝑘 ‖ is conserved. Still, 𝑘 ⊥ can be obtained using a nearly free-electron approximation for the final states if photon energy is larger than 10 eV, yielding:

𝑘 ⏊ ,𝑖 = √ 2𝑚 ħ (𝐸 𝑘𝑖𝑛 𝑐𝑜𝑠 2 𝜃 + 𝑉 0 ), (2.9)
Here, 𝑉 0 is named as the inner potential of the solid and can be determined from theoretical calculation or from photon-energy-dependent measurements. For the particular case of ARPES, the expression of the normal component can be simplified since it is always larger than the probed in-plane one. Hence, the dependence on 𝜃 is only at the first order and 𝑘 ⊥ can be expressed:

𝑘 ⏊ ,𝑖 = √ 2𝑚 ħ (ℎ𝑣 -𝛷 -𝐸 𝐵 + 𝑉 0 ), (2.10)
Therefore, if one measures the kinetic energy and the emission angles (𝜃 and 𝜑), the electron state in the solid with 𝐸 𝐵 and wave-vector 𝑘 𝑖 can be traced. Finally, the photocurrent is reduced by the probability of transmission through the surface 𝑇 (𝐸 𝑘𝑖𝑛 , 𝑘 ‖ ):

𝐼 𝑓𝑖𝑛𝑎𝑙 = 𝐼 (𝐸 𝑘𝑖𝑛 , 𝑣, 𝑘 ‖ ) 𝐷 (𝐸 𝑘𝑖𝑛 , 𝑥) 𝑇 (𝐸 𝑘𝑖𝑛 , 𝑘 ‖ ), (2.11) From this expression, one can note that the outgoing photocurrent can be obtained from the photon energy, the kinetic energy and the parallel wave-vector component, all being measurable quantities with a proper analyzer. Furthermore, apart from the electrons emitted in the photoelectric process, Auger electrons can be emitted due to the relaxation of ionized atoms: an electron from an outer higher energy level falls into an inner orbital, simultaneously emitting a second electron carrying the excess energy.

X-ray Photoelectron Spectroscopy

The Auger electron has a kinetic energy equal to the difference between atomic levels and is independent of the energy of the incident photon. Therefore, photoionization normally leads to the simultaneous emission of both photoelectrons and Auger electrons, which can be differentiated by changing the energy of the incident photon. This Auger electron emission occurs typically 10 -14 seconds after the photoelectric event.

It is worth mentioning that, in addition to Auger and photoelectron lines, one should also consider:

X-ray satellites: When one uses a non-monochromatic source for irradiation, the X-ray emission not only shows the characteristic X-ray but also some minor X-ray components at higher photon energies. Therefore, using Mg and Al sources, there will be a family of minor peaks at lower binding energy accompanying each photoelectron, since the radiation is not purely monochromatic. Moreover, the intensity and spacing of those peaks are characteristic of the Xray anode material used.

X-ray ghost lines: These lines are the result of Mg impurities on the Al anode or vice versa, or even oxidation of the anode. When x-ray radiation from an element other than the anode is incident on the sample, small peaks can be produced, sometimes more intense, but shifted by a characteristic energy range. Sometimes, but rarely, such lines can be originated from the sample itself.

Shake-up lines: Occasionally there are photoelectric processes that do not lead to ion formation in the ground state. There is always a finite probability that the ion remains in an excited state, which is a few eV above the ground state. Thus, the kinetic energy of the photoelectron is reduced, and the difference corresponds to the energy difference between the ground state and the excited state.

Multiplet-splitting: An electron from a core-level having unpaired electrons in the valence levels (spin) is able to create a vacancy in two or more ways, giving rise to a photoelectron line split asymmetrically into several components. The same can occur in the ionization of 𝑝-, 𝑑and 𝑓-levels, leading, in favorable cases, to a slight increase of the spin-orbit splitting (e.g., the 2𝑝 1/2 and 2𝑝 3/2 lines of the transition metals in the first row), and to a slight increase in the asymmetry of the line shape of the components.

Energy loss lines: These lines can be observed mostly in conductive materials. They are due to the interaction of the photoemitted electron with other electrons. The energy difference between the primary peak (photoelectron line) and the loss peak is called the plasmon energy.

The spectrum from a mixture of elements is approximately the sum of the peaks of the individual constituents. Thus, XPS can be used to identify and determine the concentration of elements in the surface, since each element has its own and unique set of binding energies, much like a fingerprint. Quantitative data can be extracted from peak heights or peak areas, and identification of chemical states often can be made from exact measurement of peak position and separations, as well as from certain spectral features. The exact binding energy of an electron does not only depend on the level from which photoemission is occurring, but also from the formal oxidation state of the atom and/or the local chemical and physical environment. Further, as the mean-free path of electrons through solids is of the order of a few nm (<10 nm), the detected electrons come from the top few atomic layers, which makes XPS a surface-sensitive technique.

In this thesis we have used XPS to determine the reduction of STO or KTO after the deposition of metals with high affinity for oxygen, as well as to elucidate both the formation and reoxidation process of 2DEG. On the one hand, the redox reaction between the oxide and the substrate leads to a change of the valence state of both the oxide and the deposited metal. Therefore, XPS allows us to determine the degree of reduction of STO and KTO to subsequently correlate it with the transport properties of the 2DEGs. This study has been carried out as a function of the thickness of the deposited metal which, as will be seen later, is a key factor in the properties of these heterostructures.

On the other hand, thanks to the connection under vacuum conditions between the sputtering magnetron and the XPS characterization chamber, as shown in Fig. 2.1, this study has not only been performed as a function of the deposited metal thickness for different metal/STO and Al/KTO 2DEGs, but also before and after exposing the samples to ambient conditions. This, in turn, will allow us to clarify the role of the reoxidation process.

In particular, these measurements were performed at room temperature using an Omicron NanoTechnology GmbH system with a base pressure of 5 x 10 -10 mbar, using Mg 𝑘𝛼 source As deduced previously for photoemission-based techniques, ARPES is a very surface sensitive technique, which makes it a powerful tool to study the band structure of solids and surfaces but represents its major disadvantage when measuring the bulk properties of the materials. However, this is still possible by using x-ray of higher energies (> 1 keV), which can probe depths up to 10 nm [START_REF] Cancillieri | [END_REF].

During the measurements, a source of VUV or soft X-rays is focused on the sample surface to investigate the valence band electronic states close to the Fermi level. By filtering the photoelectron intensity by the emission angle and the kinetic energy of the electron with an electron analyzer, the dispersion of the energy bands in the wave-vector space can be detected.

The kinetic energy will reflect the binding energy in the solid, shifted by the photon energy and the work function as deduced from equation (2.7).

On the other hand, from equation (2.10) we deduce that 𝑘 ⏊ is fixed by the photon energy by equation (2.9) and 𝑘 ‖ is related to the photoemission angle. Thus, the output of an ARPES electrons according to their kinetic energy and output angle. For a fixed value of kinetic energy, the analyzer spreads electrons with different angular component along a fixed axis 𝜃 𝑥 (with corresponding wave vector 𝑘 𝑥 ). It is also possible to use internal deflectors to shift the scattering axis to a certain value 𝜃 𝑦 (with the corresponding 𝑘 𝑦 component). In particular for our measuring instrument, the angular acceptance of the analyzer is 30 o for the 𝜃 𝑥 and 𝜃 𝑦 directions. This value can be translated into the probing ranges for 𝑘 𝑥 and 𝑘 𝑦 , respectively, using Eq. (2.8).

An ARPES spectrum 𝐼(𝐸 𝑘𝑖𝑛 , 𝑘 𝑥 ) is constructed by acquiring the photocurrent dispersion along 𝜃 𝑥 while scanning the selected kinetic energy. The energy selection is performed by suitable electrostatic lenses located in front of the analyzer. In addition, the 3D data set 𝐼(𝐸 𝑘𝑖𝑛 , 𝑘 𝑥 , 𝑘 𝑦 ) can be compiled by measuring for different values of 𝜃 𝑦 . The 3D maps provide a complete picture of the band dispersion, which is relevant for the high symmetry points of the first Brillouin zone.

Furthermore, band symmetry can be appreciated from sections at fixed binding energy (constant energy maps, CEM).

Magnetotransport Properties Characterization

This section deals with the characterization methods used to gain insight into the transport properties of different metal/oxide 2DEGs. In particular, here we describe the main types of measurements and configurations used for a primary characterization of these systems (resistivity, magnetoresistance and Hall effect measurements), as well as to evaluate the ability of metal/oxide 2DEGs for spin-charge interconversion (bilinear magnetoresistance measurements and spin-pumping ferromagnetic resonance experiments) and to exert a torque on an adjacent ferromagnetic film (second-harmonic Hall voltage measurements).

Resistivity, Magnetoresistance and Hall Effect Measurements

In this dissertation, a basic characterization of the magnetotransport properties of metal/STO and Al/KTO 2DEGs has been carried out. These measurements (resistivity, magnetoresistance and Hall effect) have been performed on thin films using the van der Pauw configuration. This configuration was proposed in 1958 [START_REF] Van Der Pauw | A method of measuring specific resistivity and Hall effect of discs of arbitrary shape[END_REF], as a tool to measure resistivity and Hall effect in samples with an arbitrary shape, if it is homogeneous in terms of thickness and transport properties, as well as the contacts are sufficiently small and located on the perimeter. Under these conditions, and in contrast with the four-point probe, the van der Pauw method provides an average value of the sample resistivity. where 𝑡 is the thickness, and 𝜌 is the resistivity. This expression, as a function of 𝜌, can be simplified as:

𝜌 𝑡 = π ln(2) 𝑅 𝑥𝑥 + 𝑅 𝑦𝑦 2 𝑓, (2.16)
with 𝑓 being the van der Pauw correction factor, which takes a value between 1 and 0.2, that is given by the ratio between 𝑅 𝑥𝑥 and 𝑅 𝑦𝑦 . Therefore, for an ideally isotropic sample and configuration, this equation can be reduced to:

𝑅 𝑠 = 𝜌 𝑥𝑥 𝑡 = 𝜋𝑅 𝑥𝑥 𝑙𝑛 (2) , ( 2

.17)

where the sheet resistance, 𝑅 𝑠 , is expressed in Ω/□, i.e., ohm per aspect ratio. Therefore, this method allows to determine the resistivity of the sample, and its variation with the applied magnetic field, also known as magnetoresistance. On the other hand, the van der Pauw configuration also allows the Hall effect to be measured.

That is, in panel (b) of Fig. 2.3.1, the potential drop across contacts 2 and 3 (𝑉 23 ) when a current flows through contacts 1 and 4 (𝐼 14 ), or vice versa, in the presence of a magnetic field perpendicular to the motion of electrons. This potential drop, the so-called Hall voltage (𝑉 𝐻 ), is caused by the Lorentz force and allows to determine the transverse resistivity in 2D materials, (𝜌 𝑥𝑦 2𝐷 ), as:

𝜌 𝑥𝑦 2𝐷 = 𝜌 𝑥𝑦 3𝐷 𝑡 = 𝑉 𝐻 --𝑉 𝐻 + 𝐼 --𝐼 + , (2.18)
From now on, since 𝜌 𝑥𝑦 2𝐷 gives the resistivity of a two-dimensional sheet in which the thickness is negligible with respect to the width, we will refer to this value as 𝑅 𝑥𝑦 .

Traditionally, the Hall effect is used to determine the density, mobility and type of carriers in both conductors and semiconductors. On the one hand, the type of carriers can be deduced directly from the experimental curve, being positive for holes and negative for electrons. On the other hand, assuming that there is only one type of carriers, it allows us to estimate the carrier density in a 2D system (𝑛 𝑠 ) and the corresponding mobility (𝜇) by means of the expressions:

𝑛 𝑠 = 𝐵 |𝑒|𝑅 𝑥𝑦 , (2.19)
and,

𝜇 = 𝐵 |𝑒|𝑅 𝑠 𝑛 𝑠 , (2.20)
where 𝑒 is the electron charge, 𝐵 is the applied magnetic field, and 𝑛 𝑠 represents electrons per unit area (i.e., cm -2 ), and 𝜇 is given in cm

𝑅 𝑠 (0) = 1 𝑒(𝑛 1 𝜇 1 + 𝑛 2 𝜇 2 ) , (2.21𝑎) 𝑅 𝑥𝑦 (𝐵) = - 𝐵 𝑒 ( (𝑛 1 𝜇 1 2 + 𝑛 2 𝜇 2 2 ) + (𝜇 1 𝜇 2 𝐵) 2 (𝑛 1 + 𝑛 2 ) (𝑛 1 𝜇 1 + 𝑛 2 𝜇 2 ) 2 + (𝜇 1 𝜇 2 𝐵) 2 (𝑛 1 + 𝑛 2 ) 2 ), ( 2

.21𝑏)

where 𝑛 1 and 𝜇 1 , and 𝑛 2 and 𝜇 2 are the carrier densities and mobilities for the two different bands, respectively.

In addition, in view of the mode explained in Sec. 1.2.4, we have performed bilinear magnetoresistance measurements in Al/KTO 2DEGs to determine the Rashba coefficient. These measurements have been performed at 2 K by rotating 360 o with the magnetic field always inplane. The measurements were carried out on a 1.58 x 10 mm 2 sample in order to achieve a better definition of the angle between the injected charge current and the in-plane magnetic field. For such characterization we used different DC current values up to 1 mA, in both directions, and magnetic field values up to 9 T.

Experimental set-up

The primary characterization of metal/STO 2DEGs was performed using a Quantum Design Dynacool PPMS capable of applying a maximum field of 9 T and reaching a minimum temperature of 1.8 K. All measurements have been performed with DC current applying an out-of-plane magnetic field, if necessary. For this purpose, the samples are fixed with a double-sided adhesive tape, suitable for vacuum conditions, to a standard resistivity puck that allows the measurement of three samples in parallel. The samples were contacted in the van der Pauw configuration with Al microwires using a Kulicke & Soffa 4523AD bonding machine.

Spin-Pumping Ferromagnetic Resonance Experiments

To evaluate the spin-to-charge conversion efficiency for different metal/oxide 2DEGs, in this work we have performed spin pumping experiments by ferromagnetic resonance (SP-FMR). To perform these experiments, we use a resonance cavity that allows us to obtain an accurate value of the spin-to-charge conversion efficiency. The setup and the methodology used to eliminate some spurious effects are explained in detail below. In this way, a better definition of the angle between the current direction 𝐼 and the applied magnetic field 𝐵 is achieved, maximizing the effect.

FMR measurements in a microwave cavity

Ferromagnetic resonance can be obtained by two methods: i) using a stripline or ii) using an Electron Paramagnetic Resonance (EPR) microwave cavity system. The former allows materials to be characterized over a wide frequency range, whereas measurements in a cavity-based system are restricted to the resonance frequency of the microwave cavity (or RF cavity), while sweeping with external RF magnetic fields. The cavity acts as a hollow resonator for the RF magnetic field, which is strongly amplified by the quality factor (𝑄) of the cavity and its intensity is orders of magnitude higher than that obtained using striplines. Importantly for our purposes, the cavity system not only enhances the signal-to-noise ratio of the FMR spectrum, but also generates a more efficient spin injection efficiency due to its higher power absorption. Therefore, measurements in a cavity are more convenient to know the spin-to-charge conversion efficiency of the different 2DEGs involved in this thesis.

In Fig. to the measurements, a calibration is necessary to couple the cavity and make sure that the power absorbed outside the resonance is the same as the power returning to the detector. The measurement is then performed in a similar way as for microstriplines, i.e., a DC magnetic field is swept until the resonance condition is reached, where the power absorbed by the cavity is maximized.

The

Spurious effects

Due to the geometry of the experiment, the voltage is measured at opposite sides of the sample, so we are also detecting magnetoresistance effects coming from the ferromagnet. Therefore, the output voltage may contain other components that we must also consider. In the following, we will briefly explain the main spurious effects and offer solutions to avoid them.

Spin rectification effects: Microwave radiation can generate two contributions in the ferromagnetic material: a RF electric field (𝐸 𝑟𝑓 ), which produces a RF current in the cavity (flowing in the sample), and a RF magnetic field (ℎ 𝑟𝑓 ), which exerts a field torque on the magnetization and induces its precession around the equilibrium direction. The latter leads to a time-dependent magnetoresistance effect in the ferromagnet, adding a RF modulation to the intrinsic resistance.

Thus, spin rectification effects arise as a consequence of the nonlinear coupling between the RF current and the oscillating resistance at the resonant frequency, resulting in a non-vanishing DC voltage [6][6]. More specifically, these effects may be due to the existence of anisotropic magnetoresistance (AMR), anomalous Hall effect (AHE) and planar Hall effect (PHE) in the sample.

These effects are not desirable when trying to analyze the conversion efficiency of metal/oxide 2DEGs by the inverse Edelstein effect (IEE), as they add to the output signal. To avoid them, good cavity optimization is needed, as well as good sample alignment within the cavity, thus minimizing 𝐸 𝑟𝑓 and maximizing ℎ 𝑟𝑓 (maximizing the inverse spin Hall effect/IEE signal). However, even after a proper sample placement, a small contribution from spin rectification effects is expected.

Separating the ISHE-generated voltage from spin rectification effects in FMR spin pumping experiments is an arduous task that has been addressed by several authors in recent years [START_REF] Harder | Electrical detection of magnetization dynamics via spin rectification effects[END_REF]- [START_REF] Soh | An angular analysis to separate spin pumping-induced inverse spin Hall effect from spin rectification in a Py/Pt bilayer[END_REF].

The first approach is to separate the output signal into a symmetric and antisymmetric component. As mentioned above, the signal from spin-to-charge conversion is purely symmetric, since it is proportional to the absorption intensity of the FMR. However, the signal from spin rectification effects is usually dominated by the antisymmetric part, as is the case in ferromagnetic materials. However, this is only true for an ideal situation and both, symmetric and antisymmetric contribution of spin rectification effects in CoFeB, has been previously reported and attributed to current dissipation phenomena [START_REF] Wigner | On unitary representations of the inhomogeneous Lorentz group[END_REF]. Therefore, to accurately assess and avoid spin rectification effects, it is necessary to perform a complete angular dependence measurement and/or use reference ferromagnetic layer as demonstrated by Rojas-Sánchez et al. [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF].

Thermal effects: The microwave radiation absorbed at the resonance frequency causes heating of the sample, leading to a thermal gradient along the out-of-plane axis of the specimen.

Therefore, thermoelectric effects such as the spin Seebeck effect (SSE) or the anomalous Nernst effect (ANE) can be added to the spin pumping signal. The contributions from ordinary Seebeck and ordinary Nernst effects can be extracted from the angular dependences, but other effects such as SSE and ANE show very similar angular dependence as inverse spin Hall effect (ISHE), being very difficult to disentangle them. Moreover, they also generate a symmetric peak at resonance (where the thermal gradient is maximum), contributing undesirably to the symmetric component of the output signal. Therefore, it is necessary to find a method or technique to verify that the thermal contribution is negligible.

In this sense, the separation of the thermal effect from the ISHE contributions is possible following the protocol recently proposed by Noël et al. [START_REF] Noël | Negligible thermal contributions to the spin pumping signal in ferromagnetic metal-platinum bilayers[END_REF]. This procedure consists in inserting a thick insulating barrier between the ferromagnetic layer and the non-magnetic layers to avoid spin injection, and allows to observe only the ANE coming from the ferromagnetic layer (note that both ISHE and SSE are related to the spin current). Next, to separate ISHE from SSE, we can distinguish between the effects due to their different time scales. While the thermal effects occur in the range of seconds, the spin-to-charge conversion is in the range of nanoseconds.

Consequently, for slow sweeps SSE would increase the output intensity, while for fast FMR sweeps the same peak intensity should be found.

Spin-Orbit Torque Measurements

In Sec. 3.4.2, spin orbital torque (SOT) measurements have been performed to determine the SOT exerted on a single Co layer by spin current generation in the 2DEG. For this purpose, we performed a harmonic Hall voltage measurement technique to quantify the two components (damping-like and field-like) of the current-induced torques. This technique, originally developed by Pi et al. [START_REF] Pi | Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layer[END_REF] and subsequently studied by Garello et al. [START_REF] Garello | Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures[END_REF], has become a standard technique to evaluate the "effective magnetic field" generated by the SOTs on magnetization.

To perform these experiments, a lithography process (detailed in the next section) has been carried out to obtain Hall bars and inject a low-frequency alternating current (𝑓=17Hz) sweeping an external magnetic field in the (𝐻) plane either along the direction of the current or transverse to it. Injection of the alternating charge current of frequency '𝑓' into the 2DEG results in the generation of spins that pass through the TaOx tunneling barrier layer. The spin current exerts SOTs on the Co layer through the s-d exchange interaction before decaying to zero that induces effective fields (∆𝐻 𝑠𝑖𝑛 2𝜋𝑓𝑡), which give rise to the oscillation of the magnetization around its equilibrium position (𝜃, 𝜙) in synchronization with the frequency of the AC current (𝑓).

The magnitude of these oscillations (∆𝜃, ∆𝜙) depends on the effective field, but also on the external magnetic field, the anisotropy of the ferromagnetic layer, etc. It is possible to extract the components of ∆𝐻 if one measures the variation of the oscillations as a function of applied fields and then, by using a Taylor's expansion, ∆𝜃 and ∆𝜙 can be expressed as the total energy density of the ferromagnetic thin film using following: From these equations, we can deduce that the voltage of the first harmonic voltage, 𝑉 𝑓 , provides The current-induced effective field has two orthogonal contributions, the damping-like (𝐻 𝐷𝐿 ) and field-like (𝐻 𝐹𝐿 ) terms (see Introduction for more details), which can be measured by applying the magnetic field along or transverse to the current direction, respectively, as sketched in panels (b) and (c) in Fig. 2.9. In order to avoid a multidomain state, the in-plane magnetic field was applied slightly off-plane by tilting the sample 𝛿𝜃 𝐻 ≈ 7°. Thus, by applying the magnetic field parallel to the current direction (± 𝑥-axis), 𝜃 𝐻 = 𝜋 2 ⁄ + 𝛿𝜃 𝐻 and, 𝜙 = 𝜙 𝐻 = 0. By combining equation (2.24a), (2.24b) and (2.27b), we can express the damping-like component of the second harmonic voltage as: with 𝜉 = 𝑅 𝑃𝐻𝐸 𝑅 𝐴𝐻𝐸 ⁄ . The magnitude of PHE can be determined by measuring the Hall effect as a function of in-plane angle between magnetization and current. The large in-plane magnetic field (greater than the anisotropy field) drags the magnetization in-the plane i.e., 𝜃 = 𝜋/2 and the variation in hall resistance solely arises due to the planar Hall effect according to 𝑅 𝑃𝐻𝐸 sin 2Ф (by replacing 𝜃 = 𝜋/2 in equation (2.25). From 𝑉 𝑓 , 𝜃(𝐻) can be directly determined as 𝜃 = 𝑐𝑜𝑠 -1 (𝑉 𝑓 ), and the value of 𝐻 𝑘 and 𝛿𝜃 𝐻 can be extracted from cos 𝜃 by fitting the Stoner-Wohlfarth model as indicated in ref. [START_REF] Wood | Exact solution for a Stoner-Wohlfarth particle in an applied field and a new approximation for the energy barrier[END_REF].

∆(
𝑉 2𝑓 𝐷𝐿 =
Finally, note that the injection of an AC electric field through the Hall bar devices originates a temperature increase of the sample by Joule heating. Such thermal gradient also exhibits a second harmonic term, which is expected to add some artifact signals related to magnetothermal effects. In Hall bar devices, the thermal gradient can be produced in-plane or along the out-of-plane direction. The former arises from asymmetries in the Hall bar mostly due to the patterning process, and the latter is due to non-uniform current distribution and/or asymmetric heat dissipation caused by the difference of thermal conductivities between the different layers in the heterostructure [188]. It is therefore important to remove such thermal effects, to eliminate spurious signals and perform accurate analysis of the spin-orbit torque measurements.

The procedure to remove the thermal effects performed in this thesis will be explained in Sec.

3.4.2.

Sample Patterning

The optical lithography process aims to obtain Hall bars, which allow the measurement of multiple electrical properties (resistivity, Hall effect, magnetoresistance, spin-torque measurements, etc.) minimizing current drift and favoring specific geometries. In particular, although the use of devices would have been also suitable for BMR measurement, in this dissertation the lithography process has been performed only for the torque spin experiments in Sec. 3.4.2. As can be seen in Fig. 2.4.1, the fabrication of the devices presents several steps. We start from a substrate previously cleaned by immersing the sample in ultrasound consecutively with distilled water, acetone and isopropanol as solvents. Subsequently, the substrate is dried of possible moisture (with a N2 gun and previous at 115 o C) and then coated with a positive photoresist SPR700-1.0, ideally with a thickness of 1 μm at 4000 rpm. Subsequently, the photoresist is cured briefly at 95 o C for 45'', followed by exposure with UV light, i.e., the lithography process. In practice, the exposure has designed by a suitable program (e.g., KLayout).

The objective used (10x) results in a resolution of 1.4 μm, restricting the details of our devices to somewhat more than this value.

After the exposure of the samples, another bake-out of the sample is performed, this time for 45'' at 115 o C. This process is done in order to define the chemical differences between the exposed and unexposed areas, achieving a better definition of the devices during the development process. For this, it is necessary to immerse the sample in a suitable developer, in this case for 45'' in MF-319. Once this process has been carried out, the sample is dried and the quality of the lithography is checked, typically by optical microscopy.

If the result is as expected, the desired materials are then deposited after cleaning with O2 plasma at very low power (7 W), and the process is concluded by lifting-off the photoresist using a As practical details, it is preferable to minimize the permanence of patterned samples under UHV conditions, since long times make the removal of the photoresist more difficult. On the other hand, although this process has the main advantage of handling the devices as little as possible, avoiding the heating processes and solvents involved, the use of photoresists prevents the growth of materials at high temperature, which may be preferable in other systems.

For these purposes, the reverse procedure is more favorable, leaving the operational areas covered by the resin, and then depositing an inert material that acts as a hard mask. Thus, after removal of the photoresist from the regions corresponding to the Hall bar, the formation of the 2DEG can be favored only in these regions, and not in those covered by this inert material. This alternative process has been successfully used for the growth of Al/KTO 2DEGS, which have been found to be superconducting for certain crystallographic orientations and growth at higher temperature, around 500 o C. With respect to the materials used, they should be insulating and inhibit the formation of the 2DEG. With these constraints we decided to use Al2O3, MgO and LaAlO3.

Magnetic Properties Characterization

With respect to the last chapters of this thesis, several magnetic microscopy techniques have been used to optimize the heterostructures used in Sec. 3.4.2 and 3.4.3 in order to favor a strong perpendicular magnetic anisotropy (PMA), as well as the stabilization of magnetic textures with skyrmionic character. This characterization has been performed by magneto-optical Kerr effect (MOKE) microscopy, magnetic force microscopy (MFM) and x-ray photoemission microscopy (X-PEEM). The fundamentals and main characteristics of the different techniques will be explained below.

Magnetic Force Microscopy

Magnetic force microscopy (MFM) is a variant of the atomic force microscopy (AFM) technique, which takes advantage of magnetostatic interactions between the tip and the sample surface to image magnetic domains.

In 1986, Binning and Rohrer invented the AFM, an adaptation of scanning tunneling microscopy (STM) capable of measuring the atomic force between a tip attached to a soft cantilever and the surface of a sample of any material. The deflection of the tip caused by electrostatic forces is recorded by a laser focused on the cantilever, and its reflection is amplified and recorded by a photodiode array, providing an accurate profile of the height of the sample surface. It can detect forces as small as pN and the in-plane resolution ranges from 1-10 nm, while it is between 0.1-100 nm along the out-of-plane direction, depending on the size and characteristics of the tip used.

A year after the discovery of the AFM, Martin and Wickramasinghe developed the MFM by changing the standard AFM tip to a magnetic one. In this case, magnetic dipole forces between a magnetic tip and a magnetic sample cause cantilever deflection and allow mapping of the domain structure of the sample surface (see Fig. 2.5.1). In this technique, the tip-surface interaction becomes crucial, as the tip is also magnetized and may induce changes in the magnetic sample.

Unlike electrostatic forces, magnetic forces are long-range, so the resolution of MFM is lower compared to AFM, typically tens of nanometers. Because of its sufficient sensitivity to weak scattering fields, the MFM technique is now widely used to map magnetic domains in magnetic thin films and other microstructures. Like other magnetic imaging techniques, MFM has a relatively long measurement time, which does not make it suitable for studying superparamagnetic systems. The MFM can operate in both DC and AC modes. On the one hand, in DC mode, the cantilever reacts to the static force between the tip and the sample, according to Hooke's law: 𝐹 = -𝑘𝛥𝑧,

where k is the tip spring constant and 𝛥𝑧 represents the tip displacement. On the other hand, the AC mode uses a different approach: the cantilever vibrates close to its natural resonance frequency, which for an approximation as a classical harmonic oscillator can be expressed as [START_REF] Abelmann | Encyclopedia of Spectroscopy and Spectrometry[END_REF], [START_REF] Bonnell | Scanning Probe Microscopy and Spectroscopy: theory, techniques, and applications, Second[END_REF]:

𝐹 = 1 2 𝜋 √ 𝐾 𝑒𝑓𝑓 𝑚 ⁄ , (2.30)
Where 𝑚 is the effective mass of the tip and 𝐾 𝑒𝑓𝑓 is the effective spring constant, which is composed by two components:

𝐾 𝑒𝑓𝑓 = 𝑘 - 𝛿𝐹 𝛿𝑧 , (2.31)
Here, there is a correction term to the actual spring constant, which depends on the force gradient with respect to the separation between the tip and the sample. Due to the force gradient, a shift in the resonance frequency will be produced:

𝐹 = 𝑓 0 √ 1 - 𝛿𝐹 𝑘𝛿𝑧 , (2.32)
Where 𝑓 0 represents the natural resonance of the cantilever. As the tip scans the sample surface, any interaction between the tip and the sample causes a shift of 𝑓 0 . Thus, the magnetic force measurement is made by detecting changes in the amplitude of such resonance or in the resonance frequency itself. In general terms, a magnetized sample creates a magnetic stray field (𝐻 ⃗ ⃗ ) and the magnetized tip will be subjected to such field. Then, the magnetic potential between the tip and the sample can be expressed as:

𝐸 𝑆-𝑇 = -𝜇 0 ∫ 𝑀 ⃗⃗ 𝑇 • 𝐻 ⃗ ⃗ 𝑆 𝑑𝑉 𝑇 , (2.33)
Where 𝜇 0 is the vacuum permeability and the integration is taken over the volume of the tip (𝑉 𝑇 ).

