Electronic properties of materials

The electronic properties of materials are the basis for all technological applications. In solids, the organization of the valence electrons dictates the interatomic distances and the nature of the chemical bonds, hence determining the hardness or ductility of the material. Beyond mechanical aspects, all the physical properties such as conductivity, magnetism or optical behaviour originate from the electronic band structure. That's why, since the advent of electronics, microelectronics, optoelectronics or even spintronics, all kinds of devices (transistors, diodes, solid-state lasers, magnetic read-head...) operate an electronic band structure tailored by the scientist/engineer.

Semiconductors are a perfect illustration of this approach. In alloys like Al x Ga 1-x As, the band gap is controled by changing the value of x [START_REF] Allali | Experimental determination of the GaAs and Ga 1-x Al x As band-gap energy dependence on temperature and aluminum mole fraction in the direct band-gap region[END_REF]. Those alloys are made by Molecular Beam Epitaxy (MBE), a technique which emerged in the late sixties to produce artificial single-crystalline materials by slow rate deposition on a substrate [START_REF] Cho | Molecular Beam Epitaxy[END_REF]. Mainly used for semiconductors at the beginning, it opened the way to many other applications.

Indeed, beyond simple bulk materials, MBE allowed for the creation of heterostructures, a pilings of thin films of different materials, which created a whole new playground for scientists. As a successful example of this approach, when a different (or differently doped) semiconductor is grown on another one, the electronic bands of the two partners have to bend to match at the interface. This creates a potential well where conduction electrons fill 2D-quantized states, confined close to the interface but with a high lateral mobility [START_REF] Delagebeaudeuf | Two-dimensional electron gas m.e.s.f.e[END_REF]. This 2D-electron gas (2DEG) owes its remarkable properties (necessary for high performance transistors) to the spatial separation of electron and donors which reduces the scattering processes. After metallic superlattices, oxide heterostructures also came recently on the forefront, the archetypical system being LaAlO 3 /SrTiO 3 , where a high mobility metallic 2D electron gas appears at the interface between those two insulating materials [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF]. The success of the semiconductors physics inspired the quest for new materials, able to push forward the performances of existing devices or to create new ones, using, e.g. 2D high conductivity materials like graphene [START_REF] Sprinkle | First direct observation of a nearly ideal graphene band structure[END_REF]. [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF]. Graphene is just an example among the emerging materials with new striking properties due to a unique band structure showing massless electrons close to the Fermi Level (see figure 1.2). Superconductivity is still a fascinating field, with materials like cuprates, cobaltates or pnictides. Beyond the quest of the highest T c , the understanding of the appearence of superconductivity is still an issue, hidden in subtle alterations of their band structure. Materials presenting phase transitions, with temperature or under the influence of an external magnetic field (magnetism, metal-insulator transition) are also widely studied. All these phase transitions often rely on subtle changes in their electronic structure. Ferroelectricity, magnetoresistance, edge states, influence of defects on physical Figure 1.2 -Band structure of multilayered graphene measured by ARPES on CAS-SIOPEE. After reference [START_REF] Sprinkle | First direct observation of a nearly ideal graphene band structure[END_REF].

properties are some of the other fields under scrutiny in the endless list of the solid state physicist.

Surfaces and thin films

The improvements of vacuum techniques and the ability to prepare an atomicaly clean and well cristallized surface in ultra-high vacuum led to the development of surface science. Material evaporation methods, like aforementioned MBE, allowed to control thin films deposition at the angström scale. These progress opened the way to explore new fascinating areas of research : the surface of materials, materials as thin films and later, nanostructures.

At the surface, the atomic environment is truncated at the interface with vacuum. The missing chemical bonds sometimes force the solid to reorganize its first atomic planes which gives rise to structural reconstructions of the surface. But it also has an effect on the electronic structure. In a tight binding approach, the missing neighbours should lower the hoping possibilities for the electrons and reduce the band width. A consequence could be, e.g., an enhancement of the magnetic moment carried by the surface atoms with respect to bulk ones [START_REF] Richter | Spin Separation in a Metal Overlayer[END_REF][START_REF] Fu | Prediction of Strongly Enhanced Two-Dimensional Ferromagnetic Moments on Metallic Overlayers, Interfaces, and Superlattices[END_REF]. New electronic states, called surface states, can appear close to the surface. They are new solutions of the Schrödinger equation in the presence of the surface, where the atomic potential periodicity is broken.

Thin films are also of great interest. Some atomic layers of a material deposited on another one can form a whole new system with its own original properties.

From the crystallographic point of view, what will be the structure of the adsorbate ? Will it be the same as in its bulk form, or will it be influenced by the structure of the substrate ? Will there be some strains induced by the epitaxy on the substrate ? What will be the growth mode of the adsorbate ? Atomic layer by atomic layer ? Or will it form clusters on the surface ? Can we take advantage of the growth mode and of the substrate morphology to grow nanostructures ? Will the growth conditions, like temperature or possible annealings, influence all these parameters ? Those issues, along with many others, are those the surface scientist has to tackle when studying a new system.

Structural considerations are closely linked to the electronic properties of the thin film. Magnetic properties are a good example. They are strongly influenced by the surface and the interface through magnetocrystalline anisotropy, or by structural strains due to the epitaxy on the substrate inducing magnetoelastic contributions. All these parameters influence the magnetization easy axis direction, which can even be stabilized perpendicular to the film plane, despite the demagnetizing field [START_REF] Bruno | Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers[END_REF]. A film of a ferromagnetic material (in its bulk form) can be ferromagnetic or not, or with a different Curie temperature, depending on its thickness. In the field of oxide thin films, the changing of the transport properties of iridates thin films with the structural strains is another example of the interplay between structure and electronic properties.

Synchrotron radiation for the study of structural and electronic properties of materials

The solid-state physicist needs as many tools as possible to study the various structural and electronic properties of solids, thin films or heterostructures. For more than 45 years, many synchrotron radiation-based experimental techniques like X-ray Absorption Spectroscopy (XAS) or Photoelectron Spectroscopy provided us with priceless information on our favorite systems.

Structural properties can be investigated by diffraction, with the high angular resolution allowed by the high brilliance of the X-ray beam emitted by storage rings, or by Extended X-ray Absorption Fine Structure (EXAFS), taking advantage of the continuous emission spectrum. For thin films, Surface EXAFS is a powerful and convenient technique, whereas grazing incidence diffraction, or even photodiffraction, allow for the study of both thin films and reconstructed surfaces.

Electronic structure can also be probed using synchrotron radiation. Angle-Resolved PhotoElectron Spectroscopy (ARPES) gives a direct image of the band structure. With respect to a classical laboratory experiment, the possibility to vary the photon energy allows to change the modulus of the photoelectron wave vectors and also to optimize the cross sections. The light polarisation is of key importance to identify the symmetry of the different observed electronic states. For the study of magnetism, the use of circularlypolarised light in X-ray Magnetic Circular Dichroism (XMCD) measurements provides an element-selective probe of the magnetic moment in magnetic materials.

Those are only few exemples of what synchrotron radiation offers for the study of condensed matter. New techniques, like Resonant (or non-resonant) Inelastic X-ray Scattering (RIXS or IXS), magnetic scattering (both in the soft or hard X-ray domains) also emerged in the last decade. Throughout the years, the classical techniques available on a storage ring have been improved in terms of energy resolution, thanks to the progresses made both on accelerators and on the beamlines. Spatial resolution reaches values in the nanometer range and time-resolved experiments probe phenomenons taking place in less than a femtosecond.

Outline of this dissertation

I spent my whole career on synchrotron radiation beamlines. I was first involved in SEXAFS study of the crystallographic structure of magnetic thin films. This will be described in the second chapter of this dissertation.

I then moved to electron spectroscopy in resonant conditions. Our studies were closely related to X-ray absorption, and the goal was to better understand absorption edges by studying resonant-Auger lines or resonant photoemission. This will be described in the third chapter.

Last, I was involved in the building of the CASSIOPEE beamline, dedicated to ARPES and Spin-Resolved Photoemission (chapter 4). Results obtained on metallic 2D-electron gas at the surface of insulating oxides are presented in the fifth chapter.

CHAPITRE 2

Structure of magnetic thin films by X-ray absorption spectroscopy

Magnetism of thin films

At the beginning of the eighties, recent progresses in single crystal surface preparation and characterisation techniques, as well as in material deposition techniques, allow the elaboration of epitaxially grown thin films with a thickness accuracy at the monolayer scale.

In a pionneering work published in 1954, Louis Néel already predicted a surface contribution to the magnetic anisotropy, due to the missing neighbours around the surface atoms [START_REF] Néel | Anisotropie magnétique superficielle et surstructures d'orientation[END_REF]. Together with magnetocristalline anisotropy (induced, e.g., by structural strains due to epitaxy on a substrate), it could induce a magnetization easy axis perpendicular to the film plane, despite the demagnetizing field. Néel stated that these contribution should be negligible, except for objects with a size of the order of, or smaller than 100 Å. Following these first predicitions, new calculations were published about the expected magnetic properties in bidimensionnal systems like surfaces of magnetic materials, or thin films of ferromagnetic metals like cobalt or iron. The troncated environment at the surface should locally reduce the bandwith and enhance the magnetic moment [START_REF] Richter | Spin Separation in a Metal Overlayer[END_REF][START_REF] Fu | Prediction of Strongly Enhanced Two-Dimensional Ferromagnetic Moments on Metallic Overlayers, Interfaces, and Superlattices[END_REF]. Furthermore, these new works confirmed Néel predictions for a possible magnetization easy axis perpendicular to the film plane [START_REF] Gay | Spin Anisotropy of Ferromagnetic Films[END_REF].

In order to check the validity of such predictions, many experimental works were carried out by numerous groups throughout the world. Thin films of magnetic materials like iron, cobalt or nickel were deposited on non-magnetic substrates like copper, platinum, gold or silver. The magnetic properties were mainly probed by Magneto-Optical Kerr Effect (MOKE) [START_REF] Beier | Magnetic Hysteresis Loop of One Monolayer of Co on Cu(100)[END_REF][START_REF] Schneider | Curie temperature of ultrathin films of fcc-cobalt epitaxially grown on atomically flat Cu(100) surfaces[END_REF], Vibrating Sample Magnetometry (VSM) or spin-resolved photoemission [START_REF] Pescia | Ferromagnetism of thin epitaxial fcc cobalt films on Cu(001) obesrved by spinpolarized photoemission[END_REF][START_REF] Schneider | Spin-and angle-resolved photoemission from single crystals and epitaxial films using circularly polarized synchrotron radiation[END_REF], but there were discrepancies between the results obtained in different groups.

The growth conditions strongly varied from one group to the other. The deposition temperature could be 77 K, room temperature or slightly above. Some were using annealings after deposition to improve the crystallographic quality of the films (but favouring a possible interdiffusion at the interface) and other weren't. The crystallographic structure and morphology of the deposits were mainly investigated by the classical surface science techniques like LEED (including I(V ) measurements) [START_REF] Gonzalez | Experimental and theoretical study of Co adsorbed at the surface of Cu : Reconstructions, charge-density waves, surface magnetism, and oxygen adsorption[END_REF][START_REF] Clarke | A LEED determination of the structure of cobalt overlayers grown on a single-crystal Cu(001) substrate[END_REF], photoemission-based technique like photodiffraction [START_REF] Tonner | Structure of Co films grown on Cu(111) studied by photoelectron diffraction[END_REF], or the newly available near field microscopy method of Scanning Tunneling Microscopy (STM) [START_REF] De La Figuera | Scanning-tunnelingmicroscopy study of the growth of cobalt on Cu(111)[END_REF].

Those studies were of key importance since it was hard to predict was would be the growth mode of one material on another. Will it be atomic layer by atomic layer, or by forming islands ? Will the adsorbate adopt the crystallographic structure of the substrate or will it keep its stable bulk crystallographic structure ? What will be the influence of the lattice mismatch between the substrate and the adsorbate ? It should certainly compress or stretch the structure of the adsorbate, which could strongly influence the magnetic anisotropy through magnetoelastic effects. Up to which thickness will the film be able to store these elastic energy before it relaxes by dislocations ? All these structural parameters depends on the growth technique, are function of the growth temperature and are sensitive to possible annealings.

A clear exemple is the growth of Fe on Cu(001) where the magnetic properties strongly depends on the growth conditions. Iron grows in a metastable face-centered cubic (fcc) structure (bulk iron is body-centered cubic (bcc) at room temperature) and the film can be either ferromagnetic with an easy magnetization axis perpendicular to the surface when deposited at low temperature [START_REF] Pappas | Reversible transition between perpendicular and in-plane magnetization in ultrathin films[END_REF], or paramagnetic when deposited at 500 K [START_REF] Macedo | Magnetism of Epitaxial fcc-Fe(100) Films on Cu(100) Investigated in situ by Conversion-Electron Mössbauer Spectroscopy in Ultrahigh Vacuum[END_REF]. These different magnetic properties were linked to the crystallographic order in the film. Furthermore, this crystallographic order was shown to change when the film is coated with copper, often used as a protective capping layer [START_REF] Magnan | Structure of thin metastable epitaxial Fe films on Cu(100) : Reconstruction and interface ordering by coating[END_REF].

Back to magnetic properties, thin magnetic films or multilayers held all their promises in terms of technological applications. Thin films with perpendicular magnetic anisotropy were used to increase the storage density in magnetic hard drives [START_REF] Iwasaki | Co-Cr recording films with perpendicular magnetic anisotropy[END_REF], but the most spectacular achievement was obtained with magnetic multilayers [START_REF] Baibich | Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices[END_REF]. Those are Figure 2.1 -Magnetoresistance of three different Fe/Cr superlattices at 4.2K. After reference [START_REF] Baibich | Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices[END_REF]. heterostructures, alterning thin magnetic and non-magnetic layers and, if the thickness of the non-magnetic material is correctly chosen, the magnetic layers couple antiferromagnetically. When applying a magnetic field, the magnetization configuration switch to ferromagnetic and the electrical resistance drops down. This was shown to be due to a spin-dependant scattering at the interfaces, only one spin direction being scattered in the ferromagnetic configuration. This so-called giant magnetoresistance makes these systems highly efficient as sensitive sensors, which are now massively used as read-head in magnetic hard-drive. Moreover, this use of the spin in an electronic component opened the door to spin-based devices (like non-volatile memory chips) giving birth to spintronics.

If the engineer is satisfied when he improves the magnetoresistance of a spin valve by 10% by changing by chance the composition of one of the electrodes, the scientist's job is to understand the process in detail for possible future breakthroughs. As discussed above, this requires a complete characterisation of the sample beyond its magnetic properties, including a good knowledge of its crystallographic structure.

Among the synchrotron radiation techniques available for structure characterisation, Surface EXAFS, or SEXAFS, is a very well suited technique for the study of thin cobalt or iron magnetic films. It consists in measuring the X-ray absorption coefficient at one of the adsorbate's edge ; the oscillations of the X-ray absorption coefficient above the edge will then give information on the lattice, including possible distortions due to the epitaxy.

In the first part of this chapter, we will briefly describe this technique and its advantages for the study of epitaxially-grown thin films. In the second part, I will present the results we obtained on thin cobalt films deposited on Cu(001). In the third part, we will show that, thanks to SEXAFS measurements, it is also possible to describe the very first steps of the growth of cobalt on Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF].

EXAFS and Surface EXAFS 2.2.1 X-ray Absorption Spectroscopy

X-ray Absorption Spectroscopy consists in a measurement of the X-ray absorption coefficient of a material as a function of the energy of the incident photons. Let us explain this technique for photon energies around the binding energy of the 1s electronic shell of one of the components of the material. On a X-ray absorption spectrum, as presented in figure 2.2, one can define three regions :

1. When the photon energy is smaller than the 1s-shell binding energy, the photons cannot excite a 1s electron : the X-ray absorption coefficient is weak and monotonous.

2. The photon energy reaches the value of the 1s-shell binding energy, the absorption probability suddenly increases as the photon is now able to excite a 1s electron to the first empty states just above the Fermi level. This photon energy region is called the absorption edge, or XANES, for X-ray Absorption Near Edge Structure.

3. For larger photon energies, the X-ray absorption coefficient globally decreases, but it also strongly oscillates. These are the Extended X-ray Absorption Fine Structure (EXAFS) oscillations.

The EXAFS oscillations

EXAFS oscillations are not oberved in absorption spectra recorded on isolated atoms. They are therefore due to the crystallographic structure around the excited atom (the one who absorbed the photon). When the photon is absorbed, a photoelectron is ejected from the excited atom by photoelectric effect and its wave function is an outgoing spherical wave centered around the excited atom. This wave wave can be scattered by surrounding atoms and the scattered part interferes with the outgoing wave. While scanning the photon energy, the kinetic energy increases, and so is the frequency of the associated electronic wave ; the interferences between the outgoing and the scattered waves are then alternatively constructive and destructive (see figure 2.3). It is the origin of the EXAFS oscillations, clearly linked to the local crystallographic structure around the excited atom.

In 1975, Sayers et al. gave an expression of these EXAFS oscillations, as a function of k, the wave vector of the photoelectron [START_REF] Sayers | New Technique for Investigating Noncrystalline Structures : Fourier Analysis of the Extended X-Ray Absorption Fine Structure[END_REF] :

χ(k) = - i N * i kR 2 i e -k 2 σ 2 i e -2R i /λ B i (k) sin(2kR i + φ i (k)) (2.1)
Some assumptions/approximations have to be made to reach this formulation. We are not going to discuss them here, except the so-called single-scattering approximation, which assumes that the outgoing wave is only scattered once (backscattered) before it goes back to the excited atom. We will come back on this later, when we will discuss multiple scattering calculations which allow to go beyond this approximation.

χ(k) appears as a sum of sinus runing over the different shells of neighbours i of the excited atom, each sinus oscillating with a frequency R i , the distance between the absorbing atom and the neighbour shell i. Each sinus is multiplied by a function B i (k), the backscattering amplitude for each neighbour shell, and two damping terms due the mean free path of the electron λ and thermal vibrations and disorder (σ 2 i is the mean square relative displacement between the absorbing atom and the neighbours i (including static and thermal disorder. It is often called the Debye-Waller factor, even if it differs from the one accounted in diffraction experiments). φ i (k) is a phase shift due to the crossing of the atomic potentials by the electronic wave. The two B i (k) and φ i (k) functions are usually extracted from an experimental spectrum recorded on a known sample. In the case of our study of thin cobalt films, they will be determined from a bulk cobalt EXAFS spectrum. Each sinus is also multiplied by N * i , the apparent number of neighbours in shell i. For a K-edge, it can be calculated using

N * i = j 3 cos 2 α j i (2.2)
The sum runs over all the atoms j of the i th neighbour shell, and α j i is the angle between the electric field vector of the linearly polarised X-rays and the direction of the bond between the absorbing atom and the neighbour j of the shell i. As we will see later, this polarisation dependence of the EXAFS oscillations makes it possible to more or less select the direction of the bonds which are going to contribute to the signal. Obviously, this is a strong asset for the study of thin epitaxial films, whose structure might be distorted.

To summarize, EXAFS is sensitive to the crystallographic structure of a solid. Contrary to diffraction, it doesn't require a long range order. The photoelectron having a small mean free path, it will only probe the first four or five nearest neighour shells. EXAFS can then be used on powders or polycrystals, and even on amorphous materials, where one can determine radial distribution functions (including their possible anisotropy) [START_REF] Magnan | Determination of the local order in amorphous cobalt films[END_REF].

The main strength of EXAFS is its element-selectivity. By working at one edge of an element, one is sensitive only to the environment of this element in the solid. Indeed, the probe is the photoelectron emitted by the excited atom. We will later use this elementselectivity to probe the crystallographic structure of a thin film deposited on a substrate.

Last, the incident photon polarisation can be used to select the bond directions contributing to the signal. This is useful in distorted structures like in epitaxially grown thin films, but also, generally speaking, in any structures where the three crystallographic axis are not equivalent.

Data analysis -Which information in the EXAFS oscillations ?

In their paper describing the EXAFS oscillations, Stern et al. also gave a method to extract the structural information from the EXAFS oscillations [START_REF] Sayers | New Technique for Investigating Noncrystalline Structures : Fourier Analysis of the Extended X-Ray Absorption Fine Structure[END_REF]. The beginning of data analysis is described in figure 2.4.

First, one needs to extract χ(k) from the raw absorption spectrum. χ(k) is defined as

χ(k) = µ -µ 0 µ 0 (2.3)
where µ is the absorption coefficient and µ 0 is the atomic absorption, i.e. without any atoms around the absorbing atom. µ 0 is determined by a polynomial fit of the EXAFS oscillations, and χ(k) is calculated as

χ(k) = µ -µ 0 J (2.4)
where J is the edge jump (see figure 2.4(c)). Since χ(k) is a sum of sinus functions, a Fourier transform gives a series of peaks roughly at the positions of the different neighbour shells (see figure 2.5). An inverse Fourier transform of the first peak of the Fourier transform allows to extract the contribution of the first nearest neighbour shell to the EXAFS signal, i.e. the first term of the sum in the χ(k) formula 2.1 (See figure 2.6). One can perform a fit of this inverse Fourier transform using the formula

χ 1 (k) = - N * 1 kR 2 1 e -k 2 σ 2 1 e -2R 1 /λ B 1 (k) sin(2kR 1 + φ 1 (k)) (2.5)
and R 1 , N * 1 and σ 1 as free parameters. In a 3d element like cobalt in its metallic form, the oscillations are large as compared to the edge jump and can be seen on a very large photon energy range (typically 700 eV). R 1 is thus determined with an accuracy of 0.01 Å, whereas the accuracy on N * 1 is roughly 10%. The value of the Debye-Waller factor σ 1 is also given by the fit. We won't discuss much this quantity in this dissertation, but it can be used for different purposes. It contains both a contribution from static disorder in the solid and a contribution from atomic vibrations [START_REF] Roubin | Experimental and Theoretical Evidence for a Strong Anisotropy of the Surface Debye-Waller Factor as Determined for a Monolayer of Cobalt on Copper (111) by Surface Extended X-Ray-Absorption Fine Structure[END_REF]. The disorder contribution can be inferred from an EXAFS spectrum recorded at a temperature sufficiently low to neglect the phonons (i.e. well below the Debye temperature of the considered material).

The phonon contribution can be studied by considering two spectra recorded at low (77 K) and room temperature (300 K). As described in figure 2.7, the amplitude

A (k) = e -k 2 σ 2 1 e -2R 1 /λ B 1 (k) is extracted from both spectra.
When plotted as function of k 2 , the logarithm of the ratio give a straight line whose slope -2∆σ 2 , and ∆σ 2 = σ(300K) -σ(77K) can be determined by a fit. Light polarisation allows to characterise the bond stiffness in the different crystal directions and/or an anisotropy of the vibrational properties [START_REF] Roubin | Experimental and Theoretical Evidence for a Strong Anisotropy of the Surface Debye-Waller Factor as Determined for a Monolayer of Cobalt on Copper (111) by Surface Extended X-Ray-Absorption Fine Structure[END_REF].

Single scattering and multiple scattering

As indicated above, the EXAFS formula is derived making the assumption that the electronic wavefunction of the photoelectron is only scattered once before it comes back to the absorbing atom ; this is the so-called single scattering approximation. To better understand when it is justified or not, the EXAFS oscillations can be described by a generalized form of formula 2.1.

In formula 2.1, each sinus oscillates with a frequency 2R i , where R i is the distance between the excited atom and the i th shell of neighbours. 2R i therefore represents the length of the single-scattering path of the electronic wave, after a round trip between the excited atom and the i th shell (see figure 2.8).

In a generalized formula, the sum would run over all the possible scattering path of length D, each scattering path contribution being a sinus oscillating with a frequency D.

Hence, the first peak of the Fourier transform is due to the shortest possible scattering path, whose length is 2R 1 , a single scattering path involving the first nearest neighbour shell. It is thus perfectly correct to interpret this peak within the single scattering approximation. This peak being the most intense in the Fourier transform, this first nearest neighbour shell contribution represents the main part of the EXAFS signal. For the distant peaks of the Fourier transform, these single scattering path contributions can be mixed with multiple scatterring path involving several neighbours shell (see figure 2.8), and a complete interpretation requires to take them all into account using dedicated programs.

Surface EXAFS

Surface EXAFS is a simple EXAFS experiment, but done in ultra-high vacuum at the edge of an element deposited as a thin film on a substrate. Hence, using the elementselectivity of X-ray absorption, only the environment of the deposited atoms is probed. X-ray absorption is not intrinsically a surface sensitive technique ; at a K-edge of a 3d-element, one uses 3 to 10 keV photons, whose penetration depth in matter is of the order of some micrometers, i.e. much larger than the thickness of some atomic layers which is of the order of some angströms. Surface EXAFS takes advantage of the chemical selectivity of X-ray absorption measurements to study the first atomic layers of a system made of a thin film on a substrate.

Apart from the ultra-high vacuum environment, another specificity of SEXAFS is the detection mode to be used for the measurements. In a classical XAS experiment, the X-ray absorption coefficient is obtained in the transmission mode, which consists in measuring the photon flux before (I 0 ) and after the sample (I). µ is then given by

χ(k) = 1 d ln( I 0 I ) (2.6)
where d is the thickness of the sample, which has to be of the order of some micrometers. This detection mode is not adapted for SEXAFS. First, the substrate is often a single crystal with a thickness of the order of 1 mm, too thick for a transmission experiment. Moreover, even if the substrate is thin enough, the contribution of the thin film to the absorption coefficient would be drowned in the total signal, the substrate being orders of magnitude thicker.

For SEXAFS measurements, more surface-sensistive detection modes have to be used, like total electron yield (the total number of electrons emitted by the sample) or fluorescence yield (the intensity of a fluorescence line of the adsorbate). Total electron yield is an easy to implement method (a connexion to the sample to measure the drain current or a simple channeltron placed in front of the sample provide high count rates) and probes a depth of the order of 100 Å. The signal due to the thin film is therefore superimposed on a background due to the absorption of the substrate (see figure 2.9). Depending on the film thickness and on the respective absorption cross section of the substrate and the adsorbate, the signal to background ratio changes, and this detection mode is usable as Figure 2.9 -The total electron yield detection mode probes around L=100 Å of the sample constituted by the thin film and the substrate (left). They both contribute to the signal : the substrate contribution gives a monotonous background whereas the thin film contribution is the signal of interest. Depending on the respective absorption cross sections of the two elements (here Co and Cu) and on the film thickness, the signal to background ratio varies, but has to be larger than 10-20%. long as it is larger than 10-20%. If it is smaller, one has to turn to fluorescence detection. The signal to background ratio is nearly ideal, since one measures a signal coming purely from the thin film, but the detector is more expensive and more difficult to handle (with, in particular, limited count rates).

in the following section, Surface EXAFS will be used for the study of thin Co films deposited on Cu(001) and Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF].

Thin cobalt films on Cu(001)

Introduction

Metastable films of cobalt grown on Cu(001) were the subject of many magnetic and structural studies. Angle-resolved X-ray photoemission scattering [START_REF] Li | Structure and growth mode of metastable fcc cobalt ultrathin films on Cu(001) as determined by angle-resolved x-ray photoemission scattering[END_REF], X-ray diffraction [START_REF] Ferrer | Epitaxial submonolayer cobalt films on Cu(100) studied by X-ray diffraction[END_REF] or in situ STM experiments [START_REF] Schneider | Spin-and angle-resolved photoemission from single crystals and epitaxial films using circularly polarized synchrotron radiation[END_REF] showed that cobalt grew to a well ordered fcc(001) film via a layer-by-layer growth mode, except for the first two layers. The films are always ferromagnetic [START_REF] Pescia | Ferromagnetism of thin epitaxial fcc cobalt films on Cu(001) obesrved by spinpolarized photoemission[END_REF], independent of the film thickness, and the remanent magnetization is always parallel to the interface, with a strong in-plane anisotropy : the [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF] direction is the easy axis [START_REF] Schneider | Curie temperature of ultrathin films of fcc-cobalt epitaxially grown on atomically flat Cu(100) surfaces[END_REF][START_REF] Heinrich | Magnetic anisotropies and exchange coupling in ultrathin fcc Co(001) structures[END_REF][START_REF] Krams | Magnetic anisotropies of ultrathin Co(001) films on Cu(001)[END_REF]. The Curie temperature of films evaporated at 450 K is strongly increasing with the film thickness from 130 K for 1.5 ML to 500 K for 2.5 ML [START_REF] Schneider | Spin-and angle-resolved photoemission from single crystals and epitaxial films using circularly polarized synchrotron radiation[END_REF].

The interpretation of the photoemission spectra [START_REF] Schneider | Spin-resolved electronic bands of FCT cobalt[END_REF] and of the magnetic properties [START_REF] Heinrich | Magnetic anisotropies and exchange coupling in ultrathin fcc Co(001) structures[END_REF] is often made assuming a tetragonal distortion of the structure. But the supposed tetragonalization has not been precisely measured for the whole Co film and for different Co-thicknesses. Quantitative analysis of the intensity of Low-Energy Electron Diffraction (LEED) spots is the only surface sensitive crystallographic technique which had been used to give the lattice spacing perpendicular to the surface : it indicates that cobalt epitaxially grows on Cu(001) in a tetragonal structure [START_REF] Clarke | A LEED determination of the structure of cobalt overlayers grown on a single-crystal Cu(001) substrate[END_REF]. But the sensitivity of LEED decreases very quickly with depth : it characterises the first two or three surface layers and the information in the direction perpendicular to the interface is indirect, since it requires a full electron multiple scattering calculation of the intensity variations of the LEED spots as a function of the incident electron energy (I(V ) measurements).

Surface EXAFS is a very attractive technique to measure the crystallographic structure of metastable thin films. As explained above, it is a selective method : by measuring the EXAFS oscillations above the K-edge of cobalt, the measurement will be sensitive only to the local order in the cobalt film, and, thanks to the large X-ray penetration depth in matter, each layer of the film gives the same contribution to the total signal. Then, films of any thickness, coated films and multilayers can be characterised with the same accuracy.

Surface EXAFS is a local atomic structure probe, and cannot solve alone a complete crystallographic structure : it is complementary to long-range order diffraction techniques like LEED. However, by performing a Fourier transform (FT) of an EXAFS spectrum, one can separate the contribution of the different shells of neighbours of the absorbing atom, each shell giving a well defined peak in the FT. The relative intensities of the different shells of neighbours are characteristic of a crystallographic structure : fcc, bcc or hexagonal close packed (hcp) structures can be identified unambiguously (see figure 2.10). Moreover, in systems where one can expect a structural anisotropy, the linear polarisation of the synchrotron radiation is used to isolate the contributions to the EXAFS signal of the bonds in different directions.

This section is organized as follows. In subsection 2 the experimental procedure is described. In subsection 3, experimental results deduced from a quantitative first shell analysis of the polarisation dependent EXAFS spectra are presented. In subsection 4, we present how we introduce a polarisation dependence in a multiple scattering calculation using the FEFF code to simulate EXAFS results on a cobalt single-crystal and on our cobalt films grown on Cu(001).

Experimental conditions

The EXAFS experiments were performed at the Laboratoire pour l'Utilisation du Rayonnement Electromagnétique (LURE) on the Surface EXAFS set-up, using a Si(311) double-crystal monochromator installed on the wiggler beamline of the DCI storage ring. The Cu(001) surface is prepared by argon ionic bombardment of the crystal maintained at about 500 • C. The crystallographic quality of the surface is checked by LEED and its cleanliness by Auger spectroscopy. The Co/Cu(001) films are prepared in a UHV chamber connected to the X-ray beamline. Cobalt is evaporated from a high-purity wire heated by electron bombardment in a vacuum better than 5×10 -10 mbar (base pressure is 2×10 -10 mbar). It is deposited at a rate of about 1 monolayer per minute on a clean Cu(001) surface. The films are grown at room temperature. The evaporation rate is calibrated prior to the evaporation with a quartz microbalance. The thickness of the film is controlled by Auger spectroscopy and by measuring the X-ray absorption edge jump of the sample at the K-edge of cobalt. Using this calibration, we estimate the thickness of the grown film with an accuracy of 10%. The local atomic structure of the films is then studied in situ.

We will only discuss here the EXAFS measurements performed on samples maintained at 77 K in order to reduce the thermal disorder and improve the precision of the crystallographic characterisation of the cobalt films. The variations of the X-ray absorption coefficient of the samples are measured above the K-edge of cobalt (7709 eV) in the total yield mode, which, for this system, gives better results than fluorescence detection. Due to the two-dimensional character of thin films, we can expect nearest-neighbour (nn) bonds of different length, depending if they are in-plane bonds (parallel to the interface plane) or out-of-plane bonds (see figure 2.11). The linear polarisation of the synchrotron radiation allows to separate these two contributions since the contribution of each bond is weighted by a factor cos 2 α, where α is the angle between the bond and the polarisation direction of the X-rays (see formula 2.2). For each film, EXAFS spectra are recorded both in normal incidence of the X-rays (electric field of the X-rays parallel to the surface) and in grazing incidence (electric field is about 20 • from the surface normal).

Analysis of the first nearest neighbour shell

Some raw EXAFS spectra of cobalt films are reproduced on figure 2.12. On figure 2.12(a), we directly see the tetragonal distortion of the 3 ML thick film : the frequency of the main EXAFS oscillations is higher in normal incidence than in grazing incidence which means a longer nn distance for intralayer bonds. On the other hand, on figure 2.12(a), we clearly see that in normal incidence, the frequency of the EXAFS oscillations is the same for a 3 and an 8 ML thick film. The anisotropy is also clear on the Fourier transforms of the EXAFS spectra of the 3 and 15 ML thick films which are shown on figure 2.13 in normal incidence. The position of the different shells of neighbours is similar to what is found for a well ordered fcc structure but the intensity of the fourth peak is reduced, and, in grazing incidence, both the second and the fourth peak are shifted to the shorter distances.

We first extract information from the first peak of the FT. It is done using a single scattering formalism since the multiple scattering contributions appear at larger distances. The FT spectra were filtered in real space to isolate the first peak and finally backtransformed in k-space. Quantitative analysis of this first shell contribution to the EXAFS data is done using the general formula giving the EXAFS modulation function, χ, in the plane wave approximation, in the case of a linear polarised light and for a K-edge (see formula 2.5).

In our case, the situation could be more complicated, since we are dealing with an epitaxial system whose structure might be distorted. If we assume a perfect fcc epitaxy, every cobalt atom has four nn in its plane, four above (missing for the top layer) and four below (See figure 2.11). When the polarisation of the light is perpendicular to the surface (grazing incidence) only the interlayer bonds contribute to the EXAFS signal (the intralayer bonds being perpendicular to the polarisation, the cos 2 α in formula 2.2 are all zero) but in normal incidence (polarisation parallel to the surface) both interlayer bonds and intralayer bonds are contributing with the same weight.

For each sample, we therefore begin by a fitting of the grazing incidence spectrum assuming a single shell of neighbours, since only the interlayer bonds give a significant contribution. The backscattering amplitude B 1 (k) (including the mean free path damping term) and phase shift φ 1 (k) amplitude are determined experimentally from reference EXAFS spectra measured on bulk cobalt at 77 K. The first shell radial distribution function Gaussian parameters are then obtained by a least-mean-square fitting of these spectra using equation 2.5. The free parameters are the number of neighbours, the mean nn distance and the Debye-Waller factor. For all the samples, the number of neighbours deduced from the experiment is very close to the effective coordination numbers calculated for a perfect epitaxial fcc thin film of the same thickness. The out-of-plane nn distance R out is 2.50 (±0.01) Å in all the samples with a low static disorder.

Then, the fitting procedure is applied to the normal incidence spectra where both intralayer and interlayer bonds contribute with about the same weight. The formula takes therefore the two R out and R in (in-plane nn distance) distances into account :

χ 1 (k) = - N * out kR 2 1 e -k 2 σ 2 out e -2Rout/λ B 1 (k) sin(2kR out + φ 1 (k)) (2.7) + N * in kR 2 1 e -k 2 σ 2 in e -2R in /λ B 1 (k) sin(2kR in + φ 1 (k))
The effective coordination number of each type of bond is fixed to its value calculated assuming a perfect fcc epitaxy of the film, as well as the interlayer bond length and Debye-Waller factors determined from the analysis of the grazing incidence spectrum. Then, in the fitting procedure, the free parameters are just the nn intralayer bond length and its associated Debye-Waller factor. For all the samples, we measure an intralayer nn distance of 2.55 (±0.01) Å with a quite low static disorder. The agreement between the experimental inverse Fourier transform spectrum and its simulation with the results of the fitting procedure is presented on figure 2.14 for the 15 monolayers thick film. For all the samples, the in-plane nn distance is 2.55 (±0.01) Å which is exactly the nn distance in bulk copper, and the out-of plane nn distance is 2.50 (±0.01) Å. So the tetragonal deformation of the films appears to be an expansion of the fcc crystal parallel to the interface to adapt exactly the in-plane nn distance of the film to the substrate one. These values give an in-plane lattice parameter a // = 3.61 ± 0.02 Åand an out-of plane lattice parameter a ⊥ = 3.46 ± 0.02 Å. The lattice parameter perpendicular to the interface is contracted by 4% with respect to the parallel one. This tetragonal deformation is the same for all the thicknesses up to 15 ML. If we assume a perfect cobalt fcc lattice built using the first nn distance in bulk cobalt (a=3.543 Å), an analysis of these results in a simple elastic model demonstrates that out-of plane contraction of the lattice parameter is a direct consequence of the in-plane expansion of a due the epitaxy on the Cu-substrate [START_REF] Heckmann | Crystallographic structure of cobalt films on Cu(100) : elastic deformation to a tetragonal structure[END_REF].

The tetragonal deformation is therefore the elastic accommodation of the film to the lateral strain induced by the epitaxy on the monocrystal of copper. This distortion means that there is an evident loss of symmetry : there is no more [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] symmetry axis. All the films are well ordered, and their elastic properties are neither strongly anisotropic, nor very different from those of bulk cobalt, coherent with the fact that the deformation is elastic. The constant magnetic properties measured in these films (always ferromagnetic and in-plane easy axis) are certainly due to this unique structure.