Consequently, the force acting on an MFM tip can be calculated by the following equation:

𝐹 = -𝛻 ⃗ 𝐸 𝑆-𝑇 = 𝜇 0 ∫ 𝛻 ⃗ ( 𝑀 ⃗⃗ 𝑇 • 𝐻 ⃗ ⃗ 𝑆 ) 𝑑𝑉 𝑇 , (2.34)
In order to remove surface topography features from the magnetic image, a dual-pass technique is normally used. In the first scan, the tip scans the surface topography in tapping mode. After that, the tip is lifted to reach the distance in which is affected only by the magnetic forces, and the magnetized tip scans again the surface following the topography line acquire from the first scan, generating the MFM image.

In this thesis we have profited from the high magnetic sensitivity of MFM to determine the configuration of domains in Pt/Co/AlOX(TaOX)/STO heterostructures, in Sec. 3.4.3. In particular, these images were acquired by Karim Bouzehouane, together with others obtained by the nitrogen vacancy magnetometer (NV magnetometer), a much more complex technique, but more powerful in terms of magnetic sensitivity and resolution.

Magneto-Optical Kerr Effect Microscopy

The first magneto-optical effect was discovered by Michael Faraday in 1845. He showed that if a magnetic field was applied to a glass sample, the transmitted light rotated its plane of polarization. Years later, John Kerr discovered the same effect but for light reflected from a polished electromagnet pole. The underlying physical mechanism is the same in both cases: the magneto-optical Kerr effect (MOKE), in which the interaction of in-plane polarized light with a magnetic material changes the polarization plane of the reflected light depending on the orientation of the magnetization of the material. Although the effect had been known since the 19th century, it was not until the 1980s that digital image processing was introduced, and Kerr microscopy became a widely used technique for imaging magnetic domains.

The magneto-optical effect can be explained in terms of macroscopic dielectric theory and microscopic quantum theory. The rotation of in-plane polarized light after being reflected by magnetic material can be expressed by the dielectric law 𝐷 = 𝜀 • 𝐸, with 𝜀 being an antisymmetric tensor. Therefore, the relation can be written as follows:

𝐷 = 𝜀(𝐸 + 𝑖𝑄𝑚 × 𝐸), (2.35)
The second term of the equation is reminiscent of the Lorentz force equation. From classical considerations, it is known that when a beam of polarized light propagates through a medium, its electric field promotes the movement of electrons. Thus, without an external magnetic field the direction of polarization will remain the same, but the presence of a left-polarized electric field will lead the electrons to a left circular motion, or vice versa. Since the electric dipole moment is proportional to the radius of the circular orbit, there will be no difference between the dielectric constants, so there will be no Faraday rotation. However, when light hits a sample surface that exhibits a magnetization in a certain direction, the Lorentz force acting on each electron will rotate the polarization by an angle θ that depends on the direction of the sample magnetization.

Therefore, it is the Lorentz force that generates the Faraday effect.

According to Voight's classification) [191], three types of Kerr effect are distinguished based on the relative orientation of the light with respect to the plane of incidence, the plane of polarization of the light and the orientation of the magnetization. These three types of Kerr effect are known as longitudinal, polar and transverse, and give rise to three characteristic configurations, schematized in Fig. 2.5.2. The first two effects lead to an effective rotation of the polarization plane (rotation and ellipticity), while the transverse one only results in an amplitude variation [START_REF] Loughran | Enhancing the magneto-optical Kerr effect through the use of a plasmonic antenna[END_REF].

For the transverse configuration, the magnetization is parallel to the plane of the sample but perpendicular to the plane of polarization of the incident light, while for the longitudinal case, it is also in the same plane of the sample but parallel to the plane of polarization of the incident light. The polar Kerr effect will be explained in more detail below, since it is the configuration used for the characterization of heterostructures in Sec 3.4.1.

Polar magneto-optical Kerr effect (p-MOKE)

In the polar Kerr effect, the magnetization is perpendicular to the plane of the sample and parallel to the direction of incidence. The Kerr effect in the polar configuration increases as the angle of incidence with the direction of magnetization decreases, reaching a maximum at normal incidence but disappearing in the longitudinal and transverse configurations. Among the three types of configurations, the p-MOKE shows the most pronounced Kerr effect and is therefore the most useful for practical applications. Thus, in the polar Kerr effect, the reflected light undergoes a rotation with an angle 𝜃 𝑘 and an ellipticity of 𝜀 𝑘 , which charged proportionally with the perpendicular component of the magnetization.

This effect has been used in order to optimize the heterostructures used in Sec. 3.4 in terms of magnetic properties, and more specifically, to determine whether these heterostructures exhibit perpendicular magnetic anisotropy (PMA), and the determination of the spin reorientation transition (SRT) of Co. Therefore, for these objectives it is not crucial to derive the more complex expressions for the Kerr effect. In practice, the polar Kerr effect is used, adjusting the analyzer to obtain the maximum magnetic contrast between opposite directions, blocking the light reflected/rotated by one of the magnetization directions, while the one corresponding to the opposite magnetization direction reaches the camera of the microscope. The magnetic contrast is maximized in situ by adjusting the analyzer in the presence of an AC out-of-plane magnetic field

X-ray Photoemission Electron Microscopy

Photoemission electron microscopy (PEEM) dates back to 1932, when Brüche built the first operational PEEM that used UV light to image photoelectrons emitted by a metal [START_REF] Feng | Photoemission Electron Microscopy[END_REF]. The technique has evolved rapidly and today, almost every major synchrotron facility is equipped with a PEEM instrument, making it a powerful tool for materials science, surface physicochemistry and magnetic thin films.

A spatial resolution of less than 10 nm can be routinely achieved using UV light, and tens of nm when using X-rays. Moreover, by means of aberration correction schemes it is possible to improve the resolution down to a few nanometers, very close to the physical limit given by the mean free path (𝜆 𝐼𝑀𝑃𝐹 ) of low-energy secondary electrons. Regarding probing depth, it should be noted that X-PEEM is also a surface-sensitive technique as it is limited by the mean free path of the lowenergy secondary electrons. Typically, the probing depth is around 2 nm for metals and oxides, however, image contrast can still be obtained even in the presence of coating layers with a total thickness of up to three times the effective mean free path.

In X-PEEM, a beam of photons with energies between 100 and 1000 eV is focused onto the sample surface, exciting the electrons in the outer shells of the atoms to be imaged. Once the secondary electrons generated in the electron cascade escape into the vacuum leaving empty core states, they are collected by the corresponding PEEM optics. Thus, a photoemission electron microscope forms an image of a solid surface based on the spatial distribution of the emitted electrons, allowing the local X-ray absorption of the sample to be mapped as a function of X-ray energy. In particular, the image contrast arises from the element-specific absorption, chemistry and magnetism of the different materials, which makes of this technique This technique has enormous potential in magnetism, as it is sensitive to magnetism coming from individual elements and allows a proper study of heterostructures, so often used in this field.

It is intrinsic to a ferromagnet that the filling of the majority and minority states is unbalanced.

Therefore, when the angular momentum of the photon is transferred to the angular momentum of the photoexcited electron, the spatial distribution of the electrons collected by the PEEM optics reflects the different density of empty states, as depicted in Fig. 2.5.4. Such phenomena give rise to strong XMCD effects at the L edges (2p → 3d transition) of transition metal ferromagnets (e.g., Fe, Co and Ni), since the d states carry most of the magnetic moment, and allow to correlate the direction of the atomic magnetic moment relative to the x-ray polarization vector.

However, a single X-PEEM image contains both magnetic and non-magnetic contribution and it is necessary to enhance the magnetic contrast by using the sum rules of XMCD [START_REF] B T Thole | X-ray circular dichroism as a probe of orbital magnetization[END_REF], [START_REF] Altarelli | Orbital-magnetization sum rule for x-ray circular dichroism: a simple proof[END_REF], after acquiring two images with the same photon energy but with opposite polarization or opposite magnetization. Since the magnetic dichroism presents an opposite sign at these edges due to the opposite sign of the spin-orbit coupling in the 2p states, this procedure reveals the magnetic contrast and suppresses non-magnetic effects.

In the framework of this thesis, X-PEEM experiments have been performed to image the magnetic textures of the heterostructures studied in Sec.

Chapter 3. Results

In the framework of this work, we have carried out the synthesis of 2DEGs by depositing metals with magnetron sputtering on oxoperovskites. In particular, 2DEGs have been formed by the deposition of different metals (Al, Ta or Y) on strontium titanate (STO) or Al on potassium tantalate (KTO).

The systems, i.e., metal/STO and Al/KTO, have been characterized by X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and transport measurements as a function of temperature and magnetic field, i.e., magnetoresistance and Hall effect. The characterization has been carried out systematically as a function of deposited metal thickness, enabling a direct comparison between the different systems. The results obtained from such primary characterization are presented and discussed in Section 3.1.

In addition, we have studied the band structure of KTO which, unlike STO, remains quite unexplored to date. Therefore, Section 3. The optimization of the heterostructures has been performed in terms of thickness and perpendicular magnetic anisotropy (PMA). Lastly, the use of microscopy techniques such as magneto-optical Kerr effect microscopy (MOKE microscopy), magnetic force microscopy (MFM) and X-ray electron photoemission microscopy (X-PEEM), has allowed us to directly visualize the spin textures within the cobalt layer.

. Synthesis and Characterization of Metal / Oxide 2DEGs

In this Section, we will refer to the synthesis process and characterization of metal/STO and Al/KTO 2DEGs. In particular, this section aims to determine the effect of depositing different metals (Al, Ta or Y) on STO, or the same metal (Al) on KTO, on the properties of the 2DEG. For this purpose, we have decided to work with the simplest systems, i. e., metal/STO and Al/KTO, since we consider that the addition of other layers, either conductive or insulating, could considerably affect the properties of such heterostructures.

It should be noted that the ideal comparison between 2DEG properties is only possible within a certain range of deposited metal thicknesses, where the deposited metal thickness is not thick enough to form a metallic layer due to overgrowth (upper limit to deposit), but thick enough to protect the 2DEG against reoxidation (lower limit to deposit). Therefore, our first approach is to determine these critical thicknesses, between which the properties of the different systems can be more adequately compared. A priori, we can assume that these critical thicknesses are different for the different metals, and are closely related to the thickness of the metal oxidized by contact with the oxide through the red-oxide reaction (tredox), as well as to the thickness of the metal naturally oxidized by air (tnative), as graphically depicted in Scheme 3.1.

Logically, a correct comparison between the properties of the 2DEGs requires that the properties of the deposited metal layer are the same within the same system (Al, Ta or Y), and similar deposition conditions for the different metals (same T, P, etc.). However, the properties of 2DEG

do not depend exclusively on the properties of the coating layer, and this is reflected in the need to carry out a more systematic process.

From preliminary results, we concluded two very important details regarding the know-how of these 2DEGs: (i) the transport properties were highly dependent on the origin of the substrate; and (ii) the spectroscopy and transport results were more reproducible for samples measured within similar time intervals. While the former can be explained by considering that 2DEG is very susceptible to any change in the host material (e.g., surface area, permittivity, etc.), the latter can be understood by considering the kinetics of red-ox reactions, which are involved in both the 2DEG formation and its reoxidation process.

According to such findings, a proper comparison between the systems requires also a control over the substrates (same batch) and the time interval between the synthesis process and the characterization steps (similar for all samples).

The results obtained from the primary characterization of these systems by XPS, AFM and magnetotransport are shown in the following Section. These are divided into two subsections, one dedicated to the different metals on STO (Section 3.1.1) and the other for Al/KTO (Section 3.1.2.).

Metal Thickness Dependence of AlOx, TaOx or YOx / STO

XPS characterization

Prior to any deposition, XPS measurements were performed on several non-terminated STO (001)

substrates obtaining similar spectra for all of them, an example of which is shown in the inset of Fig. 3.1.1 (a). During the fitting of the spectra, adventitious carbon was used as a charge reference to obtain the Ti 4+ 2p3/2 peak position at ~458.6 eV that is consistent with previously reported values [196], [START_REF]NIST X-ray Photoelectron Spectroscopy Database[END_REF],. The fits of the spectra suggest the presence of Ti 4+ only, as expected for asreceived insulating STO single crystals.

From now on, due to the shift of the peaks towards higher binding energies caused by charging effects and to facilitate the comparison between the different systems, the Ti 2p core-level spectra will be represented in energy values relative to the Ti 4+ 2p3/2 peak position. The XPS has been used to determine the relative fraction of valence states, obtaining their evolution with increasing metal deposited thickness. Note that no mention will be made of the displacement in binding energies after metal deposition on STO. Since both the charging effects during the Tab. 3.1.1: Constrains applied during the fits of Ti 2𝑝 core-level spectra. ∆𝐸 = (2𝑝 1/2 -2𝑝 3/2 ) refers to the spin-orbit splitting energy, FWHM to the full width at half maxima, and GL to the Gauss/Lorentzian product, where GL (100) denotes a pure Lorentzian line-shape.

measurements, as well as the controversy associated with the use of the C 1s peak as a charge reference [START_REF] Greczynski | X-ray photoelectron spectroscopy: towards reliable binding energy referencing[END_REF], prevent us from obtaining reliable values that can be correlated with the thickness of metal deposited.

The Ti 2p core-level spectra collected in-situ just after depositing several metal thicknesses on STO are shown in Fig 3 .1.1, for Al (a -c), Ta (d -f) and Y (g -h). The reduction of STO is visible from the spectra as peaks at lower binding energies with respect to Ti 4+ , related to a reduced valence state of Ti in STO (Ti 3+ and Ti 2+ ), arise upon deposition of the different metals. Importantly, the same constrains were applied during the fitting of all spectra. These constrains are in good agreement with reported values [START_REF] Gonbeau | XPS study of thin films of titanium oxysulfides[END_REF], [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF] and are summarized in Table 3.1.1.

Note that, for the Ta case, the Ta 4p1/2 binding energy region overlaps with that of the Ti 2p. This photoelectron line is well-known to be at ~462.2 eV for metallic Ta [START_REF] Buabthong | Vanadium, niobium and tantalum by XPS[END_REF]. However, even if the photoelectron lines for the corresponding oxide, and suboxides, are expected at slightly higher binding energies, we could not find enough information to constrain such contribution from the values reported in literature. Ta is a polyvalent cation and thus, gives rise to complex spectra which is usually approached by analyzing the most intense 4d and 4f lines rather than the 4p corelevel. The contribution from Ta to the spectra had to be determined experimentally and consequently, is subjected to a higher degree of uncertainty. For the Ta case, we measured a wider range of energies so that the Ta 4p3/2 peak at ~401 eV was included in the spectrum. The constrains during the fitting were imposed by considering an area ratio 4p1/2: 4p3/2 equal to 0.5, and the relative fraction of valence states deduced from the analysis of the spectra collected insitu for the Ta 4f core-level.

From Fig 3 .1.1 we observe that STO is reduced differently depending on the metal being deposited and that the contribution from reduced valence states Ti 3+ and Ti 2+ increases with increasing deposited metal thickness until a saturation value seems to be reached. Such a saturation value of reduced species appears to be different for the three different systems and seems to be the highest for Y, then for Al, and lastly for Ta.

In addition, it is important to determine the stability of the samples once they are exposed to ambient conditions. For that, the Ti 2p core-level spectra were collected ex-situ after a short states can be understood by considering the reoxidation of STO in ambient conditions. At higher deposited metal thicknesses, however, such reoxidation seems to be prevented and the contribution from Ti 3+ and Ti 2+ becomes comparable for both in-situ and ex-situ collected spectra.

In addition, the thickness of metal at which the contribution of reduced species becomes comparable for both spectra set appears to be different for the three metals.

For the case of Ta, the effect of exposing the sample to air on the Ta 4𝑝 1/2 photoelectron line can also be deduced from Fig. 3.1.2. The large difference between in-situ and ex-situ spectra can be attributed to the oxidation of residual metallic Ta or suboxides, which results in a larger contribution from Ta 4𝑝 1/2 peaks at higher binding energies.

For ease of comparison, Fig. As it was deduced from the in-situ spectra, Fig. 3.1.3 shows different saturation values for the reduced valence states Ti 3+ and Ti 2+ depending on which metal is being deposited. Respectively for the relative concentrations of Ti 3+ and Ti 2+ , these saturation values are approximately 25% and 10% for Al, 20% and 10% for Ta, and 35% and 15% for Y. Thus, we found that the reduction of STO is higher for Y than for Al deposition, as well as it is higher for Al than for Ta deposition. The higher reduction of STO after depositing Y can be related to the higher reactivity of this metal given its lower reduction potential, lower work function and lower oxide formation enthalpy per mol of oxygen compared to the cases of Al and [START_REF] Posadas | Scavenging of oxygen from SrTiO3 during oxide thin film deposition and the formation of interfacial 2DEGs[END_REF], [START_REF] William | CRC Handbook of Chemistry and Physics[END_REF].

Further, we also found that the saturation of reduced species of Ti for in-situ collected spectra (open circles) occurs at different metal thicknesses. If we consider that such saturation is reached at the electrochemical equilibrium of, these values can be related to the metal thickness oxidized in-situ by the reaction with STO. From Fig. 3.1.3, we can estimate these values as 0.9 nm for Al, The open circles correspond to the spectra collected in-situ. The filled circles correspond to the spectra collected ex-situ for the same samples after being exposed to ambient conditions. less than 0.3 nm for Ta, and approximately 1.2 nm for Y. We found that these thicknesses are in good agreement with the reduction potential of the different metals as well as with the oxygen diffusion coefficients through the respective oxide layers [START_REF] Nakamura | Diffusion of oxygen in amorphous Al2O3, Ta2O5, and Nb2O5[END_REF], [START_REF] Ikuma | Oxygen diffusion in the fluorite-related phases of Y2O3-Ta2O5 and Ho2O3-Ta2O5 systems[END_REF]. That is, the lower the reactivity and diffusion coefficient through the native oxide layer the smaller is the extent of the redox reaction and the thickness of metal oxidized by pulling up oxygen from STO.

In Fig. 3.1.3, the reoxidation of STO can be deduced from the decrease of Ti 3+ and Ti 2+ species for ex-situ collected spectra (filled circles) when metal deposited thickness is below a certain value.

Such a critical thickness is related to the thickness of metal to be deposited and eventually protect the reduced STO region from reoxidation, which can be estimated from Fig. reported values [START_REF]NIST X-ray Photoelectron Spectroscopy Database[END_REF] and are shown in Table 3.1.2.

Similarly, due to the shift of the peaks towards higher binding energies caused by charging effects and to facilitate comparison between the spectra obtained for different thicknesses, the corelevel spectra of Al 2p, Ta 4f, and Y 3d, have been shifted in energy values. Reference ex-situ spectra were obtained on thicker layers (60 nm) grown directly on a well-grounded metallic plate, ). In addition, by further increasing deposited metal thickness for the three systems, we found that the metallic phase arises above different thickness values depending on the metal being deposited. Importantly, these spectra provide us with useful information since they can be used to determine the thickness above which a metallic overlayer emerges as a secondary conductive pathway for electrons that will compete with the 2DEG.

To facilitate the comparison between the different systems, Fig. In our samples, however, they can be easily detected because the thickness of Ta is much smaller and the relative concentration of these species considerably larger.

As previously mentioned, from Figure 3.1.5 we can estimate the critical deposited metal thickness above which a contribution of the metallic phase is detected by XPS measurements. The formation of a metallic overlayer can be considered as an additional pathway for electron conduction, and is expected to have an important effect on the transport measurements to be presented below. From Fig. 3.1.5, we observe that these thicknesses are approximately 1.3 nm for Al, 1.3 nm for Ta, and 5.2 nm for Y.

Magnetotransport measurements

In Fig. 3.1.6, we show the temperature dependence of the sheet resistance (RS), and the RS values at 300 K and at 2 K for samples with different deposited metal thicknesses of Al (a -c), Ta (d -f), and Y (g -i). For all three systems, we found a variation of RS by one order of magnitude which cannot be ascribed to the metallic capping thus implying the conduction through the reduced region of STO, in agreement with previous reports for STO-based 2DEGs [START_REF] Niu | Suppressed carrier density for the patterned high mobility twodimensional electron gas at γ-Al2O3/SrTiO3 heterointerfaces[END_REF], [START_REF] Cancellieri | Influence of the growth conditions on the LaAIO3/SrTiO3 interface electronic properties[END_REF]. For a better interpretation of the results, we will first consider the case of Y for which we have covered a wider range of thicknesses and seems to be the most complete and easiest to understand.

From the RS vs T plots in Fig. 3.1.6 (g) we find that the RS decreases, both at 300 K and at 2 K, with increasing Y thickness as well as three well-differentiated regimes at 300 K as a function of deposited metal thickness. That is, a first regime with notably higher RS in which we find the 0.9 nm Y sample, a second regime with similar RS (from now on named "saturation" regime), which includes from 1.6 nm to 6.2 nm Y samples, and a third regime characterized by a downward bending of the RS vs T curve at higher temperatures in which we find the 7.3 nm Y sample. In agreement with our previous XPS analysis (see Fig. 3.1.3), the samples with a deposited thickness below 1.6 nm of Y are susceptible to a reoxidation process which would explain not only the highest sheet resistance obtained for the sample with 0.9 nm of Y but also, that all the thinner samples were insulating. On the other hand, samples with a deposited thickness beyond 5.2 nm could give rise to a metallic overlayer that competes with the 2DEG. Therefore, we believe that the competition of the metallic overlayer with the 2DEG in terms of transport may lead to the characteristic downward bending of the RS vs T at high temperatures observed for the 7.3 nm Y sample (Fig. 3.1.6 (g)).

Accordingly, the three different regimes above mentioned would be separated by two critical thicknesses: i) The metal thickness necessary to protect the STO from reoxidation, that separates the high and the "saturation" regimes; ii) the metal thickness above which we have a metallic overlayer, that separates the "saturation" regime from that in which we observe the characteristic downturn of the RS vs T at high temperatures.

At low temperature (2 K), a slightly different trend was observed as deposited Y thickness increases (inset Fig. 3.1.6 (i)). In this case, we observed that the RS drops between 0.9 nm and 1.6 nm Y, and then remains saturated up to of 3.2 nm. Further, for samples with a thickness above 3.2 nm, the RS decreases smoothly down to the lowest value given by the thickest sample (7.3 nm of Y).

In agreement with our XPS analysis (Fig. 3.1.3(c)), the highest RS at 2 K observed for the sample with 0.9 nm Y might be attributed to the 2DEG not being fully formed nor protected. On the other hand, we could also ascribe the saturation of the RS between 1.6 nm and 3.2 nm to the saturation of reduced species of Ti at the interface around this thickness value and thus, relate the RS "saturation" regime to 2DEGs fully formed and protected. Beyond this thickness regime, the further reduction of STO with increasing deposited Y thickness becomes more unlikely and, therefore, we consider that the smooth decrease in the RS reflects a more conducting overlayer of YOX, maybe related to the formation of isolated metallic clusters. On this issue, we assume that XPS did not allow us to detect such metallic clusters in between 3.2 and 5.2 nm due to its sensitivity (0.1 -10 at%) and that such metallic clusters do not percolate until the deposited According to this interpretation, we have access to different information depending on whether we compare the RS values at high or low temperatures. It seems that at high temperature we are sensitive to the presence of an additional conduction path. Whereas at low temperature we are more susceptible to both the 2DEG formation process and the formation of the metallic layer due to overgrowth.

In the following, the same correlation between magnetotransport and XPS results will be carried out for both Al and Ta cases. For the Al case (Fig. 3.1.6 (a -c)), we can distinguish only two regimes from those previously mentioned. The high RS regime in which we find the samples with 0.9 nm and 1.3 nm of Al, and the regime in which the RS "saturates", with the samples with an Al thickness in between 1.7 nm and 2.5 nm. The transition between the two regimes is in good agreement with our XPS results (Fig. 3.1.3 (a)), from which the thickness to efficiently protect the 2DEG from reoxidation was estimated as 1.7 nm of Al, and the previous interpretation made for Y samples.

As previously assumed for the Y case in between 5.2 nm and 6.2 nm, the detection of metallic Al above 1.3 nm by XPS and the absence of a clear contribution from an additional path for conduction can be ascribed to a non-percolated metallic overlayer i.e., isolated metallic clusters.

On the other hand, Ta is a very particular case in which we could not differentiate the aforementioned regimes. The growth of samples with a thickness below 1.3 nm gave rise to insulating samples, whereas the sample with 1.3 nm of Ta already shows a small downturn of the RS at high temperatures that becomes more pronounced with increasing Ta thickness. The absence of both the high and "saturation" RS regimes can be understood by considering that the Ta thickness oxidized by the redox reaction with STO is very small, and the formation of the metallic overlayer occurs soon after exceeding the thickness necessary to form the native oxide layer i.e., 1.3 nm of Ta. A scenario which would lead to a very sharp transition from insulating samples to the regime characterized by the downward bending of the RS at high temperatures, and which is in agreement with our XPS analysis (Fig. 3.1.3 (b)) since the Ta thickness oxidized by the redox reaction with STO was estimated to be less than 0.3 nm, whereas it was considerably larger for Al and Y cases, respectively, 0.9 nm and 1.2 nm.

From the inset of Fig. 3.1.6 (e), we observe a sudden decrease of the RS by increasing Ta thickness from 1.9 nm to 2.2 nm, which looks very similar to the one observed for the sample with 7.3 nm of Y (inset Fig. 3.1.6 (h)). Thus, in concordance with the Y case and with the large concentration of metal seen by XPS for the sample with 2.2 nm of Ta, such a sudden decrease of the RS may be related to an additional path for conduction. Further, the downward bending of RS vs T plots at high temperatures seen for all samples lead us to reconsider, in particular for this case, that the characteristic downward bending can arise not only from a percolated metallic layer but also from the contribution of isolated metallic clusters (or even Ta suboxides) in transport measurements.

To further characterize these systems, we have also performed magnetotransport with an out of plane magnetic field. Fig. 3.1.7 shows the Hall resistance curves both at 300 K and at 2 K, and the magnetoresistance curves at 2 K for samples with different deposited metal thicknesses of Al (ac), Ta (d -f), and Y (g -i).

Regarding the Hall measurements, the Hall coefficients are relatively large suggesting a low carrier density for most of the samples which cannot be ascribed to the metallic layer. Further, a very clear trend is observed for all three systems. By increasing the metal deposited thickness, the Hall coefficient decreases suggesting an increase of the 2DEG carrier density, following a tendency which can be well-correlated with the reoxidation process, the saturation of reduced species and the percolation of the metallic overlayer. A tendency which is in agreement with the XPS results (Fig. 3.1.3) and the interpretation of the RS vs T plots (Fig. 3.1.6).

In addition, the transverse resistance (Rxy) at 300 K shows a linear dependence with the magnetic field for the three systems, whereas it is clearly nonlinear at 2 K. Such features can be understood by considering electron transport through the 2DEG, since it involves the conduction through lighter dxy and heavier dxz, yz bands with different carrier density and mobilities. On the other hand, the longitudinal resistance (Rxx) curves at 2 K present a parabolic shape with a similar amplitude for Al and Ta systems, whereas it is higher for Y samples.

In Fig. 3.1.8, we show the total carrier density (the sum of nxy and nxz,yz) and the mobility values within the dxy and dxz,yz bands as a function of metal deposited thickness. These values were obtained after fitting the non-linear Hall curves and the RS values at 2 K with a two-band model [START_REF] Ashcroft | Solid State Physics[END_REF], [START_REF] Kim | Nonlinear Hall effect and multichannel conduction in LaTiO3/SrTiO3 superlattices[END_REF]. For all three systems, we obtained that the carrier density increases, and saturates at different values depending on the metal, by increasing the metal deposited thickness.

For the Al case, the lower carrier concentration obtained for the samples with a deposited thickness below 1.7 nm of Al can be attributed to an insufficient metal thickness to protect the STO from reoxidation. The saturation value for the total carrier density is approximately 8.5 x 10 13 cm -2 and is achieved at 1.7 nm, in good agreement with our XPS and transport results from which we estimated that the 2DEG is fully formed and protected above 1.7 nm of Al.

The case of Ta, however, is a bit more controversial. From XPS measurements we estimated that through the 2DEG), we cannot neglect a possible additional contribution and we believe that the value of 5.3 x 10 13 cm -2 is more accurate for the 2DEG carrier density.

The lower carrier concentration of Y samples below 1.6 nm of Y can be also understood because of the reoxidation process. The saturation carrier density value is 4.5 x 10 13 cm -2 and occurs approximately after depositing 2 nm of Y, in agreement with the interpretation of the RS vs T plots (Fig. 3.1.6) and our XPS results from which we deduced that the 2DEG was completely formed and protected from reoxidation. The saturation of the 2DEG carrier density prevails up to the sample with 5.2 nm of Y, thickness above which we observe a further increase of the carrier density values. However, since an increase of the 2DEG carrier density is unlikely beyond this thickness value, we attribute it to the formation of the metallic overlayer and its contribution in transport measurements.

According to these values, the highest 2DEG carrier density was obtained for Al, then for Ta, and lastly for Y, being respectively nAl = 8.5 x 10 13 cm -2 , nTa = 5.3 x 10 13 cm -2 and nY = 4.5 x 10 13 cm -2 .

Thus, we could not correlate a higher reduction STO with a higher carrier density into the 2DEG.