Multiple scattering simulations

In the previous section, we did a quantitative analysis of the contribution to the EXAFS signal due to the first nearest neighbours. We measured a nearest-neighbour distance longer for intralayer bonds (parallel to the interface) than for interlayer ones, resulting in a tetragonalization of a fcc structure.

In the FT of the EXAFS spectra, there are well defined peaks up to a distance of 6 Å ; they are due to single scattering on neighbours up to the sixth shell and to multiple scattering with paths of the same lengths. The position and intensity of these FT peaks are very sensitive to the structure : we shall confirm (or not) the tetragonal fcc structure of the films, if we are able (or not) to reproduce them on EXAFS data calculated using a multiple-scattering formalism. In particular, the experimental Fourier transforms are strongly anisotropic (see figure 2.13). Can this anisotropy be reproduced only considering the tetragonalization that we deduced from the first shell analysis ?

To simulate correctly the shape of an EXAFS spectrum FT up to 6 Å, we used the FEFF code developed by Rehr, Zabinsky and Albers (version 5.04) [START_REF] Rehr | Theoretical X-ray absorption fine structure standards[END_REF][START_REF] Mustre De Leon | Ab initio curvedwave X-ray-absorption fine structure[END_REF][START_REF] Rehr | High-order multiple-scattering calculations of X-ray-absorption fine structure[END_REF]. This program was first successfully tested on bulk cobalt, using the following structural parameters : a=2.51 Å and c=4.07 Å (see figure 2.15). The Fourier transforms of the calculated EXAFS spectra are plotted for the polarisation either parallel to a or c. The We then calculated with the same method the polarisation dependent EXAFS spectra of the Co/Cu(001) films, assuming that they had a face-centered tetragonal (fct) structure. To test the sensitivity of the method to the amplitude of the distortion, we tried different tetragonalizations. The results for three different structures, where the mean value of the nn distance is always 2.53 Å, are presented on figure 2.16 :

-"t1" is a fcc crystal with a lattice parameter a=3.58 Å, which means a nn distance R=2.53 Å. -"t2" is a fct crystal with lattice parameters a =3.62 Åand a ⊥ =3.45 Å,which means nn distances R in =2.56 Å and R out =2.50 Å. -"t3" is a fct crystal with lattice parameters a =3.64 Åand a ⊥ =3.37 Å,which means nn distances R in =2.58 Å and R out =2.48 Å. We then compare the FEFF simulations with the experimental FT for Co/Cu(001) films. Since the simulations are made for bulk crystals without surfaces, we consider the experimental results on the thickest 15 ML film. The best agreement is obtained for the "t2" structure, as shown on the lower part of figure 2.16. The FEFF calculations reproduce very well most of the positions, intensities and polarisation dependence of the different peaks. The results of the FEFF simulations agree with the first shell analysis : the structure "t2" gives values for the first-neighbour distances R in =2.56 Å and R out =2.50 Å, very close to those found with the first shell analysis, R in =2.55 Å and R out =2.50 Å.

Conclusion

In this section, we have studied the local order in thin cobalt films of different thicknesses grown on Cu(001) by Surface EXAFS. The analysis of the first nearest neighbour shell shows that all the films, from 2 to 15 ML, have the same fcc tetragonalized structure. The first nearest neighbour distances are 2.55 Å for bonds lying in planes parallel to the interface, and 2.50 Å for bonds out of these planes. That leads to lattice parameters of a = 3.61 Å parallel to the interface, and a ⊥ = 3.46 ± 0.02 Å perpendicular to the interface. Assuming a "fcc cobalt" with an nn distance of 2.505 Å, this tetragonal distortion is an elastic accommodation to the strain imposed by the copper substrate, which has a nn distance of 2.55 Å. This lateral expansion induces a contraction along the surface normal. The experimental measurement of this deformation is in very good agreement with that predicted by the continuum elastic theory [START_REF] Heckmann | Crystallographic structure of cobalt films on Cu(100) : elastic deformation to a tetragonal structure[END_REF]. Multiple scattering calculations of the EXAFS data using the FEFF code confirm the lattice parameters extracted from the first shell analysis. In systems like Fe/Cu(001), the magnetic properties of the iron films strongly depend on their thicknesses and on their growth temperature : it was shown that their crystallographic structure was changing with these parameters. The constant magnetic properties measured in the cobalt films grown on Cu(001) are certainly due to the unique structure of these films, not depending on their thickness.

2.4 Adsorption site, growth and structure of thin cobalt films on Cu(111)

Introduction

Since the discovery of giant magnetoresistance in Fe/Cr multilayers [START_REF] Baibich | Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices[END_REF], numerous systems have been tested in the quest of the maximum variation of the electrical resistance when applying a magnetic field. The Co/Cu system was studied both with the (001) [START_REF] Cebollada | Antiferromagnetic ordering in Co-Cu single-crystal superlattices[END_REF] and the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] orientations [START_REF] Parkin | Oscillatory magnetic exchange coupling through thin copper layers[END_REF][START_REF] Harp | Growth temperature dependence of magnetoresistance in Co/Cu(111) wedged superlattices[END_REF][START_REF] Mosca | Oscillatory interlayer coupling and giant magnetoresistance in Co/Cu multilayers[END_REF]. In the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] orientation, at least in samples made by sputtering, magnetoresistance values of the order of 115% were measured at 4 K [START_REF] Parkin | Giant magnetoresistance in antiferromagnetic Co/Cu multilayers[END_REF], comparable to what was obtained on the pioneering Fe/Cr system.

On Cu(100), we showed that cobalt is in perfect epitaxy on copper in a tetragonal facecentered structure. From the structural point of view, the problem is different on Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] since the symmetry of the fcc Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] surface is that of the hcp Co(0001) surface. The structure of the deposited cobalt film can therefore be either fcc or hcp, the difference between the two structures lying only in the stacking sequence of the hexagonal planes, ABCABC sequence for fcc and ABAB for hcp (see figure 2.17).

Many papers were already devoted to the study of the structure and growth mode of these films. Concerning the stacking sequence, from X-ray photoelectron diffraction (XPD) studies, Scheuch et al. [START_REF] Scheuch | Investigation of the growth of Co on Cu(111) and Sb/Cu(111) using photoelectron forward scattering[END_REF] thought that the Co atoms start to grow in a fcc stacking untwinned with the substrate (ABCabc, where the upper case letters denote the Cu substrate, and the lowercase ones the Co layers), while de la Figuera et al. interpreted their scanning tunneling microscopy (STM) data as evidence for the existence of twinned fcc crystallites ( ABCabc and ABCbac) [START_REF] De La Figuera | Scanning-tunnelingmicroscopy study of the growth of cobalt on Cu(111)[END_REF]. But up to our SEXAFS study, the adsorption site of the first layer remained unknown. All the diffraction studies showed a sixfold symmetry for films thicker than 3 or 4 ML. This can be interpreted either as two twinned fcc structures or as a hcp structure. EXAFS, which is sensitive only to the local order, can solve this controversy.

fcc and hcp structures are quite similar as they both consist in stacking of hexagonal atomic planes. The differences observed in the EXAFS oscillations between the two structures could be subtle but a careful analysis should allow to distinguish between the two stacking sequences. In a fcc local environment, the first and the fourth neighbours are aligned and give the well-known focusing effect (see bottom part of figure 2.18). Its origin are the numerous scattering paths involving those aligned atoms which have all the same total length. This results in a high intensity peak in the Fourier transform of the EXAFS spectrum at the position of the fourth neighbour shell. In a hcp environment, this focusing effect exists only in the hexagonal planes. Thus, at the EXAFS scale, twinned fcc crystallites will look like bulk fcc, while hcp crystallites will look like bulk hcp.

In this Surface EXAFS study of thin cobalt films deposited on Cu(111), we will extensively use multiple-scattering (MS) analysis of the data to extract even more details on the cobalt growth. An original result will be to unambiguously establish that, at the very early stages of growth, the cobalt atoms are mainly adsorbed on fcc continuation sites (ABCa). Quantitative simulations of the X-ray absorption spectra including higher shell contributions will allows us to identify the stacking sequence as the thickness of the film increases.

Experimental conditions

The experiments were performed at the Laboratoire pour l'Utilisation du Rayonnement Electromagnetique, on the surface EXAFS setup installed on the wiggler beam line of DCI storage ring, using a Si(311) double crystal monochromator. The Co is deposited at room temperature on a clean Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] single crystal in ultrahigh vacuum. Preparation and control of the substrate, as well as the cobalt deposition technique and the determination of the film thickness were done the same way as for the study of Co/Cu(001).

The EXAFS spectra χ(k) are recorded in situ at the Co K-edge (7710 eV) in the fluorescence yield mode. During the measurements, the sample is maintained at 77 K in order to reduce the thermal disorder. We have studied films from 0.5 to 8 ML. As for the study of Co/Cu(001), spectra were recorded both in normal (polarisation of the X-rays parallel to the surface) and grazing incidence (polarisation of the X-rays is about 20 • from the surface normal) (NI and GI).

Analysis of the first-nearest neighbour shell

The angular dependence of the EXAFS signal is used once again to determine separately the lengths of the in-plane and out-of-plane bonds. Whatever the stacking is on the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] surface (hcp or fcc), each Co atom has six nearest neighbours in its plane, three above (missing for the top layer) and three below (see figure 2.17). Then, concerning the first shell of neighbours, in GI only the bonds out of the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] planes (interlayer bonds) are contributing to the EXAFS signal, while in NI, the bonds parallel to the (111) planes (intralayer bonds) have a weight three times larger than the out-of-planes ones.

The frequency of the main EXAFS oscillation is the nn distance. From the raw data presented on figure 2.19, it is clear that the NI spectrum oscillates faster than the GI one, denoting an intralayer bond longer than the interlayer one.

The first nn distances are extracted using the same procedure as for the Co/Cu(001) study. The interlayer bond length is determined from the GI spectrum, and the result is injected in the fit of the NI spectrum to determine the intralayer bond length. For all the Co thicknesses, the in-plane nn distance is 2.54 (±0.01) Å, the out-of-plane nn distance is 2.50 (±0.01) Å and the static disorder at 77 K is very similar to its value in bulk cobalt. The Cu substrate, which has a nn distance of 2.55 Å, forces the Co atoms to adopt parallel to the interface a larger in-plane parameter than in bulk Co. This distortion does not vary when the film thickness increases up to 8 ML.

Adsorption site and stacking period determined by multiple scattering calculations

As noted before, it is impossible to determine the stacking of the Co films from the analysis of the first shell. In the FT of the EXAFS spectra (see, e.g., figure 2.20) we can see well-defined peaks up to a distance of 6 Å. As in the Co/Cu(001) study, they are due to single scatterings involving neighbours located at larger distances, but also to multiple scattering phenomena. Among these multiple scattering contributions, the most important ones are those concerning three aligned atoms. In particular, in an fcc structure, each first neighbour at a distance R of the central atom is aligned with a fourth neighbour at a distance 2R of this central atom. These alignments enhance the intensity of the fourth peak in the FT, both in NI and GI. In a hcp structure, these alignments still exist in the (0001) planes, but are lost out of these planes. It causes an absence of focusing in GI, and gives the strong polarisation dependence of the fourth peak in the FT of bulk hcp cobalt (see figure 2.15). It should therefore be possible to conclude on the structure of the cobalt films, fcc or hcp, by measuring the polarisation dependence of the EXAFS spectra and comparing it to simulations involving multiple scattering phenomena.

We did the calculations using the FEFF code (Version 6) [START_REF] Rehr | Theoretical X-ray absorption fine structure standards[END_REF][START_REF] Mustre De Leon | Ab initio curvedwave X-ray-absorption fine structure[END_REF][START_REF] Rehr | High-order multiple-scattering calculations of X-ray-absorption fine structure[END_REF], considering the single-, double-, and triple-scattering processes. The only free parameter is the amplitude reduction factor S 0 (it is between 0.65 and 0.80), the Debye temperature being fixed to its bulk value (445 K for Co and 343 K for Cu). We first consider the 8 ML-thick film. The first-shell analysis has determined that the Co in-plane nn distance is 2.54 (±0.01) Å and the out-of-plane one is 2.50 (±0.01) Å. The Co crystals constructed for the FEFF calculation with the two stacking sequences (distorted hcp and distorted fcc) are supposed in perfect epitaxy on Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] with an in-plane nn distance of 2.55 Å and an out-of-plane nn distance of 2.50 Å.

As expected, the NI calculations are very similar for the two simulations and well reproduce the NI experimental data (they are both very similar to the NI spectra presented further for the 3 ML-thick film). On the other hand, in GI, there is a dramatic decrease of the high distant peaks of the FT for the distorted hcp simulation as compared to the distorted fcc one. These results are presented in figure 2.20 and compared to the experiment. Unambiguously, the distorted hcp simulation fits much better the experiment. We cannot exclude the presence of some "defects" with local fcc stacking, but we can say that they represent less than 20% of the total signal. We did also calculations on a non-distorted hcp Co : the FT is in disagreement with the experiment. This multishell analysis therefore confirms the first-shell analysis, i.e., the non-isotropic shape of the nn shell, and demonstrates clearly that an 8 ML film has already a mainly hcp structure, a result in agreement with XPD measurements [START_REF] Scheuch | Investigation of the growth of Co on Cu(111) and Sb/Cu(111) using photoelectron forward scattering[END_REF].

The X-ray Absorption Near-Edge Structure (XANES) are also very sensitive to the local structure and to the polarisation effects. The XANES spectra of fcc Cu are isotropic and present two bumps in the region from 10 to 20 eV above the edge, while for an hcp cobalt single crystal with a (0001) free surface, there are two bumps in NI, but only one bump in GI (figure 2.21(a)). These results are totally expected since in the hcp structure, the full point group (D 6h ) confers to the electric dipole K-edge absorption cross section a dichroic dependence, whereas in the fcc structure, i.e., in a cubic symmetry (O h ), the electric dipole absorption cross section is isotropic. Convergence of the cluster size (about 200 atoms) has been thoroughly checked for both structures. The accuracy of the FEFF6 code in the XANES region for such edges is demonstrated in figure 2.21 : the XANES spectra anisotropy measured on a bulk hcp Co(0001) is very well reproduced by the calculation, with the two bumps in NI, and only one in GI. The experimental spectra on the 8 ML-thick film present the same anisotropy, confirming the hcp stacking in this film.

What happens now at the very beginning of the Co growth ? Cu is fcc, and has a ABCABC stacking sequence of the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] planes. If we assume that the surface plane is of C type, the first deposited Co atoms can be located either on A sites ("fcc sites") or on B sites ("hcp sites"). In a fcc site, a cobalt adatom will have its fourth Cu neighbour aligned Finally, the study of a 3 ML-thick film is of great interest, since we have established that the first Co layer was adsorbed on fcc sites, but also that, at high coverage, the structure is mainly hcp. What is the stacking at this intermediate thickness ? Starting on a C surface and the first layer on the A site, the stacking can be ABCabc (fcc stacking type) or ABCaba or ABCaca (hcp stacking types). We proceeded the same way as for the study of the adsorption site by comparing FEFF6 simulations on 3 ML of Co/Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] with experiment. The crystals are constructed again with an in-plane nn distance of 2.55 Å (for Co-Co and Cu-Cu) and out-of-plane nn distances of 2.50 Å (for Co-Co and Co-Cu) and 2.55 Å (for Cu-Cu). For each configuration, a total absorption spectrum is the average of three calculations with the absorbing atom on each different Co layer. The FT of the results for both NI and GI are presented in 2.23, together with the FT of the spectra recorded on a 3 ML-thick film. In NI, the agreement between calculation and experiment is very good and quite independent of the stacking sequence. In GI, the positions of the peaks are well reproduced by the three simulations, but the relative intensities are better reproduced by the ABCaba simulation. Other stacking sequences like ABCbcb and ABCbab give simulations with very small high distant peak clearly different form the experiment.

To confirm the aba stacking, we have compared the XANES spectra of the different simulations. As can be seen on figure 2.21, the experimental spectra recorded on the 3 ML film present a clear anisotropy, with two bumps in NI and mainly one in GI, while the XANES of a 1.5 ML film is isotropic. The anisotropy measured on the 3 ML film is only described by the ABCaba simulation, whereas the XANES of the ABCabc simulation is nearly isotropic with two bumps in the two incidences, and looks more alike the fcc Cu ones. Here also, the XANES spectra confirm the result of the EXAFS multishell analysis. Both the 0.5 ML and the 1.5 ML-thick films have two bumps in the XANES region in the NI and in the GI : this is the signature of fcc continuation sites for the two first layers. The 3 ML film has anisotropic XANES spectra well reproduced assuming a third layer in hcp sites.

Conclusion

We found that thin Co films are in epitaxy on Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] and that, for all the thicknesses, they have a distorted structure with in-plane nn distances of 2.54 Å very close to the Cu one, and out-of-plane nn distances of 2.50 Å. A polarisation-dependent of both EXAFS and XANES data allows us to determine the Co first location on the Cu surface and the structure of the films. This result shows that, while cobalt adopts the fcc structure of copper on a (100) surface (which has a square two-dimensional symmetry not existing in hcp structures), cobalt grows with its own hcp bulk structure on the (111) copper surface, the sixfold symmetry of the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] fcc surface becoming the (0001) basal plane of the cobalt film. The hcp stacking starts at the third deposited layer, as soon as the Co has to choose between the fcc and the hcp structure.

Conclusion

In this section, we showed that SEXAFS was a useful tool for the structural characterisation of thin epitaxial films. We used it for the study of thin cobalt films, deposited on Cu(001) and Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF]. In these systems, the first nn distance can be measured with an accuracy of 0.01 Å, and the linear polarisation of the synchrotron radiation, used as a photon source, allows to probe possible distortions of the unit cell due to the epitaxial stress. Moreover, multiple scattering simulations of the experimental data makes it possible to extract even more precise details about the structure, the adsorption site or stacking period of the deposited atomic planes, pieces of information which are only accessible if one can go further than the first nn shell in the interpretation. At this time, we used versions 5 (Co/Cu(001)) and 6 (Co/Cu(111)) of FEFF. Since these studies, the program evolved a lot and now includes a full multiple scattering calculation method, i.e. an exact calculation of the absorption coefficient where older versions of FEFF used only a limited number of scattering processes [START_REF] Rehr | Parameter-free calculations of X-ray spectra with FEFF9[END_REF]. It now also goes beyond the muffin-tin approximation. Using FEFF, one can calculate angular momentum projected densities of states, X-ray emission spectra and X-ray scattering amplitudes, as well as results from other spectroscopies like Electron Energy Loss Spectra (EELS) and Non-Resonant Inelastic X-ray Scattering (NRIXS).