The non-correlation of these results can be attributed to differences in the distribution profile of oxygen vacancies in the STO and thus, to a different degree of confinement for the different 2DEGs. We consider that the confinement of the 2DEG is closely related to the electric field at the interface, which depends not only on the STO but also on the properties of the oxide. The higher the ability of the oxide to retain electrons near the interface, i.e., to induce a positive charge, the higher the electric field at the interface and the confinement of the 2DEG. A higher confinement of electrons near the interface for the Al case, and therefore a narrower oxygen vacancies distribution profile, could explain the higher carrier density obtained for these samples compared to those of Y, where the STO reduction was substantially higher. Fig. 3.1.8 also shows the mobilities for the majority (nxy) and minority carriers (nxz,yz) obtained when fitting the non-linear Hall curves and the sheet resistance at 2 K into a two-band model. As previously deduced from the magnetoresistance curves at 2 K, we can observe some similarities between Al and Ta cases which cannot be extended to the Y case. From this figure, we see that the mobilities for the majority carriers in the Ti-dxy band for Al and Ta samples are in between 100 cm 2 /V•s to 200 cm 2 /V•s, whereas they are in between 350 cm 2 /V•s to 750 cm 2 /V•s for the Y samples. On the other hand, the mobilities of minority carriers in Ti-dxz,yz bands for Al and Ta samples are in between 750 cm 2 /V•s and 1500 cm 2 /V•s, whereas they are higher for Y samples, in between 1000 cm 2 /V•s and 2250 cm 2 /V•s. The higher mobilities of the heavier dxz, yz bands can be understood by considering the longer scattering time of electrons since these bands are located farther from the interface, as was previously reported by Delugas et al. [START_REF] Delugas | Spontaneous 2-dimensional carrier confinement at the n-type SrTiO3/LaAlO3 interface[END_REF].

In Fig. 3.1.9 we show the mobility as a function of carrier density within the lighter dxy (a) and heavier dxz, yz (b) bands. We see that Al and Ta cases present a similar behaviour, the values for the lighter dxy bands are in between 100 cm 2 /V•s and 200 cm 2 /V•s and are higher for the Ta case.

The Y samples show higher mobilities, in between 350 cm 2 /V•s to 750 cm 2 /V•s, but smaller carrier density values. The mobility values for the heavier dxz, yz bands increase by increasing carrier density for all three systems. In this case, they are slightly higher for Al than for Ta, and the highest for Y samples. The higher mobilities obtained for Y samples can be also related to the lower confinement of these 2DEGs and a larger contribution from dxz, yz, which extend farther in the STO lattice.

AFM imaging

In Fig. 3.1.10, it is shown the most representative AFM images for samples with different Al thicknesses. From the analysis, we observed that the surface of Al samples is smooth up to a 1.7

nm, thickness at which a clear transition on the topography is observed. Above this thickness, much larger particles appear, reaching a height of up to 40 nm. These particles are isolated and become smaller as the Al thickness increases, tending to a topography similar to that given by the reference sample on which we grew 30 nm of Al on SiO2.

The evolution of the topography as a function of Al thickness agrees with our XPS and magnetotransport results. From which we deduce that the metallic phase appears for samples with a thickness equal to or greater than 1.3 nm (see Fig. forming isolated metallic clusters since we could not see a clear contribution derived from a metallic layer during transport measurements i.e., the downward bending in the RS vs T plots (see Fig. 3.1.6 (a)). Furthermore, if percolation of the metallic layer occurs, we would expect a topography similar to that of the reference sample. Therefore, the differences between the images obtained for the thicker sample and the reference sample further support our interpretation of the magnetotransport results in which non-percolation of the metallic layer is assumed within the range of thicknesses studied (up to 2.6nm).

Accordingly, the formation of the metallic layer is also revealed by the topography of the samples and, therefore, the AFM images allow us to estimate above which deposited thickness the metallic phase arises. In addition, comparison of the topography with thicker reference samples (i.e., 30 nm) on which we are certain of the presence of the metallic layer below the native oxide, allows us to determine whether the percolation of the metallic layer has occurred. As we would expect a similar topography of the samples when the percolation of the metallic layer occurs, regardless of the substrate used for deposition.

On the other hand, Fig. 3.1.11 shows the AFM images obtained for samples with different Ta thicknesses. The surface of all samples is relatively smooth, however, we found that the surface of the sample with 1.3 nm Ta presents a large number of small particles that decrease in number with increasing Ta thickness up to 1.6 nm. According to our XPS and magnetotransport results, where we attribute the observed downward bending at higher temperatures to the contribution of metallic clusters. By further increasing the deposited thickness of Ta, we observed that the surface of the samples flattened again, resulting in a roughness comparable to that of the reference sample (30 nm Ta on SiO2) and suggesting the percolation of the metallic clusters when a thickness equal to or greater than 1.9 nm of Ta is deposited. We found that the percolation at this thickness is in agreement with the sudden decrease of the RS observed at high temperature Lastly, the variation of the topography observed for the Y samples is more complex. Fig. 3.1.12 shows the AFM images obtained for samples with different thicknesses of Y on STO. We found that for very low Y thicknesses (0.6 nm) the surface presents many particles whose height cannot be explained by considering the low metal deposited thickness (ranging from 40 nm up to an impressive 200 nm in height in some cases) (a). If we further increase the thickness of Y to 0.9 nm, we continue to observe these particles although this time in smaller numbers, with an apparent smaller size, and showing a clear directionality (b). Surprisingly, by increasing the thickness up to 1.2 nm, the particles disappear giving rise to a very smooth topography that prevails up to a deposited Y thickness of 4.2 nm. Above this thickness, we observed how the surface roughness increased for the samples with 5.2 and 6.2 nm of yttrium, to become as smooth as the reference sample upon deposition of 7.3 nm of Y (d -g). . In agreement with our previous interpretation of XPS and magnetotransport measurements, we can easily relate the increase of roughness for the samples with 5.2 nm and 6.2 nm of Y to the formation of metallic clusters, as well as the flattening of the surface to the percolation of the metallic clusters for the sample with 7.3 nm of Y.

However, the drastic evolution of the topography observed for the thinner samples remains unclear i.e., in between 0.3 nm and 1.2 nm of Y. On this issue, it is worth noting that Srijani et al.

[210] have reported a similar topography after Gd deposition on STO. Further, the authors performed transmission electron microscopy measurements which allow them to explain the discordance of the topography features with the deposited metal thickness by the blistering of the surface i.e., the formation of gas bubbles. They also reported very large magnetoresistance and high mobility values which they attributed to the presence of these blisters.

All this is reminiscent of what was observed for the Y samples, which can be understood if one considers the similarities between these metals. They both have very low reduction potential, work function and oxide formation enthalpy values and, therefore, the deposition of Y and Gd leads towards a more aggressive reaction with STO compared to the deposition of Al or Ta.

Further, since these bubbles were not observed on the other samples, we assume that the large features observed by AFM are oxygen bubbles, arising from a more aggressive redox reaction of these metals with STO.

The formation of oxygen bubbles can be understood by considering that electrochemical equilibrium with the STO cannot be reached by the mere oxidation of the metal layer if the deposited Y layer is not thick enough. To reach this electrochemical equilibrium it is necessary to create more oxygen vacancies in the STO than the metal layer can accommodate. Resulting in an excess of oxygen at the interface, which can recombine into molecular oxygen and lead to subsequent gas bubble formation. On the other hand, the flattening of the surface can be understood if we consider that the thickness of the deposited metal becomes sufficient to accommodate all the oxygen released by the STO in order to reach electrochemical equilibrium with Y. This scenario would explain that the size of the bubbles decreases with increasing Y thickness until they disappear upon deposition of Y thickness equal to or greater than 1.2 nm.

This would also have major consequences for the synthesis process of these systems since the formation of bubbles would take place during deposition (in situ) and could affect the quality of the interface in heterostructures, and their properties.

Another possible scenario is that the formation of these bubbles takes place upon exposure of the samples to ambient conditions. According to our XPS results, the reoxidation of the STO is much more pronounced for Y, which can be attributed to both the higher substrate reduction, which causes this region to have a higher affinity for oxygen, and the higher amount of metal that needs to be deposited to protect it. Thus, for smaller thicknesses of Y, oxygen diffusion through the thin oxide layer is favored and may lead to a more aggressive reoxidation reaction compared to Al or Ta. We consider that this reaction could also deform the oxide layer and lead to areas where molecular oxygen is trapped in the interlayer. It should be noted that this process would occur ex situ and would have fewer consequences in terms of heterostructure synthesis.

Metal Thickness Dependence of AlOx / KTO

XPS characterization

As in the case of the samples grown on STO in the last section, the XPS spectra of the nonterminated KTO (001) substrates were obtained prior to Al deposition. An example of which is shown in the inset of Fig. 3.1.13 (a). Similarly, adventitious carbon was used as a charge reference to obtain the Ta 5+ 4f7/2 peak position at ~26.2 eV, which is in agreement with previously reported values [START_REF] Thomas | The motion of the spinning electron[END_REF]. The fits of the spectra could be carried out considering only the presence of Ta 5+ and are therefore consistent with the corresponding valence state of Ta within the KTO crystal lattice.

In the following, due to the shift of the peaks towards higher binding energies caused by charging effects and to facilitate comparison between the spectra obtained for samples with different Al thicknesses, the Ta 4f core-level spectra will be plotted in energy values relative to the position of the Ta 5+ 4f7/2 peak. Again, XPS has been used only to determine the relative fraction of the valence states for the different samples, and to obtain the evolution of valence states with increasing Al thickness. Leaving aside any interpretation that can be made on the shift of the is important to note that the same constrains were applied during the fitting of all spectra. Those constrains are in good agreement with the reported values [START_REF] Sheng Moo | An XPS depth-profile study on electrochemically deposited TaOx[END_REF] and are summarized in Tab.

3.1.2 (see previous section). In addition, Fig. 3.1.13 (g -h) shows the ex-situ collected Al 2p corelevel spectra which have been fitted according to the values summarized in the same table (Tab.

3.1.2) for the Al case.

From the in-situ Ta 4f collected spectra shown in Fig 3 .1.13 (a -c), we find out that the contribution from reduced valence states of Ta i.e., Ta 4+ and Ta 2+ , increases with deposited Al thickness. Furthermore, if we compare the spectra collected in-situ (a -c) with those collected ex situ (d -f), it is observed that the exposure of the samples to air leads to reoxidation of KTO. Such reoxidation is represented in the spectra as a decrease of the contribution arising from Ta 4+ and Ta 2+ , and is mainly observed for samples with low Al thicknesses. Moreover, the reoxidation of the samples appears to be prevented by further increasing the Al thickness since the contribution from Ta 4+ and Ta 2+ becomes comparable for both in-situ and ex-situ spectra at higher Al thicknesses.

On the other hand, with respect to the ex-situ collected Al 2p spectra shown in Fig. 3.1.13 (g -i),

these have been plotted so that the binding energy of the metallic phase matches the position in from reference spectrum. We find that the Al is fully oxidized at low thicknesses as well as that the metallic phase emerges when a certain Al thickness is exceeded, similarly to what was observed for the Al/STO samples.

For better interpretation of the XPS spectra, the relative concentration of the valence states of Ta deduced from the analysis of the spectra collected in-situ (open circles) and ex-situ (filled circles) is provided in Fig. 3.1.14 (a). From the analysis of the spectra collected in-situ, we observe that the relative Ta 4+ concentration scales up to 6% after depositing 0.4 nm Al and gradually increases with further increasing Al thickness, while the relative concentration of Ta 2+ increases linearly up to 4% within the whole range of thicknesses, i.e., up to 2.6 nm Al.

Note that, the non-saturation of reduced species was also observed, although to a lesser extent, in the case of depositing Ta on STO (see Fig. 3.1.3 (b)). Such behavior can be understood by considering that the probing depth of XPS decreases with increasing metal deposited thickness, and that such phenomenon is more pronounced when depositing heavy metals, such as Ta.

Consequently, a decrease in XPS probing depth leads to a greater contribution from the interface and reduced species near the interface, which occurs more markedly with the thickness of Ta than with the thickness of other lighter elements such as Al or Y. Likewise, the fact that Ta is a heavier element than Ti implies that the probing depth in KTO is less than in STO. This makes us more sensitive to the interface and favors the increase of the relative concentration of reduced species with the thickness of deposited metal even when depositing lighter elements such as Al.

Moreover, from the XPS spectra collected ex-situ, it could be determined that samples with Al thicknesses below 1.7 nm are susceptible to reoxidation, resulting in a lower contribution of reduced Ta species compared to the spectra obtained in-situ. For samples with Al thickness higher than 1.7 nm, however, the relative concentration of reduced species becomes similar for both set of spectra. Thus, indicating that when depositing above 1.7 nm of Al the region of KTO reduced upon Al deposition remains protected against the reoxidation when the samples are exposed to ambient conditions. samples with low deposited Al thickness, which probably corresponds to its most stable oxide i.e., Al2O3. By further increasing deposited Al thickness, a second contribution related to the appearance of the metallic phase appears. This metallic phase is clearly detected for samples with 1.7 nm of Al, and its contribution becomes larger for thicker samples. A trend that is expected to continue until the benchmark for the Al case is reached i.e., the relative concentration of valence states given by the native oxide layer and the metal underneath. Notably, we find that such trend looks very similar, if not same, to the one obtained for the samples of Al grown on STO (see Fig

), from which we deduced that the metallic phase arises after depositing 1.3 nm of Al.

The higher reduction, as well as the higher Al thickness required to reach saturation of reduced species for the case of STO, can be attributed to a higher reducibility of this substrate compared to KTO. Furthermore, from the analysis we deduce that the Al thickness to protect the 2DEG from reoxidation is the same for KTO and STO samples. Therefore, supporting that the thickness of Al required to protect the 2DEG is only related to the thickness necessary to form the native oxide layer which mostly depends on the deposited metal, and not on the substrate nor on the amount of metal oxidized by the redox reaction.

Magnetotransport measurements

In Fig. 3.1.15 we show the temperature dependence of the RS (a) and the Hall curves obtained at 300 K (b) for samples with different deposited Al thicknesses. Also, the RS values deduced from the RS vs T plots at 300 K (c) and at 2 K (d) are shown as a function of deposited Al thickness.

From the RS vs T plots, we find that the RS drops by more than one order of magnitude as the temperature decreases. This variation of RS occurs even for samples where the metallic phase was not detected by XPS measurements and thus, suggest conduction through the 2DEG formed when KTO is reduced upon Al deposition. Moreover, as a general tendency, the RS decreases as the deposited Al thickness increases. A trend that occurs at both 300 K and 2 K and which can be appreciated more clearly in figures (c) and (d), respectively. It is noteworthy that the downward bending of RS vs T at high temperatures is not distinguishable for these samples, which would suggest a competition between two conduction paths for electrons as inferred in the previous section for the Ta and Y samples on STO.

Regarding the Hall measurements at 300 K, the obtained Hall curves show a linear dependence with the magnetic field regardless of deposited Al thickness. The variation of the transverse resistance (Rxy) as a function of magnetic field is large for all samples, indicating that the carrier density is much lower than what is expected for a metal and, therefore, confirming that electron transport takes place mainly through the region of KTO reduced upon Al deposition. Further, we note that the Hall coefficients for the thinner samples are larger and thus, can be related to a decrease of the 2DEG carrier density caused by the reoxidation of KTO. In Fig. 3.1.16, it is shown the Hall (a) and magnetoresistance (b) curves at 2 K for the samples with different thicknesses of Al grown on similar KTO substrates. From the Hall curves, we find that the Hall coefficient decreases with increasing deposited thickness, suggesting an increase of carrier density in the 2DEG. Further, the magnetoresistance curves exhibit a parabolic shape and there is also a decrease of the amplitude as we increase deposited Al thickness.

The nonlinearity of the Hall curves suggests two types of carriers. Hence, we have fit these curves together with the longitudinal resistance (Rxx) at 2 K in the absence of magnetic field in a twoband model, to finally extract the total carrier density (c) (sum of nxy and nxz,yz) and the mobilities (d) within the Ta-dxy and Ta-dxz,yx bands. The carrier density of these samples saturates around 6

x 10 13 cm -2 and we believe that this value is representative of the 2DEG carrier density, since we do not find any sign in the RS vs T plots suggesting an additional contribution from a metallic overlayer, clusters or suboxides, i.e., the downward bending of the RS plots at high temperatures.

As for the mobility values, we obtained that the lighter dxy bands show a mobility ranging between 300 and 400 cm 2 /V•s, while the heavier dxz, yz bands show a higher mobility, ranging between 850 and 2200 cm 2 /V•s. Remarkably, these values are higher than those deduced for STO-based 2DEGs in the previous section, and can be attributed to the larger overlapping of Ta-5d orbitals with the O-2p orbitals compared to Ti-3d. Again, the higher mobility of the heavier bands is related to the longer scattering time as these bands are farther away from the interface. Furthermore, we have determined from ex situ XPS above which deposited thickness value the metallic phase appears. We found that this second critical thickness is higher for Y (5.2 nm), while it is quite similar for Al and Ta (1.3 nm). According to the scenario by which the metallic phase lies in between two oxides, the one formed by direct contact with the oxide and the one formed by air, the higher critical thickness of Y can be related to a higher thickness of these two, in agreement with our previous results.

Again, we note that the critical thickness at which the metallic phase arises is the same for the Al/KTO and Al/STO cases (1.3 nm), suggesting that the metal oxidized, both by contact with oxide and by air, are very similar for the two systems.

Regarding transport measurements, these were performed within an interval of less than 48h after synthesis, as a function of temperature and magnetic field. For all systems, the RS vs T plots show signatures of 2DEG formation, exhibiting a very pronounced RS change with temperature, as well as low carrier density and high mobilities at low temperature. First, we highlight that for the thicker samples the RS vs T curves bend at high temperature. This phenomenon is attributed to the competition between the 2DEG and a secondary path for conduction. RS variations, both at high and low temperature, are discussed in terms of reoxidation of the 2DEG, as well as the contribution to the transport from metallic clusters, suboxides, or a percolated metallic layer due to overgrowth. This reasoning also explains the evolution of the carrier density with deposited metal thickness, where clear saturation regimes are observed from 1.7 nm of Al, 1.6 nm of Ta and <3 nm of Y. These values coincide relatively well to the critical thickness to protect the 2DEG from reoxidation: 1.7 nm for Al, 1.3 nm for Ta, and >1.5 nm for Y. The saturation densities of the 2DEGs are finally estimated as: nAl = 8.5 x 10 13 cm -2 , nTa = 5.3 x 10 13 cm -2 and nY = 4.5 x 10 13 cm -2 . On the other hand, the carrier mobilities for Al and Ta are very similar, and lower than those obtained in Y/STO 2DEGs. The higher mobilities and lower carrier densities, obtained for the Y case, are attributed to the lower confinement of the 2DEG.

Magnetotransport measurements for Al/KTO 2DEGs gave rise to similar trends with Al thickness.

Carrier density saturation occurs around 1.7 nm, yielding to 6 x 10 13 cm -2 . It is worth noting that these 2DEGs present a higher mobility than those obtained for Al/STO, which can be attributed to the higher overlap between 5d orbitals in KTO.

Finally, from AFM imaging of metal/STO samples, we observed clear transitions of the topography as a function of the deposited metal thickness for the three systems. While Al and Ta grow smoothly in the early stages, the topography of the Y samples show huge features that cannot be related to the deposited metal thickness. This is attributed to the more aggressive reaction of Y with STO, and surface blistering when the Y thickness is not sufficient to accommodate all the oxygen released by the oxide to reach electrochemical equilibrium. By increasing metal thickness, we observe further changes on the topography of the samples, which seems to reflect the percolation process of the metallic overlayer.

. Investigation of the Rashba Bands in AlO x / KTO 2DEGs

As discussed in Sec. 3.1.2, the use of KTO substrates for sputtering deposition of reactive metals allows the formation of high-mobility 2DEGs, which in turn can be used to efficiently interconvert charge and spin currents through direct (DEE) and inverse Edelstein effects (IEE). As discussed in the introduction (Sec. 1.4.3), the interconversion efficiency (λEE) depends on the product between the electron-momentum scattering time (τm) and the Rashba coefficient (αR) of the different band pairs. Recently, a record value of λEE (± 30 nm) has been reported for STO-based 2DEGs from SP-FMR experiments under the application of a suitable gate voltage [START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF]. However, to date, it has not been possible to observe the STO Rashba bands because the value of the Rashba splitting predicted for STO (αR ̴ 50 meV•Å) is below the energy resolution limit of the techniques used for this purpose.

In this context, since Ta is a 5d element, KTO-based 2DEGs are expected to exhibit a considerably larger αR due to the larger spin-orbit interaction. Note that the SOC of KTO is ̴ 0.47 eV and thus, an order of magnitude larger than that of STO ( ̴ 0.02 eV). In fact, from density functional theory (DFT) calculations performed by Zhang et al. [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF] a Rashba coefficient of about 310 meV•Å has been predicted for a band pair with a predominant Ta-dxz and Ta-dyz (Exz-yz) orbital character. This makes the KTO really promising for a direct visualization of the bands and resolving their splitting by spectroscopy techniques. Moreover, the fact that the SOC magnitude in KTO is comparable to the Fermi energy and the energy between subbands leads to strong hybridization between orbitals, which makes the physics behind the band structure of KTO 2DEGs more complex and richer compared to their counterparts in STO [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF]. The strong orbital reconstruction renders KTO attractive for a better understanding of the spin-orbit physics underlying the interconversion process, which is essential for predicting the interconversion efficiency in different systems, such as their response to a gate voltage or to the variation of other parameters, e.g., the crystal symmetry.

The aim of this chapter is, therefore, to obtain more detailed information about the band structure of KTO, which remains rather unexplored compared to that of STO. In fact, there is currently a great controversy about the magnitude of αR in terms of the large values expected from theoretical calculations [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF], and those obtained from magnetotransport measurements [START_REF] Nakamura | Electric field tuning of spin-orbit coupling in KTaO3 fieldeffect transistors[END_REF]or the non-observation of Rashba splitting by ARPES [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF], [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO3[END_REF]. In order to shed some light on this debate, in this work we have carried out the synthesis of Al/KTO 2DEGs by molecular beam epitaxy (MBE) for subsequent characterization by ARPES. These experiments were performed at CASSIOPÈE beamline (synchrotron SOLEIL, in France), under the supervision of Julien Rault, Patrick Lefèvre and François Bertran. The results obtained will be discussed and combined with theoretical calculations based on the tight-binding model, which were performed by Ingrid Mertig's group at the University of Halle.

Synthesis of Al/KTO 2DEGs for ARPES measurements

To present date, studies of KTO surface states have been based on the use of doped [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF] or vacuum cleaved substrates [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF], [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO3[END_REF], [START_REF] Bruno | Band structure and spin-orbital texture of the (111)-KTaO3 2D Electron Gas[END_REF], and on the modulation of oxygen vacancy concentration by UV light [START_REF] King | Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3[END_REF], [START_REF] Bruno | Band structure and spin-orbital texture of the (111)-KTaO3 2D Electron Gas[END_REF]. In this work we adopt the procedure followed by Rödel et al. for STO [START_REF] Rödel | Universal fabrication of 2D electron systems in functional oxides[END_REF] and we create the 2DEG by Al deposition to subsequently characterize its band structure. As will be shown below, this process allowed us to resolve the Rashba splitting more clearly than in previous work and therefore, we will carefully explain the synthesis procedure, which we hope will be useful to the scientific community.

As introduced in section 2.2, ARPES is very surface sensitive and requires UHV, very clean surfaces and an Al layer thinner than the escape depth of electrons from the solid (about 4.5 Å for an energy of 30 eV). Nonetheless, ARPES is especially sensitive to charging effects and requires a proper assembly that allows charge compensation during the photoemission process. Because of these and other factors, sample preparation and synthesis play a critical role for the visualization of the 2DEG band structure.

Our first concern is thus to ensure a clean surface. To this end, a common cleaning protocol has been followed based on short immersions in ultrasonic baths, using deionized water, acetone and isopropanol as solvents, and drying with a N2 gun. The procedure is repeated until AFM confirms that sample surface is clean.

Regarding the mounting of KTO substrates, to avoid possible surface deterioration we have refrained from using the holed metallic plates, commonly employed to ensure good electrical contact and minimize charging effects during measurements. For this, we have solely used silver paint qualified for UHV applications, really pushing it up to the edges of the substrate. The silver paint has been dried gradually by increasing the temperature up to 270 o C (limit of our hotplate), which is found below typical decarbonation temperatures (i.e., below 300-350 o C). Subsequently, after gradual cooling, the substrate is introduced into the MBE chamber for pre-annealing at about 300 o C to ensure further decarbonation of the sample. Note that during the synthesis, the system is not heated to higher temperature to avoid the formation of oxygen vacancies and potassium volatilization. The temperature ramps are relatively smooth (<10 K/min), and the time at the maximum temperature is determined empirically, i.e., the pressure is monitored and the process is considered completed when the pressure saturates at the lowest value.

Once the substrate is at room temperature, low energy electron diffraction (LEED) measurements were performed to confirm the surface quality of KTO, which is verified upon obtaining sharp diffraction patterns, in Fig. 3.2.1 (a).

Thereafter, a thin layer of Al is deposited at RT (1 or 2 Å for the samples present in this work), with the MBE system previously conditioned and calibrated. The deposition is performed with the Al source at 1000 o C and a pressure of about 7.9 x 10 -10 mbar, corresponding to a growth rate of 0.6 Å/min. After growth, we perform LEED again and observe a fainter diffraction pattern (see parabolic bands (Eα n=1 , Eα n=2 , Eβ n=1 ), as previously reported by Santander et al. [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO3[END_REF] for in situ cleaved KTO. Assuming that these bands (indicated in figure by dotted lines) are parabolic, we estimate the effective masses from their curvature (m* = 0.23m0 for Eα n=1 and Eα n=2 , m* = 0.52m0 for Eβ n=1 ), and the carrier densities from the area enclosed by each Fermi surface (n = 4.1x10 13 cm - 2 for Eα n=1 , n = 1.9x10 13 cm -2 for Eα n=2 , n = 1.3x10 13 cm -2 for Eβ n=1 ). We note that such values result in a total carrier density of 7.3x10 13 cm -2 , matching relatively well with that extracted from magnetotransport measurements (6x10 13 cm -2 from Fig. 3.1.16 (c)). We further note that the band which is expected to show the highest Rashba splitting, according to theoretical calculations [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF], is the heavier Eβ n=1 band.

In order to resolve the Rashba-like splitting, we performed an additional ARPES characterization at low temperature (15 K) on a sample with 1 Å of Al, minimizing both thermal noise and electron scattering across the aluminum oxide overlayer. First, by tuning the photon energy at normal emission (see Fig. 3.2.3), we found that electronic states near the Fermi level do not disperse along kZ, confirming the quasi-2D nature of the KTO-based electron gas. We again obtained the maximum photoemission intensity at about 31 eV, and we found that intensity decreases as we move farther from 002, i.e., 31 eV. This gradual decrease of the photoemission intensity occurs over one third of the reciprocal lattice (2π/a = 1.58 Å -1 ) and thus, indicates that the bands with predominant dxy orbital character (to which the most intense lines in the spectra at |ky| = 0.1 Å -1 can be assigned) extend over a distance equivalent to three unit cells of KTO beyond the interface.

Second, also from the photon energy scans, we observed a strong photon polarization-dependent cross-section effect (i.e., linear and circular dichroism), which arises from the d orbital symmetry in KTO. Due to dipole selection rules, the corresponding dipole matrix element between the initial and final states must have an even symmetry with respect to the xz plane for the electron emission probability to be non-zero at normal emission. Thus, for linear vertical polarization (LV) only the odd initial states dxy and dyz can be measured, whereas only the initial states dxz can be detected with linear horizontal polarization (LH).

Similarly, circular dichroism refers to the phenomenon whereby the response of a system differs depending on whether the light is circularly polarized to the left (CL) or to the right (CR). This effect can be inferred from Fig. 3.2.3, where the spectral density in the inner part of the band structure differs depending on whether the spectrum was obtained with a CL (a), or CR (b) polarization. That is, the photoemission intensity is higher at negative values of ky for CL polarization (a), while it is higher at positive values of ky for CR polarization (b). It should be noted that circular dichroism may also reflect an orbital angular momentum (OAM) [START_REF] Park | Orbital Rashba effect and its detection by circular dichroism angle-resolved photoemission spectroscopy[END_REF] arising from electron's orbital motion and the self-rotation of their wave packets [START_REF] Chang | Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands[END_REF], [START_REF] Johansson | Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces[END_REF], which tends more readily to form chiral structures in momentum space than the electron spin momentum within the ideal free-electron Rashba model (always perpendicular to k). Therefore, the contrast difference between spectra (a) and (b) could a priori be related to a non-zero OAM for a pair of momentum-splitted bands whose wave functions appear to extend farther away from the interface, approximately 6 cells according to their extension in kZ (h). The larger extension of these bands, as well as their momentum splitting, lead us to consider that the circular dichroism could originate from the pair of bands with an equal admixture of dxz-yz character and from which the highest value of Rashba-like splitting is expected [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF], [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO3[END_REF]. However, above all, both the linear and circular dichroism observed during the measurements highlights the need to use different polarizations to resolve the band structure in detail, as well as the strong orbital reconstruction of KTO band structure due to the confinement potential.

In line with the above, we have compiled a detailed map of the band structure by probing with From the combination of the experimental spectra and the simulations, we identified four pairs of bands. Near the  point, the subbands with higher binding energy (pink and green) show mainly dxy character. In particular, the green bands are not clearly visible around 002 due to the dipole selection rules, but can be resolved them by performing the second derivative of the intensity maps [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO3[END_REF]. The extent of the pink bands in ky, as well as their high photoemission near the Fermi level, can be related to the external features of the band structure observed in the photon energy scan. Therefore, it is worth noting that these bands are the ones that presumably extend over the first three TaO2 monolayers from the interface. At higher binding energies, we distinguish that the next pair of bands near the  point has a predominant dxz-yz character and shows a very large Rashba-type splitting. The filling of these bands leads to a strong interaction between orbitals enhancing the splitting of the outer subbands, something reminiscent of STO 2DEGs. The increased overlap of the dxz-yz orbitals along the z-direction, as well as the magnitude of the splitting of this band pair near the Fermi level, led us to attribute to these bands the circular dichroism in the photon energy scan. Finally, it is worth mentioning that at lower binding energies, a new band composed dxy character is observed. We find that this band structure and the theoretical calculations performed by our collaborators agree quite well with previous simulations and interpretations [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF].

To gain insight into the splitting between the different band pairs, we show in panels (b), (c), and the spin splitting to decrease rapidly as the Fermi level increases. This behavior differs from STObased 2DEGs, where the dispersion of the curves is always parabolic, and prevents the definition of a Rashba coefficient for the system in fixed terms of Rashba energy (ER) and wave vector (kR).

The effective Rashba coefficient is defined by the averaged radius of the Fermi surfaces, which was found to vary as a function of energy for each band pair. It is noteworthy that from tight binding fits, our collaborators obtained a maximum effective Rashba coefficient of about 330 meV•Å for the band with the largest Rashba splitting, in good agreement with previous DFT simulations [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF].

On the other hand, the maps at constant energy have been reconstructed from the sum of LH and LV dispersion curves at EB = 50 meV (e), 25 meV (f) and 5 meV (g). From these figures, it can be inferred how the appearance of the heavier band lifts the spin degeneracy in the outermost bands. These maps show a good agreement between the data and the theoretical fits, indicating that the effective masses, hopping parameters and spin-orbit coupling values extracted from the tight-binding model are the ones that correctly describe the system, as they allow predicting the band structure along all directions.

The correct determination of these parameters allows the simulation of spin and orbital textures of the band structure, which are essential for determining the interconversion efficiencies through the spin (𝜒 𝑠 ) and orbital (𝜒 𝑙 ) Edelstein tensors [START_REF] Johansson | Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces[END_REF]. From very preliminary calculations (not shown in this thesis), we find that this system exhibits very complex textures regarding both spin and orbital moments. Like their STO counterparts, the eigenspinors in the band structure of KTO-based 2DEGs are not always perpendicular to the wave vector in contrast with the ideal free-electron Rashba model. In terms of orbital contribution, the KTO band structure presents a large orbital momentum, which makes this system a promising candidate not only for transporting spin currents but also orbital currents. Further, both spin and orbital contributions strongly depend on the position of the Fermi energy within the band structure and thus, enables their tunability by a gate voltage and increases the versatility of this system for spinorbitronics.

In Sec. 3.3.2 and 3.3.3, we will show the gate dependence of the spin to charge interconversion efficiency for Al/KTO, which together with the experimental results present in this chapter, and the combination with theoretical calculations may allow us to disentangle the role of the different bands of KTO in the spin-charge interconversion process, as was done previous for STO-based 2DEGs.

. Spin-Charge Interconversion in Metal / Oxide 2DEGs

As shown in Sec. 3.1.1, the deposition of reactive metals (Al, Ta or Y) on STO under UHV conditions results in the formation of 2DEGs as a consequence of a redox reaction, whereby the deposited metal is oxidized and the STO is reduced. Furthermore, we found that the magnetotransport properties of metal/STO 2DEGs differ for different systems, suggesting that they are not only governed by the substrate in which they are embedded, but also depend on the properties of the deposited metal and its corresponding oxide. On the other hand, while previous work on Al/STO 2DEGs demonstrated that the dependence of the conversion efficiency on gate voltage is intimately related to the band structure of the 2DEG host material (i.e., STO), the effect of the metal and its corresponding oxide on the conversion efficiency remains unknown.

Thus, our next step in Sec. 3.3.1 is to determine how the properties of these two, the deposited metal and its corresponding oxide, influence the spin-to-charge conversion efficiency by SP-FMR experiments. These experiments have been performed for the Ta and Y cases as a function of back-gate voltage, following a procedure very similar to that in previous work for Al/STO 2DEGs [START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF]. Finally, the response of the systems is compared, and the differences and similarities discussed in terms of 2DEG band structure, degree of confinement, and properties of the different metal oxides.

In addition, in previous sections we have also carried out the synthesis and characterization of Al/KTO 2DEGs, as well as studied their band structure by ARPES. From these experiments, we have obtained 2DEGs with higher mobility than the STO counterparts, as well as observed a band structure that is subjected to strong orbital interactions, and which exhibits a much larger Rashbalike splitting. These results render KTO a very promising candidate for spin-charge interconversion, as well as a rich platform for further understanding of the role of the band structure in the conversion process.

Therefore, in order to investigate the potential of KTO for spinorbitronics, we will now focus on the spin-charge interconversion efficiency of Al/KTO 2DEGs. On the one hand, Sec. shows the results obtained by anisotropic magnetoresistance (BMR) measurements to determine the charge-to-spin conversion efficiency by the reciprocal effect, the direct Edelstein effect (DEE).

Spin-to-Charge Conversion of AlOx, TaOx or YOx / STO

The aim of this section is to compare the spin to charge current conversion efficiency of 2DEGs obtained after the deposition of Al, Ta, or Y on STO. For this purpose, we have prepared samples by depositing same thickness of Ta or Y (1 nm) for SP-FMR experiments, which were performed by the group of Laurent Vila and Jean-Philippe Attané in Spintec (Grenoble). The results will be compared to those obtained by the same group for a sample with a similar thickness of Al (0.9 nm) prepared by Diogo C. Vaz [START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF].

Importantly for a proper comparison of the spin to charge conversion efficiencies, all heterostructures have similar metal thicknesses and have been grown and measured under the same conditions. The samples have been coated with 20 nm of NiFe, which is used as spin current injector during the experiments, and an Al capping to avoid oxidation of the magnetic layer in ambient conditions. All depositions, including the deposition of 1 nm of metal, were carried out during the same vacuum cycle to avoid the reoxidation of the 2DEG and to allow the correlation of these results with those presented in Section 3.1.1.

Note that, in contrast to the samples with just 1 nm of Al, Ta or Y, the samples used for SP-FMR experiments are completely protected against reoxidation due to the presence of the top capping layers of NiFe and AlOx. Thus, in order to correlate the spin to charge conversion efficiencies with the previous results, we will refer to the saturation values of the 2DEG carrier density for the three systems (in Tab. 3.3.1) and not to the values obtained ex-situ for samples with only 1 nm of metal. Consideration of the saturation carrier density for each system is performed according to the in-situ XPS results (Fig. 3.1.3), from which we infer the practically complete saturation of reduced Ti species upon deposition of 1 nm of any of these metals, either Al, Ta or Y. As for the experimental procedure, the 2DEGs were first subjected to a forming process by sweeping the back-gate voltage from +200 V to -200 V [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO3(X = Al, Ti)/SrTiO3[END_REF]. The SP-FMR measurements were carried out in a cavity at 15 K and different back-gate voltages, ranging from +200 V to -200 V.

The output signals were seen to increase linearly with r.f. power up to 5 mW confirming a negligible contribution from thermal effects such as anomalous Nernst (AHE) [START_REF] Avery | Observation of the planar nernst effect in permalloy and Nickel thin films with in-plane thermal gradients[END_REF] and spin Seebeck (SSE)) [START_REF] Uchida | Observation of longitudinal spin-Seebeck effect in magnetic insulators[END_REF]. In addition, angle-dependent measurements were performed to rule out spin rectification effects [START_REF] Bai | Universal method for separating spin pumping from spin rectification voltage of ferromagnetic resonance[END_REF]. Consequently, most of the large symmetric contribution to the spin-pumping signal can be attributed to the charge current generated by the inverse Edelstein effect (IEE) in the 2DEG. [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF]- [START_REF] Martin-Rio | Suppression of spin rectification effects in spin pumping experiments[END_REF] (see Sec. 2.3.4 for more details). agreement with previously reported values for STO-based 2DEGs [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF]- [START_REF] Ohya | Efficient intrinsic spin-to-charge current conversion in an all-epitaxial single-crystal perovskite-oxide heterostructure of L a0.67 S r0.33Mn O3/LaAl O3/SrTi O3[END_REF], we found that these systems produce large voltages which are one or two orders of magnitude higher than those reported with, e.g., Pt [START_REF] Zhang | Determination of the Pt spin diffusion length by spin-pumping and spin Hall effect[END_REF] or Ta [START_REF] Yu | Determination of spin Hall angle and spin diffusion length in β -phasedominated tantalum[END_REF]. Moreover, the charge current produced varies significantly and even changes several times of sign within this voltage range, following for all cases a similar trend with two minima separated by about 200 V. This ability to alter the conversion efficiency as well as the sign of the generated charge current with gate voltage provides an additional degree of freedom which, together with the higher efficiency for spin-tocharge conversion, makes STO-based 2DEGs more appealing for application in platforms to perform spin to charge conversion compared to spin Hall effect-based devices [START_REF] Liu | Spin-torque switching with the giant spin hall effect of tantalum[END_REF], [START_REF] Pai | Spin transfer torque devices utilizing the giant spin Hall effect of tungsten[END_REF], other

Rashba systems [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF] and 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].

On the other hand, from Fig. 3.3.2 (d) we observe that the output signals differ as a function of the metal used to create the 2DEG, being higher for the case of Al, then for Ta, and finally for Y.

In addition, the relative position of the curves with respect to the voltage scale varies for the three systems, as well as the distance between the two minima varies slightly, being about 210 V for Al, 200 V for Ta, and 230 V for the Y samples. We also note that these minima are more pronounced for the Al and Ta cases, than for Y.

The similarities and differences between the three systems offer the possibility to better understand the spin to charge conversion process in STO-based 2DEGs, as well as highlight the need for a wise choice of materials in order to optimize the conversion efficiency for spinorbitronic devices. To this end, these features will be addressed in more depth below.

Regarding the similar non-monotonic dependence of the conversion efficiency on gate voltage, we refer to the previous work for the AlOX/STO sample [START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF]. In this paper, we combined SP-FMR and ARPES results with theoretical calculations to show that each Rashba-split band pair contributes differently, and may even show opposite signs, to the spin to charge conversion process. Moreover, the contribution of the bands varies non-monotonically with the Fermi level, and it is the consideration of all of them what finally accounts for the effective conversion efficiency of the system [START_REF] Johansson | Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces[END_REF]. As a result, the complex dependence of the conversion efficiency on gate voltage obtained for AlOX/STO 2DEGs (blue in Fig. 3.3.2) could be successfully correlated with the features of the band structure of STO (onset of the different bands, avoided crossings, etc.). With this in mind, the observed similarities with respect to the gate dependence, such as the presence of several sign changes and two minima within the same voltage range, can be attributed to a similar band structure, which is to be expected considering that STO is the host material for all the 2DEGs studied in this section.

However, although similar, these trends are not exactly the same and it can be distinguished that features of the different curves, such as the two minima, are more pronounced for the Al and Ta increase of the Rashba coefficient due to a larger electric field at the interface, which in turn, also favors the formation of more confined 2DEGs. We note that the higher efficiency was found for Al and Ta 2DEGs which, in agreement with our previous interpretation regarding the features of the curves i.e., expansion/contraction in voltage scale and position of maxima and minima, are more confined.

Furthermore, according to the equation above, the different conversion efficiencies depend on the momentum relaxation time, which is determined by [START_REF] Drude | Zur Elektronentheorie der Metalle[END_REF]:

𝜏 = 𝜇𝑚 * 𝑒 , (3.3)
From this equation, it follows that the higher the mobility in the 2DEG, the higher the efficiency of the spin to charge conversion process. However, it is not possible to correlate the efficiencies with the experimentally determined mobilities for these systems (Fig. 3.1.9) since, even if Y deposition results in 2DEGs with the highest mobilities, this system shows the lowest efficiency.

It is worth mentioning that, in agreement with previous reports [START_REF] Dey | Conversion of spin current into charge current in a topological insulator: Role of the interface[END_REF], the 2DEG scattering time (τ2DEG) by itself does not adequately represent our system, as we must consider the scattering time across the entire heterostructure. The effective scattering time (τeff) is determined by the scattering time within the 2DEG (in the ps range), the NiFe (fs) and the transparency of the tunnelling oxide barrier in between. On this issue, the possibility of electrons leaking into the ferromagnetic layer through the oxide layer severely decreases the conversion efficiency and thus, the transparency of the oxide barrier may become decisive. According to Simmon's model [START_REF] Simmons | Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film[END_REF], the tunneling current density through a barrier can be expressed as:

𝑗 𝐵 = 𝑉 𝐺 √2𝑚 𝑒 𝜑 𝑑 ( 𝑒 ℎ ) 2 𝑒𝑥𝑝 [- 4𝜋𝑑 ℎ √2𝑚 𝑒 𝜑], (3.4)
Where VG is the applied gate voltage, d is the oxide barrier thickness, 𝜑 is the mean barrier height above Fermi level and 𝑚 𝑒 is the electron mass. From this equation, it can be seen how the current passing through the barrier depends exponentially on both the thickness and the height of the barrier. In principle, we could estimate the transparency of the oxide barrier by considering the theoretical values for 𝜑, and computing the thickness of the oxide barrier from the thickness oxidized by the redox reaction with STO (from Fig. 3.1.3) together with the oxide formation expansion coefficients for each oxide [START_REF] Dorneles | The use of Simmons' equation to quantify the insulating barrier parameters in Al/AlOx/Al tunnel junctions[END_REF]- [START_REF] Dimopoulos | Tunnel junctions with yttrium oxide barrier and various ferromagnetic electrodes[END_REF]. However, such estimation would be far from being accurate since it is necessary a statistical study to determine less theoretical factors such as the presence of "hot spots" (effective area), the role of image forces or metallic clusters in the oxide layer, the dielectric constant of the metal oxides, etc. [START_REF] Simmons | Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film[END_REF]. From experimental works and literature, it is well-know that the AlOX shows higher barrier height than Ta or Y oxides [START_REF] Rottländer | Tantalum oxide as an alternative low height tunnel barrier in magnetic junctions[END_REF], [START_REF] Dimopoulos | Tunnel junctions with yttrium oxide barrier and various ferromagnetic electrodes[END_REF] and therefore, it is expected to display a lower transparency for a similar barrier thickness and higher spin-to-charge conversion efficiency, in agreement with our results. where 𝐽 𝐶 is the charge current generated by the IEE. From these values, we find a conversion efficiency of λIEE = -3.5 nm, which has a magnitude comparable to the values obtained for LAO/STO 2DEGs [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF], [START_REF] Chauleau | Efficient spin-to-charge conversion in the 2D electron liquid at the LAO/STO interface[END_REF], [START_REF] Ohya | Efficient intrinsic spin-to-charge current conversion in an all-epitaxial single-crystal perovskite-oxide heterostructure of La0.67Sr0.33MnO3/LaAlO3/SrTiO3[END_REF] (in between 2 nm and -6.4 nm depending on gate voltage) and among the highest values reported so far. However, this value is still lower than expected for KTO-based 2DEGs, and considerably lower than that of Al/STO 2DEGs [START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF], where the maximum efficiency reached a value of about 30 nm under application of a suitable gate voltage.

On the other hand, more comprehensive studies versus voltage with other Al/KTO 2DEGs supported that the magnitude of the conversion efficiency was an intrinsic property of this system. Fig. Hence, the lower efficiency of KTO for spin to charge conversion can be attributed to the nature of the substrate itself. On the one hand, the relaxation time τ is presumably shorter in KTO than in STO because, even though the mobilities are comparable, the effective masses are lower. Thus, such band pair of about 320 meV•Å from theoretical calculations, the interaction between orbitals and compensation between bands hinders a direct relation of these with the conversion efficiency. In fact, although not specifically mentioned in Sec. 3.2, preliminary theoretical calculations carried out by our collaborators in Halle suggest that the in-plane spin momentum component is considerably smaller for the largely momentum-splitted pair of bands (dxz-yz), whereas it is higher for the lighter (dxy) ones. Also, very complex orbital momentum and spin textures were deduced from these simulations, pointing out the strong interactions and compensation effects between bands. It is noteworthy that, although the computed spin Edelstein tensor was slightly smaller, the orbital Edelstein tensor of KTO was found to be four times larger compared to that of STO [START_REF] Johansson | Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces[END_REF]. This suggests that KTO is a very good candidate for interconversion between orbital currents and charge currents by means of the orbital Edelstein effect, an emerging field of research in spinorbitronics [START_REF] Park | Orbital Rashba effect and its detection by circular dichroism angle-resolved photoemission spectroscopy[END_REF], [START_REF] Jo | Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals[END_REF]- [START_REF] Go | Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals[END_REF]. Further, KTO still presents fascinating properties and could find its place in other applications, as well as it still continues to be of utility in unraveling the effect of the band structure on the interconversion processes.

In this sense, we believe that further experiments could be directed to the improvement of the spin-to-charge conversion efficiency in KTO by proper optimization of its band structure (e.g., other heterointerfaces, voltage, strain). Moreover, KTO could be exploited for efficient interconversion between charge and orbital currents, as well as to elucidate the interaction between spin and orbital momentum. We consider that the interaction between spin and orbital momentum may give rise to compensation effects which have an effect on conversion processes, although its proper study requires the development of new methods capable of reliably ruling out the contribution of one or the other. Such experimental techniques would allow a more complete understanding of the underlying spin-orbit physics, and bring us a little closer to the control and application of these phenomena in real devices.

In view of the last two sections, a broader and more systematic study involving a wider variety of metals and substrates would be desirable. On the one hand, such a study could unravel the effect of the metal and its corresponding oxide on the 2DEG band structure as well as on the conversion efficiency. But also, the use of different substrates, as seen in this section, would allow access to very different playgrounds and a more general picture of these systems.

Charge-to-Spin Conversion of AlOx / KTO

So far, we have explored the spin-to-charge conversion efficiency of Al/KTO 2DEGs and found that this system does not seem, a priori, as attractive as Al/STO for such a purpose. Moreover, supported by the results in Sec. 3.2, our collaborators in Halle were able to compute the orbital and spin textures, whose complexity suggests strong interactions and compensation effects between bands which could be detrimental to conversion efficiency. The unexpected lower efficiencies of Al/KTO compared to Al/STO 2DEGs, is thus attributed in the previous section to the lower relaxation time τ due to the lower effective masses in this system, and compensation phenomena and related to the nature of the substrate, taking into account that the properties of the upper layers were similar for both systems during the SP-FMR experiments.

These results highlight the role of the 2DEG host material, and prompt further study of KTO band structure. For the sake of completeness, our next step will be to investigate the potential of Al/KTO 2DEGs for charge-to-spin conversion via the direct Edelstein effect (DEE), which remains rather unexplored in oxide 2DEGs. For example, Wang et al. [START_REF] Wang | Room-temperature giant charge-to-spin conversion at the SrTiO3-LaAlO3 oxide interface[END_REF] demonstrated through spintorque ferromagnetic resonance (ST-FMR) measurements that a spin density propagates perpendicularly toward a ferromagnetic top layer when an r.f. charge current flows through LAO/STO 2DEGs. Also, other groups [START_REF] Narayanapillai | Current-driven spin orbit field in LaAlO3/SrTiO3 heterostructures[END_REF] performed anisotropic magnetoresistance (AMR) measurements as a function of current, determining the Rashba fields induced in LAO/STO 2DEGs. However, apart from these few works, studies on charge-spin conversion in oxide 2DEGs are still scarce [START_REF] Vaz | Oxide spin-orbitronics: new routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF].

In this work, we have determined the ability of Al/KTO 2DEGs to perform charge-spin conversion using a simple method based on the analysis of the bilinear response of these systems during angle-resolved magnetotransport measurements, recently proposed by Vaz et al. [START_REF] Vaz | Determining the Rashba parameter from the bilinear magnetoresistance response in a two-dimensional electron gas[END_REF] for Rashba 2DEGs. As explained in Section 2.3.3, this method allows us to determine the effective Rashba coefficient of a rather well-known system, STO. However, KTO remains quite unexplored compared to STO, and this fact led us to assume certain values in order to estimate the effective Rashba coefficient of this system, which will be finally compared with the values previously reported for 2DEGs based on KTO and the effective Rashba coefficient computed from theoretical calculations for the band with larger splitting.

These measurements were performed for a sample with 2.1 nm of Al on KTO (001) and, therefore, we can assume that the carrier density of the 2DEG is the saturation value (i.e., 6.1 x 10 13 cm -2 ), since the Al thickness is sufficient to completely reduce KTO and protect the interface from reoxidation (see Sec. 3.1.2). Angle-dependent magnetotransport experiments were carried out at 2 K using a 1.5 x 10 mm slab of the sample to better define the current direction with respect to the magnetic field. shows a linear dependence with magnetic field, whereas AQMR scales quadratically. Further, if we look into the current dependence of the ABMR, we also find a linear dependence but showing a small negative offset.

Note that spurious thermal effects such as Nernst effect [START_REF] Guillet | Observation of large unidirectional Rashba magnetoresistance in Ge(111)[END_REF] and spin Seebeck effect [START_REF] Nakai | Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals[END_REF], due to a vertical temperature gradient from the heating by the applied current, could be the source of the BMR signal. In order to discard such possibility, we also measured the angular dependence of the longitudinal and transverse resistance using AC current. Thus, the QMR and BMR signals should appear at 1f and 2f longitudinal signals, respectively. If thermal effects are taking place, a voltage at 2f will develop along the longitudinal and transverse direction, which should be present. Therefore, we can continue the analysis excluding the presence of significant spurious effects and assuming that the BMR signal is mainly attributed to inversion symmetry breaking and Rashba spin-orbit interaction.

To estimate the Rashba coefficient (𝛼 𝑅 ), we can use the expression that relates the amplitude of BMR and QMR as follows [START_REF] Vaz | Determining the Rashba parameter from the bilinear magnetoresistance response in a two-dimensional electron gas[END_REF]:

𝐴 𝐵𝑀𝑅 𝐴 𝑄𝑀𝑅 = 2𝜋ℏ |𝑒|𝑔𝜇 𝐵 𝛼 𝑅 𝜀 𝐹 𝑗 𝐵 , (3.6)
where ℏ is the reduced Planck constant, e is the electron charge, 𝜇 𝐵 is the Bohr magneton, 𝜀 𝐹 is the Fermi energy and g is the g-factor. Thus, to give an estimation value of 𝛼 𝑅 , we only need to determine the Fermi energy and the g-factor for this system. As seen in Sec. 3.2, the band structure of KTO 2DEGs is very complex and complicates the analysis. As a first approximation, due to the higher mobilities and higher Rashba splitting of the band pair with predominant character dxz/yz we can assume that the major contribution to the conversion process will be given by this band pair. An assumption that allows us to roughly estimate 𝜀 𝐹 from the ARPES spectra (Fig. 3.2.4) as the minima for the dxz/yz band pair (i.e., 𝜀 𝐹 = 55meV).

On the other hand, to the best of our knowledge, the g-factor has not been measured for KTO.

As an approach, we can use a value within the range of those obtained for STO, [START_REF] Caviglia | Tunable Rashba spin-orbit interaction at oxide interfaces[END_REF], i.e., in between 0.5 to 2. Note that 𝜀 𝐹 and g-factor values are the biggest source of error when estimating the Rashba coefficient, since we rely on the estimated value from ARPES measurements and the g-factor of STO. We found that the minimum value of g = 0. 𝛼 𝑅 ≈ -280 meV• Å, which is consistent with preliminary theoretical calculations by the group of Ingrid Mertig (|𝛼 𝑅 |= 320 meV.Å), and the one computed by Zhang et al. [START_REF] Zhang | Unusual electric and optical tuning of KTaO3-based two-dimensional electron gases with 5d orbitals[END_REF].

We can now use the estimated αR values to compute the conversion efficiency λIEE ≈ αR• 𝜏/ℏ. For that, we estimate 𝜏 as 0.6 ps from the effective mass and mobility carriers for the band with the larger Rashba-like splitting, i.e., m* = 0.52m0 and μ2 ≈ 2000 cm 2 .V -1 s -1 (in Fig. 3. 1.16 (d)). This value leads to a conversion efficiency λIEE in between -6 nm and -25 nm, depending on the g value.

Among these values, the closest to the experimental value extracted from SP-FMR experiments (λIEE ≈ -3.5 nm) is -6 nm, assuming 𝛼 𝑅 ≈ -70 meV• Å. We note that an effective Rashba coefficient comparable to the value obtained from theoretical calculations would result in higher efficiency (around -25 nm), which is significantly larger than the one obtained from SP-FMR.

The discrepancy between the experimental values of |𝛼 𝑅 | (in between 70 and 100 meV• Å) and the theoretically predicted values for the largely splitted band pair (of about 300 meV• Å) manifest that the conversion efficiency is not dominated by the contribution of a single band pair, even if this one presents a much larger Rashba splitting and higher mobilities compared to the others.

As previously discussed, different band pairs may contribute with opposite signs, and the interaction between bands may give rise to complex spin and orbital textures as well as compensation effects which may strongly affect both the effective Rashba coefficient and subsequently, the interconversion efficiency. Further, such discrepancy is also favored by slight differences between the 2DEG properties of the samples, the simplicity of the BMR model, and the lack of an experimental value for the g-factor of KTO.

Nevertheless, the values of spin-charge interconversion efficiency obtained by both SP-FMR and BMR experiments for Al/KTO 2DEGs are still among the highest reported in the literature to date [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF], [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF], [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], [START_REF] Noel | Highly efficient spin-to-charge current conversion in strained HgTe surface states protected by a HgCdTe layer[END_REF], even being one order of magnitude larger than the one found for heavy metals such as Pt [START_REF] Zhang | Determination of the Pt spin diffusion length by spin-pumping and spin Hall effect[END_REF] (comparing the efficiency with the product of the spin Hall angle and spin diffusion length).

Further experiments should aim to determine the value of the g-factor at KTO, and perform these experiments as a function of a gate voltage. The results obtained from these experiments could be used to estimate a more accurate effective Rashba coefficient for different points of the band structure, which in turn could be combined with other techniques (SP-FMR, ARPES measurements, simulations, etc.) to elucidate the complex spin-orbit physics in KTO.

. Magnetization Control by Spin-Orbit Torque

As discussed in the introduction, the direct Edelstein effect (DEE) results in a spin accumulation transverse to the current, which can diffuse as a spin current able to exert a torque on the magnetization of an adjacent ferromagnetic film. This effect, together with SHE, are related to a strong spin-orbit interaction (SOI), thus falling into the category of so-called spin-orbit torques (SOT). Unlike spin-transfer torques (STT), SOTs allow current-driven magnetization control without the need for an additional ferromagnetic material acting as a spin polarizer, which favors the development of spin-logic devices with lower energy consumption, faster response time and higher scalability and storage capacity. Moreover, as an additional degree of freedom, the SOT could also be tailored under the application of a suitable gate voltage, further increasing the versatility of these devices compared to STT-based counterparts.

Thus, after confirming in Sec. 3.3.1 the great potential of metal/STO 2DEGs for spin-charge interconversion, this section addresses the ability of these systems to generate a torque in a ferromagnetic thin film by the DEE, as well as to deterministically control chiral magnetic textures.

With these objectives in mind, section 3.4.1 focuses on the optimization of Pt/Co/metal/STO heterostructures (with Al or Ta as the metal) in order to obtain suitable magnetic and transport properties. With respect to Sec. 3.4.2, this optimization will be performed in terms of metal thicknesses, pursuing simultaneously both their minimization in order to maximize the effect of 2DEG during torque characterization, and obtaining samples with strong perpendicular magnetic anisotropy (PMA). On the other hand, this optimization process also concerns the stabilization of chiral magnetic textures and the results presented in Sec. 3.4.3.

In Sec. 3.4.2 the results regarding the characterization of the torque exerted on the Co thin film will be presented. Specifically, this characterization has been performed by measuring the second-harmonics in the Hall voltage (explained in Sec. 2.3.5). It is worth mentioning that in this section we are dealing with a complex system in which the presence of heavy metals (such as Pt or Ta) in the heterostructure can also have an effect on the ferromagnetic film together with the 2DEG. Therefore, these experiments have been performed as a function of a gate voltage in the hope of being able to distinguish both contributions.

Finally, in section 3. In this subsection we face the optimization of the heterostructures used, respectively in sections 3.4.2 and 3.4.3, in order to study the ability of metal/STO 2DEGs to exert a torque on an adjacent magnetic film, as well as to be combined with magnetic textures of chiral character able to be manipulated by electric current. With this aim, in this thesis we work with Pt/Co/metal/STO heterostructures, using Al or Ta as the metal for the generation of the 2DEGs in STO. Thus, in these heterostructures the symmetry breaking is preserved and the incorporation of Co/Pt allows to obtain PMA, besides introducing an antisymmetric exchange interaction (DMI) in the ferromagnetic that favors the stabilization of the chiral magnetic textures. In fact, the Co/Pt interface is a common factor in most of the multilayers where skyrmion stabilization is sought in systems with PMA [START_REF] Karayev | Interlayer exchange coupling in Pt/Co/Ru and Pt/Co/Ir superlattices[END_REF]- [START_REF] Yang | Controlling Dzyaloshinskii-Moriya interaction via chirality dependent atomic-layer stacking, insulator capping and electric Field[END_REF].

However, due to the competition in electron transport between Co/Pt and 2DEG, this system forces us to reduce the thickness of these metallic components to maximize the current passing through the 2DEG, and maximize the effect of SOT produced by the latter on the magnetization of the ferromagnetic thin film. In turn, the thickness limitation of these components prevents us from using multilayers, making it difficult to obtain the desired magnetic properties by forcing us to work with individual trilayers (Pt/Co/metal) and restricting us to an inverse stacking order to that commonly used. On the other hand, the presence of heavy metals such as Pt (or Ta) implies a possible additional contribution to the torque during magnetotransport measurements, which we address in Sec. 3.4.2 by performing the corresponding measurements as a function of a gate voltage. In this sense, the torque from heavy metals should be less susceptible to gate voltage, whereas for metal/STO 2DEGs we can expect a priori a considerable magnitude change.

It is worth mentioning that there are probably other combinations of materials more suitable to carry out this study, based on the use of more insulating materials that avoid additional contributions to the torque by SHE, and allow to obtain the desired magnetic properties. In this work we have decided to combine metal/STO 2DEGs with Co/Pt bilayers, which has the great advantage of being exhaustively studied and relatively simpler than these other systems.

However, everything mentioned in the previous paragraph implies a proper optimization process.