In the systems studied here, it is fair to say that we were finaly more interested in pushing the limits of the experimental technique we were using, Surface EXAFS, for the study of epitaxial thin films. In this prospect, we even worked on the polarisation dependence of the EXAFS signal at the L 2,3 edges, where the EXAFS formula is more complicated, since one has to take into account the two p → s and p → d excitation channels for the photoelectron [START_REF] Le Fèvre | X-ray absorption at the L 2,3 edge of an anisotropic single crystal : Cadmium (0001)[END_REF]. Nevertheless, the highlighted motivation was to correlate structure and magnetic properties, and there are systems, like Fe/Cu(001) [START_REF] Magnan | Structure of thin metastable epitaxial Fe films on Cu(100) : Reconstruction and interface ordering by coating[END_REF], Fe-films patterned into stripes by the so-called "atomic-saw method" (a compression of the substrate induces dislocations cuting the deposited film) [START_REF] Jaffrès | Anisotropy in metallic thin films patterned by the atomic saw method[END_REF][START_REF] Jaffrès | Correlation between magnetism and structural relaxation in thin Fe(001) films patterned by the atomic saw method[END_REF] or cobalt films deposited on vicinal Cu-surfaces [START_REF] Chaumin-Midoir | Structure and morphology of thin cobalt films deposited on vicinal surface Cu(1 1 11)[END_REF][START_REF] Chaumin-Midoir | Magnetism, structure and morphology of thin cobalt films deposited on Cu(115)[END_REF][START_REF] Chaumin-Midoir | Crystallographic structure and morphology of cobalt films on Cu(1 1 11)[END_REF] where the relationship was clearly established by SEXAFS maesurements.

The results presented here were mainly published in references [START_REF] Heckmann | Crystallographic structure of cobalt films on Cu(100) : elastic deformation to a tetragonal structure[END_REF] for Co/Cu(001) and [START_REF] Le Fèvre | Adsorption site, growth, and structure of Co on Cu(111) determined by multiple-scattering analysis of x-ray-absorption spectra[END_REF] for Co/Cu [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF].

CHAPITRE 3

Interpretation of X-ray absorption edges by high-energy resonant electronic spectroscopies

Introduction

In the previous chapter, it was shown that X-ray absorption could provide important pieces of information on the crystallographic structure. In particular, we were able to extract information about the stacking period of hexagonal atomic planes from the XANES region of the absorption spectrum. In this photon energy region, the photoelectron probes the very first empty electronic states above the Fermi level. In a metallic system like our Co/Cu films, at a K-edge where the photoelectron is excited towards very delocalized p states, the photoelectron is sensitive to the shape of the interatomic potential and hence, to the crystallographic structure. In more complicated systems, like rare-earth compounds or oxides, the electronic structure of these empty states may be much more complex, with localized states possibly embedded in the continuum formed by delocalized states and more or less hybridized with them.

The physical properties of materials like magnetism, conductivity, or reactivity are due to these outermost electronic levels of atoms. Spectroscopies like X-ray photoelectron spectroscopy (XPS) or X-ray absorption spectroscopy (XAS) are powerful tools to probe the electronic structure, but their analysis is not straightforward when correlations between electrons become important in the case of correlated electronic states, as in some of the 3d levels of the first series of transition metals (TM) and their oxides. In XPS or Auger measurements, another problem to tackle is surface sensitivity of the technique due to the small escape depth of the electrons in the commonly used photon energy range between 10 and 1500 eV. The lowering of the coordination number for surface atoms leads to a narrowing of the electronic bands, thus changing their hybridization and the relative weights of the different possible electronic congurations with respect to the bulk. Hence, the interpretation of XPS spectra must account for the relative bulk and surface contribution to the total spectrum. If one is interested in the bulk electronic structure, surface sensitivity is clearly a drawback.

In cerium compounds, XPS spectra with varying photon energy or with different electron collection angles have been performed [START_REF] Braicovich | Surface effects on the 4f hybridization in Ce intermetallics as seen with Ce 3d XPS[END_REF][START_REF] Braicovich | Highenergy Ce -3d photoemission : Bulk properties of CeM 2 (M=Fe, Co, Ni) and Ce 7 Ni 3[END_REF]. However, the most efficient way to suppress the surface contribution to a large extent is to signicantly increase the electron kinetic energy by raising the photon energy into the hard X-ray range [START_REF] Lindau | X-ray photoemission spectroscopy[END_REF], while keeping the energy resolution available at lower photon energy and reasonable count rates. This can now be achieved thanks to progresses of synchrotron radiation sources, beamlines and instrumentation. It also opens the possibility to perform resonant electronic spectroscopy around deep thresholds like the K-edges of 3d-TM or the L 2,3 edges of 4d-TM and rare earths with high bulk sensitivity [START_REF] Sekiyama | Probing bulk states of correlated electron systems by high-resolution resonance photoemission[END_REF].

Resonant spectroscopies are powerful tools to probe the electronic states near the Fermi level as well as the atomic electronic conguration. These spectroscopies consist in observing a selected decay process (fluorescence, Auger decay or autoionization interfering with direct photoelectron emission) with photon energies around an absorption edge.

In this chapter, we will only focus on non-radiative processes like Auger or autoionization. After a short introduction to these spectroscopic techniques, we will use them to better understand the L 3 -edge of cerium in mixed-valent compounds and the prepeaks of the Ti-K-edge in TiO 2 -rutile. We will see that the analysis of the Auger or photoemission lineshape in the resonant regime will allow us to attribute precise final states to each XANES structure. In the last part of this chapter, we will summarize applications of resonant spectroscopy in the soft X-ray range for other purposes like the interpretation of Auger lineshape, or amplification of spectral features to allow valence-selective photoelectron diffraction.

Resonant spectroscopies

Introduction

In this section, we will briefly describe the principles of resonant spectroscopies. Although we will focus on non-radiative decay processes in the following, we will introduce them on fluorescence measurements. They are indeed easier to understand since only one electron is involved in the decay process.

Decay processes-Principle of a resonant experiment

Once an atom has absorbed a photon, a photoelectron is emitted leaving the atom in an excited state with a hole in its electronic cloud. The atom can decay via two different processes (figure 3.1) :

-A radiative process : in such a process, an electron from an outer level fills the photohole, and the atom emits a photon whose energy is roughly the difference between the binding energies of the concerned electronic levels. This is the fluorescence decay. -A non-radiative process : an electron from an outer level fills the photohole, and another electron is ejected with a kinetic energy which depends on the the binding energies of the involved electronic levels. This is the Auger decay. The idea of resonant spectroscopies, at least for the interpretation of absorption edges, is to take advantage of the information contained in those decay processes and to combine it to the sensitivity of X-ray absorption to the electronic empty states. In this prospect, fluorescence or Auger spectra are recorded for photon energies corresponding to an absorption edge. The goal will be to use the lineshape of decay process spectra to have an idea of the electronic configuration of the atom in the absorption final state, and hence, to precisely identify the origin of each structure in the absorption edge.

Resonant fluorescence

Experimental observation

When increasing the excitative photon energy, one could expect the fluorescence to appear suddenly, at the expected energy, once the photon has enough energy to create the photohole, i.e., to excite the photoelectron towards the first empty state above the Fermi level. This not what is experimentaly observed. One can identify two different regimes :

-The normal regime : When the incident photon energy is larger than the energy needed to excite the photoelectron, we are in the normal fluorescence regime described above, where the fluorescence photon is emitted at a constant energy which does not depend on the incident photon energy. -The Raman regime : When the incident photon energy is smaller than the energy needed to excite the photoelectron (but close to it), one does observe a fluorescence line. It appears at an energy lower than normal fluorescence and its energy increases with the incident photon energy, until it reaches the energy of normal fluorescence when the incident photon energy reaches the energy needed to excite the photoelectron to an empty state above the Fermi level. In this regime, the fluorescence line are also observed with a reduced energy width (as compared to normal fluorescence) [START_REF] Cullie | Inelastic Resonance Emission of X-Rays : Anomalous Scattering Associated with Anomalous Dispersion[END_REF]. Resonant fluorescence spectra are often plotted as a function of the transfer energy, E T , defined by where E is the fluorescence energy and hν the incident photon energy. In this representation, similar to the binding energy plot in photoemission, Raman lines appear at fixed energy positions, whereas normal fluorescence appears at a transfer energy which varies as the incident photon energy.

E T = hν -E (3.1)

A simple picture

One can give a simple (but false !) picture of this Raman regime as a two-step process, sketched on figure 3.2. In this picture, when the incident photon energy is smaller than the photoelectron excitation threshold, one considers that it is actually excited to an empty state above E F , although it doesn't have enough energy for that. The missing energy is then taken from the Raman photon emitted in the decay process. When increasing the incident photon energy, this missing energy is smaller and smaller, and the Raman photon energy increases as the incident photon energy and gets closer and closer to the normal fluorescence one, until it reaches it when the incident photon energy reaches the ionization threshold.

A correct picture

In the Hamiltonian describing the interaction between photons and matter, the interaction term is usualy treated as a first order perturbation of H 0 describing the solid and its electrons. A first order development is sufficient to describe X-ray absorption or photoemission. The Raman regime was first observed by Sparks in 1974 [START_REF] Cullie | Inelastic Resonance Emission of X-Rays : Anomalous Scattering Associated with Anomalous Dispersion[END_REF], and, from the photon energy dependence of the process cross section, he suggested that it should be explained by taking into account the second order term in perturbation. This gives a probability for the emission of a photon with energy ω with incident photons ω [START_REF] Åberg | Resonant anomalous X-ray scattering : theory and applications[END_REF] :

I(ω, ω ) ∝ f n f |H int | n n |H int | i E i + ω -E n -iΓ n 2 × δ(E f -ω -E i -ω) (3.2)
known as the Kramers-Heisenberg formula. H int is the photon-matter interaction Hamiltonian, and n| is the intermediate state which appears in the second order perturbation In this formula, the first and second brackets remind of the two steps in the simple model presented above, but the description of the process appears to be more complex, with cross-terms to take into account. It is often say that the excitation and the decay are treated coherently, in a one-step picture. This is sketched in figure 3.3, with an incident photon with an energy close to the K-edge and a decay involving a L-electron. On the right, the process is sketched as we described it up to now (excitation and decay) ; on the left, it is presented as a one-step process, where part of the photon energy is absorbed to excite a L-electron, as in a Raman process. This second picture is the correct one, which explains the name of Raman-regime for the below-the-edge photon energy domain and the name of this technique : Resonant Inelastic X-ray Scattering (RIXS) or Resonant Raman Scattering (RRS).

Dispersion and energy width

Both the dispersive behaviour and the reduced energy width have been explained by Armen and Åberg by energy conservation arguments, in a formalism which applies both for radiative and non-radiative decays [START_REF] Bradley Armen | InnerShell Photoionization : Teijo Åberg's Concept of RRRS[END_REF].

Let's illustrate this theory by the simple case of a Kα fluorescence decay at a K-edge, the photoelectron being excited to continuum delocalized states. In the normal regime, the fluorescence line can be considered as a lorentzian with an energy width Γ (given by the 1s core hole lifetime) and centered at

ω KL = E K -E L (3.3)
where E K and E L are the binding energies of the 1s and 2p levels, respectively (see figure 3.4).

Let us consider the excitation of the atom by a photon with an energy ω, and let's define

E exc = ω -E K (3.4)
E exc is the excess energy. It is is negative in the Raman regime (below the K-edge), and positive in the normal regime (above the K-edge).

Let's now write the energy E of the system constituted by the atom of ground state energy E i and the incident photon, i.e., before the photon absorption

E = E i + ω (3.5)
and in the final state, where a 2p photoelectron has been excited above the Fermi level with a kinetic energy >0 and a photon with an energy ω has been emitted, neglecting any multielectronic effects due to the core hole

E = E i + (E L + ) + ω (3.6)
Energy conservation then writes

E i + ω = E i + (E L + ) + ω (3.7) ω = (E L + ) + ω (3.8)
Introducing E K in formula 3.8 gives

ω -E K = E L -E K + + ω (3.9)
Using the expressions of ω KL and E exc , one finaly obtains

E exc + ω KL = + ω (3.10)
At E exc = 0, i.e. exactly at the K-edge, equation 3.10 writes

ω KL = + ω (3.11)
which shows that the normal fluoresence photon energy is shared in between the emitted photon and the photoelectron.

In the Raman regime, is positive and we therefore have, according to equation 3.10, ω < E exc + ω KL . Since E exc is negative this regime, that means that the emitted fluorescence spectrum shows a cut-off at E exc below ω KL . When the incident photon energy increases, E exc decreases as ω and this cut-off moves towards high emission energy, until the total emission spectra is revealed (see figure 3.4). This explains the apparent dispersion of the fluorescence line in the Raman regime, as well as its apparent smaller energy width. Those simple energy conservation arguments also shows that the Raman regime will exist on an incident photon energy range of the order of two times the lifetime Γ of the 1s core hole.

Spectator lines

In addition to the Raman line, resonant fluorescence spectra can also show separate additionnal dispersive lines, the spectator lines, due to transitions to a localized state.

Transitions to continuum delocalized states in the resonant regime give rise to the Raman line descibed above, but there can also be an empty localized state accessible to the photoelectron. In this case, one observes another fluorescence line, emitted while the photoelectron is still located on the atom, as a spectator of the decay process. In the following, we will see what are the energy and intensity of these spectator lines when scanning the incident photon energy around the transition energy, and some exemples of experimental observations. First, why do those lines appear at a different energy from the Raman line ? Let's assume that for a given atom with a ground state |i of energy E i and for an incident photon energy ω, a photoelectron can be excited either to a continuum delocalized state (final state |f cont with energy E cont f ) or to a localized state (final state |f loc , with energy E loc f ). One can write

|i + ω → |f cont + ω Raman |i + ω → |f loc + ω Spect
where ω Raman and ω Spect are Raman fluorescence line or spectator line, respectively. Energy conservation writes

E i + ω = E cont f + ω Raman = E loc f + ω Spect
In the case of the transition to the localized state, since the photoelectron is still located on the atom, it participates to the screening of the core hole and lowers the final state energy, with respect to the case of a transition to a delocalized state, where the photoelectron leaves the atom. Hence, E cont f > E loc f , and ω Raman < ω Spect . The spectator lines therefore always appear at an energy lower than the Raman line.

Experimentaly, those spectator lines always appear at constant transfer energy (i.e. with their energy varying like the incident photon energy). This can be understood in the simple two-step picture presented at the beginning of this section (or from the more rigorous formula 3.11). If the incident photon energy is smaller than the transition energy, some energy is taken from the fluorescence photon ; if it is larger than the transition energy, some energy, taken from the photoelectron, is transfered to the fluorescence decay. The spectator line thus always appears at constant transfer energy, the transition to the localized state being favored to lower the final energy of the atom (see figure 3.5).

The dispersive behaviours of a Raman and a spectator line are sketched in figure 3.6. The intensity of the spectator line will obviously be maximum at the photon energy corresponding to the involved electronic transition.

These spectator lines were first evidenced at the Mn-K-edge in KMnO 4 [START_REF] Briand | X-ray raman and compton scattering in the vicinity of a deep atomic level[END_REF]. A nice exemple is observed at the copper K-edge of CuO (see figure 3 are spectator lines due to 1s → 3d quadrupolar transitions and 1s → 4p dipolar transitions, respectively, whereas line A is the Raman line. B and C appear for photon energies corresponding to well-defined structures in the absorption edge, which can therefore be attributed to those electronic transitions [START_REF] Hayashi | Hidden electronic state of CuO revealed by resonant inelastic X-ray scattering[END_REF]. Another exemple is given on figure 3.8, where 2p → 4f quadrupolar transitions are detected at the L 3 -edge of gadolinium. Transitions towards the very localized 4f -states are highlighted by the A spectator line in the resonant fluorescence spectra, while the B and B* lines are due to 2p → 5d dipolar transitions ; C is the Raman line [START_REF] Krisch | Evidence for a Quadrupolar Excitation Channel at the L III Edge of Gadolinium by Resonant Inelastic X-Ray Scattering[END_REF].

Resonant Auger

The non-radiative Auger decay process basicaly shows the same behaviour as fluorescence in resonant measurements. If the overall kinetic energy resolution (including the energy resolution of the excitative photons) is smaller than the natural energy width of the core hole (due to its lifetime), so-called resonant Raman Auger lines with a subnatural linewidth and at constant binding energy can be observed. First discovered in gas phase [START_REF] Brown | Ice. Observation of the Auger resonant raman effect[END_REF][START_REF] Bradley Armen | Threshold excitation of short-lived atomic inner-shell hole states with synchrotron radiation[END_REF][START_REF] Kivimäki | Subnatural linewidths in the Kr M 5 N 2,3 N 2,3 and Xe N 5 O 2,3 O 2,3 resonant Auger spectra[END_REF], such measurements were performed on solids in the nineties [START_REF] Drube | Density of State Effects in Ag L 3 M 4,5 M 4,5 Threshold Auger Spectra[END_REF]. As in resonant fluorescence spectra, dispersive spectator lines can be observed in the presence of a core electron excited in a localized empty orbital [START_REF] Brown | Ice. Observation of the Auger resonant raman effect[END_REF].

The simple (false) two-step picture we gave for fluorescence also applies for the Auger decay, as shown in figure 3.9. As for fluorescence, the results can be rigorously described using the Kramers-Heisenberg formula 3.2.

Resonant photoemission

In addition to the resonant Auger process, the other non-radiative process which can occur upon photoexcitation near an absorption edge is autoionization. In this process, which can only take place at an absorption edge, the photoelectron itself fills the core hole and an electron from an outer level is ejected. As can be seen on figure 3.10, the atomic final state is thus exactly the same as in a direct photoelectron emission process from this outer level, with only one core hole, unlike in the case of an Auger decay, and with a photoelectron emitted at excactly the same kinetic energy as in a direct photoemission process (figure 3.10).

Hence, autoionization cannot be observed separately, since the electrons emitted via this process are mixed with photoemitted electrons. One are only sensitive to this resonant process through its interferences with photoemission. These interferences between the two processes (autoionization and direct photoelectron emission) were described by Ugo Fano in 1961 [START_REF] Fano | Effects of configuration interaction on intensities and phase shifts[END_REF], who predicted a characteristic resonance behaviour of photoelectron emission lines near an absorption edge.

Fano starts from a set of continuum states ψ E of energy E which, in our case will represent the final state after a direct photoemission process. A discrete state ϕ is introduced into this continuum of states. For a resonant photoemission experiment, it will represent the transition to a localized state at the absorption threshold. The Hamiltonian describing the system is diagonal for the ψ E continuum state (

ψ E |H| ψ E = E × δ(E -E )),
but is perturbed by the discrete state :

ϕ |H| ϕ = E ϕ and ψ E |H| ϕ = V E
A diagonalization of H gives a set of new eigenstates Ψ E and shows that the discrete state ϕ is modified by an admixture of continuum states to form a Φ state with a finite energy half-width of 1 2

Γ = π |V E | 2 .
Its energy E φ is also shifted from a quantity

F = P.P. dE |V E | 2 E -E
The ratio of the transition probabilities from the initial state to the unperturbed or perturbed continuum states is given by a series of curves, called Fano profiles, whose general formula is

| ψ E |T | i | 2 | Ψ E |T | i | 2 = (q + ) 2 1 + 2 where = E -E 0 -F 1 2 Γ
and

πq 2 = | Φ |T | i | 2 2Γ | Φ E |T | i | 2
The q parameter appears as the ratio of the transition probabilities to the discrete state (autoionization) or to a continuum state (photoemission). Some Fano profiles, calculated for different q values are presented on figure 3.11. The shape of the resonance profile strongly depends on q. For large values of q (strong probability of autoionization, i.e. transition to a very localized state), the profile looks like a Lorentzian. For weak q-values, the profile presents a dip around the resonance position.