The main objective of this optimization process is to ensure the maximum effect of the 2DEG on the magnetization of the ferromagnet during SOT characterization, and magnetic texture manipulation. For this purpose, the thickness of the overlayer has been minimized while preserving adequate magnetic properties, both in terms of PMA and in relation to the stabilization of chiral magnetic textures. The synthesis of heterostructures with different thicknesses of Al, Co and Pt has been performed by magnetron sputtering (Sec. 2.1), and the characterization by MOKE polar microscopy (Sec. 2.4.2) and magnetotransport measurements.

From preliminary results, we discovered two very important technical details regarding the knowhow of these heterostructures. First, the properties were more reproducible for heterostructures grown on similar substrates (from the same batch), as seen above for 2DEG properties in Sec.

3.1.1; and second, a short exposure of the samples to air after the first deposition of Al or Ta on STO clearly favored PMA, compared to unexposed heterostructures with equivalent metal thicknesses. It is noteworthy that during this optimization process very few samples with PMA at room temperature were obtained in which the metal (Al or Ta) and the Co/Pt bilayer were consecutively deposited in situ (in fact, none for the case of Ta). This phenomenon can be attributed to the fact that the exposure of the samples to air prior to Co/Pt deposition prevents the formation of intermetallic compounds (Al-Co or Ta-Co) and favors the formation of a betterdefined oxide interlayer which can further enhance the PMA [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF], [START_REF] Benguettat-El Mokhtari | Interface phenomena in ferromagnet/TaOx-based systems: damping, perpendicular magnetic anisotropy, and Dzyaloshinskii-Moriya interaction[END_REF].

In agreement with such findings, the results shown below have been obtained for heterostructures grown on similar substrates (from the same batch, or from the same cleaved substrate) and briefly exposed to ambient conditions after the first deposition of Al or Ta. On the other hand, the Al and Ta thicknesses have been adjusted to the minimum necessary to protect the 2DEG against reoxidation, forcing a closer proximity/interaction between the 2DEG and the ferromagnetic, as well as avoiding as much as possible the presence of the metallic phase in these layers. More specifically, these thicknesses correspond to 1.7 nm for Al, and 1.3 nm for Ta, which have been chosen according to the XPS results obtained ex situ after a similar exposure time (see previous section, Fig. 3.1.3).

From here, the optimization process is divided into two stages: the optimization of the Co thickness in heterostructures with a relatively thick Pt layer, and the subsequent minimization of Pt thickness with the optimal Co thickness. The first of the stages allows us to determine the thickness range in which the spin reorientation transition (SRT) occurs in Co, i.e., the region in which the ferromagnetic magnetization easy axis of the magnetization changes from in-plane (IMA) to out-of-plane (PMA). In relation to our objective in Sec. 3.4.3, it is well known that within this range of thicknesses there is a strong competition between PMA and in-plane magnetic anisotropy (IMA) which renders both terms negligible and favors the stabilization of skyrmions) [START_REF] He | Evolution of topological skyrmions across the spin reorientation transition in Pt/Co/Ta multilayers[END_REF]. On the other hand, during the second stage, the Pt thickness has been minimized to such an extent that, although not at room temperature, the samples exhibit PMA at the measurement conditions of Sec. 3.4.2, i.e., at 10 K.

Regarding the characterization process, the first stage of optimization has been performed at room temperature by polar MOKE microscopy, which allows to monitor the change of magnetization upon application of a magnetic field and to obtain the corresponding hysteresis cycles. Therefore, this characterization technique has been used in order to determine the suitability of these samples for the experiments of Sec. 3.4.2 and 3.4.3. That is, whether they have strong magnetic anisotropy (PMA), or whether they lie within the spin reorientation transition (SRT) zone where stabilization of skyrmions is expected to be favored. From these results, the SRT is found within the same range of Co thicknesses for both systems, i.e., in between 0.8 and 1.2 nm. Moreover, we obtained samples with PMA after depositing 0.8 nm of Co in both heterostructures, whatever the Pt thickness between 3 and 6 nm. Also, we observe that an increase of Pt thickness favors an out-of-plane magnetization for the samples with 1 nm Co, as can be deduced from the comparison between panels in the same row. It is worth mentioning that we also synthetised heterostructures with 0.6 nm of Co which, in contrast to the samples with 0.8 nm, did not show 100% remanence. Here, the lower remanence could be reflecting the presence of regions below a critical Co thickness that exhibit a superparamagnetic behavior. A fact that is favored in our heterostructures by a higher roughness of the metal oxide compared to most other works where the ferromagnetic layer is grown on presumably smoother surfaces [START_REF] Gweon | A very large perpendicular magnetic anisotropy in Pt/Co/MgO trilayers fabricated by controlling the MgO sputtering power and its thickness[END_REF]. In particular, the samples in Fig. 3 function of temperature and an out-of-plane applied magnetic field, i.e., Hall effect and magnetoresistance measurements.

Finally, after further reducing the Co thickness to 0.7 nm and the Pt thickness to 1.7 nm, we obtained the results shown in Fig. 3.4.2. In this figure, the top row corresponds to the heterostructures with 1.7 nm Al, while the bottom row corresponds to the heterostructures with 1.3 nm Ta. For both systems, we find that the sheet resistance decreases markedly with temperature, which reflects the contribution of 2DEG in transport. In fact, the low-temperature sheet resistance for both heterostructures is quite comparable to that obtained for the simpler metal/STO 2DEGs systems (see Fig. 3.1. 6), effectively suggesting that both conduction channels (2DEG and Pt) can compete with each other.

In addition, Fig. 3.4.2. shows the transverse resistance (Rxy) as a function of an out-of-plane magnetic field, both at 300 K and at 10 K. For both systems, we observe that the Rxy is dominated by the anomalous Hall effect (AHE) in the ferromagnet, which allows us to determine whether these samples have PMA, i.e., 100% remanent magnetization in the out-of-plane direction. We find that, although this is not deduced from room temperature measurements, panels (b) and (d), panels (c) and (f) confirm the presence of PMA at 10 K as thermal fluctuations decrease. All of the above, a sheet resistance of the heterostructure comparable to that of metal/STO 2DEGs and a total remanence of the samples in the out-of-plane direction at 10 K, is sufficient to qualify these heterostructures as suitable for SOT characterization in Sec. 3.4.2, and terminate the optimization process. However, we cannot leave this section without mentioning that the minimization of the Pt thickness reveals very singular effects with respect to the longitudinal resistance (Rxx).

Antisymmetric magnetoresistance

For a better understanding of this singularity, Fig. 3.4.3 shows a superposition of Rxy and Rxx as a function of an out-of-plane magnetic field for the same heterostructures with Al (a) or Ta (b). In particular, these measurements have been obtained at 2 K after performing the same demagnetization process for both systems (while applying same DC current as used during the transport measurements), and sweeping the magnetic field at lower velocity to resolve these signatures in the magnetoresistance. Moreover, the first sweep of the magnetic field was performed from 0 to 9 T, allowing to see the first magnetization curve.

First of all, considering that the observed opening in Rxx is due to contacts misalignment (note that we are measuring thin films) we can assume the same resistance for both magnetic saturation states, i.e. for high absolute values of magnetic field. In fact, this was subsequently confirmed on microdevices. Thus, we found that the Rxx presents an antisymmetric anomaly with respect to the applied field, resulting in three resistance states: an intermediate resistance state corresponding to the magnetic saturation state (monodomain configuration), and high and low resistance states in the demagnetized state (multidomain configuration), as deduced from the coincidence of the maxima (minima) with the coercive field (Hc) in Rxy.

This phenomenon is commonly explained with a very simple model, in which the motion of a single domain wall along a ferromagnetic track with PMA is considered [START_REF] Cheng | Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy[END_REF]. This model explained schematically in Fig. 3 Despite the good fit, the simplicity of the model does not allow to extend it to a multidomain configuration, which we can assume for our samples due to the area of the thin films, i.e. 5 x 5 mm 2 . Although the single-wall model may be valid for microdevices [START_REF] Hai | Electrical characterization of magnetic domain wall via distinctive hysteresis and magnetoresistance[END_REF] or in samples where a magnetic shape anisotropy gradient is induced [START_REF] Cheng | Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy[END_REF], we find that this antisymmetric anomaly does not require the magnetization, the domain wall, and the current direction to be mutually perpendicular. It can occur in multidomain configurations in which wall propagation takes place in more than one direction [START_REF] Desrat | Antisymmetric magnetoresistance anomalies and magnetic domain structure in GaMnAs/InGaAs layers[END_REF], and even in heterogeneously magnetized samples [START_REF] Su | Antisymmetric magnetoresistance due to domain-wall tilting in perpendicularly magnetized films[END_REF]. From these reports, we found that the magnitude of the effect depends on the inclination of the domain walls, and it is enhanced when the in-plane component of these domain walls is larger, changing sign depending on their relative orientation with respect to the current direction. The in-plane component of the domain walls is therefore attributed to be the origin of this effect, which in the presence of a current gives rise to a non-zero perpendicular component of the current density which, if treated as a perturbation, can be considered as a contribution of the Hall effect to Rxx and explain the antisymmetrical nature of the effect.

In terms of materials, the antisymmetric magnetoresistance has been previously reported and attributed to the presence of domain walls in Co/Pt multilayers [START_REF] Sheng Moo | An XPS depth-profile study on electrochemically deposited TaOx[END_REF], Pt/Co0.85Tb0.15/Pt [START_REF] Su | Antisymmetric magnetoresistance due to domain-wall tilting in perpendicularly magnetized films[END_REF], and Hf/GdFeCo/SiN trilayers [START_REF] Hai | Electrical characterization of magnetic domain wall via distinctive hysteresis and magnetoresistance[END_REF], GaMnAs/InGaAs [START_REF] Desrat | Antisymmetric magnetoresistance anomalies and magnetic domain structure in GaMnAs/InGaAs layers[END_REF] with PMA and GaMnAs/GaAs with IMA [START_REF] Tang | Negative intrinsic resistivity of an individual domain wall in epitaxial (Ga,Mn)As microdevices[END_REF] epilayers. Although more recently such anomaly has been also found in more exotic systems pinning of isolated spins with opposite magnetization, we find that this mismatch between the variation of Rxy and Rxx is also found on the opposite side (|Hoop|<|Hc|). In this sense, since the variation of Rxy is relatively small, we think that the mismatch at lower absolute magnetic field values can be attributed to the early stages of magnetic domain nucleation with opposite magnetization, during which the presence of domain walls is still negligible.

Regarding the asymmetry with respect to the magnetic field applied out-of-plane, up to this point we have ignored that an isotropic multidomain configuration in the demagnetized state would lead to compensation phenomena. This effect therefore implies that there are two distinct domain configurations for the demagnetized state, with a different in-plane component of the magnetization. In these two configurations, the contribution of the domain walls to the longitudinal resistance has opposite sign giving rise to two different states of resistance. In this sense, we consider that to achieve this effect in a multi-domain configuration, certain essential ingredients are necessary to favor both the decompensation of the domain walls along a given direction, and its detection by magnetoresistance measurements.

On the one hand, to be able to detect the effect it is necessary to be sensitive to the change of resistance due to the orientation of magnetic domain walls. According to this approach, we found that the magnitude of the effect is clearly more visible in more resistive materials, such as semiconductors [START_REF] Desrat | Antisymmetric magnetoresistance anomalies and magnetic domain structure in GaMnAs/InGaAs layers[END_REF], [START_REF] Tang | Negative intrinsic resistivity of an individual domain wall in epitaxial (Ga,Mn)As microdevices[END_REF], than in other heterostructures with more conductive materials [START_REF] Cheng | Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy[END_REF], [START_REF] Hai | Electrical characterization of magnetic domain wall via distinctive hysteresis and magnetoresistance[END_REF], [START_REF] Su | Antisymmetric magnetoresistance due to domain-wall tilting in perpendicularly magnetized films[END_REF]. Also, we observed that this effect was significantly less visible as we increased in our heterostructures the Pt thickness from 1.7 nm to 2.2 nm, suggesting that the contribution of the domain walls during transport measurements was being screened by parallel transport in the Pt layer.

On the other hand, with respect to the tilting of the domain walls, we noted that all the systems in which this phenomenon has been reported present a material with SOC. In this sense, it is possible that the flow of an electric current through these heterostructures favors a decompensation of the domain walls by its interaction with the spin accumulation at the interface, induced either by the spin Hall effect (SHE) or by the direct Edelstein effect (DEE). The decompensation of the domain walls along this direction could explain the two resistance states depending on whether the tilt favors, on average, a more "parallel" or "antiparallel" configuration with respect to the electrically driven spin polarization at the interface(s), as depicted in Fig. 3.5.5.

In fact, assuming this scenario allows us to explain some more features in panel (b) of Fig. 3.4.3.

On the one hand, spin accumulation would favor the perseverance of the demagnetization state, since it would favor the in-plane component of the magnetization, explaining the remarkable plateau obtained during the first magnetization curve in panel (b). Moreover, this hypothesis would explain why we were able to induce the high resistance state by considering that the domain walls can be textured by passing a DC current during a demagnetization process. From panel (b) we also observe that only the high resistance state is stable for magnetic field values H=+Hc, preserving the asymmetry with respect to the applied magnetic field. Note that the transition to the monodomain state during the first magnetization curve is completed at H=+Hc, while in the rest of the traces |H|=|Hc| coincides with the transition from a monodomain to a multidomain configuration. On the other hand, the change of sign cannot be understood by considering only the SHE in Pt, and makes it necessary to assume a contribution from the DEE in STO, with opposite sign for the two heterostructures, a very promising finding in relation to the characterization of the SOT in the next section.

Unfortunately, more experiments are still needed to confirm the role of spin-orbit coupling in antisymmetric magnetoresistance, particularly in these heterostructures. To this end, the Ta sample could be demagnetized while the current flows in the opposite direction, expecting to obtain the opposite resistance state. In addition, measurements could be made as a function of the angle, hoping to favor this anomaly and the broadening of the peaks when the magnetic field is applied in-plane and transversal to the current direction. Measurements could also be made as a function of gate voltage expecting to clarify the role of the 2DEG, since a priori we expect both a change of magnitude and a change of sign of the spin polarization induced by the DEE in STO. If this is confirmed, simulations based simultaneously on magnetic microscopy and magnetotransport observations would be desirable to elucidate the factors governing the process. A proper understanding of such a phenomenon would allow not only the application of these systems to manipulate the magnetization, but also to exploit this anomaly as a powerful tool to understand and characterize both magnetic properties and SOC phenomena. The deposition of a Ti/Au electrode on the bottom of the substrate allows us to apply a gate voltage and thus modulate the carrier density of the 2DEG as well as the shape of the quantum well. From resistance measurements during the 2DEG formation process, in which successive voltage cycles between +200 V and -200 V are performed, we find a hysteretic behavior and a saturation regime. From the first polarization curve, we find that the heterostructure resistance decreases with increasing voltage towards positive values, indicating an increasing contribution from the 2DEG in transport as the voltage is increased up to +200 V. From this point, the decrease in gate voltage causes the resistance curve not to follow the trajectory of the first bias curve, but to increase more rapidly reaching the saturation value at 80 V, which is maintained up to -200 V.

When the voltage is increased again, the resistance remains constant from -200 V to -25 V and decreases following the path of the first bias curve. After several cycles, the results overlap, thus defining a hysteresis cycle.

In order to study the torque exerted by the 2DEG, and to be able to differentiate it from the contribution of Pt, these experiments have been performed as a function of gate voltage. So far, the analysis has been carried out at two extreme gate voltages, at -25 V where the resistance is in saturation and the role of the 2DEG is negligible, and at +175 V where the total heterostructure resistance is considerably lower suggesting that the 2DEG comes into play. Thus, assuming that resistance saturation occurs when the contribution of the 2DEG is practically zero and current flows only through the metal (𝐼 𝐶𝑜/𝑃𝑡 ), we can estimate the proportion of current flowing through the 2DEG (𝐼 2𝐷𝐸𝐺 ) as:

𝐼 2𝐷𝐸𝐺 = 𝐼 𝑡 (1 - 𝑅 𝑡 𝑅 𝐶𝑜 𝑃𝑡 ), (3.7)
where, 𝐼 𝑡 is the total current injected in the channel, 𝑅 𝑡 is the total resistance of heterostructure, and 𝑅 𝐶𝑜/𝑃𝑡 is the resistance of metal (i.e., at -200V). Within this approach, the current flowing through the 2DEG at -25 V is 0%, while at +175 V it is approximately 24%.

Panel (b) of Fig. 3.4.5 shows the first harmonic signal when the magnetic field is swept in the plane along the direction of current flow at both -25 V (in red) and 175 V (in black). From the superposition of both hysteresis cycles, we observe that the change in resistance at -25 V is larger, indicating that the contribution of the anomalous Hall effect is larger than at 175 V due to a higher current flowing through the Co layer, whereas a negligible current is flowing through the 2DEG at -25 V.

On the other hand, panel (c) shows the normalized first harmonic Hall data for gate voltages of -25 V (red) and 175 V (black). The good overlap of both curves indicates that the anisotropy of the ferromagnetic layer is constant upon the application of gate voltages, confirming the quality of the sample and of the measurements, and enabling the comparison between both voltage values.

As for the characterization of the damping-like torque, we have simultaneously measured 1 st and 2 nd harmonics of the Hall voltage while sweeping the in-plane field along the current direction.

However, the in-plane magnetic field is applied with a slight tilt of 7 o to avoid a magnetic multidomain state. Measurements were performed for various currents ranging from 1 mA to 3.5 mA at 10 K. Panel (d) shows the raw data of 1 st harmonic Hall voltage (Vω) as a function of in-plane magnetic field for different currents. These measurements allow us to determine the anisotropy field, as well position of magnetization at each field which are required for the fitting of the second harmonics, in panel (e). An example of these fits is shown in panel (f), trying to highlight that, compared to other approaches, both the curve at high and low values of magnetic field are m is the magnetization direction and σ is the spin polarization direction. We perform a linear fit to extract the 𝐻 𝐷𝐿 for a current of 1mA.

On the other hand, Fig. 3.4.6 shows the results obtained at +175 V for which we estimated a current through the 2DEG of 24%. From the comparison of these results with those obtained at -25 V, we observe that the curves corresponding to the first harmonic exhibit similar shape and, as expected, an amplitude that increases with current intensity.

In contrast, the 2 nd harmonic Hall voltages at 175 V in panel (b) are different with respect to those at -25 V, although the signature of the torque peaks is still distinguishable for some of the curves. We note that these differences could arise from Joule heating in 2DEG due to a temperature gradient. Next, we assume that this contribution could arise from the anomalous Nernst effect producing an additional magnetization-dependent voltage at 2f, which can be we quantified using the expression:

𝑉 2𝜔 = 𝑉 𝑟𝑎𝑤 -𝑉 𝐴𝑁𝐸 𝑉 𝑓 2𝑉 𝐴𝐻𝐸 , (3.8)
In this sense, we return to the configuration with the out-of-plane magnetic field to characterize the ANE and to be able to subtract its contribution properly. Panel (c) shows V2f as a function of the out-of-plane magnetic field, while panel (d) shows the signal corresponding to the 2 nd harmonic after subtracting the ANE contribution. After correction, we obtain a curve very similar to the previous ones obtained at -25 V, thus confirming that the origin of these differences is mainly dictated by a temperature gradient at this voltage value. in a potential gradient by the IEE, the injection of an electric current results in a spin accumulation by the DEE that can interact with the magnetization of a ferromagnet. Therefore, these materials are potentially useful not only for the much-needed conversion platforms between spin and charge currents, but could also be used to read (IEE) and manipulate (DEE) the state of an adjacent magnetic material in a very efficient way [START_REF] Lee | Direct observation of spin accumulation and spin-orbit torque driven by Rashba-Edelstein effect in an InAs quantum-well layer[END_REF], [START_REF] Manchon | Theory of spin torque due to spin-orbit coupling[END_REF]. In this context, the combination of these materials with skyrmions would have a great technological implication since it would allow the development of logic devices more easily integrated in Si technology and with incredible features such as an enormous information storage capacity, very low energy consumption, great robustness and high speed [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF], [START_REF] Kang | Skyrmion-electronics: an overview and outlook[END_REF].

In particular, skyrmions can be treated as magnetic particles in which the spins point upward at the periphery and downward at the center, or vice versa, being defined by a topological number

𝑆 = 1 4𝜋 ∬ 𝑚 ( 𝜕𝑚 𝜕𝑥 × 𝜕𝑚 𝜕𝑦
) 𝑑𝑥𝑑𝑦 [START_REF] Thiaville | Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films[END_REF], [START_REF] Rohart | Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii-Moriya interaction[END_REF], that is, the topology is protected since the spins inside the skyrmions cannot be rotated to another state with a different 𝑆. Currently, skyrmions are receiving a great deal of research interest due to several properties, namely, the requirement of a low threshold current density (compared to DWs) for passivity, being highly shielded due to their solitonic nature, intrinsic randomness to aid in probabilistic and neuromorphic computation, etc. [START_REF] Fert | Skyrmions on the track[END_REF], [START_REF] Pinna | Skyrmion gas manipulation for probabilistic computing[END_REF]- [START_REF] Song | Skyrmion-based artificial synapses for neuromorphic computing[END_REF].

With the ultimate goal of stabilizing chiral-skyrmionic textures, we have carried out the characterization of Pt/Co/AlOX(TAOX)/STO heterostructures using various magnetic microscopy techniques. A priori, these heterostructures fulfill the basic requirements for the stabilization of magnetic textures with chiral character, such as strong DMIs induced by the inversion symmetry breaking and the strong SOC of the heavy metal adjacent to the ferromagnet [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF], which are probably enhanced by the presence of the 2DEG. The microscopic energy for an ultrathin film in presence of DMI can be written as [START_REF] Thiaville | Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films[END_REF], [START_REF] Rohart | Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii-Moriya interaction[END_REF]: The formation of such worm-like domains, the so-called stripe domain phase, is characteristic of two-dimensional systems with PMA and arises from the competition between short-range (exchange) and long-range interactions (dipole-dipole). Moreover, in the presence of DMI, this domain configuration is intimately related to the generation of nontrivial spin topological textures, such as skyrmion lattices or chiral bubbles [START_REF] Fert | Magnetic skyrmions: advances in physics and potential applications[END_REF], [START_REF] Kang | Skyrmion-electronics: an overview and outlook[END_REF], [START_REF] Büttner | Theory of isolated magnetic skyrmions: from fundamentals to room temperature applications[END_REF], [START_REF] Meyer | Isolated zero field sub-10 nm skyrmions in ultrathin Co films[END_REF]. As can be seen in panels (b) and (c), this domain configuration breaks up as the out-of-plane magnetic field increases, giving rise to bubble-shaped domains whose diameter is approximately 1 m at 0.56 mT. In the presence of low anisotropy and DMI in our samples, these bubbles could be indicating the formation of skyrmionic textures. Therefore, this new domain pattern could present a chiral character, sharing many properties with compact skyrmions, such as the possibility to manipulate them without external magnetic fields. However, it is worth mentioning that a final confirmation is needed, which would be possible by observing the Hall effect of skyrmions or by demonstrating the deterministic manipulation by purely electrical means.

Despite these promising observations, the significant reduction of the domains together with some optical artifacts (e.g., Faraday effect, interface-induced interferences) do not allow us to resolve them using MOKE microscopy. Therefore, in the following we resort to higher resolution techniques (MFM, NV, X-PEEM).

Next, we explore a wider range of Co thicknesses, choosing to work with Pt(4.5)/Co(𝑥)/AlOX/STO heterostructures, with 𝑥 equal to 0.8, 1.0 and 1.2 nm. We note that, increasing Co thickness should further reduce the anisotropy of the system, obtaining a state with 𝐾 𝑒𝑓𝑓 ~0 near the SRT of Co. This should present the optimal situation to stabilize the skyrmions in the presence of finite DMI in the system [START_REF] He | Evolution of topological skyrmions across the spin reorientation transition in Pt/Co/Ta multilayers[END_REF]. From Fig. 3.4.9 we observe small circular-shaped magnetic perturbations in all samples, whose size (100 -200 nm) is considerably smaller than previously observed by MOKE microscopy. On the one hand, the average size of these perturbations is around 175 nm in panels (a) and (c), i.e., in heterostructures with 0.8 and 1.2 nm Co. In contrast, panel (b) corresponding to a sample with 1 nm Co shows considerably smaller diameters, around 100 nm. These differences in the mean diameter of these features may do not reflect the effect of an increase in Co thickness, since they can be argued in terms of the resolution of the MFM. It should be noted that the thickness of the scan line is twice as large for the 4 x 4 m 2 images (a and c) compared to that of 2 x 2 m 2 , i.e., (a) and (c). Therefore, these images show the importance of carrying a proper parameterization to resolve these features and make a proper comparison between the heterostructures. From previous reports [START_REF] Brandão | Observation of magnetic skyrmions in unpatterned symmetric multilayers at room temperature and zero magnetic field[END_REF], we find that the size of these perturbations could be reflecting the stabilization of skyrmions at high temperature in the absence of a magnetic field, although complementation with other techniques is necessary for a final confirmation of their chiral nature as well as their possible manipulation by applying electric currents. Finally, comparing panels (a)

and (c), we find that there is a higher density of these perturbations for the 1.2 nm Co sample (c), as well as that they are slightly thicker and more defined in this heterostructure, indicating that their stabilization is more favored when the PMA is lower.

On the other hand, Fig. Subsequently, experiments were performed as a function of polarization and photon flux without being able to find a direct relationship between these factors and changes in magnetic anisotropy, ruling out a priori angular momentum transfer or heating as the origin of this effect.

Panels (d -f) show some of the XMCD images acquired in an attempt to demonstrate the large variation in the configuration of the magnetic domains under standard measurement conditions.

Each image corresponds to an acquisition time of 10 minutes and, although they are not consecutive, they show the poor stability of these heterostructures with increasing radiation time in the same area (from left to right). In the first measurements (d), magnetic domains characteristic of an out-of-plane magnetization are observed [START_REF] Boulle | Room temperature chiral magnetic skyrmion in ultrathin magnetic nanostructures[END_REF], in which the rounded domains are dispersed in a matrix with the opposite magnetization. In particular, some of these It is found that this effect whereby the domains become smaller, and may even induce an anisotropy change, is favored at the absorption edges and depends on the exposure time [START_REF] Guang | Creating zero-field skyrmions in exchange-biased multilayers through xray illumination[END_REF].

This effect is therefore dependent on the number of photons, which has been minimized as much as possible to study the evolution of the domains in the presence of an applied field. Again, these results highlight the challenge of characterizing these systems and the need to carry out a correct optimization of the parameters for a proper characterization. Nonetheless, it is worth mentioning that this interaction represents an added potential of these systems in terms of the development of optically controlled devices and promotes further study of this interaction and the factors that govern it. Among other advantages, these optically controlled devices would have the great advantage of being able to be controlled remotely, as well as to work at higher frequencies [START_REF] Ogawa | Ultrafast optical excitation of magnetic skyrmions[END_REF]- [START_REF] Gerlinger | Application concepts for ultrafast laser-induced skyrmion creation and annihilation[END_REF]. further increased these domains percolate, enclosing oppositely shaped magnetized domains with a rather circular shape (e and f). In contrast to the domains present in the first stages, these circular-shaped domains are smaller in size. From a statistical analysis for the image obtained at -3.75 mT, in panels (a) and (b) of Fig. 3.4.12, we find that the average diameter of these domains is around 153 nm, reasonably in agreement with previous images obtained from MFM.

Finally, this heterostructure was also characterized by NV magnetometry in the demagnetized state, obtaining a diameter for these perturbations in the magnetization much smaller, only 50 nm in diameter.

In summary, in this work we have taken the first steps to investigate that we are able to stabilize skyrmionic magnetic textures, as well as their manipulation when combined with Rashba 2DEGs.

As a positive result, we have been able to distinguish that the competition between internal hand, we observed magnetic textures reminiscent of skyrmions by using several magnetic microscopies, although their chiral character is still to be confirmed.

Outlook

This work stimulates the study of other metal/STO 2DEGs to consolidate the role of the overlayer in the 2DEG formation process and its properties in terms of the spin-charge interconversion process. On the other hand, this work also prompts further study of the role of the band structure on the spin-charge interconversion properties of KTO-based 2DEGs, in order to better understand the underlying physics and be able to tailor them.

In addition, our laboratory is currently investigating the possibility of combining these systems with materials with a ferroelectric or ferromagnetic order, which could greatly increase their versatility for spintronics. In this sense, the use of ferroelectric substrates would add another degree of freedom to switch the sign of the conversion through the switching of the ferroelectric order. Among the ferroelectric candidates for hosting 2DEGs, we find Ca:SrTiO3, BaTiO3 and Nb:KTaO3. Alternatively, the direct coupling of 2DEGs with ferromagnetic materials may allow the development of devices able to carry out write and read operations in a more efficient way and with lower energy consumption. Currently, our laboratory is taking the first steps towards direct 2DEG/ferromagnetic coupling, with no oxide tunnel barrier in between. For this purpose, it has been decided to work with Eu since it shows a high affinity for oxygen and one of its stoichiometric oxides is ferromagnetic.

Based on the results obtained in this thesis, in the near future we will try to confirm both the ability of the 2DEG to efficiently exert a torque on the magnetization of the ferromagnetic layer, and the chiral character of the magnetic textures observed in this work. With this objective, it would be interesting to study other systems with a less conductive overlayer, which does not involve an additional contribution to the torque, as it is the case of Pt. Finally, if the effect of the 2DEG on the magnetization is found to be modulable by back-gating, this would pave the way towards the manipulation of skyrmions by electric currents.