Apart from the fact that autoionization can only be detected through its interferences with photoelectron emission, resonant photoemission is not formally different from resonant Auger or resonant fluorescence : near an absorption edge, possible transitions towards localized states just above E F gives rise to an additional process which will strongly modify the intensity of photoelectron emission peaks and satellites lines corresponding to the same final states than those reached by autoionization.

Conclusion

In this section, we briefly presented the different resonant spectroscopic techniques. They combine the sensitivity of X-ray absorption to the empty sates and the hability of spectroscopic methods, like fluorescence, photoemission or Auger, to give an additionnal information about the final electronic configuration. They are therefore completely 3.3 Quadrupolar transitions at the Ti-K-edge in TiO 2rutile evidenced by resonant Auger

Introduction

Since it obeys strict selection rules, X-ray absorption is an element and orbital-selective probe of both crystallographic and electronic structures of materials. Beyond the dominant features of the absorption spectra arising from excitations which can be interpreted within the dipolar approximation, the absorption pre-edge and near-edge features commonly involve second order quadrupolar transitions (QT) [START_REF] Brouder | Angular dependence of x-ray absorption spectra[END_REF]. Although these are of weak intensity, their corresponding terms in the interaction Hamiltonian often contain valuable information. For instance, the magnetism of selected orbitals can be probed via the analysis of QT by X-ray magnetic circular dichroism, as at the L 2,3 edges of rare earths. At these edges, QT from the 2p-levels towards the 4f -orbitals (which generally carry most of the magnetic moment in rare earth compounds) give a signal of the same order of magnitude as that due to the dipolar 2p → 5d transitions [START_REF] Baudelet | Study of 5d magnetism in rare-earth-transition-metal (Fe, Co) intermetallic compounds by magnetic circular X-ray dichroism[END_REF]. In resonant X-ray magnetic scattering, the quadrupolar 2p → 4f component dominates the Sm-L 3 -edge and allows a description of the 4f magnetism [START_REF] Dumesnil | Magnetic ordering in a (001) Sm layer and a Sm/Y superlattice studied by resonant X-ray magnetic scattering[END_REF]. Pre-K-edge features are often observed in the case of 3d compounds. Associated with transitions towards p or d orbitals, they involve both dipolar and quadrupolar transitions and are also important in magne-tic measurements [START_REF] Neubeck | K-edge resonant x-ray magnetic scattering from CoO[END_REF]. A picture of the occurrence of QT is therefore of prime interest to achieve a description of the electronic structure of these compounds and to fully account for their physical properties. A common way to discriminate between dipolar and quadrupolar transitions is based on the interpretation of the angular dependence of the XAS cross section, since the electric dipolar ( . r) and quadrupolar ( . rk. r) terms of the interaction Hamiltonian are sensitive either to the polarization direction of the X-rays or to both and the direction of the photon wave vector k [START_REF] Richter | Spin Separation in a Metal Overlayer[END_REF]. However, this method suffers from severe drawbacks. It can only be applied to single crystals and to ensure that the weak quadrupolar contributions can be distinguished from the more intense dipolar components, its use is restricted to the study of pre-edge features well separate from the main absorption threshold.

We show here that QT can be detected thanks to spectator lines in the resonant Auger decay process. This is illustrated on the pre-K-edge of titanium in rutile-TiO 2 by discriminating the various components of each of the features of the pre-edge spectrum.

Experimental conditions

The experiments were performed using the tunable high energy X-ray photoemission station at the BW2 wiggler beam line of HASYLAB, equipped with Si(220) crystals monochromator and a Scienta SES-200 analyzer (total energy resolution of 0.6 eV at the Ti K-edge). Data were collected on a TiO 2 (110)-rutile single crystal, prepared according to standard procedures in order to obtain the stoichiometric composition [START_REF] Pétigny | Superficial defects induced by argon and oxygen bombardments on (110) TiO 2 surfaces[END_REF]. The angular dependence was studied by rotating the sample around a vertical axis. The electron collection direction is fixed in the horizontal plane at 45 • from the incoming X-ray beam.

Angular dependence of XAS spectra

The Ti K-edge XAS spectrum is presented on figure 3.12. Before the main edge, it exhibits a series of three prepeaks called A 1 , A 2 , and A 3 . In the following, the photon energy is referenced relative to the maximum of A 2 whose absolute energy position was measured to be 4968.9 eV. A 1 and A 3 are thus peaking at -2.75 and +3.0 eV relative photon energy, respectively.

Previous studies used polarisation dependent XAS to elucidate the origin of these structures [START_REF] Uozumi | Experimental and Theoretical Investigation of the Pre-Peaks at the Ti K-Edge Absorption Spectra in TiO 2[END_REF][START_REF] Poumellec | Angular Dependence of the Ti K-Edge in Rutile TiO 2[END_REF]. Total electron yield spectra were recorded for two different X-ray incident angles with respect to the (110) surface. The wave vector of the X-rays is either parallel to the [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF] surface normal (0 • , at 45 • from the a axis), or at 45 • from it (45 • , parallel to the a axis). At a K-edge, due to the highly directional character of the reached p orbitals, the electric dipolar absorption cross section possesses the symmetry of the crystal [START_REF] Brouder | Angular dependence of x-ray absorption spectra[END_REF]. It is thus not expected to vary with the X-ray incidence angle (transitions to p x and/or p y orbitals). On the contrary, quadrupolar contributions are expected to have the largest possible intensity variation between 0 • and 45 • , since the d symmetry of the probed orbitals confers to their intensity a cos(4Φ) dependence (where Φ denotes the rotation of and k in the (100) plane) [START_REF] Brouder | Angular dependence of x-ray absorption spectra[END_REF]. All the angular dependences are therefore due to intensity variations of QT. In rutile, the first coordination shell of Ti atoms is composed of six oxygen atoms which form a distorted octahedron [START_REF] Poumellec | Angular Dependence of the Ti K-Edge in Rutile TiO 2[END_REF]. Using the electric quadrupolar Hamiltonian formula, in a basis linked to the octahedron, the only allowed QT in the 0 • geometry are towards d xz and d yz orbitals which belong to the t 2g -like representation. In the 45 • geometry, the main allowed transitions are towards the d x 2 -y 2 and d z 2 orbitals, which belong to the e g -like representation (transitions towards the d xy t 2g -like orbital are also allowed). For the A 1 prepeak, the maximum intensity at 0 • and the minimum at 45 • are indicative of t 2g -like QT. The reversed behaviour of the A 2 prepeak shows that its quadrupolar component is mostly e g -like, while the absence of any angular dependence of A 3 is assigned to a purely dipolar origin. The data meet the previously published results [START_REF] Poumellec | Angular Dependence of the Ti K-Edge in Rutile TiO 2[END_REF][START_REF] Uozumi | Experimental and Theoretical Investigation of the Pre-Peaks at the Ti K-Edge Absorption Spectra in TiO 2[END_REF]. However, these results did not allow an experimental decomposition of the pre-edge into its various quadrupolar and dipolar contributions. In this goal, an analysis of the Ti-KLL resonant Auger lines was undertaken in the pre-edge region of the Ti K-edge.

Resonant Auger

The normal Auger spectrum, recorded for a photon energy well above the ionization threshold, exhibits three lines. in the following, we will focus on the most intense, located at 4006.3 ±1 eV.

Chosen spectra collected in both 45 • and 0 • geometry of the X-rays are shown in figure 3.13. The series of resonant exhibit three components, labeled To examine the intensity of the Q 1 , Q 2 , and D peaks, the Auger spectra were assumed to be a simple sum of these three components with Lorentzian lineshapes and an integral background. The results are presented in figure 3. [START_REF] Schneider | Spin-and angle-resolved photoemission from single crystals and epitaxial films using circularly polarized synchrotron radiation[END_REF].

Q 1 , Q 2 ,
Q 1 has a maximum intensity on the maximum of the A 1 prepeak (-2.75 eV) and follows the same angular dependence : it is more intense at 0 • than at 45 • . Considering both resonant behaviour and angular dependence, Q 1 is assigned to an Auger decay following the quadrupolar excitation of a 1s electron in the t 2g -like orbitals. Moreover, since it appears at constant binding energy, it can be identified as a spectator line.

The intensity of Q 2 shows a maximum just below A 2 (-1.0 eV) roughly where the difference between the two XAS spectra recorded at 0 • and 45 • is maximum (see figure 3.14). Unlike for Q 1 , its intensity increases from 0 • to 45 • . Q 2 can therefore be attributed to a spectator line due to an additional valence electron promoted in the e g -like orbitals via a QT.

Last, the D peak is attributed to decay following a dipolar transition of the 1s electron towards the p empty states of continuum, since it finally stabilizes at the position of the classical Auger line. Consistently, its intensity does not show any significant angular variation (bottom of figure 3.14). Very weak (almost zero) in the A 1 region, it is roughly twice that of Q 2 in the A 2 region.

Assuming equal Auger decay rates for the different intermediate states, this intensity analysis of the different Auger components gives an estimate for the relative contributions of quadrupolar and dipolar transitions in the prepeaks. Thus, as can be seen on figure 3.14, A 1 has a purely quadrupolar origin and due to 1s → 3d(t 2g ) transitions, A 3 is purely dipolar, and dipolar transitions have equal contributions in A 2 and A 3 ; a quadrupolar contribution to A 2 , due to 1s → 3d(e g ), is detected on its low-photon-energy side, 1 eV before its maximum. All these results are in agreement with calculations presented in reference [START_REF] Uozumi | Experimental and Theoretical Investigation of the Pre-Peaks at the Ti K-Edge Absorption Spectra in TiO 2[END_REF] or [START_REF] Joly | Electron Population Analysis by Full-Potential X-Ray Absorption Simulations[END_REF]. In this latter calculation, the 3d-population is adjusted and the energy positions of the quadrupolar transitions are shown to be very sensitive to this parameter. They find a quadrupolar part for A 2 slightly shifted with respect to our work with a maximum at the same energy position as the dipolar contribution.

Conclusion

In the region of the Ti K-edge in TiO 2 , the resonant behaviour of the KLL Auger lines has been used to unravel the different contributions to the absorption spectrum. Raman Auger lines following dipolar excitation towards p-states, and spectator lines following

51

QT towards e g and t 2g states are clearly discriminated. These decays are unambiguously identified by their angular dependence. Resonant Auger spectra therefore offer direct and separate fingerprints for the different transitions occurring in the studied absorption edge, either to the continuum or to bound states, such as, e.g., quadrupolar transitions to d-states at K-edges. In rutile-TiO 2 , resonant Auger spectra allows also a quantitative determination of the respective weights of the dipolar and quadrupolar transitions in the A 2 prepeak, where both contributions are mixed.

High-energy resonant photoemission in CeRh 3 -

Interpretation of the Ce L 3 -edge in mixed-valent compounds

Introduction

In the description of the physical properties of transition metal, lanthanide and actinide compounds, electronic correlations play an important role : the quite high localization of the d or f orbitals leads to an intermediate situation where it is not clear whether the band-like or atomic-like model is more appropriate. For these d or f states, the intra-atomic Coulomb interaction is important, but the direct overlap of the orbitals on different sites and their hybridization with the other bands have also to be considered.

High-energy spectroscopies such as X-ray photoelectron spectroscopy and X-ray absorption spectroscopy applied to the electronic structure of matter are powerful techniques but due to the presence of multielectronic effects, the interpretation of the experimental results is not straightforward. In mixed-valent cerium compounds, spectroscopic data have been interpreted in terms of band-like [START_REF] Weschke | Bandlike character of 4f electrons in CeRh 3[END_REF] or localized [START_REF] Grioni | Resonant inverse photoemission in cerium-based materials[END_REF][START_REF] Witkowski | Configuration-dependent hybridization in electron spectroscopies of Ce-based compounds[END_REF] models. We present here the results of core-level resonant photoemission and Auger spectroscopy in a CeRh 3 compound, which support the localized many-body approach for the description of L 3edge XAS spectra.

The unusual physical properties of cerium compounds are connected to the cerium electronic structure : the high density of 4f states at the Fermi level can lead to a partial delocalization of the 4f electrons, which gives an intermediate valent ground state. XAS at the L 2,3 -edges has been widely performed to study the electronic properties of intermediate valent compounds, since it is not surface sensitive and does not need ultrahigh-vacuum environment. From absorption data, one has deduced the 4f occupancy of Ce, using phenomenological interpretation of the edge profiles [START_REF] Röhler | Chapter 71, X-ray absorption and emission spectra[END_REF]. On the other hand, with circularly polarised light (X-ray magnetic circular dichroism, XMCD), absorption thresholds give also access to the magnetic properties of Ce [START_REF] Giorgetti | Magnetic circular X-ray dichroism in Ce intermetallic compounds[END_REF]. L 2,3 -edges therefore contain a valuable information, but their interpretation is complicated : in the final state, the interaction between the photoelectron and the excited atom cannot be neglected. Resonance experiments were a new way to assign the main structure of the absorption edge to precise final electronic configurations, for relatively localized states. In a classical absorption experiment, one simply measures the total absorption cross section, which represents all the transition probabilities from an initial state to different final states, leading to different decay processes. In a resonance experiment, one selects only one decay process, corresponding to a well-defined final state, and the intensity of this decay is monitored across the absorption edge. Thus, fluorescence decay has allowed to detail the understanding of the L 3 -edge and the XMCD of Gd (see figure 3.8) [START_REF] Krisch | Evidence for a Quadrupolar Excitation Channel at the L III Edge of Gadolinium by Resonant Inelastic X-Ray Scattering[END_REF]. In this section, Ce-3d resonant photoemission is used to study the Ce-L 3 edge in mixed-valent compounds.

Mixed-valent Ce-compounds

In its atomic configuration, cerium possesses one 4f electron. In some compounds, the 4f states strongly hybridize with the more delocalized 5d6s valence states. The ground state has then to be described as a linear combination of 4f 0 , 4f 1 and even 4f 2 electronic configurations. These are the mixed-valent compounds.

In these compounds, Ce-3d photoemission spectra exhibit well-defined satellites for each 3d 3/2 and 3d 5/2 line. They have been described assigning the different peaks to the relaxation of the 4f electrons in the core-hole potential [START_REF] Fuggle | Electronic structure of Ce and its intermetallic compounds[END_REF]. In a simple picture, in the 3d-photoemission final state, it is energeticaly favourable to have more localized electrons in order to efficiently screen the 3d-core hole and reduce the ion final energy. Introducing the ground state |i (energy E i ) and the photoemission final state with n 4f electrons 3d 9 4f n (5d6s) 4-n (energy E 4f n ), one can write |i + hν → 3d 9 4f n (5d6s) 4-n + photoelectron (3.12)

If E n K is the kinetic energy of the photoelectron corresponding to the 4f n configuration of the final state, energy conservation writes

E i + hν = E 4f n + E n K (3.13)
Since the addition of one electron in the 4f shell reduces the final state energy, one has E 4f 2 < E 4f 1 < E 4f 0 , and therefore

E 2 K > E 1 K > E 0 K .
Hence, the three lines in the 3d photoemssion spectrum can be attributed to the different possible final electronic configurations.

The same influence of the core hole in the final state is observed in XAS measurement at the Ce-L 3 edge. in the Ce 7 Rh 3 purely trivalent (4f 1 ) compound, the spectrum shows a unique white line, whereas in the CeRh 3 mixed-valent compound, it shows two bumps attributed to 4f 1 and 4f 0 final states (see figure 3.16). A careful examination of the spectrum reveals a 4f 2 component hidden in the rise of the edge [START_REF] Bianconi | Experimental evidence for the shake-down peak in L III (and L II )-XANES of light rare earth intermetallics[END_REF], that we will clearly evidenced using resonant 3d-photoemission in the following.

Experimental conditions

The samples were scraped in situ under UHV conditions. The spectra presented here were obtained at the ESRF, on the ID32 beamline using a Si [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] double-crystal monochromator. The good energy resolution available on this beamline, even at this high energy (better than 1 eV at 5 keV), allowed us to isolate the peaks corresponding to 4f 0 , 4f 1 and 4f 2 character of the final state in the CeRh 3 3d-photoemission spectrum.

Interpretation of the Ce-L 3 absorption edge using highenergy resonant 3d-photoemission

To better understand this Ce-L 3 XAS profile, Ce-3d photoemission spectra were recorded for photon energies around the Ce L 3 -edge, located around 5728 eV. The first advantage of using such high energy photons is to increase the escape depth of the electrons in matter. In a classical XPS-setup, with photons around 1200 eV, Ce-3d photoelectrons are emitted with a kinetic energy around 300 eV which makes the measurement quite surfacesensitive. The lowering of the coordination number for surface atoms leads to a narrowing of the electronic bands. In Ce-compounds, this effect should decrease the hybridization between the 4f -states and the valence band, and give a more localized character to the 4f electron. If one is interested in the bulk electronic structure, one has to evaluate the relative bulk and surface contributions. Several groups have tried this, varying the escape depth of the photoelectrons by varying the energy of the photon excitation [START_REF] Braicovich | Highenergy Ce -3d photoemission : Bulk properties of CeM 2 (M=Fe, Co, Ni) and Ce 7 Ni 3[END_REF][START_REF] Laubschat | Surfaceelectronic structure of α-like Ce compounds[END_REF]. The mean free path being of the order of 10 Å, the surface contribution cannot be neglected and has been estimated by the authors. The estimation is difficult and inaccurate results can lead to a wrong determination of the bulk ground-state parameters [START_REF] Sekiyama | Probing bulk states of correlated electron systems by high-resolution resonance photoemission[END_REF]. In our study, the 3d photoemission spectra were recorded with photon energies around the L 3 absorption edge of Ce (5728 eV). The kinetic energy of the photoelectrons is then around 4800 eV, and their mean free path is larger than 50 Å. The surface contribution can therefore be neglected which is an important advantage of this very high-energy spectroscopy : it procures a real probe of the Ce-compound bulk electronic structure.

The experiment consisted in measuring the intensities of the Ce-3d photoemission peaks while sweeping the photon energy across the Ce-L 3 absorption edge (Constant Initial State spectra, CIS). As explained above, around the L 3 -edge, the direct photoemission process interferes with the resonant autoionization process which leads to the same final state. The two processes are 2p 6 3d 10 4f n (5d6s) 4-n + hν → 2p 6 3d 9 4f n (5d6s) 4-n + e - and 2p 6 3d 10 4f n (5d6s) 4-n + hν → 2p 5 3d 10 4f n (5d6s) 5-n → 2p 6 3d 9 4f n (5d6s) 4-n + e - As explained above, these interferences were described by Fano [START_REF] Fano | Effects of configuration interaction on intensities and phase shifts[END_REF] and can give rise to strong variations in the photoemission cross section for relatively localized electronic states. CIS spectra comparable to Fano profiles were measured by monitoring the raw photoemission peak intensities ; a background, measured as the intensity at the bottom of the photoemission spectrum, was then substracted. CIS spectra are presented on figure 3.17 for CeRh 3 where Ce has an intermediate ground state, together with the Ce-L 3 absorption edge. The CIS spectra were recorded for three lines of the XPS spectrum, due to final states of the Ce atoms with zero, one, or two 4f electrons labeled 4f 0 , 4f 1 and 4f 2 . The results show different resonance energies for the contributions of the different final states. The resonances are quite intense, of the order of 30%, although less spectacular than what can be observed in case of transitions towards very localized states, e.g. 3d → 4f resonance in rare earths. It shows that the 5d states of rare-earth compounds, which are less localized than the 4f , can also give rise to resonant effects. In figure 3.17, the CIS spectra of the 3d 5/2 -4f 2 , 3d 5/2 -4f 1 and 3d 3/2 -4f 0 photoemission peaks of Ce in CeRh 3 are reported, together with fits to a Fano function. A clear result that comes out directly from the raw experimental data is a different resonance energy for each line. In figure 3.17, straight lines correspond to the resonance energies E 0 of the Fano fits. The photoemission line due to 4f 2 final state resonates at 5725 eV, slightly before the first structure of the L 3 -edge, the 4f 1 contribution resonates at 5728 eV, on the first hump of the L 3 -edge, whereas the 4f 0 satellite resonates at 5737 eV, on the second hump of the L 3 edge. So, in the intermediate valent compounds, the position of the resonances makes it possible to assign unambiguously the two main lines in the XAS profile to mainly 2p 5 4f 1 and 2p 5 4f 0 final states, and the shoulder in the rise at the absorption edge to a 2p 5 4f 2 final state, as already suggested by Bianconi et al. [START_REF] Bianconi | Experimental evidence for the shake-down peak in L III (and L II )-XANES of light rare earth intermetallics[END_REF].

This simple atomic-like interpretation of the shape of the XAS profiles of cerium compounds explains well the XMCD signal at the Ce-L 3 -edge. Giorgetti et al. suggested that an atomic picture was the most suited, with a 4f 1 contribution at the edge, and 4f 0 and 4f 2 contributions at, respectively, +9.6 and -3 eV, in full agreement with the energy positions we observed in our resonant photoemission experiment [START_REF] Giorgetti | Magnetic circular X-ray dichroism in Ce intermetallic compounds[END_REF].

Conclusion

We showed here that quite strong resonances occur in Ce-3d photoemission when varying the energy of the excitative photons across the Ce-L 3 edge. The resonance energies of the different satellites in the 3d photoemission spectrum allow us to assign the main structures in the XAS spectra to the corresponding 4f 2 , 4f 1 and 4f 0 final electronic configurations.

Here we used the good knowledge of the photoemission spectrum to better understand XAS profiles. Moreover, the use of high energy photons, while keeping a good overall energy resolution, made our measurements bulk-sensitive, which is crucial in the case of those compounds. In this chapter, we have up to now focused on the XAS profile interpretation but applications of resonant spectroscopies are numerous. Instead of using the Auger decay to better understand absorption edges, one can also use resonant measurements to better understand the Auger profiles. The Ti-LM V Auger decay in rutile-TiO 2 is a good case to investigate.

Other applications of resonant measurements

Indeed, the ability to produce a correct diagnosis about the nature and the amount of chemical defects is a central need of chemistry of ceramic surfaces because they create new electronic states, in particular in the gap, and perturb the reactivity. We will also see later, that defects like oxygen vacancies play a key-role in the creation of 2D-electron gases at the surface of oxides. In this respect, the lineshape of Auger decay has been used to determine, at least qualitatively, the surface stoichiometry of some transition metal oxides [START_REF] Rao | Studies of solids and surfaces by Auger electron spectroscopy [and discussion[END_REF]. As an example, in Ti-oxides, the relative intensities of the two main lines of the Ti-L 2,3 M 2,3 V Auger decay were shown to be clearly correlated to the surface stoichiometry of the compound [START_REF] Rao | Interatomic Auger transitions in transition-metal oxides[END_REF][START_REF] Victor | Surface defects and the electronic structure of SrTiO 3 surfaces[END_REF]. This Auger spectrum mainly involves two components (see figure 3.18). Due to its appearance when the metal is oxidized, and its growing intensity while increasing the cation oxidation state, the low kinetic energy component has been assigned to a so called "interatomic L 3 M V (O)" decay, while the other component has been associated to an "intra-atomic L 3 M V (T i)" process [START_REF] Rao | Interatomic Auger transitions in transition-metal oxides[END_REF][START_REF] Göpel | Surface defects of TiO 2 (110) : A combined XPS, XAES and ELS study[END_REF][START_REF] Sadeghi | Electronic interactions in the rhodium/TiO 2 system[END_REF]. Here, V(O) and V(Ti) refer to the O and Ti contributions to the oxide valence band, respectively. This well-documented Ti-LM V intensity ratio has been widely used to determine changes in the stoichiometry of Ti compounds surfaces as well as variations in surface oxygen stoichiometry after metal deposition [START_REF] Pétigny | Superficial defects induced by argon and oxygen bombardments on (110) TiO 2 surfaces[END_REF]. Rao et al. [START_REF] Rao | Interatomic Auger transitions in transition-metal oxides[END_REF] showed the coherent evolution of the Ti-L 2,3 M 2,3 V Auger spectra through a series of compounds presenting a gradual reduction of the titanium ion from TiO 2 to metallic titanium. The spectrum evolves from mostly a unique line around 408 eV in TiO 2 to a unique line at around 414 eV in metallic titanium, the intermediate spectra presenting these two lines with varying relative intensities. Auger spectra from samples under examination herein are shown in figure 3.18. To understand the link between the Auger line shape and the stoichiometry of titanium oxides, a detailed study of the Ti-L 2,3 M 2,3 V Auger resonant behaviour at the Ti-L 2,3 edges has been undertaken on a series of three samples : a stoichiometric rutile-TiO 2 crystal, a reduced rutile-TiO 2 sample (TiO 2-x ) and polycrystalline metallic titanium. and TiO 2-x spectra were recorded at 542 eV photon energy. On metallic titanium, the spectrum was recorded at 465.6 eV. The feature seen at 407 eV kinetic energy in metallic titanium spectrum is the Ti-3s photoemission. The two other Auger spectra, which were recorded at higher photon energies are not contaminated by this photoemission peak.

Experimental conditions

Data were collected at the ALOISA beamline of the Elettra Synchrotron Light Source in Trieste. The s-polarised light was impinging on the sample at grazing incidence (∼ 6 • ). The resolving power was around 5000 in the 450-810 eV photon energy range used herein. The resonant Auger spectra were recorded using the ALOISA 33 mm hemispherical analyzers whose energy resolution was set to 360 meV, leading to an overall experimental resolution of 380 meV. The TiO 2 -rutile(110) sample was previously heated in vacuum at 900 K during 1 h. As a result, the rutile took a dark blue color and became conductive enough to avoid charging effects. The stoichiometric surface was obtained by further annealings at 800 K under an oxygen pressure of 1×10 -6 mbar. Further details on the sample preparation are given in reference [START_REF] Pétigny | Superficial defects induced by argon and oxygen bombardments on (110) TiO 2 surfaces[END_REF]. The TiO 2-x sample was prepared by sputtering the stoichiometric TiO 2 (110) crystal with 1 keV Ar + ions during 15 mn in order to create oxygen vacancies near the surface, followed by a 15 mn annealing at 400 • C in ultrahigh vacuum. The polycrystalline titanium sample was prepared by several argon sputterings followed by annealings at 670 K.

In order to determine precisely the origin of the different contributions of the complex Ti-L 2,3 M 2,3 V Auger spectra in TiO 2 , we have recorded these spectra in resonance at the Ti-L 2,3 absorption edges. The goal is, by increasing the probability for the creation of a well defined core hole, to enhance the relative weight of a given contribution in the Auger profile.

In non-resonant conditions, the L 2,3 M 2,3 V Auger process can be described as follows : first, a 2p core hole is created by a photon whose energy is higher than the 2p binding energy, and a core electron is photoemitted. Then, the excited ion decays via the Auger process involving a 3p electron and a valence electron. The first electron fills the 2p hole, and the second one is emitted (see figure 3.19). In resonant conditions, when the photon energy corresponds to the maximum of the L 3 part of the XAS profile, only 2p 3/2 core holes are created and only the L 3 M 2,3 V part of the Auger decay is present in the resonant Auger spectra. At higher photon energies, in the L 2 part of the XAS profile, the creation of a 2p 1/2 core hole is allowed. Then, in the resonant Auger spectra, the L 2 M 2,3 V part of the Auger profile appears. Since at this higher photon energy the excited atom can also decay via a (very fast) L 2 L 3 V Coster-Kronig process, some resonance of the L 3 M 2,3 V can also occur at the L 2 XAS threshold through some kind of three-step process : creation of a 2p 1/2 core hole, a Coster-Kronig decay with creation of a 2p 3/2 hole, and then a L 3 M 2,3 V Auger decay. Finally, we also recorded resonant valence-band photoemission spectra. Since the LM V Auger process involves valence electronic states, the knowledge of the valence-band lineshape for the different samples is of major interest. At resonance, the direct photoemission of a valence-band electron interferes with the two-step autoionization process leading to the same final state [START_REF] Fano | Effects of configuration interaction on intensities and phase shifts[END_REF]. The incident photon induces the transition of a 2p electron to an empty 3d state above the Fermi level. Then, the excited atom decays, the photoelectron filling back the core hole and a valence electron being emitted (see Section 3.2.5). The photon energy dependence of the valence band spectra allows to emphasize the local density of states on the Ti-atoms by the enhancement of its relative weight at the Ti-2p → 3d excitation threshold.

Main results

Ti-LM 2,3 V Auger spectra recorded on stoichiometric TiO 2 -rutile, TiO 2-x and metallic titanium at the Ti-L 2,3 absorption edges for different photon energies, are presented in Figure 3.20, as well as resonant measurements of the valence band.

For stoichiometric rutile, concerning the L 2,3 M 2,3 V Auger decay, it is clear that, if the low-energy structure of the Auger spectra appears above the L 3 -edge, the high kinetic energy structure (labelled A) only shows up near the L 2 -edge, confirming the attribution of these lines to the L 3 M V and L 2 M V components of the Auger spectrum, respectively. The valence band spectra from the stoichiometric oxide show a dominant structure due to the mixing of the O-2p and Ti-3d states [START_REF] De Groot | Oxygen 1s x-ray absorption of tetravalent titanium oxides : A comparison with single-particle calculations[END_REF][START_REF] Woicik | Hybridization and Bond-Orbital Components in Site-Specific X-Ray Photoelectron Spectra of Rutile TiO 2[END_REF][START_REF] Thomas | Resonant photoemission of anatase TiO 2 (101) and (001) single crystals[END_REF] peaking between 5 and 10 eV binding energy. The resonant Ti-L 3 M 2,3 V Auger spectra on stoichiometric TiO 2 can be modeled by two peaks labeled B and C on figure 3.20. Indeed, the splitting of roughly 1.7 eV between the two features V B and V C (see figure 3.20) of the valence band is similar to the B-C energy separation in the Auger spectra (2.4 eV). Furthermore, it is clear that the C structure is always more intense than B, except for photon excitations around the second peak of the Ti-L 3 edge (which corresponds to the transition of the 2p photoelectron towards the 3d states of e g -like symmetry [START_REF] Van Der Laan | Polaronic satellites in x-ray-absorption spectra[END_REF][START_REF] De Groot | L 2,3 x-rayabsorption edges of d 0 compounds : K + , Ca 2+ , Sc 3+ , and Ti 4+ in O h (octahedral) symmetry[END_REF]), as for the V B and V C components of the valence band.

In these valence band spectra, the small peak which shows up near the Fermi level, especially visible around a photon energy of 462 eV is attributed to the filled 3d states of titanium associated to the presence on the surface of a small amount of oxygen vacancies [START_REF] Prince | 2p resonant photoemission study of TiO 2[END_REF][START_REF] Thomas | Resonant photoemission of anatase TiO 2 (101) and (001) single crystals[END_REF]. The much smaller intensity of this so-called defect peak in our measurements indicates that the surface of our sample was closer to the perfect TiO 2 stoichiometry than that used by Prince et al. in their experiment [START_REF] Prince | 2p resonant photoemission study of TiO 2[END_REF]. This type of defects releases electrons in the surface region which can give birth to a well-organized confined 2D electron gas in oxides like SrTiO 3 . This will be studied in details in chapter 5 of this dissertation.

In the TiO 2-x sample (central panel of Figure 3.20), the valence band involves a broad band between 5 and 10 eV binding energy and a sharp feature peaking just below the Fermi level. This is the defect peak described above. As expected, it is much more intense than in stoichiometric TiO 2 and it exhibits a strong resonance behaviour at the Ti-L 2,3 thresholds. Consequently, it adds a component in the resonant Ti-L 3 M 2,3 V Auger spectra as evidenced by the 6.2 eV separation in energy between the two valence band structures which nearly matches that between the two L 3 M 2,3 V lines (∼ 5.7 eV). This new structure is certainly superimposed on the Ti-L 2 M V Auger decay which should appear above the L 2 -edge roughly at this kinetic energy (see results on stoichiometric TiO 2 above).

As discussed in the introduction of this section, there seems to be a gradual evolution in the Ti-L 2,3 M 2,3 V Auger spectra from TiO 2 to metallic Ti [START_REF] Rao | Interatomic Auger transitions in transition-metal oxides[END_REF][START_REF] Göpel | Surface defects of TiO 2 (110) : A combined XPS, XAES and ELS study[END_REF][START_REF] Sadeghi | Electronic interactions in the rhodium/TiO 2 system[END_REF]. It is therefore relevant to analyze spectra from bulk titanium (see Figure 3.20, right panel). The valence band spectra is now only made from the Ti-3d states. A L 3 V V (respectively L 2 V V ) Auger decay appears in the valence band resonant spectra at constant kinetic energy when the photon energy reaches the L 3 (L 2 ) ionization threshold. Associated with this valence-band profile, the Ti-L 2,3 M 2,3 V Auger decay is dominated by a unique component, at the kinetic energy of the Auger structure due to the defect peak in the TiO 2-x sample. A weak feature at 420 eV kinetic energy appears around the L 2 edge and could be the Ti-L 2 M 2,3 V Auger decay.

Conclusion

The L 3 and L 2 parts of the Ti-LM V Auger decay in TiO 2 can be disentangled by scanning the photon energies across the Ti-L 2,3 edges. The evolution of the Auger lineshape was also studied as a function of the stoichiometry, from TiO 2 to metallic Ti. The interpretation of the two main lines in the Ti-LM V Auger decay in terms of inter and intra-atomic Auger decay is not completely correct. Indeed, in stoichiometric TiO 2 , those two lines clearly corresponds to the Ti-L 3 M 2,3 V and the L 2 M 2,3 V lines. On the other hand, as soon as the TiO 2 crystal is reduced, the high kinetic energy Auger line is clearly a probe of the reduction of the Ti ion, as it is linked to the defect state peak appearing close to the Fermi level when oxygen vacancies are created. More details about this study can be found in reference [START_REF] Danger | Intra-atomic versus interatomic process in resonant Auger spectra at the Ti L 2,3 edges in rutile[END_REF] and [START_REF] Le Fèvre | Stoichiometry-related Auger lineshapes in titanium oxides : Influence of valence-band profile and of Coster-Kronig processes[END_REF]. In these papers, the conclusions drawn thanks to resonant electron spectroscopy measurements are also confirmed by photoelectron-Auger electron coincidence measurements.

Introduction

As described in the previous section, defects play an important role in many chemical reactions at oxide surfaces. The understanding of their structural and electronic properties is a major issue of surface chemistry. The rutile-TiO 2 [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF] surface is often considered as a model system for oxide surfaces and has been the subject of extensive studies [START_REF] Allali | Experimental determination of the GaAs and Ga 1-x Al x As band-gap energy dependence on temperature and aluminum mole fraction in the direct band-gap region[END_REF]. Under standard preparation conditions, for the (1×1) surface, the major defect type in the near surface region is oxygen vacancies at the bridging (O1) site ("V" in figure 3.21). Each oxygen vacancy gives rise to two excess electrons and the appearance of new electronic states in the TiO 2 band gap at about 2 eV above the valence band maximum (see valence band spectra in Figure 3.20 of the previous section). These defect states are mainly of Ti-3d character as it was shown by resonant photoemission experiments [START_REF] Zhang | Cation-ligand hybridization for stoichiometric and reduced TiO 2 (110) surfaces determined by resonant photoemission[END_REF][START_REF] Le Fèvre | Stoichiometry-related Auger lineshapes in titanium oxides : Influence of valence-band profile and of Coster-Kronig processes[END_REF]. However, the distribution of the excess charge, which is crucial in modeling the TiO 2 (110) surface and its chemical and photochemical behaviour, remained an open issue.

By theoretical calculations, the defect states are found either as delocalized over several Ti-sites in the surface and subsurface layer [START_REF] Lindan | First-principles spin-polarized calculations on the reduced and reconstructed TiO 2 (110) surface[END_REF][START_REF] Paxton | Electronic structure of reduced titanium dioxide[END_REF] or in the surface layer, the two excess electrons being localized on two specific surface Ti-sites [START_REF] Bredow | Electronic structure of an isolated oxygen vacancy at the TiO 2 (110) surface[END_REF][START_REF] Di Valentin | Electronic structure of defect states in hydroxylated and reduced rutile TiO 2 (110) surfaces[END_REF]. On the experimental side, there is some evidence that the excess electrons are unpaired and localized [START_REF] Serwicka | Localization of conduction band electrons in polycrystalline TiO 2 studied by ESR[END_REF]. The organization (or not) of the excess electrons into a 2D electron gas also gives clues on their localized or delocalized character. It was recently shown that their behaviour was very different in rutile and anatase, the two polymorphs of TiO 2 (see Supplemental Material of reference [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF]). Generally speaking, the study of 2D metallic electron systems at the surface of oxide, or at the interface between two oxides, triggered many other theoretical investigations on the nature of these defect states (see chapter 5).

It is very challenging to experimentally locate these excess electrons, coming from a very low density of defects in the crystal structure. For the surface layer, it can be achieved by Scanning Tunneling Microscopy (STM) [START_REF] Setvin | Direct view at excess electrons in TiO 2 rutile and anatase[END_REF], but it is impossible to have information on the subsurface layers by this technique. In this section, we will show that PED is a technique consisting in measuring the intensity of a photoemission peak (or an Auger line) as a function of the electron emission angle (see figure 3.22). As first explained by K. Siegbahn [START_REF] Siegbahn | Electron Spectroscopy For Atoms, Molecules And Condensed Matter[END_REF] and later by other authors like C. S. Fadley [START_REF] Fadley | The Study of Surface Structures by Photoelectron Diffraction and Auger Electron Diffraction[END_REF], this intensity map shows modulations which are linked to the local order around the excited atom. As for EXAFS, this is due to the scattering of the photoelectron wave function by the surrounding atoms. For high kinetic energy electrons, the scattering is more likely in the forward direction. Hence, a high photoemission intensity is measured along the dense atomic directions of the crystal and the interpretation of the PED patterns is quite direct and simple. On the other hand, for low kinetic energy electrons, the scattering probability is more isotropic, making the experimental results more complex to interprete. Complete multiple scattering calculations are then mandatory. PED patterns are therefore very sensitive to the photoelectron kinetic energy.