Titre:

  photoémission à résolution angulaire (ARPES) ont été réalisées pour mettre en évidence le rôle de la structure de bande complexe du KTO dans l'efficacité de l'interconversion spin/charge. Après cette caractérisation, l'applicabilité des différents systèmes dans les plateformes d'interconversion spin-charge a été déterminée. À cette fin, des expériences de pompage de spin à résonance ferromagnétique (SP-FMR) et des mesures de magnétorésistance anisotrope (AMR) ont été réalisées. Le dernier chapitre de la thèse se concentre sur la capacité des différents systèmes à exercer des couples spin-orbite (SOT) la magnétisation d'un film ferromagnétique adjacent. Tout d'abord, les détails de l'optimisation des hétérostructures en termes d'épaisseur et de propriétés magnétiques seront donnés, suivis de la quantification du SOT par des mesures de magnétotransport. Enfin, des résultats préliminaires seront présentés sur l'observation de textures magnétiques, très probablement de caractère skyrmionique, qui pourraient être directement manipulées par un courant électrique exploitant l'effet Edelstein direct/inverse. La visualisation de ces textures de spin skyrmioniques a été réalisée par microscopie magnéto-optique à effet Kerr (MOKE), microscopie à force magnétique (MFM) et microscopie électronique à photoémission de rayons X (X-PEEM).

Outline Chapter 1 .

 1 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 Part I

Fig. 1 . 1 . 1 :

 111 Fig. 1.1.1: Graphical representation of the density of states (DOS) as a function of energy for a normal material (a) and a ferromagnetic material (b). Note that the DOS available at Fermi

Fig. 1 . 1 . 2 :

 112 Fig. 1.1.2: An electron orbiting around a nucleus at distance 𝑟 and with linear momentum 𝑝 feels an induction magnetic field 𝐵 that couples the spin momentum 𝑆 with the orbital momentum 𝐿 (a). The total angular momentum 𝐽 is then described by the sum of 𝑆 and 𝐿 (b).

Fig. 1 . 1 . 3 :

 113 Fig.1.1.3: Representation of the Elliot-Yafet and D'yakonov-Perel' spin relaxation mechanisms.In the Elliot-Yafet mechanism (a), the spin change events occur after a certain number of scattering events within a period of 𝜏 𝑝 . In contrast, in the D'yakonov-Perel' mechanism (b) spin relaxation occurs progressively due to the action of a fluctuating magnetic field, and is inhibited by a higher collision frequency (motional narrowing phenomenon).

Fig. 1 . 2 . 1 :

 121 Fig. 1.2.1: Anomalous Hall effect (a): injection of a charge current (𝑗 𝑐 ) into a homogeneously magnetized out-of-plane ferromagnetic material (𝑀) produces a transverse 𝑗 𝑐 due to the deflection of majority and minority spins in opposite directions. Spin Hall effect (b): injection of 𝑗 𝑐 into a material with SOC results in the scattering of oppositely polarized electrons in opposite directions, i.e., a transverse spin current (𝑗 𝑠 ). Inverse spin Hall effect (c): injection of a pure 𝑗 𝑠 through a spin-orbit coupled material results in the generation of a transverse 𝑗 𝑐 .

Fig. 1 . 2 . 2 :

 122 Fig. 1.2.2: Schematic illustration of the extrinsic (a and b) and intrinsic (c) spin-orbit coupling mechanisms responsible of the SHE of anomalous Hall effect. (a) Skew scattering, (b) sidejump scattering at a charge impurity (Q), and (c) intrinsic Berry phase mechanism.

. 24 )

 24 This expression thus implies a momentum-dependent splitting for the two spin subbands equal to 𝑘 𝑅 = ±𝛼 𝑅 𝑚/ħ 2 for |𝛼 𝑅 | > 0. In the free electron approximation, this is equivalent to two non-equivalent Fermi circular contours, with rotation of the in-plane (𝑘 𝑥 , 𝑘 𝑦 ) spins in opposite directions (either clockwise or counterclockwise) as depicted in Fig.1.2.3 (b).

Fig. 1 . 2 . 3 :

 123 Fig. 1.2.3: Schematic illustration of non-splitted (a) and Rashba type splitted subands (b) in the free electron model. Rashba-type splitting of Au (111) surface (c)

. 28 )

 28 With respect to the reciprocal effect, the IEE, the injection of a constant spin density along the 𝑦axis into Rashba 2DES (e.g., by spin pumping, spin injection, etc.), induces a shift of the Fermi contours in opposite directions by ±∆𝑘 𝑥 (see panel (b) of Fig.1.2.

Fig. 1 . 2 . 4 :

 124 Fig.1.2.4: In the free electron model, the Rashba spin-orbit interaction gives rise to two concentric circles (a) with spins rotating in opposite directions for the outer (+) and inner (-) contours. Injection of a charge current along -𝑥 results in spin accumulation along the 𝑦direction by the direct Edelstein effect (b), due to the non-compensation of out-of-equilibrium spin populations (shaded areas). Injection of a spin current with polarization along 𝑦 results in displacement of the Fermi contours in opposite directions (c), giving rise to a charge current density along -𝑥.

Fig. 1 . 2 . 5 :

 125 Fig. 1.2.5: Illustration of magnetization dynamics. Precession of the magnetization around an effective magnetic field (𝐻 ⃗ ⃗ 𝑒𝑓𝑓 ) according to Landau-Lifshitz equation (a), and with the additional damping torque introduced by Gilbert (b). Notice that the damping-like toque tends to align 𝑀 ⃗⃗ with 𝐻 ⃗ ⃗ 𝑒𝑓𝑓 . Two energy eigenstates arise as a consequence of the Zeeman splitting when an external magnetic field (𝐻 ⃗ ⃗ 0 ) is applied (c). This splitting increases as a function of 𝐻 ⃗ ⃗ 0 .At ferromagnetic resonance, a radio frequency field with energy ℏ𝜔 = 𝑔𝜇 𝐵 𝐻 induces the transition between the two energy eigenstates.

Fig. 1 . 2 . 6 :

 126 Fig. 1.2.6: Graphical representation of spin injection from a ferromagnetic (FM) to a nonmagnetic (NM) layer. In the presence of spin accumulation, represented by the black arrows in (a), a torque (𝜏) is exerted on the magnetization of the ferromagnetic layer, resulting in precession of the magnetization. (b) If an RF magnetic field (ℎ 𝑟𝑓 ) forces the precession of the magnetization to keep on ferromagnetic resonance, part of the angular momentum is transferred to the NM layer, i.e., a spin current (𝑗 𝑠 ) is injected.

  Fig. 1.2.7: The Fermi contour shifts due to the bias current 𝑗. A non-equilibrium spin density arises due to the direct Edelstein effect. Blue and orange arrows in panel (a) and (b) represent the polarization of the spin accumulation when flowing a charge current in opposite directions. A sketch of the BMR measurement setup where 𝐵 is a rotating in-plane magnetic field is shown in panel (c). 𝛷 denotes the angle between the current and the magnetic field.

Fig. 1 . 2 . 8 :

 128 Fig. 1.2.8: Spin Hall effect (a) and direct Edelstein effect (b): a charge current flowing through a heavy metal (HM) generates a spin accumulation at the interface with a ferromagnetic material (FM) transferring its angular momentum and generating a SOT upon magnetization.

Fig. 1 . 3 . 1 :

 131 Fig. 1.3.1: Dzyaloshinskii-Moriya interfacial interaction (iDMI) at the interface between an FM layer and a heavy metal with strong SOC, in this case Fe and Ir (a). The iDMI is mediated by an asymmetric exchange interaction between the strongly orbitally coupled electrons in the heavy metal (Ir), and the spins of the atoms in the magnetic layer (Fe). 𝑆 1 and 𝑆 2 are the spins of the neighboring atoms and 𝑑 12 is the corresponding DMI vector. The DMI favors the canting of otherwise parallel or antiparallel spins. Example of additive DMI at the Pt/Co/Ir interface.

Fig. 1 . 3 . 2 :

 132 Fig. 1.3.2: Types of magnetic skyrmions. Néel-type (a) and Bloch-type (b) skyrmions with the magnetization rotating from the downward direction at the center of the skyrmion to the upward direction at the edge. In Néel-type skyrmions the spins rotate within the plane of symmetry, while in Bloch-type skyrmions this rotation presents a transverse component giving rise to a swirling spin configuration. Lattice of skyrmions observed by scanning tunnelling microscopy in a monolayer of Fe grown on Ir(111) (c). The colour wheel indicates the in-plane magnetization and the square unit cell has a side length of 1 nm. Individual skyrmions observed by the same technique in a PdFe bilayer on Ir(111). The out-of-plane magnetization is colour-coded from red for 'up' to blue for 'down' magnetization. Panels (a -d) are

  crystal structure very flexible in terms of composition. It allows the relatively free substitution of cations, which becomes crucial when developing new materials, and leads to a large variety of perovskite-type metal oxides. Further, the introduction of active interfaces formed by perovskite oxides is expected to generate a new technological revolution in the coming years. The development of powerful deposition techniques such as pulsed laser deposition (PLD), magnetron sputtering or molecular-beam epitaxy (MBE) in the past decades have allowed the growth of well-defined interfaces of these complex oxides and the discovery of new surprising phenomena, such as the well-known two-dimensional electron gas (2DEG) at the interface between two strongly insulating materials: strontium titanate (SrTiO3, STO) and lanthanum aluminate (LaAlO3, LAO)[START_REF] Ohtomo | A high-mobility electron gas at the LaAlO3 /SrTiO3 heterointerface[END_REF]. This atomic-scale engineering has opened a world of possibilities to explore and make use of the fundamental properties of such interfaces, with new and more fascinating properties awaiting to be discovered and studied.

Fig. 1 . 4 . 1 :

 141 Fig. 1.4.1: Transition metals are highly correlated systems in which properties are dictated by interactions between the crystal field, band gap, Hund's coupling and Coulomb repulsion forces.

  agreement with BCS theory (see panel (c) of Fig. 1.4.2) and several unconventional scenarios have been proposed to explain the superconductivity in this material, but to date a definitive explanation for the dome-shaped behavior is still lacking. The electronic properties of STO can be understood by considering the hybridization of Ti-3d states with O-2p states, since Sr 2+ cations are strongly electropositive and have a secondary role in the electronic structure. Such hybridization leads to the formation of a valence band which is mainly anionic, composed of O-2s and O-2p orbitals, and to the formation of a conduction band which is mainly cationic, composed of Ti-3d orbitals. The valence and conduction bands are separated by an indirect bandgap of 3.25 eV (R → Г) and a direct bandgap of 3.75 eV (Г→ Г).

Fig. 1 . 4 . 2 :

 142 Fig. 1.4.2: Resistivity (a) and Hall mobility (b) temperature dependence of doped-SrTiO3 samples. (c) Evolution of the critical temperature for superconductivity (Tc) with the charge carrier concentration for reduced-SrTiO3 bulk samples. Reprinted by permission from[START_REF] Tufte | Electron mobility in semiconducting strontium titanate[END_REF]

Fig. 1 . 4 . 3 :

 143 Fig.1.4.3: Schematic of SrTiO3 perovskite structure (left) and orbital energy levels under the cubic crystal field due to oxygen ions (right).

1

 1

  .4.4 (a) and (b)).

Fig. 1 . 4 . 4 :

 144 Fig.1.4.4: Resistivity (a) and Hall mobility (b) temperature dependence of KTaO3 samples. (c) Measurement of the resistivity as a function of temperature for a 2DEG at the interface of EuO/KTO (111), showing the superconducting transition and critical temperature (TC) at low temperatures, which varies with the carrier concentration. Panels (a) and (b) are reprinted

1

 1

  .4.4 (c)), and similarly, Chen et al. reported a 2DEG in[START_REF] Scheel | Crystal growth technology[END_REF]

Fig. 1 . 5 . 1 :

 151 Fig. 1.5.1: Heats of formation of the most stable oxides as a function of the work function for common metals. The metals are grouped in three of the quadrants with respect to the dashed lines. The lines are based on empirical reports of the oxidation of metals on STO and correspond approximately to the formation energy of an oxygen vacancy in STO and electronic affinity (work function) of n-type TiO2-terminated STO. Reproduced with permission from[START_REF] Posadas | Scavenging of oxygen from SrTiO3 during oxide thin film deposition and the formation of interfacial 2DEGs[END_REF]

Fig. 1 . 6 . 1 :

 161 Fig. 1.6.1: Bulk STO band structure along 𝑘 𝑦 (a). Sketch of the allowed motion of an electron between 𝑑 𝑥𝑦 orbitals in a cubic structure (b). The hopping along 𝑧 is more impeded resulting in heavier 𝑑 𝑥𝑧 /𝑑 𝑦𝑧 bands. Subband structure obtained using the approximated solution of a particle of mass 𝑚 𝑧 in a wedge potential to define the subband confinement energies at the 𝛤-point. The inset shows the wedge potential profile. (d) Electronic band structure of the 2DEG at the (001) surface of STO, in particular the plot represents the energy momentum dispersion measured within the second Brillouin zone. The data represents the sum of measurements performed with 𝑠and 𝑝polarized light at 52 eV photon energy at 10 K. (e) Top panel represents the constant energy map at EF in the 𝑘 𝑥 𝑘 𝑧 plane. The 𝑘 𝑧 range shown is approximately one Brillouin zone perpendicular to the sample surface. The front panel shows the energy-momentum subband dispersion of the 2DEG. (a), (b) and (c) are reprinted

Fig. 1 .

 1 Fig. 1.6.2: (a) Experimental Fermi surface around the Γ11 point for the 2DEG formed at the Al/STO interface. (b) Band dispersion along the (100) direction. The cyan in (a) denotes the (100) direction. Solid lines indicate the theoretical bands obtained from an eight-band tight binding model. Reprinted with permission from [213].

Fig. 1 .

 1 Fig. 1.6.3 shows the results obtained in LTO/STO by applying the voltage to -200 V, returning to zero, increasing to 50 V and returning to zero. It was observed that the curve is reversible as soon as the maximum applied voltage is not exceeded. The same was observed at the LAO/STO interface. The exact capacity of the well and thus the maximum number of carriers depends on the growth conditions and may vary from sample to sample. While it is possible to fully deplete

  figure it can be clearly seen how the curves are linear below 40 V, showing a decrease of the slope as the gate voltage is increased. This behavior is expected according to the tuning of the carrier density by the electric field effect. However, above 40 V a kink appears that moves progressively towards lower magnetic field values. Zooming into the low magnetic field region (Fig.1.6.4 (b)), one can find that the Hall slopes undergo a significant change at this voltage value: from slopes that gradually decrease with increasing gate voltage, to slopes that are practically constant and even increase slightly above this critical voltage. The linear regime is thus attributed to a lower carrier density, in which the transport is measured by a single band contribution, while the nonlinear regime is associated with the presence of carriers with different mobilities, which obviously show a different dependence on the applied magnetic field (Fig.1.6.4 (c)). The transition between the two regimes is therefore the point from which the dxz/yz bands start to be populated, i.e., the Lifshitz transition.

Fig. 1 .

 1 Fig. 1.6.4: (a) Hall resistance, 𝜌xy, as a function of the magnetic field, B, for several back-gate voltages, Vg, for a 2DEG formed at the LAO/STO interface. (b) Zoom-in on the low-field region of (a). It can be seen that the low-field slopes reverse their gate dependence at VC = 40V (see inset). (c) Carrier densities extracted from Hall effect measurements at zero magnetic field (red) and 14 T (blue) as a function of the gate voltage. The measurement without applied magnetic field reflects the density of high mobility carrier, while the one measured with 14 T

Fig. 2 .Fig. 2 . 1 :

 221 Fig.2.1 shows a panoramic picture of the ultravacuum system (UHV, 10 -9 mbar range) used for sample growth and photoemission measurements, which some of them were performed in situ.The system consists of two clusters connected through a tunnel to transfer the samples between the different chambers without the need to break the vacuum. The clusters are equipped with three pulsed laser deposition (PLD) systems, two magnetron sputtering systems (one of them confocal), and chambers dedicated to X-ray and ultraviolet photoelectron spectroscopy (XPS/UPS), low-energy electron diffraction (LEED), and hard-mask placement.

Fig. 2 .

 2 Fig. 2.1.1: Sketch of the sputtering process (a) and picture of the plasma generated from a sputtering target (b).

Fig. 2 . 2 . 1 :

 221 Fig.2.2.1: Schematic of the three-step model commonly used to describe the photoemission process: i) photoexcitation of the electron from the valence band to the conduction band after being irradiated by photons, ii) propagation of the photoexcited electron to the surface (in this process additional secondary electrons can be excited), iii) emission of photoexcited

Fig. 2 . 2 . 2 :

 222 Fig. 2.2.2: Universal curve representing the electron inelastic mean free path as a function of kinetic energy (bottom axis). The top axis shows corresponding photon energy (the work function is assumed about 4eV for all materials). Coloured regions indicate the VUV and X-ray

XFig. 2 . 2 . 3 :

 223 photoexcited electrons can escape from the surface and be collected by an electron energy analyzer, where their characteristic 𝐸 𝑘𝑖𝑛 is determined according to equation (2.7). The analyzer functions as an energy filter, allowing only those electrons with an energy within a certain range to reach the detector. Therefore, the XPS spectrum obtained represents the number of detected photoelectrons as a function of 𝐸 𝑘𝑖𝑛 , which is directly related to the characteristic binding energy

(ℎ𝑣=1253. 6

 6 eV) operating at 20 mA and 15 kV. The pass energy, slits and sweep rate were adjusted for a balance between intensity and resolution during measurements2.2.3. Angle-Resolved Photoelectron SpectroscopyThanks to the capability of angle-resolved photoemission spectroscopy (ARPES) to simultaneously probe the energy (𝐸 𝑘𝑖𝑛 ) and momentum (𝑘) of photoemitted electrons, this technique has been widely used to study the electronic band structure of materials, giving information about the collective behaviour of correlated electron systems, such as superconductors, density waves, magnetic orders and topological materials, etc. The technique has been revived in the last decades due to the rapid development of precise electron spectrometers, modern synchrotrons and better laser light sources. As a result of this progress, many variants of this technique have emerged, including soft x-ray ARPES, time-resolved ARPES, spin-resolved ARPES and spatially resolved ARPES.

  photoelectron intensity depends on the electric dipole matrix from equation (2.2).ARPES experiments were performed at CASSIOPPÉE beamline, in SOLEIL synchrotron. It is equipped with a high-resolution hemispherical analyzer (Scienta Omicron DA30), which separates

Fig. 2 .

 2 Fig.2.3.1 (a) shows the typical van der Pauw configuration on square-shaped samples, in which four ohmic contacts are placed at the corners. In practice, an electric current is injected between contacts 1 and 2 (𝐼 12 ), and the voltage difference between contacts 3 and 4 (𝑉 34 ) is measured at

Fig. 2 . 3 . 1 :

 231 Fig. 2.3.1: Example of the Van der Pauw configuration for square-shaped samples. Four ohmic contacts are placed at the corners of the sample for both resistivity and magnetoresistance (a) and Hall effect (b) measurements.

Fig. 2 . 3 . 2 :

 232 Fig.2.3.2: Illustration of the setup during bilinear magnetoresistance measurements. Current injection takes place along the longitudinal direction of a 1.58 x 10 mm 2 rectangular sample.

Fig. 2 . 3 . 3 :

 233 Fig. 2.3.3: Configuration used for spin pumping measurements using a resonant cavity. The DC magnetic field is generated by electromagnets located on opposite sides. The sample is glued on a support that allows the connection of two contacts for the detection of the voltage generated by the charging current, and another one to apply the gate voltage. The RF magnetic field (ℎ 𝑟𝑓 ) is produced by a Gunn diode, which emits a wave to the circulator. From here, the signal is sent to the cavity. At resonance, the power reflected by the cavity and the sample passes through the circulator to the detector.

  spin pumping experiments as well as the analysis of the results were carried out by the group of Laurent Vila and Jean-Philippe Attané at Spintec (Grenoble). These experiments were performed on a Brüker ESP300 X-band CW spectrometer at 9.68 GHz with a Brüker ER 4118X-MS5 cavity loop contained in a cryostat. The samples are typically 0.4 × 2.4 mm 2 and are glued on a thin PCB sample holder, bonded with Al wires on opposite sides of the sample, as shown in the schematic below. The PCB has two copper lines that allow resonance detection. The samples are also contacted on the back side using silver paste so that a back gate voltage can be applied. The RF magnetic field (ℎ 𝑟𝑓 ) is applied along the longitudinal direction, while 𝐻 0 is transverse to the sample, both being contained in plane. The generated DC voltage was measured with a Keithley 2182 A nanovoltmeter and the gate voltage was applied with a Keithley 2400 source meter. It should be noted that the good positioning of the sample in the cavity is very important to avoid nonlinearity of the spin pumping signal with power and to avoid unwanted thermal effects (see below thermal effects). This is also important if the magnetization properties of the ferromagnetic material change with increasing temperature. Fortunately, the material used in this work (NiFe) presents a high Tc and its properties do not change in a narrow range close to room temperature, thus preserving resonance field and showing a linear output signal with power. Therefore, it was first necessary to check the appropriate power to be used during the experiments to maintain a linear regime (5 mW in our case).

  information about the magnetization rotation (𝜃, 𝜙) due to the external field and the anisotropy fields of the ferromagnetic thin film, whereas the second harmonic voltage, 𝑉 2𝑓 , provides information about the amplitude of the magnetization oscillations (∆𝜃, ∆𝜙) produced by the SOT via the anomalous (AHE) and planar Hall effects (PHE). During these experiments, we measured the first and second harmonic voltage simultaneously as a function of magnetic field by using dual harmonic lock-in amplifier.

Fig. 2 . 3 . 4 :

 234 Fig. 2.3.4: Second harmonic Hall voltage technique. Panel (a) shows a schematic with the direction of magnetization and the external magnetic field in Cartesian coordinate system. The schematic of the two geometries used in this work: the magnetic field (𝐻) is applied longitudinally (b) or transversely (c) to the current direction (𝐼 𝑎𝑐 ) to determine the dampinglike (𝐻 𝐷𝐿 ) and field-like (𝐻 𝐹𝐿 ) components of the spin-orbit torque, respectively.

Fig. 2 . 4 . 1 :

 241 Fig. 2.4.1: Sketch showing the Hall bar fabrication process: (a) Substrate as-received after a careful cleaning of the surface; (b) substrate with photoresist, dark area represents the exposed region to UV light during lithography; (c) exposed regions are removed by selective chemical products; (d) deposition of the heterostructure by sputtering and (e) subsequent litoff process to eliminate the photoresist.

Fig. 2 . 4 . 2 :

 242 Fig. 2.4.2: Example of a patterned Pt/Co/Ta/STO heterostructure. Panel (a) shows a 5 x 5 mm 2 image with Hall bars whose channel width is 10 or 25 μm (in numbers on the left side), and a longitudinal distance between contacts of 50 and 100 μm. Panel (b) is a magnification of one device with 10 μm channel width.

Fig. 2 . 5 . 1 :

 251 Fig. 2.5.1: Sketch explaining the operation of magnetic force microscopy technique. The magnetic tip is sensitive to the stray fields of the magnetic domains, which are reflected as a negative (parallel) or positive (antiparallel) variation in the phase of the oscillating cantilever.

Fig. 2 . 5 . 2 :

 252 Fig. 2.5.2: Sketch for the three different configurations of MOKE microscopy: polar (a), longitudinal (b) and transverse (c). Grey arrows indicate the magnetization (𝑀) direction and the incident optical beam is assumed to be p-polarized (clockwise). 𝜃 𝑘 and 𝜀 𝑘 are angle rotation and ellipticity, respectively. The transverse MOKE configuration does not produce a change in the polarization state, only modifies the amplitude of the reflected electric field.

Fig. 2 .

 2 Fig. 2.5.3: Magneto-optical Kerr effect (MOKE) microscope image (a) and example of the obtained hysteresis cycles (b) for Pt/Co/AlOX/STO heterostructures.

3 . 4 . 3 .Fig. 2 . 5 . 5 :

 343255 Fig. 2.5.5: XMCD is proportional to the projection of the magnetization and thus, the contrast will be different for in-plane (a) and out-of plane (b) magnetic domains.

  photoemission spectroscopy (ARPES). The obtained spectra are combined with theoretical calculations based on the tight-binding model.In turn, Section 3.3 focuses on the efficiency of the different systems in terms of the spin-charge current interconversion process. The spin-to-charge conversion process by the inverse Edelstein effect (IEE) has been characterized by spin pumping experiments (SP-FMR) after combining metal/STO and Al/KTO 2DEGs in AlOx/NiFe/metal/oxide heterostructures. On the other hand, the conversion efficiency of charge currents into spin currents by direct Edelstein effect (EE) has been studied for the Al/KTO system by analyzing the bilinear response of this systems during angleresolved magnetotransport measurements (BMR).Finally, section 3.4 deals with the optimization of Pt/Co/metal/STO heterostructures to study the spin-orbit torque (SOT) induced from the 2DEG by means of magnetotransport measurements.

Sketch 3 . 1 :

 31 Schematic diagram showing the reoxidation process of STO (a), a fully protected 2DEG (b), and the formation of a metallic layer due to overgrowth (c), as a function of the thickness of metal deposited. In this sketch, tredox represents the thickness of metal oxidized by the redox reaction with STO, and tnative the thickness of metal oxidized by air.

Fig. 3 . 1 . 1 :

 311 Fig. 3.1.1: Ti 2𝑝 core-level spectra obtained in-situ when different thicknesses of Al (a -c), Ta (d -f) or Y (g -i) are deposited on STO. All the spectra have been normalized to the maximum intensity and the binding energy values are relative to the 𝑇𝑖 4+ 2𝑝 3/2 peak position. The color code is the same for all figures and it is shown in (i). Note that, for the Ta case, the Ti 2𝑝 corelevel energy region overlaps with the energy range of 𝑇𝑎 4𝑝 1/2 . Thus, for better visualization the fitted Ta peaks have been removed from the spectra.

Fig. 3 . 1 . 2 :

 312 Fig. 3.1.2: Ti 2𝑝 core-level spectra obtained ex-situ when different thicknesses of Al (a -c), Ta (d -f) or Y (g -i) are deposited on STO. All the spectra have been normalized to the maximum intensity and the binding energy values are relative to the 𝑇𝑖 4+ 2𝑝 3/2 peak position. The color code is the same for all figures and it is shown in (i).

  exposure of the samples to air (see Fig. 3.1.2 for Al (a -c), Ta (d -f) and Y (g -h)). Notably at low metal deposited thicknesses, these spectra show a lower contribution from Ti 3+ and Ti 2+ when compared to in-situ collected spectra. The decrease of the concentration of reduced valence

  3.1.3 shows the relative concentration of Ti valence states as a function of Al (a), Ta (b), or Y (c) deposited thickness, both for spectra collected in-situ (open circles) and ex-situ (filled circles).

Fig. 3 . 1 . 3 :

 313 Fig. 3.1.3: Evolution of Ti valence states with increasing the thickness of Al (a), Ta (b) or Y (c).

Tab. 3 . 1 . 2 :

 312 Constrains imposed during the fits of Al 2𝑝 (a -d), Ta 4𝑓 (e -n) and Y 3𝑑 (o -r) corelevels. LA refers to an asymmetric line-shape for metals caused by the coupling with the conduction electrons and GL to the Gauss/Lorentzian product, where GL (100) denotes a pure Lorentzian line-shape. whereas for the case of Y the reoxidation has been observed for all samples within the range of thickness studied by XPS. Whether it is necessary to deposit more Y to efficiently protect the STO from reoxidation agrees with a thicker native oxide layer for the Y case. These values were deduced by X-ray reflectometry measurements, being 1.8 nm for Al2O3, 1.5 nm for Ta2O5, and 3.4 nm for Y2O3. We found that the different native oxide layer thicknesses can also be related to the different oxygen diffusion coefficients through the oxide layers as well as to the reduction potential, work function and oxide formation enthalpy values per mol of oxygen of the different metals. Allowing us to correlate a larger thickness of the native oxide layer with a larger extent of the redox reaction at the interface.In Fig.3.1.4, we show the spectra collected ex-situ for Al 2p (a, b), Ta 4f (c, d) and Y 3d (e, f) corelevels obtained for the same samples. Note that for Y case, a wider range of thicknesses have been covered. The analysis of the spectra has been carried out by means of an active fitting process in which the appropriate restrictions have been sought to obtain coherent and meaningful trends. Finally, the same constraints were applied for Al, Ta or Y samples over the whole range of thicknesses. The constraints during the fitting are in good agreement with the

Fig. 3 . 1 . 4 :

 314 Fig. 3.1.4: Al 2𝑝 , Ta 4𝑓 and Y 3𝑑 XPS spectra obtained ex-situ after depositing 0.9 nm (a) and 2.1 nm (b) of Al, 1.3 nm (c) and 2.5 nm (d) of Ta, and 4.2 nm (e) and 6.2 nm (f) of Y on STO. It shows that Al and Y are mostly oxidized with a valence state 3+ which may correspond to Al2O3 and Y2O3 respectively, whereas in the case of tantalum several valence states (1+, 2+, 4+, 5+) are present. The color code is the same for top and bottom rows.

  3.1.5 shows the evolution of the valence states for Al, Ta and Y as the deposited layer thickness increases. As mentioned above, all three metals are fully oxidized at low thicknesses. In the case of Al and Y, these elements present a single 3+ valence state which likely corresponds to their most stable oxide form, respectively, Al2O3 and Y2O3. However, Ta has several valence states corresponding to both the most stable oxide (Ta2O5) and other suboxides (TaO2, TaO, Ta2O) and thus gives us a more characteristic trend with deposited tantalum thickness.

Figure 3 . 1 .

 31 Figure 3.1.5 also shows the relative concentration of valence states obtained from ex-situreference spectra for a 60 nm thick layer of Al, Ta, or Y deposited on a metallic plate. Such thickness is well above the probing depth of XPS (10-20 nm) and thus, provide us with a reference during the analysis which points out the relative concentration in valence states just given by the top native oxide layer and the metal underneath. A relative concentration that should be reached for any of the systems if we increase the metal thickness sufficiently to not see the oxide formed by the redox reaction with STO. From Fig.3.1.5 we see that such trend is fulfilled for all three cases. It should be noted for the case of Ta, that the presence of suboxides is not easily detectable in the reference samples. This can be explained considering that such suboxides are found at the interface of the native oxide with the metal, and their proportion compared to Ta2O5 is very small.