In our experiment on TiO 2 , PED is recorded for photoelectrons from the Ti-3d defect state which are resonantly excited at the Ti-2p → 3d transition. At this resonance, as seen in the previous section, the defect state photoemission is strongly enhanced [START_REF] Le Fèvre | Stoichiometry-related Auger lineshapes in titanium oxides : Influence of valence-band profile and of Coster-Kronig processes[END_REF], which is crucial to obtain a sufficient signal-to-noise ratio in PED.

Experimental conditions

The experiments were performed at the ALOISA beamline of the Elettra Synchrotron Light Source in Trieste, Italy. The TiO 2 (110) single crystal was cleaned by 1 keV Ar bombardment and annealed for 45 min at 870 K under ultrahigh vacuum. This standard protocol produces flat (1×1)-terminated surfaces with a bridging oxygen vacancy concentration of a few percent [START_REF] Li | Oxygen-induced restructuring of the TiO 2 (110) surface : a comprehensive study[END_REF]. The PED from the defect states was recorded for a photon energy at the maximum of the L 2 -edge resonance (462 eV). The X-ray beam was impinging in grazing incidence and the light polarisation was normal to the surface. A plot over (θ,φ) will be called a "PED pattern" in the following.

Results

As a reference, we first measured the nonresonant PED from the Ti-2p 3/2 core level taken with a photon energy of 920 eV, so that the kinetic energy of the photoelectrons was nearly the same (460 eV) as in the case of the resonant PED from the defect state. The two PED patterns are shown in figure 3.23. Since PED probes the local environment around the emitting Ti atoms, the strong difference between the two patterns immediately indicates that the defect charge is not uniformly distributed over all Ti-sites (as is the Ti-2p charge).

We calculated the PED patterns for emission from the six inequivalent Ti sites on the first three TiO layers, labeled Ti(1)-Ti [START_REF] Richter | Spin Separation in a Metal Overlayer[END_REF], taking into account a surface reconstruction as described in [START_REF] Lindsay | Revisiting the surface structure of TiO 2 (110) : A quantitative Low-Energy Electron Diffraction study[END_REF]. Among the different Ti(n) sites in the cluster, the emitter was taken to be the one closest to the O1 vacancy. Some of the calculated PED patterns are shown in figure 3.24). The main contributions to the experimental pattern are shown to mainly come from Ti(3) (34% of the total signal), whereas contributions from Ti(4), Ti(5) and Ti(6) are found to be negligible.

Conclusions

These resonant PED measurements provide a unique tool to characterise defects like O-vacancies in oxides beyond the surface layer. In rutile, we found that the defect charge is distributed over several surface and subsurface lattice Ti sites. By far, most of the charge is found on subsurface sites, with a maximum on the second layer site Ti(3). The charge on the other second layer site (Ti(4)) is completely negligible. The surface layer sites, Ti(1) and Ti(2), carry a small, but non-negligible amount of charge. this is in qualitative agreement with DFT calculations. More details about this study can be found in reference [START_REF] Krüger | Defect states at the TiO 2 (110) surface probed by resonant photoelectron diffraction[END_REF].

Conclusion

In this chapter, we showed that resonant electronic spectroscopies were well-adapted to provide a fine information on the XANES of complex materials. Resonant Auger allowed us to detect quadrupolar transitions in small prepeaks of the Ti-K in rutile-TiO 2 , whereas resonant photoemission was used in a mixed-valent Ce-compound to identify the final electronic configurations responsible from the main structures in the Ce L 3 -edge. These results were obtained in the late nineties on the ID32 (ESRF) and BW2 (Hasylab) beamlines, two pionneering experimental setups for hard X-ray photoemission. Ever since, numerous beamlines dedicated to this technique were built throughout the world. As compared to classical ARPES in the VUV or soft X-ray range, the goals are to have a more bulk-sensitive measurement as well as to probe embedded interfaces in heterostructures. The price to pay is a much reduced cross section of the valence band, making those measurements more difficult to handle.

Another popular application of resonant measurements, which we didn't explore here is XAS eliminating the core-hole lifetime broadening, by recording either fluorescence [START_REF] Hämäläinen | Elimination of the inner-shell lifetime broadening in x-ray-absorption spectroscopy[END_REF] or Auger decay [START_REF] Drube | High Resolution Ag L 3 -XANES Studies of AuAg Alloys Using the Electron Yield of a Narrow Auger Channel[END_REF].

A typical use of resonant photoemission is to choose the photon energy in order to amplify spectral features in a photoemission spectrum. The classical example is the use of the 4d → 4f resonance to amplify the 4f spectral weight in the valence band of rare-earth compounds [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF][START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF]. We used this specificity to amplify the peak which appears close to the Fermi level in rutile-TiO 2 when O-vacancies are created in the crystal. This peak, due to the filling of the Ti-3d states, is notably amplified when excited with photon energy around the Ti L 2,3 -edges [START_REF] Danger | Intra-atomic versus interatomic process in resonant Auger spectra at the Ti L 2,3 edges in rutile[END_REF], [START_REF] Le Fèvre | Stoichiometry-related Auger lineshapes in titanium oxides : Influence of valence-band profile and of Coster-Kronig processes[END_REF]. The locations of O-vacancies can then be identified by resonant photodiffraction [START_REF] Krüger | Defect states at the TiO 2 (110) surface probed by resonant photoelectron diffraction[END_REF].

The results presented here were mainly published in references [START_REF] Le Fèvre | High-energy resonant photoemission and resonant Auger spectroscopy in Ce-Rh compounds[END_REF], [START_REF] Danger | Quadrupolar transitions evidenced by resonant Auger spectroscopy[END_REF], [START_REF] Danger | Intra-atomic versus interatomic process in resonant Auger spectra at the Ti L 2,3 edges in rutile[END_REF], [START_REF] Le Fèvre | Stoichiometry-related Auger lineshapes in titanium oxides : Influence of valence-band profile and of Coster-Kronig processes[END_REF] and [START_REF] Krüger | Defect states at the TiO 2 (110) surface probed by resonant photoelectron diffraction[END_REF].

CHAPITRE 4

Angle Resolved Photoelectron Spectroscopy-The CASSIOPEE beamline

Introduction

The results presented in the second chapter of this dissertation were obtained on the DCI (Dispositif de Collisions dans l'Igloo), one of the two storage rings operated by the LURE (Laboratoire pour l'Utilisation du Rayonnement Electromagnétique), the former French synchrotron radiation facility which was located in Orsay. This light source as well as our experimental setup were not efficient enough for the resonant measurements in the X-ray range (Ti-K-edge or Ce-L 3 -edge) presented in chapter 3. These results were obtained either at HASYLAB (HAmburger SYnchrotronstrahlungsLABor, Hamburg, Germany), an upgraded first generation storage ring, or at ESRF (European Synchrotron Radiation Facility, Grenoble), the european third generation source. At this time (late nineties), DCI, which started operation in 1976, was clearly overtaken by more modern sources.

Super ACO, the other storage ring at LURE, started to deliver photons in 1988. Unlike its predecessors (ACO (Anneau de Collisions d'Orsay) and DCI, built for particle physics), it was devoted only to synchrotron radiation. It was an efficient machine in the VUV and soft X-ray ranges, working with positrons at 800 MeV. Nevertheless, shortly after its starting, it was already clear that higher energy machine (working around 1 or 2 GeV) were promissing and able to produce photon beams with a much higher brilliance. Our data at the Ti-L 2,3 -edges were taken at Elettra, the Italian synchrotron radiation source located close to Trieste, whose operation energy at this time was between 1 and 2 GeV.

The size of a storage ring (and consequently, its price) is quite proportionnal to the energy of the stored particles. Super ACO (800 MeV) was a relatively cheap machine with a diameter of around 23 m as compared to ESRF (6 GeV, 320 m diameter). An intermediate energy machine (between 2 and 3 GeV) rapidly appeared as an ideal solution for an "average" European country. Indeed : 67 -It is expensive, but still affordable.

-VUV, soft X-ray and hard X-ray beamlines can be implemented, although hard X-ray beamlines are certainly less efficient than on high energy machines. -In France, the country which was already hosting the European synchrotron radiation facility optimized for hard X-rays, such an intermediate energy machine would be complementary and could satisfy both the hard X-ray and the VUV communities, formerly gathered around DCI and Super-ACO, respectively. Numerous intermediate energy machines have therefore florished all over Europe : Elettra in Italy, SLS in Switzerland, BESSY II in Germany, ALBA in Spain, DIAMOND in Great Britain, MAX IV in Sweden... The French project was called SOLEIL, for Source Optimisée de Lumière d'Energie Intermédiaire de LURE. As indicated in the name, it was studied at LURE between 1989 and 1999. The story of the SOLEIL project and the final political decision to finally build this new French machine is a rich and lively story which is told in reference [START_REF] Traverse | Le projet SOLEIL, chronique et analyse d'un combat. Acteurs de la science[END_REF]. Nevertheless, it was accepted by the French government in 2000, the first beam was stored in the machine in 2006 and the first experiments started in 2008.

The CASSIOPEE beamline, dedicated to angle resolved photoemission and spinresolved photoemission was one of the first eleven beamlines of the construction phase (so-called phase I beamlines). It was positively evaluated by the Scientific Advisory Committee and the Council of SOLEIL in 2002. The building of the CASSIOPEE beamline started in 2002 ; the first photons were delivered by the beamline in February the 8 th 2007 and the experiments started in June 2008.

In this section, I will first present the Angle-Resolved PhotoElectron Spectroscopy technique (ARPES). I will then describe the CASSIOPEE beamline and its main characteristics.

Angle-Resolved PhotoElectron Spectroscopy

-ARPES

The ARPES equations

In a photoemission experiment, a sample (a solid in our case) is irradiated with monochromatic photons of energy hν. By photoelectric effect [START_REF] Einstein | Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt[END_REF], a photon can be absorbed by an atom of the material which then emits an electron with a kinetic energy E kin given by

E kin = hν -Φ -|E B | (4.1)
where E B is the binding energy of the electron and Φ is the work function of the material, i.e. the height of the potential barrier that the electron has to cross to go from the solid to the vacuum. This work function is a characteristic constant of the sample surface [START_REF] Einstein | Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt[END_REF].

It can be determined by photoemission experiments, but it is easier to refer the binding energy to the measured Fermi level E F as a reference, i.e. to use it as the zero for binding energies. The kinetic energy of an emitted electron can be measured by an electrostatic electron analyzer. Such a photoemission experiment is sketched on figure 4.1. A kinetic energy scan gives a measurement of the density of states at the corresponding binding energy of the electron in the solid, broadened by lifetime effects (∆E = ∆τ ), as sketched in figure 4.2. This figure also introduces some notions which are useful for ARPES measurements.

ARPES focuses on valence electrons. It consists in measuring both the kinetic energy and the emission angle of the photoemitted electrons, the goal being to determine both their wave vector k and their binding energies inside the solid E B to plot the band structure. To achieve that, one uses the conservation laws of energy and momentum.

Figure 4.3 shows the principle of an ARPES experiment. One measures outside the solid both the kinetic energy of a collected electron and its emission angle with respect to the sample surface normal θ. Let's call k out and E out kin the wave vector and the kinetic energy of a photoemitted electron outside the solid.

As seen at the begining of this section, the energy conservation equation written in equation 4.1 immediately gives

E B = hν -Φ -E kin (4.2)
Can we now determine the wave vector of the photoelectron in its initial state k, before the excitation by the photon ? To reach this goal, one has to go deeper into the description of the photoemission process. The electron initial state is described by its binding energy E B and its wave vector k and belongs to the occupied states of the solid band structure. Once excited by the photon, the electron is promoted to an empty state of the band structure inside the solid, defined by its energy E f and its wave vector k in . The momentum conservation therefore writes

k in = k + k photon (4.3)
Taking a photon energy and an electron kinetic energy of 50 eV (a typical value for ARPES measurements), the ratio

k k photon (with k = √ 2mE kin and k photon = E photon c ) is
of the order of ∼ 10 -2 . We can therefore safely neglect k photon , at least in this photon energy range and make the approximation

k in ∼ k (4.4)
This is summarized on the left part of figure 4.4. The conservation of k during the photoexcitation process results in a "vertical" transition of the electron in the band structure.

Our ARPES measurement provides the kinetic energy of the photoelectron E kin . The photoelectron being a free electron, its kinetic energy can be written as

E kin = 2 (k out ) 2 2m (4.5)
k out is therefore given by

k out = √ 2mE kin (4.6)
By measuring E kin , one is therefore able to determine the modulus of the wave vector of the photoelectron outside the solid, k out . We now show that k out is slightly different from k in and k, due to the crossing of the surface potential barrier by the photoelectron. In its initial state, defined by its binding energy E B and its wave vector k, the electron belongs to the occupied states of the solid band structure (black solid line), below the Fermi level. The excitation by the photon promotes it to an empty state of the band structure inside the solid, whose energy is E f but with the same wave vector k. This final state is approximated by a free-electron-like parabola (red dotted line)

E f = 2 k 2 2m -E 0 .
When it crosses the surface to reach the vacuum, the electron loses an energy Φ and is now a free electron, belonging to a parabolic dispersion shifted in energy by V 0 = E kin + Φ with respect to the approximated final state inside the solid. V 0 is called the inner potential.

k out can be decomposed into its two components parallel and perpendicular to the surface (see figure 4.3) :

k out || = √ 2mE kin sin θ (4.7) k out ⊥ = √ 2mE kin cos θ (4.8)
The k || component is conserved when the electron crosses the surface as the whole process is invariant under translations parallel to the sample surface. Hence

k || = k out || = √ 2mE kin sin θ (4.9)
On the other hand, the k ⊥ component is affected by the crossing of the surface potential barrier. k out ⊥ is therefore not a direct measurement of k ⊥ , the component perpendicular to the surface of the electron wave vector in its initial state. A determination of k ⊥ requiers the so-called free electron approximation. It consists in assuming a free electron-like dispersion of the electron in its intermediate state, i.e. after it has been excited by the photon but when it is still inside the solid. This free electron-like dispersion is the red dotted line in figure 4.4. It should approximate as well as possible the final state dispersion to give a parabola bottom at an energy E 0 . This final state dispersion is therefore given by

E f = 2 k 2 2m -E 0 (4.10)
As described by equation 4.2, the electron loses an energy Φ when crossing the surface potential barrier and

E f = E kin + Φ (4.11)
Equation 4.10 therefore becomes

E kin + Φ = 2 k 2 2m -E 0 (4.12)
Introducing the inner potential

V 0 = E 0 + Φ and expressing k 2 as k 2 = k 2 || + k 2 ⊥ one obtains E kin = 2 (k 2 || + k 2 ⊥ ) 2m -V 0 (4.13) k 2 ⊥ = 2m 2 (E kin + V 0 ) -k 2 || (4.14)
Using the expression of k || given by equation 4.9, one directly obtains

k 2 ⊥ = 2m 2 (E kin + V 0 ) - 2m 2 E kin sin 2 (θ) (4.15) k 2 ⊥ = 2m 2 E kin cos 2 (θ) + V 0 (4.16) k ⊥ = 2m 2 E kin cos 2 (θ) + V 0 1/2 (4.17)
Hence, the electron is sligtly refracted when it leaves the solid, the component of its wave vector perpendicular to the surface being reduced by the potential barrier at the interface between the solid and vacuum (see figure 4.5).

Putting together equations 4.2, 4.9 and 4.17 gives a set of three equations, allowing to determine the binding energy and the wave vector of the photoelectron in its initial state as a function of the measured values of E kin and θ : Those equations show that it is possible to explore the reciprocal space (i.e. to probe different values of k) either by changing the collection angle θ or by changing the photon energy hν (and then the photoelectron kinetic energy). Modern electron analyzers make it possible to collect photoelectrons simultaneously over a large θ-range (of the order of 30 • , i.e. ±15 • around the surface normal) along a precise direction defined by the entrance slit of the analyzer. The result is then an image, as shown on figure 4.6.

E B = hν -Φ -E kin (4.18) k || = √ 2mE kin sin θ (4.19) k ⊥ = 2m 2 E kin cos 2 (θ) + V 0 1/2 (4.20)

ARPES : assets and problems

In an ARPES experiment, the main problems to tackle are : -The samples have to be single crystals.

-ARPES is very surface sensitive. For the kinetic energies useful for ARPES (between 10 and 100 eV), the electron mean free path in matter is of the order of 5-10 Å. That means that the probed depth of the sample is of the order of a few atomic planes. The electronic structure being likely to change close to the surface, this is a strong drawback of the technique when one wants to characterize the bulk electronic structure. There are now attemps to use higher energy photons (soft [START_REF] Sekiyama | Probing bulk states of correlated electron systems by high-resolution resonance photoemission[END_REF] or even hard X-rays [START_REF] Gray | Probing bulk electronic structure with hard x-ray angle-resolved photoemission[END_REF]) to increase the kinetic energy of the photoelectrons and hence their mean free path, while keeping energy resolutions good enough for ARPES. -The study of 3D systems is not straightforward, due to the inner potential V 0 involved in the k ⊥ formula. In practice, the inner potential V 0 can be determined by measuring the periodicity of the electronic structure along k ⊥ . Based on this measurement, V 0 is adjusted so that the k ⊥ values of high symmetry points of the measured electronic structure correspond to the momenta of high symmetry points of the reciprocal lattice. Nevertheless, the study of 2D-systems (where only k || is of interest) is much easier. On the other hand, the assets of ARPES are numerous : -It is a unique tool to image the band structure of a solid. With a state-of-the-art 74 -The Hamiltonian describing the interaction between the photon and the electron can be written (in the dipolar approximation) as .r, where is the polarisation of the incident light and r is the electron position. That means that if one uses a polarised photon source (like synchrotron radiation), the relative orientation of the electric field and of the electron orbital will play a role in the photoemission intensity. Practically, the contribution of some orbitals can be cancelled or enhanced by choosing the right experimental conditions. In a simple experimental geometry, where the horizontal plane is a mirror plane for the sample and also the incidence plane (containing both the incident photons and the collected electrons, see figure 4.7), a simple rule says that only the orbitals with the same parity as the polarisation with respect to this plane contribute to the signal. Hence, a s-polarisation, which is odd with respect to the incidence plane will reveal orbitals which are odd with respect to this plane. On the contrary, p-polarisation (even with respect to the incidence plane) will reveal even orbitals. This is a very useful asset of ARPES to also provide information on the symmetry of the observed bands. -The matrix element describing the photoemission process is

w f i ∝ 2π | < Ψ f |H int |Ψ i > | 2 δ(E f -E i -hν) (4.21)
where H int is the photon-atom interaction Hamiltonian, Ψ i is N -electron wave function (of energy E i ) of the atom in its initial state, whereas Ψ f describes the (N -1)-electron system and the photoelectron in the final state (after the excitation by the photon of energy hν) of energy E f . The sudden approximation consists in assuming that the photoelectron is decoupled from the remaining (N -1)-electron system in the final state. This approximation results in the factorization of the final state Ψ f in two independent factors corresponding to the (N -1)-electron system and the photoelectron. As a consequence, the N -electron wave functions can be written as

|Φ i Ψ i (N -1) and |Φ f Ψ f (N -1)
, where Φ i the initial one-electron wave function of the electron before the optical excitation and Φ f the final one-electron wave function of the electron in the solid after the optical excitation. Hence, using equation 4.21, the total photocurrent W (E, hν) = i,f w f i emitted by the sample can be re-written as

I(E, hν) ∝ |M f i | 2 A( k, E)δ(E f -E i -hν) (4.22)
where

|M f i | 2 ∝ | < Φ f |H int |Φ i > | 2
is a one-electron matrix element describing the optical transition of the photoelectron and

A( k, E) = m | < Ψ m (N -1)|Ψ i (N -1) > | 2 (4.23)
is the so-called spectral function [START_REF] Hüfner | Photoelectron Spectroscopy : Principles and Applications[END_REF].