Fig. 3 . 1 . 6 :

 316 Fig. 3.1.6: Top row: Temperature dependence of the sheet resistance for samples with different thicknesses of Al (a), Ta (d) or Y (g). Middle row: Sheet resistance at T = 300 K as a function of Al (b), Ta (e) or Y (h) deposited thickness. Bottom row: Sheet resistance at T = 2 K as a function of Al (c), Ta (f) or Y (i) deposited thickness.

Fig. 3 . 1 . 7 :

 317 Fig. 3.1.7: Top row: Hall resistance curves obtained at T = 300 K for samples with different thicknesses of Al (a), Ta (d) or Y (g). Middle row: Hall resistance curves obtained at T = 2 K for the same samples with Al (b), Ta (e) or Y (h). Bottom row: Magnetoresistance curves obtained at T = 2 K for the same samples with Al (b), Ta (e) or Y (h).

1. 3 Fig. 3 . 1 . 8 :

 3318 Fig. 3.1.8: Carrier density and mobility values of the 2DEG estimated by fitting the Hall and the sheet resistance value at 2 K into a two-band model. Top row: Total carrier density as a function of Al (a), Ta (c) and Y (e) metal thickness. Bottom row: Mobilities as a function of Al (b), Ta (d) and Y (f) metal thickness.

  Fig. 3.1.9: Mobility as a function of carrier density for Al, Ta and Y samples for the lighter dxy (a) and heavier dxz, yz (b) bands.

Fig. 3 .

 3 Fig. 3.1.11: AFM images obtained after depositing 0.6 nm (a), 1.3 nm (b) and 1.6 nm (c) of Ta on STO. (d) Reference image obtained after depositing 30 nm of Ta on SiO2. Images are 5x5 m. The scale bar in each image represents 2 m.

(

  see inset Fig. 3.1.6 (e)) and the large amount of metal detected by XPS (see Fig. 3.1.5 (b)).

Fig. 3 .

 3 Fig. 3.1.12: AFM images obtained after depositing 0.3 nm (a), 0.6 nm (b), 0.9 nm (c), 1.2 nm (d), 4.1 nm (e), 5.2 nm (a), 7.3 nm (b) of Y on STO. (h) Reference image obtained after depositing 30 nm of Y on SiO2.

  photoelectron lines in binding energy values due to Al deposition. The Ta 4f core-level spectra collected in-situ just after depositing different thicknesses of Al are shown in Fig 3.1.13 (a -c), while the spectra collected ex-situ are shown in Fig. 3.1.13 (d -f)). It

Fig. 3 . 1 . 13 :

 3113 Fig. 3.1.13: Ta 4𝑓 core-level spectra obtained in-situ (a -c) and ex-situ (d -f) when different thicknesses of Al are deposited on KTO. Al 2𝑝 core-level spectra obtained ex-situ for the same samples (g -i)

Fig. 3 .

 3 Fig.3.1.14 (b) shows the relative concentration of the valence states of Al deduced from the analysis of ex-situ collected spectra. From this figure, it is observed that Al is present as Al 3+ for

Fig. 3 . 1 . 14 :

 3114 Fig. 3.1.14: Relative concentration of valence states for Ta (a) and Al (b) when increasing Al thickness on KTO.

Fig. 3 . 1 . 15 :

 3115 Fig. 3.1.15: Temperature dependence of the sheet resistance (a) and Hall resistance curves obtained at T = 300 K (b) for samples with different deposited Al thickness on KTO. Plots for the sheet resistance at T = 300 K (c) and at T = 2 K (d) for the same samples.

Fig. 3 . 1 . 16 :

 3116 Fig. 3.1.16: Hall resistance (a) and magnetoresistance (b) curves obtained at T = 2 K (b) for samples with different Al thicknesses on KTO. Plots for the 2DEG carrier density (c) and mobilities (d) as a function of Al thickness.

Fig. 3 .

 3 Fig. 3.2.1: LEED pattern obtained before (a) and after (b) the deposition of 2 Å of Al on KTO (001) by MBE.

Fig. 3 .

 3 Fig.3.2.1 (b)), suggesting that the atomic order at the interface is preserved, as well as that the deposited Al layer is indeed very thin. The sample is then inserted into the ARPES chamber without breaking the vacuum from the MBE chamber and it is ready to be characterized by ARPES.

  different polarizations (LH, LV, CL and CR). Panel (a) of Fig.3.2.4 shows the band dispersion obtained along the [001] direction (i.e.,  ̅̅̅̅ ) with LH polarization, on which the theoretical bands calculated by Ingrid Mertig's group using the tight-binding model have been superimposed (on the right-hand side).

Fig. 3 . 2 . 3 :

 323 Fig. 3.2.3: Photon energy spectra obtained at normal emission for AlOX/KTO, with left (CL, (a)) and right circularly polarized light (CR, (b)).

Fig. 3 . 2 . 4 :

 324 Fig. 3.2.4: Band dispersion along the [001] direction obtained at 15 K with LH (a) for AlOx/KTO. The bands obtained with the tight-binding fit are highlighted by colors and superimposed on the spectrum on the right-hand side. The sum of the spectra obtained with linear (LH+LV) and circular (CL+CR) polarizations are shown, respectively, in (b) and (c, d). The tight binding bands have been superimposed on the spectra in figure (d). The energy range corresponds to the area enclosed by the red box in (a). Constant energy maps (e -g) reconstructed from the band dispersion spectra obtained with LH polarization along the [001] direction, for energies of 50 meV (e), 25 meV (f) and 5 meV (g) below the Fermi level.

  3.3.2 shows the results obtained by SP-FMR experiments by which the ability of Al/KTO 2DEGs to convert spin currents into charge currents by means of the inverse Edelstein effect (IEE) is determined. These experiments have been performed as a function of a gate voltage and are expected to be useful for disentangling the role of different bands in the conversion process by its combination with the ARPES spectra (Sec. 3.2) and theoretical calculations (ongoing). On the other hand, Sec. 3.3.3

Tab. 3 . 3 . 1 :

 331 Relative fractions of reduced Ti valence states after the deposition of 1 nm of Al, Ta or Y on STO, and the saturation carrier density values for the different metal/STO 2DEGs at higher metal thicknesses, which were estimated in Sec. 3.1.1.

Fig. 3 .

 3 Fig. 3.3.2 shows the charge current produced by the IEE as a function of gate voltage for Al (a), Ta (b) and Y (c) samples. To facilitate the comparison of the results obtained for the different 2DEGs, panel (d) shows the same data replotted in a single figure. Some similarities and differences between the three systems are apparent from this figure. On the one hand, in

Fig. 3 . 3 . 2 :

 332 Fig. 3.3.2: Symmetric contribution to the DC voltage obtained at 15 K by spin-pumping FMR experiments. The voltages are normalized by the rf power in the cavity. Data is shown as a function of a gate voltage for the AlOx /NiFe (20 nm)/metal (1 nm)//STO samples: for Al (a), Ta (b) and Y (c) as metal. The data for the Al case was obtained previously by the same group, see ref.[213]. For comparison, the data are replotted in the same figure (d).

Fig. 3 . 3 . 4 :

 334 Fig. 3.3.4: Derivative of the FMR spectra at 10 K for negative (a) and positive (b) magnetic fields. Charge current generated transverse to the magnetization normalized by the applied r.f. power in the cavity, for negative (c) and positive (d) magnetic fields as depicted in the corresponding insets. The data in (b) and (d) are shown as symbols and the result of the fit as a thick solid line. The symmetric and antisymmetric components are shown as thin solid and dashed lines, respectively. The measurements were obtained while back-gating at -120 V.

  Fig. 3.3.5: Maximum symmetric contribution to the DC voltage measured at 10 K by SP-FMR experiments. The voltages are normalized by the rf power in the cavity. Data is shown as a function of gate voltage for the AlOx /NiFe (20 nm)/AlOX (~ 1nm)/KTO sample.

Fig. 3 .

 3 Fig.3.3.6 shows the results obtained by measuring the longitudinal resistance while rotating the sample within the plane defined by the current and applied magnetic field directions. In this

Fig. 3 .

 3 Fig. 3.3.6: (a) Normalized longitudinal magnetoresistance for two opposite currents as a function of the angle (ϕ) between the applied current and the magnetic field. The measurements were done by increasing the magnetic field from 1 T to 9 T and at 2 K. (JC = ± 0.64 A/m) and fixed magnetic field B = 2 T at 2 K. Bilinear (b) and quadratic (c).

  Fig. 3.2.7: (d) Current dependence of the BMR amplitude (ABMR) at 9 T. Magnetic field dependence of the BMR amplitude (e) and QMR amplitude (AQMR) (f). The current is fixed at JC = 0.64 A/m in (e) and (f). All data was obtained at 2 K.

4 . 3

 43 we have used magnetic microscopy techniques to evaluate the possibility of stabilizing magnetic textures with chiral character, although their coupling and manipulation by the SOT generated by the 2DEG will be subject of future work. More specifically, imaging of the magnetic textures has been carried out by magneto-optical Kerr effect microscopy (MOKE), magnetic force microscopy (MFM) and nitrogen vacancy magnetometer (NV) by Karim Bouzehouane, and by X-ray photoelectron emission microscopy (X-PEEM) by Sergio Valencia and Mohamad-Assaad Mawass at BESSY II, in Berlin.

3. 4 . 1 .

 41 Synthesis Optimization of Pt / Co / AlOx (TaOx) / STO

Fig. 3 .

 3 Fig. 3.4.1 shows the most representative hysteresis cycles for the SRT of Co in Pt/Co/metal/STO heterostructures, where metal denotes 1.7 nm Al for the top row (a -c), and 1.3 nm Ta for the

Fig. 3 . 4 . 1 :

 341 Fig. 3.4.1: Hysteresis loops obtained by polar MOKE microscopy at 300 K for Pt/Co/metal/STO heterostructures, applying an out-of-plane magnetic field. Metal in the top row denotes 1.7 nm Al, while in the bottom row denotes 1.3 nm Ta. Within each panel, heterostructures with different Co thicknesses (0.8 -1.2 nm) but the same Pt thickness are compared. Pt thickness increases from left to right (3 -6 nm) for heterostructures with equivalent Co thicknesses.

Fig. 3 . 4 . 2 :

 342 Fig. 3.4.2: Temperature dependence of sheet resistance (RS, first column), and transverse resistance (Rxy) as a function of an out-of-plane magnetic field at 300 K (middle column) and at 10 K (third column). The data is shown for Pt/Co/metal/STO heterostructures, in which metal denotes Al (top row) or Ta (bottom row).

Fig. 3 . 4 . 3 :

 343 Fig. 3.4.3: Longitudinal (Rxx) and transverse (Rxy) resistance as a function of an out-of-plane magnetic field at 2 K. The data is shown for Pt(1.7)/Co(0.7)/metal/STO heterostructures, being metal 1.7 nm of Al (a), or 1.3 nm of Ta (b), and the numbers in between brackets the thickness in of Pt and Co in nanometers. In panel (b), the red arrows indicate the magnetic field sweep direction, while the numbers in brackets denote the saturation (|H|>|HC|) and demagnetized states (|H|=|HC|).

Fig. 3 . 4 . 4 :

 344 Fig. 3.4.4: Sketch of the single-wall model for explaining the antisymmetric magnetoresistance effect in a system with PMA. The appearance of a DW divides the channel into two domains with opposite magnetization alignment where the Hall resistance exhibit an opposite sign. Inverse configurations (b and d) lead to a change of sign magnetization in the longitudinal direction

Fig. 3 . 4 . 5 :

 345 Fig. 3.4.5: Sketch of the model proposed for explaining the antisymmetric magnetoresistance in a system with PMA and SOC. The high and low resistance states correspond to the parallel or antiparallel orientation of the spin accumulation, generated by the IEE, with respect to the orientation of spins in domain walls uncompensated along this direction

Fig. 3 . 4 . 5 :

 345 Fig. 3.4.5: Scheme of transport and harmonic Hall measurements (a). Panel (b) shows the 1 st harmonic Hall voltage as a function of in-plane magnetic field for Vg= -25 V (red) and Vg = 175 V (black) to compare Hall resistance at two extreme gate voltages. Panel (c) shows the normalized 1 st harmonic Hall resistance as a function of in-plane magnetic field to compare the anisotropy field at Vg= -25 V (red) and Vg = 175 V (black). 1 st (d) and 2 nd (e) harmonic Hall voltages with sweeping in-plane magnetic field for various currents. Fitting of second harmonic Hall voltage to extract the damping like effective fields (𝐻 𝐷𝐿 ) (f) showing the experimental data (green), simulations fitting of DL and FL torques (black), considering that there is no FL torque in DL geometry (dashed-yellow), and fitting in the linear regime (pink).

Fig. 3 . 4 . 6 :

 346 Fig. 3.4.6: Raw data of 1 st (a) and 2 nd (b) harmonic Hall voltages as a function of in-plane magnetic field for Vg= 175 for various currents. V2f as a function of the out-of-plane magnetic field for various current values to estimate the thermal effects (c). 2 nd harmonic after subtracting the ANE contribution (d).

Fig. 3 .

 3 Fig.3.4.6 shows the damping-like effective fields as a function of current for two magnetization states, at -25 V (a) and 175 V (b). After performing a linear fit of the obtained data, we find that the effective field of the damping torque is very similar at both gate voltage values. The estimated value at -25 V is 26.8 Oe, while the estimated value at 175 V is 24.6 Oe. This result is a priori surprising since the current distribution has been estimated to be very different for both voltage values, i.e., while at -25 V the current through the Co/Pt layer is 100%, at 175 V only 76% of the current flows. This could be reflecting the role of 2DEG, suggesting that it has a similar order of magnitude to that exerted by Pt, but of opposite sign. This could be confirmed by further voltage analysis, which is currently being carried out.

Fig. 3 . 4 . 7 :

 347 Fig. 3.4.7: Both panels show the damping-like effective field as a function of current for two magnetization states in the channel, for two gate voltages: (a) Vg = -25 V and (b) 175 V. The solid lines are the linear fit forced to cross through (0,0) with uncertainty shown in shadow.The slope of the linear fit is used to estimate the damping-like effective field for 1 mA current in the channel.

1 2

 1 𝐸 = 𝐸 𝑒𝑥 + 𝐸 𝑎𝑛𝑖 + 𝐸 𝑍𝑒𝑒𝑚𝑎𝑛 + 𝐸 𝑑𝑒𝑚𝑎𝑔 + 𝐸 𝐷𝑀𝐼 , 𝑠 𝑚 • 𝐻 𝑑 -𝐷 • [𝑚 𝑧 ∇ ⃗ ⃗ • 𝑚 -(𝑚 • ∇ ⃗ ⃗ ) • 𝑚 𝑧 ],(3.9b)being 𝐴 the isotropic exchange constant, 𝐾 𝑢 is the uniaxial anisotropy constant with 𝑧 being the easy axis (perpendicular magnetization), 𝐻 𝑎 is the external applied field, 𝐻 𝑑 is the demagnetizing field, and 𝐷 is the magnitude of DMI. In static case (𝐻 𝑎 =0), the micromagnetic energy can be rewritten as:𝑒𝑓𝑓 • (𝑚 • 𝑧) 2 -𝐷 • [𝑚 𝑧 ∇ ⃗ ⃗ • 𝑚 -(𝑚 • ∇ ⃗ ⃗ ) • 𝑚 𝑧 ],(3.10)where 𝐾 𝑒𝑓𝑓 is the effective anisotropy constant which also incorporates the shape anisotropy (demagnetization energy), expressed as 𝐾 𝑒𝑓𝑓 = 𝐾 𝑢 -𝜇 0 𝑀 𝑠 2 , 𝑀 𝑠 being the saturation magnetization of the system. Thus, since the exchange of the systems is intrinsic, one can tune the generation of magnetic textures by controlling the 𝐾 𝑒𝑓𝑓 and 𝐷 strength.Considering the above conditions, we have prepared Pt(6)/Co(𝑥)/AlOX(TaOX)/STO heterostructures (the numbers in parentheses are the thicknesses in nanometers) using the magnetron sputtering technique in an HV chamber. The Co layer thickness has been selected after careful characterization of the hysteresis behavior to satisfy the energy requirements to stabilize the chiral textures. For the imaging of the textures, we have used magneto-optical Kerr effect (MOKE) microscopy, magnetic force microscopy (MFM), X-ray photoemission electron microscopy (X-PEEM) and nitrogen vacancy (NV) center magnetometry technique. The MFM and NV magnetometry images were acquired by Karim Bouzehouane at CNRS/Thales, while the X-PEEM characterization was performed by Sergio Valencia and Mohammed-Assad Mawaass at BESSY-II in Berlin. Finally, although the manipulation of these magnetic textures and the role of 2DEG remain to be demonstrated, these preliminary results seem very promising in terms of the possible combination of these systems, which encourages the continuation of this study. Our first approximation was performed by MOKE microscopy for Pt(6)/Co(0.8)/AlOX/STO. The aforementioned sample exhibits a moderate PMA at room temperature as can be deduced from its hysteresis cycle in previous Sec. 3.4.1 (in Fig.3.4.1 (c)). Panel (a) of Fig. 3.4.8 shows the configuration of magnetic domains after a demagnetization process with an out-of-plane magnetic field.

  The hysteresis cycles corresponding to these heterostructures are shown in panel (b) of Fig. 3.3.1 (in previous section. The images obtained by MFM are shown in panels (a), (b) and (c) of Fig. 3.4.9, for 0.8, 1.0 and 1.2 nm Co, respectively.

Fig. 3 . 4 . 8 :

 348 Fig. 3.4.8: Images obtained by MOKE microscopy for Pt(6)/Co(0.8)/AlOX/STO. Transition from a stripe domain phase (a) to a bubble domain phase as the magnetic field increases up to 0.45 mT (b) and 0.56 mT (c) in the direction perpendicular to the plane. The mean diameter (FWHM) of the bubble domains is around 1 m in panel (c).

3 . 4 .

 34 10 shows the Pt(1.7)/Co(0.7)/TaOX/STO hysteresis cycle in which the Pt thickness is thin enough to allow characterization by X-PEEM at room temperature. Panels (b) and (c) show XMCD images acquired at a photon energy coincident with the L3 edge of Co. The two panels correspond to the same point on the sample before (b) and after (c) beam overillumination, i.e., with the beam apertures opened to the maximum. These images show how the magnetization of Co within this zone changes from out-of-plane to in-plane, i.e., a striking change of the magnetic anisotropy under irradiation. It is worth mentioning that such anisotropy change only takes place in the irradiated zones, and is therefore a local beam-induced effect.

Fig. 3 . 4 . 9 :

 349 Fig. 3.4.9: Images and profile lines obtained by MFM for Pt(4.5)/Co(𝑥)/AlOX/STO heterostructures, where 𝑥 is 0.8 (a, b), 1.0 (c, d) and 1.2 nm (e, f). The mean diameter of the magnetic perturbations (FWHM) is 170 and 180 nm for the 4 x 4 m 2 images (a, e), while 100 nm for the 2 x 2 m 2 image (c).

Fig. 3 .

 3 Fig. 3.4.10: Hysteresis cycle corresponding to Pt(1.7)/Co(0.7)/AlOX/STO (a). XMCD images: transition from an out-of-plane domain configuration (b) to an in-plane magnetized configuration (c) after over-illuminating the heterostructure with X-rays; time evolution of the domain configuration (d -f) upon x-ray incidence under standard measurement conditions.

Fig. 3 . 4 .

 34 Fig.3.4.11 shows the XMCD images obtained by applying a magnetic field after minimizing the effect of the beam on the domain structure. These images were obtained after performing magnetic saturation and returning to zero magnetic field. From these images we observe rounded domains around 1 m large (a and b). As the magnetic field increases in the direction favorable to these (brighter) domains, they become narrower and more elongated, while new domains nucleate, giving rise to a structure reminiscent of a stripe-domain phase (c and d). As the field is

Fig. 3 . 4 . 11 :

 3411 Fig. 3.4.11: Evolution of the domain configuration when applying an out-of-plane magnetic field during X-PEEM measurements.

  . The relaxation time 𝑇 1 , called spin relaxation time, defines the time required for the longitudinal component of the spin to reach equilibrium, while 𝑇 2 defines the time at which the spins lose phase coherence. In nonmagnetic isotropic conducting materials, the relaxation time (𝑇 1 ) and the dephasing time (𝑇 2 ) are equal as long as 𝜔 0 𝜏 𝑐 ≪ 1,

	|𝑒|𝑔 𝑒 2𝑚 𝑒	𝐵 0

  𝜀 𝑔 )3 . Another distinction between these two mechanisms is the respective dependence of the spin diffusion length 𝑙 𝑠𝑓 = √ 𝐷𝜏 𝑠𝑓 , where 𝐷 is the diffusion constant on momentum dispersion: 𝐷~𝜏 𝑝 , for the Elliot-Yafet mechanism 𝑙 𝑠𝑓 𝐸𝑌 ~𝜏𝑝 , while for the D'yakonov-Perel' mechanism the 𝑙 𝑠𝑓 does not depend on 𝜏 𝑝 .

	1.1.3. From equations (1.14) and (1.16), one arrives at 𝜏 𝑠𝑓 𝐸𝑌 ~𝜏𝑝 for the Elliot-Yafet mechanism,
	while at 𝜏 𝑠𝑓 𝐷𝑃 ~𝜏𝑝 -1 for the D'yaknov-Perel' mechanism. Moreover, substituting equation (1.17)
	into equation (1.16) leads to 𝜏 𝑠𝑓 𝐷𝑃 (𝐵𝐼𝐴)~(1/𝜀 𝑔 ), while 𝜏 𝑠𝑓 𝐸𝑌 ~(

  al. were able to derive the 𝛼 𝑅 from these experiments.

	Starting from this model, Vaz et al. [59] developed a model to determine the Rashba coefficient
	(𝛼 𝑅 ) directly from BMR measurements, which is applicable for Rashba 2DEGs where the Rashba
	coupling is much larger than the Zeeman field, and for a very simple case, where the Fermi
	contours are circular and characterized by a Rashba parameter. Thus, it is worth mentioning that
	this model should be used with caution as it does not adequately describe highly anisotropic
	Fermi contours. Considering such an ideal case, the electronic states are described by the
	following Hamiltonian in the plane-wave basis:
	𝐻 ̂𝑅 =	ℏ 2 𝑘 2 2𝑚 * 𝜎 0 + 𝛼 𝑅 (𝑘 𝑦 𝜎 𝑥 -𝑘 𝑥 𝜎 𝑦 ),	(1.42)
	where 𝑘 2 is equal to 𝑘 𝑥 2 + 𝑘 𝑥 2 , 𝛼 𝑅 is the Rashba parameter and 𝜎 𝑗 (𝑗 = {0, 𝑥, 𝑦, 𝑧}) are the unit
	and Pauli matrices acting in spin space. The Hamiltonian above has two eigenvalues: 𝜀 ± =	ℏ 2 𝑘 2

  Therefore, by using this expression we can experimentally estimate the value of the Rashba parameter, assuming that 𝜀 𝐹 can be provided from the value of the effective mass and the charge carrier densities, after performing for instance ARPES measurements, and 𝑔 can be often found in the literature. It is worth mentioning that Vaz et al.[START_REF] Vaz | Determining the Rashba parameter from the bilinear magnetoresistance response in a two-dimensional electron gas[END_REF] found a good agreement of the Rashba

	parameter with the experimental data, providing a positive value for the Rashba coefficient of
	LAO/STO 2DEGs over a wide range of energies. This work demonstrated the potential of this
	effect to characterize conversion efficiencies and test the strength of spin-orbit coupling in 2D 1.2.6). systems. According to this work, an effective Rashba can be extracted based simply on the relative
	Thus, the in-plane anisotropic magnetoresistance for a Rashba 2DEG system can be decomposed amplitudes of the quadratic and bilinear terms of the magnetoresistance, carrier density, and
	in two components: an asymmetric bilinear component (𝐵𝑀𝑅) arising from the spin-orbit effective mass.
	interaction, which scales linearly on both electric and magnetic field; and a symmetric quadratic
	component (𝑄𝑀𝑅), which scales quadratically with the magnetic field. By following the
	definitions,	𝐵𝑀𝑅 = [𝑀𝑅(𝐵, 𝑗 𝑥 ) -𝑀𝑅(𝐵, -𝑗 𝑥 )]/2	and	𝑄𝑀𝑅 = (𝑀𝑅(𝐵, 𝑗 𝑥 ) +
	𝑀𝑅(𝐵, -𝑗 𝑥 )]/2, both components can be expressed as:
		𝐵𝑀𝑅 = 𝐴 𝐵𝑀𝑅	𝑗 𝑥 𝑗	𝑠𝑖𝑛𝜙,	(1.45𝑎)
		𝑄𝑀𝑅 = 𝐴 𝑄𝑀𝑅 cos(2𝜙),	(1.45𝑏)
	where 𝐴 𝐵𝑀𝑅 and 𝐴 𝑄𝑀𝑅 are the amplitudes of the bilinear and quadratic components,
	respectively. As can be inferred from the equations, QMR oscillates with 𝜋 periodicity, while BMR
	oscillates with periodicity 2𝜋. The angular dependence of the total magnetoresistance will then
	show an asymmetry between 𝜙 = 𝜋 2 ⁄ and 𝜙 = 3𝜋 2 ⁄ , and there will be an asymmetry for
	opposite directions of the current. Still within this model, 𝐴 𝐵𝑀𝑅 and 𝐴 𝑄𝑀𝑅 are given by:
		𝐴 𝐵𝑀𝑅 =	3𝜋 4	ℎ 𝑒 2	𝑔𝜇 𝐵 |𝑒|	𝛼 𝑅 𝜏 𝜀 𝑅 2 + 𝜀 𝐹 2 𝑗𝐵,	(1.46𝑎)
		𝐴 𝑄𝑀𝑅 =	3𝜋 4	(𝑔𝜇 𝐵 ) 2 𝑒 2	𝜀 𝐹 𝜏 𝜀 𝑅 2 + 𝜀 𝐹 2 𝐵 2 ,	(1.46𝑏)
	From these expressions, and considering the normalized magnetoresistance, which can be
	expressed as 𝑀𝑅 = [𝜌 𝑥𝑥 (𝐵) -𝜌 𝑥𝑥 (𝐵 = 0)]/𝜌 𝑥𝑥 (𝐵 = 0), the amplitudes become:
		𝐴 𝐵𝑀𝑅 =	3 2	𝜋	𝑔𝜇 𝐵 |𝑒|ℏ	𝛼 𝑅 𝜏 2 𝜀 𝐹	𝑗𝐵,	(1.47𝑎)
		𝐴 𝑄𝑀𝑅 =	3 4	( 𝑔𝜇 𝐵 ℏ	) 2	𝜏 2 𝐵 2 ,	(1.47𝑏)
	with 𝜏 is the scattering time of electrons. Note that, from the ratio between both amplitudes, we
	can extract the Rashba parameter:
		𝐴 𝐵𝑀𝑅 𝐴 𝑄𝑀𝑅	=	2𝜋ℏ |𝑒|𝑔𝜇 𝐵	𝛼 𝑅 𝜀 𝐹	𝑗 𝐵	,	(1.48)

  And the permutation between contacts makes possible to obtain average values for both the 𝑥 and 𝑦 directions:

			𝑅 12,34 =	𝑉 34 𝐼 12	,	(2.12)
	𝑅 𝑥𝑥 =	𝑅 12,34 + 𝑅 34,12 2	,	(2.13)
	𝑅 𝑦𝑦 =	𝑅 13,24 + 𝑅 24,13 2	,	(2.14)
	These resistances are in turn related for homogeneous samples with arbitrary shapes by the
	following expression:
	𝑒𝑥𝑝 (-	𝜋𝑡 𝜌	𝑅 𝑥𝑥 ) + 𝑒𝑥𝑝 (-	𝜋𝑡 𝜌	𝑅 𝑥𝑥 ) = 1,	(2.15)

[START_REF] Overhauser | Paramagnetic Relaxation in Metals[END_REF]

) is measured at the opposite edge. In this way, the resistance is determined by Ohm's law as follows:

  2

  •V -1 •s -1 . However, as will be shown later in the results, this model is too simplistic to describe the nonlinear Hall traces observed for metal/oxide 2DEGs, which can be attributed to electronic transport mediated by the contribution of different bands, and electrons with different mobility. For this reason, to obtain more precise information on carrier density and mobilities, in this work we apply the two-band Drude model, mainly based on the fact that in STO (001) and KTO (001) we can clearly discriminate lighter carriers in the conduction plane, in bands with dxy orbital character, from heavier carriers in bands with dxz,yz orbital character. In this model, 𝑅 𝑠 and 𝑅 𝑥𝑦 as a function of an applied field are determined by:

  𝐸 = -𝐾 𝑒𝑓𝑓 𝑐𝑜𝑠 2 𝜃 -𝑀 𝑆 (𝑠𝑖𝑛 𝜃 𝑐𝑜𝑠𝜙 𝐻 𝑥 + 𝑠𝑖𝑛𝜃 𝑠𝑖𝑛𝜙 𝐻 𝑦 + 𝑐𝑜𝑠𝜃𝐻 𝑧 ), (2.23) with 𝐾 𝑒𝑓𝑓 as the effective anisotropy, which is positive for out-of-plane easy axis and given by 𝐾 𝑒𝑓𝑓 = 𝜇 0 𝐻 𝐾 𝑀 𝑆 /2, and with 𝑀 𝑆 as the saturation magnetization. By combining equation (2.22) The next step is to extract the value of the amplitudes corresponding to the anomalous Hall voltage. Considering the configuration sketched in Fig. 2.3.4, the anomalous Hall voltage can be

	expressed as:
	𝑉 𝑥𝑦 = 𝐼𝑅 0 + 𝐼𝑅 𝐴𝐻𝐸 cos(𝜃) + 𝐼𝑅 𝑃𝐻𝐸 𝑠𝑖𝑛 2 (𝜃) sin(2𝜙),	(2.25)
	where 𝑅 0 represents the 𝑥-𝑦 resistance due to Hall bar misalignment (independent of the
	magnetization) and 𝑅 𝐴𝐻𝐸 and 𝑅 𝑃𝐻𝐸 are the anomalous and planar Hall effect resistances,
	respectively. If we consider the time modulation of the current at frequency 𝑓, we can replace
	(𝐼,∆𝐻) by (𝐼 0 , ∆𝐻, )sin(2𝜋𝑓𝑡) and (𝜃, 𝜙) by (𝜃 + ∆𝜃 sin (2𝜋𝑓𝑡), 𝜙 + ∆𝜙 sin (2𝜋𝑓𝑡)). Then, the
	expression for the anomalous Hall effect becomes:
		𝑉 𝑥𝑦 = 𝑉 0 + 𝑉 𝑓 sin(2𝜋𝑓𝑡) + 𝑉 2𝑓 cos(4𝜋𝑓𝑡),	(2.26)
	where the first and second harmonics are described by:
	𝑉 𝑓 = (𝑅 0 + 𝑅 𝐴𝐻𝐸 cos(𝜃) + 𝑅 𝑃𝐻𝐸 𝑠𝑖𝑛 2 (𝜃) sin(2𝜙))𝐼 0 ,	(2.27𝑎)
	𝑉 0 = 𝑉 2𝑓 =	1 2	(𝑅 𝐴𝐻𝐸 sin(𝜃) -𝑅 𝑃𝐻𝐸 sin(2𝜃) sin(2𝜙))∆𝜃𝐼 0
					-𝑅 𝑃𝐻𝐸 𝑠𝑖𝑛 2 (𝜃) sin(2𝜙) ∆𝜙𝐼 0 ,	(2.27𝑏)
	𝜃, 𝜙) =	𝜕 𝐻 𝑥 𝐸 𝜕 (𝜃,𝜙) 𝐸	∆𝐻 𝑥 +	𝜕 𝐻 𝑦 𝐸 𝜕 (𝜃,𝜙) 𝐸	∆𝐻 𝑦 +	𝜕 𝐻 𝑧 𝐸 𝜕 (𝜃,𝜙) 𝐸	∆𝐻 𝑧 ,	(2.22)
	and (2.23), we can express the amplitude of these oscillations as:
	∆𝜃 =	cos 𝜃 (∆𝐻 𝑥 𝑐𝑜𝑠 𝜙 + ∆𝐻 𝑥 𝑠𝑖𝑛𝜙) -∆𝐻 𝑧 𝑠𝑖𝑛𝜃 𝐻 𝐾 𝑐𝑜𝑠2𝜃 + 𝐻 cos (𝜃 -𝜃 𝐻 )	,	(2.24𝑎)
			∆𝜙 =	∆𝐻 𝑦 𝑐𝑜𝑠 𝜙 + ∆𝐻 𝑥 𝑠𝑖𝑛𝜙 𝐻 sin 𝜃 𝐻	,	(2.24𝑏)

where ∆𝐻 𝑖=𝑥,𝑦,𝑧 are the components of the SOT effective field. In addition, if the film presents uniaxial magnetic anisotropy, as in our case for the samples with PMA in Sec.3.4.2, the energy density is defined by:

  On the other hand, if we apply the magnetic field transverse to the current direction (± 𝑦-axis), 𝜃 𝐻 = 𝜋 2 ⁄ + 𝛿𝜃 𝐻 and 𝜙 = 𝜙 𝐻 = 𝜋 2 ⁄ , the field-like component of 𝑉 2𝑓 can be derived as:

	-	1 2	sin 𝜃 (	𝐻 𝐷𝐿 𝐻 𝐾 𝑐𝑜𝑠2𝜃 + 𝐻 sin (𝛿𝜃 𝐻 -𝜃)	+	2𝐻 𝐹𝐿 𝜉 sec(𝛿𝜃 𝐻 ) sin 𝜃 𝐻	) 𝑅 𝐴𝐻𝐸 𝐼 0 ,	(2.28)
	𝑉 2𝑓 𝐹𝐿 = -	1 2	cos θ sin 𝜃 (	𝐻 𝐹𝐿 𝐻 𝐾 𝑐𝑜𝑠2𝜃 + 𝐻 sin (𝛿𝜃 𝐻 -𝜃)	+	2𝐻 𝐷𝐿 𝜉 sec(𝛿𝜃 𝐻 ) sin 𝜃 𝐻	) 𝑅 𝐴𝐻𝐸 𝐼 0 , (2.29)

  3.1.3 as the point at which the Ti 4+ concentrations for in-situ and ex-situ spectra meet each other. Furthermore, it can be assumed that the thickness of the metal oxidized by exposure of the samples to air is always greater than the metal oxidized by the redox reaction with the STO. And therefore, that the thickness of metal to protect the STO is the same thickness of metal needed to form the native oxide layer. From Fig.3.1.3 we can estimate these values as 1.7 nm for Al and 1.3 nm for Ta,

		𝑷𝒆𝒂𝒌	∆𝑬 𝒊. 𝒆. , (𝟐𝒑 𝟏/𝟐 -𝟐𝒑 𝟑/𝟐 )	𝑭𝑾𝑯𝑴	Area	𝑳𝒊𝒏𝒆 -𝒔𝒉𝒂𝒑𝒆
	𝒂	𝐴𝑙 3+ 2𝑝 1/2	0.42 𝑒𝑉	-	𝑏 * 0.5	𝐺𝐿(30)
	𝒃	𝐴𝑙 3+ 2𝑝 3/2	-	-	-	𝐺𝐿(30)
	𝒄	𝐴𝑙 0 2𝑝 1/2	0.42 𝑒𝑉	𝑎 * 1	𝑑 * 0.5	𝐺𝐿(30)
	𝒅	𝐴𝑙 0 2𝑝 3/2	-	𝑏 * 1	-	𝐺𝐿(30)
	𝒆	𝑇𝑎 5+ 4𝑓 5/2	1.91 𝑒𝑉	-	𝑓 * 0.75	𝐺𝐿(50)
	𝒇	𝑇𝑎 5+ 4𝑓 7/2	-	𝑒 * 1	-	𝐺𝐿(50)
	𝒈	𝑇𝑎 4+ 4𝑓 5/2	1.91 𝑒𝑉	𝑒 * 1	ℎ * 0.75	𝐺𝐿(50)
	𝒉	𝑇𝑎 4+ 4𝑓 7/2	-	𝑒 * 1	-	𝐺𝐿(50)
	𝒊	𝑇𝑎 2+ 4𝑓 5/2	1.91 𝑒𝑉	𝑒 * 1	𝑗 * 0.75	𝐺𝐿(50)
	𝒋	𝑇𝑎 2+ 4𝑓 7/2	-	𝑒 * 1	-	𝐺𝐿(50)
	𝒌	𝑇𝑎 1+ 4𝑓 5/2	1.91 𝑒𝑉	-	𝑙 * 0.75	𝐺𝐿(50)
	𝒍	𝑇𝑎 1+ 4𝑓 7/2	-	𝑔 * 1	-	𝐺𝐿(50)
	𝒎	𝑇𝑎 0 4𝑓 5/2	1.91 𝑒𝑉	-	𝑛 * 0.75	𝐿𝐴(1.1,7,25)
	𝒏	𝑇𝑎 0 4𝑓 7/2	-	𝑚 * 1	-	𝐿𝐴(1.1,7,25)
	𝒐	𝑌 3+ 3𝑑 3/2	2.05 𝑒𝑉	-	𝑝 * 0.67	𝐺𝐿(30)
	𝒑	𝑌 3+ 3𝑑 5/2	-	𝑜 * 1	-	𝐺𝐿(30)
	𝒒	𝑌 0 3𝑑 3/2	2.05 𝑒𝑉	-	𝑟 * 0.67	𝐿𝐴(1.4,6,3)
	𝒓	𝑌 0 3𝑑 5/2	-	𝑞 * 1	-	𝐿𝐴(1.4,6,3)

  3.3.5 shows the results obtained by sweeping the gate voltage from 200 to -200 V, and measuring the conversion efficiency at FMR conditions. Compared to STO, the conversion efficiency of Al/KTO 2DEGs is lower but also exhibits a non-monotonic dependence on gate voltage, with more or less sharp maxima and minima. This dependence is different from that obtained for Al/STO 2DEGs and can be attributed to a different band structure. In fact, no sign change has been detected over the whole range of voltages studied, indicating even less versatility of this substrate for spin to charge conversion platforms in comparison with STO.

  3.4.3. Towards Skyrmionic Spin Textures on Pt/Co/AlOx/STO and Pt/Co/TaOx/STO As discussed in previous sections, metal/STO 2DEGs can be used for interconversion between spin currents and charge currents. While a spin current injected into these Rashba 2DEGs results

chaque système à partir de ces résultats est présentée. D'autre part, nous présentons la configuration et les détails techniques des mesures de magnétorésistance bilinéaire (BMR), grâce auxquelles nous pouvons déterminer la capacité des 2DEG métal/oxyde à convertir les courants de charge en courants de spin par l'effet Edelstein direct (DEE), et estimer la valeur du coefficient de Rashba. Des détails pratiques sur la caractérisation de l'effet Edelstein inverse (DEE) par des expériences de pompage de spin par résonance ferromagnétique (SP-FMR) sont également présentés. En particulier, nous nous concentrons sur des expériences réalisées avec un système de cavité micro-ondes à résonance paramagnétique électronique, et nous présentons les effets parasites possibles, ainsi que des solutions pour les éviter ou pour identifier leur contribution aux signaux de sortie.En outre, les principes techniques fondamentaux de la technique de tension de Hall harmonique permettant de caractériser le couple exercé par le 2DEG sur la magnétisation d'un film magnétique adjacent sont présentés. En particulier, ces expériences ont été réalisées sur des dispositifs dont le processus de lithographie optique est décrit en détail.Enfin, le chapitre sur les techniques expérimentales se termine par une présentation des microscopies utilisées pour la caractérisation des propriétés magnétiques, telles que la microscopie à force magnétique (MFM), la microscopie magnéto-optique à effet Kerr (MOKE) et la microscopie à photoémission de rayons X (X-PEEM).Le troisième chapitre comprend les résultats obtenus au cours de cette thèse. Tout d'abord, la caractérisation des systèmes métal/oxyde par spectroscopie de photoémission de rayons X (XPS),

l'épaisseur du métal nécessaires pour empêcher la réoxydation du 2DEG sont plus élevées dans le cas du Y. Ces différences sont discutées à partir des fonctions de travail des métaux déposés, de la chaleur de formation des oxydes correspondants plus stables et des coefficients de diffusion de l'oxygène à travers les couches d'oxyde. Nous constatons que la fonction de travail plus faible de Y, ainsi que la chaleur de formation plus faible de l'oxyde d'Ytrium et le coefficient de diffusion de l'oxygène plus élevé, expliquent les résultats obtenus. Quant à la caractérisation des propriétés de magnétotransport des 2DEGs métal/STO, elle a été réalisée de manière très systématique et nous avons pu corréler les résultats avec le processus de réoxydation et la percolation d'une couche métallique déduite de la caractérisation XPS précédente des mêmes échantillons. A partir de ces résultats, nous avons constaté que les 2DEGs d'Al/STO et de Ta/STO sont plus similaires dans le sens où ils présentent une densité de porteurs plus élevée et des mobilités plus faibles par rapport au cas de l'Y. Ces différences sont discutées en termes d'un confinement plus faible du 2DEG pour le cas Y, en accord avec la réduction plus importante du substrat. Enfin, à partir de la caractérisation des systèmes métal/STO par MFM, nous observons que la topographie change de façon marquée avec l'épaisseur du métal déposé. Nous constatons que le processus de percolation de la couche métallique peut être distingué ainsi que, pour le cas particulier de Y, que la réaction agressive avec le STO conduit à la formation de bulles d'oxygène lorsque l'épaisseur est inférieure à une certaine épaisseur. Une deuxième sous-section se concentre sur la réalisation de la même étude sur le système Al/KTO. Nous constatons que le dépôt d'Al conduit à une réduction du substrat. Nous constatons que l'épaisseur de l'Al oxydé par contact avec KTO est inférieure à celle oxydée par contact avec STO. Ces différences sont discutées sur la base de la réductibilité plus faible du KTO par rapport au STO. D'après les propriétés de transport, nous constatons que ces 2DEGs présentent une densité de porteurs plus faible et des mobilités plus élevées que leurs homologues STO.

Acknowledgements

Summary

In this section, we present the results obtained for metal/STO and Al/KTO 2DEGs, synthesized following a systematic process. For a proper comparison between systems, we ensured the same properties in both the deposited metal layer and the 2DEG host material. The deposition of metals (Al, Ta, or Y) has been performed by magnetron sputtering at RT and under very similar conditions, as well as on substrates presumably coming from the same single crystal. The characterization has been performed as a function of the deposited metal thickness by in situ and ex situ XPS, AFM, and magnetotransport measurements. The time evolution of these systems, attributable to the kinetics of the red-ox reactions involved in the 2DEG formation/reoxidation process, has been addressed by establishing similar time intervals between the synthesis and the characterization steps.

From in situ XPS measurements, performed just after deposition of Al, Ta or Y on STO, we determined that the STO reduction is higher for Y than for Al and Ta. We also found that the thickness of deposited metal required to achieve saturation of reduced species is greater for Y (1.2 nm), than for Al (0.9 nm) and finally Ta (< 0.3 nm). A priori, such thickness can be related to the metal thickness oxidized by direct contact with STO through a red-ox reaction. We note that the higher reduction of STO upon Y deposition, as well as a higher thickness of Y oxidized by contact with STO, is in agreement with what is expected from electrochemical potentials, work functions and enthalpies of oxide formation per mole of oxygen reported for metals [START_REF] Posadas | Scavenging of oxygen from SrTiO3 during oxide thin film deposition and the formation of interfacial 2DEGs[END_REF], [START_REF] Haynes | Handbook of Chemistry and Physics[END_REF], and the oxygen diffusion coefficients through the corresponding oxide layers [START_REF] Nakamura | Diffusion of oxygen in amorphous Al2O3, Ta2O5, and Nb2O5[END_REF], [START_REF] Ikuma | Oxygen diffusion in the fluorite-related phases of Y2O3-Ta2O5 and Ho2O3-Ta2O5 systems[END_REF].

The study performed on Al/KTO suggests that the saturation in reduced species occurs for smaller thicknesses of Al (0.4 nm) compared to Al/STO (0.9 nm), as well as the relative concentration of reduced species is lower. The results indicate a less aggressive red-ox reaction of Al with KTO and, therefore, that this oxide is more difficult to reduce than STO.

From ex situ XPS, after exposing the samples to air for approx. 10 min, we observed reoxidation of the metal/STO interface below a critical thickness. In principle, this critical value can be related to the thickness of metal needed to form the native oxide layer and efficiently protect the 2DEG from reoxidation. From X-ray reflectometry measurements, we found that the thickness of the native oxide layer is higher for Y (3.4 nm) than for Al (1.8 nm) or Ta (1.5 nm). Therefore, this could explain that the metal thickness required to protect the 2DEG against oxidation is greater for the cases of Y (> 1.5 nm) and Al (1.7 nm) than for Ta (1.3 nm), although we should consider other factors such as, for example, expansion coefficients of the different metals and the roughness of the layer.

Regarding the Al/KTO system, we found that the critical thickness of Al to prevent KTO reoxidation is the same as for STO case (1.7 nm), supporting the scenario whereby the 2DEG is protected from a deposited metal thickness that allows the formation of the native oxide layer, and which is characteristic of each metal for a given conditions.

Fermi level shift per unit voltage would imply that we are able to explore a larger energy regime of the 2DEG band structure by measuring within the same voltage range. Second, taking into account the experimental procedure by which we measured from the accumulation regime [START_REF] Biscaras | Limit of the electrostatic doping in two-dimensional electron gases of LaXO3(X = Al, Ti)/SrTiO3[END_REF], [START_REF] Scopigno | Phase Separation from Electron Confinement at Oxide Interfaces[END_REF], [START_REF] Pallecchi | Irreversible Multi-Band Effects and Lifshitz Transitions at the LaAlO3/SrTiO3 Interface Under Field Effect[END_REF], i.e., from +200 V to -200 V, equivalent points in the band structure (e.g., maxima and minima in Fig. 3.3.2 (d)) should appear at higher voltages for a more confined 2DEG since it would be necessary to decrease the electric field to a smaller extent to lower the Fermi level from the top of the quantum well down to this equivalent point within the 2DEGs band structure .

On the other hand, the confinement of the 2DEG in a smaller region of space would affect the band structure and carrier distribution within the bands [START_REF] Walker | ARPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces[END_REF], which could explain why the curves not only contract or expand, but are slightly different for the three systems. In this sense, ARPES measurements for the Ta and Y systems would be appropriate to clarify the effects of the confining potential on the 2DEG orbital reconstruction, enabling to predict the behavior of other metal/STO systems.

From Fig. 3.3.2 (d), it is observed that for the Al and Ta trends, the minima are narrower, the curves are shifted towards positive voltage values, as well as that these two systems exhibit higher spin-charge conversion efficiency compared to the Y case. All these features suggest that the band structures for Al and Ta 2DEGs are more similar to each other (than compared to the Y case), resulting in spatially more confined 2DEGs. Assuming a different band structure for the Y case would also agree with the results obtained in Sec. 3.1.1, from which we found that Y deposition gave rise to 2DEGs with lower carrier density than expected from the reduction of STO, and considerably higher mobilities as expected for a 2DEG which extends farther from the interface.

As discussed in Section 3.1.1, the confinement of the 2DEG depends not only on how much the STO is reduced by direct contact with the metal and the ability of the substrate to accommodate the charge, but also depends on the ability of the spontaneously formed oxide layer to retain as many electrons as possible close to the interface. Indeed, the oxide layer is expected to affect the electric field perpendicular to the 2DEG (E0), and may lead to different Rashba coefficients (αR), since [242]:

Where g is the g-factor, 𝜇 𝐵 is the Bohr magneton, 𝑚 * is the effective electron mass, and c is the speed of light. According to this equation, a higher electric field across the interface would not only favor a higher confinement of the 2DEG, but also an increase of the αR, increasing the conversion efficiency (λIEE) according to the equation [START_REF] Shen | Microscopic theory of the inverse Edelstein effect[END_REF]:

Where τ is the momentum relaxation time, and ħ the reduced Planck constant. Therefore, we find that the higher conversion efficiency obtained for the Al and Ta cases can be explained by an

Spin-to-Charge Conversion of AlOx / KTO

From the previous section, in which we compared the conversion efficiency of metal/STO 2DEGs, we observed some similarities regarding their response to gate voltage. In particular, we find a non-monotonic dependence that exhibits minima and maxima for the three different systems, as well as several sign changes that indeed increase their versatility for future applications. These similarities must logically stem from a common factor among the three systems, and are therefore attributed to the band structure of the substrate (i.e., STO), as was done in the previous work for Al/STO 2DEGs. Thus, while the comparison between metal/STO 2DEGs allows to elucidate the effect of the metal and its oxide on conversion efficiency, the comparison between Al/oxide 2DEGs would enable further optimization and a deeper understanding of the underlying physics occurring within completely different band structures.

In this context, this section focuses on the spin-charge interconversion efficiency of Al/KTO 2DEGs, from which we expect a higher conversion efficiency given the higher SOC and its larger Rashba-like splitting, observed in Sec. 3.2 by ARPES. The characterization has been carried out by SP-FMR experiments on heterostructures grown under the same conditions as those of metal/STO, favoring the comparison between both oxides for the Al case. Again, the samples were grown without breaking the vacuum between depositions and with equivalent metal thicknesses, i.e., 0.9 nm of Al, 20 nm of NiFe and an Al coating to protect the ferromagnetic layer against oxidation. Subsequently, SP-FMR measurements, as well as analysis of the results, were again performed by the group of Laurent Vila and Jean-Philippe Attané at Spintec (Grenoble).

The 2DEG carrier density after depositing 0.9 nm Al can be estimated from the saturation value for AlOx/KTO 2DEGs in Fig. 3.1.16 (c), which yields to 6 x 10 13 cm -2 . This assumption is possible because these samples have been capped in situ with other metallic layers (NiFe and Al capping), which prevent the oxidation of the 2DEG when the sample is exposed to ambient conditions. Also in this section, the consideration of the saturation carrier density value can be made in agreement with the XPS results in Sec. 3.1.2, from which reduced Ta species were found to saturate for thinner Al deposition (Fig. 3.1.14 (a)).

The samples were measured following a similar protocol as for STO samples but at 10 K. First, the 2DEG was subjected to a forming process and the SP-FRM measurements were carried out by configurations while applying a back-gate equal to -120 V. In both settings, it is observed how the output signal is relatively large [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF], [START_REF] Zhang | Determination of the Pt spin diffusion length by spin-pumping and spin Hall effect[END_REF]- [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 dominated by a symmetric component attributable to the IEE, while the asymmetric signal associated to the anisotropic magnetoresistance (AMR) or planar Hall effect in NiFe [START_REF] Rojas-Sánchez | Spin pumping and inverse spin Hall effect in germanium[END_REF], is very weak. Moreover, we note that the generated charge current is of the order of 40 nA and thus, higher than the value of 1 nA reported for thermal spin injection experiments [START_REF] Zhang | Thermal spin injection and inverse Edelstein effect of the twodimensional electron gas at EuO-KTaO3 interfaces[END_REF], confirming that the contribution from thermal effects is considerably smaller. Also, by comparing both figures, it is clearly seen how the reversal of the magnetic field direction leads to a change of sign in the output signal as expected from an interconversion process, i.e., the direction of the generated charge current depends on the spin polarization of the injected spin current.

Furthermore, from the sample magnetization (MS = 817 kA/m), the g-factor (g = 2.1), and the extra damping in the heterostructure (α0 = 6.94 x 10 -3 ) with respect to the damping in a reference sample with the same thickness of NiFe (α0 = 6.36 x 10 -3 ), the spin current injected into the 2DEG (𝐽 𝑆 ) can be calculated by equation (1.39). In turn, the calculated injected spin current allows computing the conversion efficiency (𝜆 𝐼𝐸𝐸 ) of the system according to [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] :

such as van der Waals AFM/FM heterostructures, and attributed to spin-orbit coupling [START_REF] Albarakati | Antisymmetric magnetoresistance in van der Waals Fe3GeTe2/graphite/Fe 3GeTe2 trilayer heterostructures[END_REF],

unsynchronized magnetic switching [START_REF] Hu | Antisymmetric magnetoresistance in a van der Waals antiferromagnetic/ferromagnetic layered MnPS3/Fe3GeTe2 stacking heterostructure[END_REF] or planar-symmetry-breaking [START_REF] Liu | Planar-symmetry-breaking induced antisymmetric magnetoresistance in van der Waals ferromagnet Fe3GeTe2[END_REF].

As for the works whose interpretation is based on the role of magnetic domain walls [START_REF] Cheng | Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy[END_REF]- [START_REF] Tang | Negative intrinsic resistivity of an individual domain wall in epitaxial (Ga,Mn)As microdevices[END_REF],

we find that the shape of these peaks is related to the nucleation and propagation processes of magnetic domains during magnetization reversal. In fact, it can be clearly seen in Fig. 3.3.3 that the shape of these peaks is very different for the heterostructures with Al (a) and Ta(b).

First, comparing both panels of Fig. 3.4.3, we observe that the peaks are broader and more symmetrical for the case of Ta (b), as well as that the beginning and the end of them (area delimited by the yellow box) coincide with the magnetic saturation, as deduced from Rxy. On the contrary, the peaks in the case of Al are clearly asymmetric, presenting a tail at the highest absolute magnetic field values, while the change in resistance is much more pronounced on the opposite side (lower field values). Moreover, for the case of Al the beginning and the end of the peaks (area delimited by the yellow box) do not exactly coincide with the saturation in the Rxy (blue box). Finally, and more clearly visible, the asymmetry of the effect with respect to the magnetic field has the opposite sign for the heterostructures with Al (a) and Ta (b). Now, considering that the point of maximum (and minimum) resistance corresponds to the demagnetized state with the highest density of domain walls, one can divide the peak in two by taking the maximum (or minimum) as the cut-off point: i) the transition from an initial monodomain configuration to a demagnetized state would correspond to the inner side of both peaks with respect to the magnetic field axis, i.e., |Hoop|<|Hc|, and ii) the transition from this demagnetized state to a final monodomain configuration would correspond to the outer side of both peaks, i.e.,|Hoop|>|Hc|). Thus, while for the case of Al (a) this demagnetized state is reached very quickly, the saturation process from this demagnetized state seems to occur more slowly.

On the contrary, the large symmetry of the peaks in the case of Ta (b) reflects a much more gradual orientation of the magnetization, which is comparable at both stages, i.e., from an initial saturation state to the demagnetized state (i), and from this demagnetized state to the opposite saturation state (ii). In addition, the greater width of these peaks for the Ta case reflects that the walls are more stable over a wider range of magnetic fields.

All this is consistent with the fact that the Al (a) heterostructure has higher PMA, which favors faster propagation of domain walls with in-plane magnetization component, and which is also reflected in the non-demagnetization of this heterostructure, in contrast to the case of Ta.

Regarding the coincidence of peak width with saturation in transverse resistance, we observe for the case of Ta that Rxx and Rxy go hand in hand and these regions coincide quite well. However, for the case of Al, we observe a variation in Rxy that is not reflected in Rxx. This implies that there is a magnetic field range where a higher orientation of the magnetization along the perpendicular direction is achieved, without implying a higher presence of magnetic domain walls. While for high absolute values of magnetic field (|Hoop|>|Hc|) this mismatch can be understood as the energies favors an out-of-plane magnetization and the appearance of bubble-like domains, as well as the stabilization of more point-like perturbations, possibly skyrmions. However, we have found that the characterization of these systems can be very challenging in terms of the susceptibility of this system to external stimuli. Future experiments will focus on confirming the presence of skyrmions or topological textures, as well as whether they can be effectively manipulated by SOT from the 2DEG, or by light sources. Image of the same sample obtained by NV magnetometry after a demagnetization process (c). The image is 1 x 1 m and the FWHM of the magnetic perturbations is about 50 nm (d).

Chapter 4. Summary and Outlook Summary

The main motivation of this thesis was to further investigate the potential of different systems to achieve efficient spin-charge interconversion. In addition, we went beyond exploring the possibility of using these materials as a tool to exert a torque on the magnetization of and adjacent ferromagnetic film, as well as their combination with chiral magnetic textures. Below, I summarize the most general conclusions of each chapter and I share some implications and perspectives of this work.

Chapter 1

The deposition of Al, Ta, or Y on STO under HV conditions leads to a redox reaction and the formation of a 2DEG at the interface. We find that the substrate reduction and the metal thickness to be deposited to protect the 2DEG against reoxidation are higher the lower the work function and the enthalpy of formation of the more stable metal oxide. Thus, a higher reduction is obtained and a higher thickness of Y needs to be deposited compared to Al or Ta. As for the transport properties, the case of Y presents significantly different properties. In particular, we have observed that despite a higher substrate reduction we have a lower carrier density and higher mobilities, which has been attributed to a lower 2DEG confinement for the Y case than for Al or Ta.

Moreover, it has been shown that the deposition of Al on KTO also leads to the formation of 2DEG at the interface, which exhibit lower carrier densities and higher mobilities than the Al/STO case.

This result is understandable considering that Ta is a heavier element than Ti and, therefore, presents a higher overlap with the 2p orbitals of oxygen.

Chapter 2

After performing the synthesis of Al/KTO 2DEGs, we have characterized their band structure by performing ARPES measurements at both high and low temperature. We have resolved for the first time the large Rashba-like splitting between the bands with dxz/dyz orbital character.

According to theoretical calculations, we found that these bands deviate from the parabolic shape, suggesting the presence of interband interactions and strong orbital reconstructions.

These results were the basis to carry out DFT calculations by our collaborators, who confirmed the complex spin and orbital textures. Furthermore, from these calculations they estimated a maximum Rashba coefficient of about 320 meV•Ǻ for the band with largest Rashba splitting.

Chapter 3

In this chapter, we have compared the charge currents generated by the inverse Edelstein effect (IEE) from Al, Ta and Y/STO 2DEGs as a function of gate voltage. The spin-pumping ferromagnetic resonance experiments and the analysis were carried by the group of Laurent Vila and Jean-Philippe. Attané in Spintec. From the gate dependence, we observed a similar non-monotonic dependence of the spin-to-charge conversion for the different systems, which has been attributed to the band structure of the STO. On the other hand, we have observed some differences in both the magnitude and the expansion/contraction of the curves, which was discussed in terms of the properties of the overlayer, the possibility of electrons escaping through the oxide layer into the ferromagnet, and a distinct 2DEG confinement.

On the other hand, we have also performed the gate dependence study for Al/KTO 2DEGs, which exhibits a different trend compared to STO-based 2DEGs. Such a different trend can be understood considering the different band structure of the substrate. In this case, the sign of the Rashba coefficient remains within the gate voltages studied. This result, together with the lower efficiency obtained for this system, suggest that KTO-based 2DEGs are less appealing for spincharge conversion compared to STO-based 2DEGs. However, we should not ignore that this system presents a very large splitting and a strong interaction between spin and orbital moments, which could be engineered to achieve higher conversion efficiency between spin and charge currents or even between orbital and charge currents.

Finally, this chapter also presents the characterization of these systems for the charge-spin conversion by the direct Edelstein effect. We have performed bilinear magnetoresistance measurements and from the analysis, we have obtained a negative sign for the Rashba coefficient and a magnitude which is in agreement with previously reported results and with theoretical calculations performed by our collaborators in Hale.

Chapter 4

This chapter focuses on the potential of 2DEG/STO metal to exert a torque on the magnetization of an adjacent ferromagnetic thin film. For this purpose, the optimization of Pt/Co/AlOX(TaOX)/STO heterostructures has been carried out to achieve perpendicular magnetic anisotropy as well as to favor the stabilization of magnetic textures with chiral character.

By using harmonic Hall technique, we found that, despite the larger contribution of the 2DEG at positive gate values, back-gating the heterostructure does not lead to very different effective field torques. This could indicate that the 2DEG has a similar magnitude and opposite sign as Pt.

However, the role of the 2DEG is yet to be confirmed and further analysis is needed for other voltage values. A more detailed study of the torque generated by the 2DEG may require further optimization of these heterostructures, or even combination with other materials. On the other