The |M f i | 2 matrix elements contain the Hamiltonian and therefore all the experimental geometry effects (like the polarisation effects described in the previous item) or the photoemission cross section.

On the other hand, the spectral function A( k, E) gives the total probability to remove one electron of energy E and momentum k from the ground-state of the solid. One directly sees that if the N -electron system is not perturbed by the removal of one electron, Ψ i (N -1) will still be an eigenstate of the (N -1)-electron system. It will have a non-zero overlap only with itself and A( k, E) will be equal to 1. On the other hand, if the (N -1) remaining electrons are perturbed, Ψ i (N -1) will no longer be an eigenstate and will have an overlap with many Ψ i (N -1)states. The spectral function hence describes electron-electron correlations and, more generally, many-body effects in photoemission spectra. Those effects appear as perturbations to the regular dispersion, like kinks or band-renormalization.

Conclusion

In this section, we have presented ARPES, a powerful experimental technique for the characterisation of band structure in solids. The band structure can be imaged in the whole reciprocal space by scanning either the photoelectron emission angle or the excitative photon energy. Synchrotron radiation is therefore the ultimate light source for ARPES measurements : it is an intense, accordable, polarised and, in the photon energy region where valence band cross-section are large (between 10 and 100 eV), energy resolutions of the order of 1 meV can be achieved. I contributed to the design, the mounting and the operation of the CASSIOPEE beamline at SOLEIL dedicated to ARPES and spin-resolved photoemission. In the following section, I will present this beamline and its main characteristics.

The CASSIOPEE beamline 4.3.1 Introduction

The CASSIOPEE beamline was mounted by François Bertran and myself under the supervision of Amina Taleb-Ibrahimi and with the technical support of Julien Pinon, Daniel Ragonnet and Françoise Deschamps. CASSIOPEE is located on the I15-M section (a 5.5 m long straight section) of the storage ring and provides a monochromatic Xray beam, tunable in the 7.5-1500 eV energy range with vertical, horizontal or circular polarisations. CASSIOPEE is equipped with two photoemission setups for ARPES and spin resolved measurements, respectively. Those measurement chambers are coupled to a very complete MBE system allowing for surface preparations and thin films deposition and characterisation. A 3D-view of the beamline, from the entrance optics to the endstations is shown on figure 4.8. In this section, we will describe the sources, the optics and the experimental chambers of the CASSIOPEE beamline.

Sources : the HU256 and HU60 undulators

Two undulators, called HU256 and HU60, are necessary to cover the large 7.5-1500 eV photon energy range available on CASSIOPEE which allows for "classical" ARPES measurements, but also for soft X-ray ARPES or core level measurements. Both undulators were designed at SOLEIL by the GMI (Groupe Magnétisme et Insertions : Magnetism and Insertion Device Group).

HU256

Photons in the 7.5-150 eV energy range are provided by a 3.6 m long elliptical electromagnetic undulator with a 256 mm magnetic period, HU256. Our HU256 was produced, tested and magnetically measured by the Budker Institute for Nuclear Physics (Novosibirsk, Russia) for Synchrotron SOLEIL. It was the first of this type and two other models were built afterwards for the ANTARES and PLEIADES beamlines. It is made of two series of coils generating a vertical or a horizontal periodic (or pseudo-periodic) magnetic field. The vertical and horizontal magnetic fields are formed by 27 B z -dipole magnets and by 28 B x -dipole magnets, respectively. HU256 can produce linearly (vertical or horizontal) polarised light as well as right or left circularly polarised light. The 7.5-150 eV photon energy range is covered by the HU256 first harmonics, for current in the coils varying from 175 to 40 A in linear horizontal polarisation, or 275 to 70 A in linear vertical polarisation. To get rid of the contribution of higher harmonics, HU256 can also work in a pseudo-periodic mode. To achieve this for linear horizontal polarised light, modulation coils are placed on all the B z dipoles to modulate the vertical magnetic field. For linear vertical polarised light, two independent power supplies modulate the horizontal magnetic field. In the aperiodic mode, although the intensity of the first harmonics is reduced, the higher harmonics are either significantly reduced, or shifted in energy (and hence filtered by the monochromator).

HU60

The HU60 undulator provides photons in the 90-1500 eV energy range. It is 1.8 m long permanent magnet APPLE II-type undulator with a 60 mm magnetic period. As can be seen on figure 4.10, it is made of four rows of magnets, placed above and below the electron beam. One can change the energy of the emitted photon lines by changing the gap in between the top and bottom rows of magnets, thus changing the magnetic field experienced by the electrons. Linearly (vertical or horizontal) polarised light as well as right or left circularly polarised light can be produced by changing the phase, i.e. by moving horizontally two rows of magnets with respect to the others (see top part of figure 4.10). In our case, a zero phase corresponds to linear horizontal polarisation. By setting this phase to half of the magnetic period (30 mm in our case), the polarisation flips to linear vertical. In between these two extreme conditions, the polarisation is elliptical, i.e. both B z and B x are non-zero. The phase corresponding to purely circular right or left polarisation (B z = B x ) depends on the chosen gap and therefore on the selected photon energy. As for HU256, the position of the first harmonics as a function of the gap was experimentally measured and tabulated. For photon energies from 90 to 950 eV, one can use the first harmonics ; from 950 to 1200 eV, the flux is larger on the second harmonics.

Optics

Entrance optics

The CASSIOPEE entrance optics is made of three Pt-coated silicon mirrors (a M1a plane mirror, and two M1b and M1c spherical mirrors) attached to the same rotating table whose rotation axis is vertical, in the plane of M1a surface. The surfaces of the three mirrors are ideally parallel. The beam first comes on M1a and is then reflected either on M1b (low energy position) or M1c (high energy position), depending on the incident angle on M1a :

-In the low energy position (7.5 eV-150 eV photon energy range, when HU256 is used), the rotating table is set for an incident angle of 5.02 • on M1a. The photon beam is then reflected towards M1b, whose radius is calculated to focus the HU256 source point onto the monochromator's gratings. -In the high energy position (100 eV-1500 eV photon energy range, when HU60 is used), the rotating table is set for a smaller incident angle of 2.44 • on M1a to improve the reflectivity of the mirrors. The photon beam is then reflected towards M1c, whose radius is calculated to focus the HU60 source point onto the monochromator's gratings. These two working positions are sketched on figure 4.11. A picture of the entrance optics is shown on figure 4.12. If the mirrors are perfectly parallel, the exit beam position should remain the same, whatever the working position is. To correct any misalignment, M1a can also be rotated individually ; practically, this has to be done each time the working position is changed. The incident and the outgoing beams are then parallel and shifted horizontally by 62 mm. This horizontal shift allows to shield the machine high energy brehmstrahlung thanks to a tungsten rod, paced on the axis of the incoming beam, whereas the useful VUV-photons, reflected by M1a, continue their route in the beamline.

The power absorbed by these first mirrors depends on the experimental conditions, but in the worst case (with a small gap on HU60), it is of the order of 300 W. The mirrors have therefore to be cooled. We chose to use a cryogenic cooling for our entrance optics, at a temperature around 100 K where the silicon dilatation coefficient is zero. This should avoid any deformation (thermal bump) of the mirror surfaces under the impact of the photon beam. This cooling is insured by a liquid nitrogen closed loop circulation with a 8 bar-pressure to keep nitrogen liquid at 100 K.

To summarize, the CASSIOPEE entrance optics has four main goals :

-Changing the incident angle allows to work at low or high photon energies.

-The different radius of the M1b and M1c spherical mirrors take into account the different position of the source when using HU256 or HU60. -It absorbs most of the parasitic power emitted by the machine thanks to its cryogenic cooling. -It shifts horizontally the useful photons, allowing the shielding of the very high energy photons on the undulators axis. This entrance optics principle was first developed for both the CASSIOPEE and the TEMPO beamlines. It was then adopted by other VUV-beamlines at SOLEIL (like PLEIADES or ANTARES). Other entrance optics rely on the same principle but are water-cooled (SEXTANT, HERMES).

Monochromator

The design of the CASSIOPEE plane grating monochromator was done by the SO-LEIL Optics Group. The starting point is the famous SX700 monochromator [START_REF] Petersen | The plane grating and elliptical mirror : A new optical configuration for monochromators[END_REF] but several modifications have been made by the Optics Group. It is a plane grating monochromator (PGM), in which both the incident and the emergent angles on the grating can be chosen independently. The working principle of the monochromator is sketched in figure 4.13. A view inside the instrument is presented on figure 4.14. One can choose the incident angle of the white beam on the plane grating by rotating the grating around a horizontal axis contained in the grating surface plane. The emergent angle can be chosen by rotating the plane mirror located above the grating. The shift in height between the incoming white beam and the outgoing monochromatic beam is constant and equal to h=20 mm. To ensure this constant shift at the exit, the mirror rotates around a horizontal axis located 10 mm ( h 2 ) below the grating plane. For a given couple (α,β), the selected wavelength is given by the gratings law :

cos α -cos β = -N kλ (4.24)
where k is the diffraction order (-1 for CASSIOPEE) and N is the number of lines/mm on the grating. The CASSIOPEE monochromator contains three different gratings with 400 l/mm, 800 l/mm and 1600 l/mm respectively. The CASSIOPEE monochromator is designed to work in the modified Petersen mode, which means that α and β are always chosen to fulfil

cos β cos α = c ≈ 0.2 (4.25)
to ensure an optimal resolution on the whole photon energy range. These two 4.24 and 4.25 conditions imply that a given photon energy corresponds to a unique (α,β) couple.

The CASSIOPEE monochromator was built in Berlin (Germany) by the BESTEC company, under the supervision of the SOLEIL Optics Group and the CASSIOPEE staff. It was the very first of this type built for SOLEIL and it was adopted by many other beamlines afterwards (PLEIADES, ANTARES, HERMES). The expected resolving power ( E ∆E ) was calculated by the Optics Group on the whole accessible photon energy range. Small variations of c around the 0.2 value have been allowed in order to optimize the resolution which was predicted to be always larger than 25000, with a peak at 70000 at 100 eV (see figure 4.15). It is hard to confirm these calculations experimentaly on the whole photon energy range. CASSIOPEE is equipped with a gas cell, placed in between the The gratings themselves also have an original design. They focus the beam vertically thanks to their varied line spacing (VLS), but the groove depth also varies along the direction perpendicular to the beam. Hence, by choosing the position of the grating with respect to the beam, one can choose the groove depth experienced by the beam and change its reflectivity. This allows to optimize either the flux or the purity of the beam (ratio between first harmonics and higher orders harmonics). They were made by the Jobin-Yvon company (Longjumeau, France), based on an idea of the SOLEIL Optics Group.

To take advantage of this varied groove depth, the gratings can be translated perpendicular to the beam. To ensure minimum parasitic angular displacements during this translation, the BESTEC company took great care of its mechanical design. Angular displacements are inevitable, but BESTEC manages to achieve a reproducibility better than 10 to 17 µrad (∼ (0.6×10 -3 ) • ). Four gratings of this type can be installed in the CASSIO-PEE monochromator, but we only use three for the moment. Gratings with 400, 800 and 1600 l/mm allow working in the 7.5-155, 35-826 and 69-1550 eV photon energy ranges, respectively. The first two gratings are optimized to focus the beam emitted by HU256, the 800 l/mm grating providing more flux and less resolution than the 400 l/mm one. The third (1600 l/mm) grating has been designed for HU60. Both the gratings and the The natural linewidth of the lines due to the core-hole lifetime being usually estimated to 115 meV, we adjusted the experimental spectrum with seven Voigt functions, combining a 115 meV wide lorentzian and a resolution gaussian. The best adjustment of the experimental spectrum is obtained for an experimental resolution of 10 meV. This value corresponds to a resolving power of 40000, which is the value expected from the Optics Group calculations. After the monochromator, the beamline is divided into two branches providing photons to the two CASSIOPEE endstations. The beam goes either directly on the ARPES setup focusing optics, or, when a deviation mirror is inserted (deviation mirror M3 on figure 4.8), to the spin-resolved photoemission.

The CASSIOPEE endstations

The CASSIOPEE beamline hosts two endstations dedicated to spin-resolved photoemission and ARPES, respectively. A third chamber (MBE chamber) allows the preparation of the samples (surfaces or thin films). These three chambers are all connected to a small crossway chamber, where up to sixteen samples can be stored on a carrousel (see figure 4.17). All this installation is in ultrahigh vacuum ; a fast entry lock mounted on the crossway chamber allows the introduction of new samples into the system.

The spin-resolved photoemission experiment

The spin-resolved photoemission setup was designed by François Bertran. The beam on the sample is focused to around 300 µm 2 by the toroidal deviation mirror used to deflect the beam towards the experiment. The setup is equipped with a SCIENTA SES-2002 spectrometer which has been modified in order to integrate a Mott detector for the spin polarisation measurement. The usual 40 mm diameter 2D detector has been replaced by a smaller one (25 mm diameter) and an electronic optics has been added at the vacant space. The spectrometer allows then to perform conventional ARPES measurements with an angular range of ±8 • and spin-resolved measurements. The electronic optics collects electrons through a small aperture located below the 2D-detector and sends them towards the Mott detector. The size of this aperture determines the contribution of the spin detector to the total energy and angular resolutions of the spin-resolved measurements, which are 1% of the spectrometer pass-energy and ±1.8 • , respectively. The Mott detector is made of a gold target towards which electrons are accelerated by a 28 kV bias and of four micro-channel plates. Each pair of micro-channel plates defines a scattering plane in which, thanks to the spin-orbit interaction, there is a spin-dependent left-right scattering asymmetry (Mott scattering). This asymmetry is proportional to the spin polarisation along an axis perpendicular to the scattering plane. In our geometry, with a sample normal parallel to the spectrometer axis (normal emission), we can measure the spin polarisations along the horizontal direction in the sample plane and along the normal to the surface. The sample holder has 4 axis of freedom (three translations and a polar rotation) and can be cooled down to 25 K thanks to a liquid helium cryostat. It also includes a manual azimuthal rotation. Finally, the sample can be magnetised in situ with a magnetic field up to 1200 Oe ; the photoemission measurements are performed in the remanent state.

The ARPES experiment

Two spherical and toroidal mirrors (pseudo-Wolter configuration, see figure 4.18(a)) focus the beam into the ARPES chamber. The size of the beam depends on the photon energy ; the larger the photon energy, the smaller the spot. Its average size is 50×30 µm 2 and figure 4.18(b) shows calculations from the Optics Group for 9, 25 and 100 eV.

The ARPES setup is a 400 mm diameter cylindrical chamber equipped with a Scienta R4000 electron analyzer. The whole chamber is mounted on a motorized movable frame to correctly position it with respect to the beam. The magnetic fields outside the chamber are shielded by a double µ-metal wall. The pumping system includes two turbomolecular pumps (mounted on the chamber and on the analyzer, respectively), an ion pump, a Ti-sublimator and a Getter cartridge pump. After a 5 to 7 days of bake-out (inside a metallic baking box), the vacuum is usually in the high 10 -11 mbar or smaller when the cryostat is cold.

We use a sample holder with only one rotation around its vertical axis. It was developed at the Laboratoire de Physique des Solides (Orsay, France) by Véronique Brouet, Gilles Guillier and Alessandro Nicolaou. It allows to cool the sample down to 5 K thanks to a liquid-He circulation cryostat. Figure 4. 19(a) shows the sample holder inside the chamber, in front of the analyzer. The golden box is a cryogenic shield cooled by the hot helium leaving the cold point of the cryostat. It is fixed with respect to the analyzer and the cold finger (on which the sample is mounted) rotates inside this shield. A door can be opened on the rear of the shield for sample transfer, but the shield can be completely closed during measurements. The simple mechanical design and this efficient shield confer very good cryogenic performances for this instrument. The sample can be cooled down to 7 K in less than one hour and down to 5 K in two or three hours. Two holes are drilled on the front of the shield to let the photons in, either from the beamline or from a UV-lamp. A vertical slit allows the electrons to travel from the sample to the analyzer. One can also see the nose of the electron analyzer on the left. This sample holder is fully motorized and computer-controlled. The beam comes at 45 • from the analyzer axis.

ARPES measurements on CASSIOPEE are performed using this single-rotation vertical sample holder. The rotation around its vertical axis is carried out by an in-air rotary platform (θ rotation). A second angular degree of freedom is provided by the Scienta analyzer, which is able to collect electrons in a 30 • angular range (±15 • around normal emission) along the direction of its entrance slit. In our setup, this slit is mounted vertically so that combined with the θ rotation of the sample holder, we can access a large part of the reciprocal space (see figure 4.19(b)).

An important parameter for the quality of the angle-resolved photoemission measurements is the overall energy resolution of the beamline (photon and electron spectrometer). This can be estimated from the width of the Fermi step on a metallic sample. We performed such measurements on polycrystalline Cu or Au surfaces, but the best results were obtained on a Ag [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF] Just to point out the difficulty of such resolution measurement, another fit using a temperature of 19 K in the Fermi function is shown in figure 4.20(b). Since part of the Fermi broadening is now accounted by temperature, the fit gives a better resolution of 2.7 meV with a roughly two times smaller residual. Let's say that the truth must be somewhere in between these two values...

The CASSIOPEE preparation chamber

One of the strength of the CASSIOPEE beamline is to propose a very complete preparation chamber for surface preparation and thin film growth. This chamber is coupled to the two endstations by an UHV transfer system. This MBE chamber is equipped with :

-Low Energy Electron Diffraction (LEED) and Reflection High Energy Electron Diffraction (RHEED) apparatus -An electron spectrometer for Auger analysis -A residual gas analyzer -A 3 keV ion gun for sputtering -A gas line where (in addition to Ar, used for the ion gun) three different gas sources can be quickly mounted -A ten-crucible (2 sets of 5) 6 kW e-gun for thin film deposition -Three quartz microbalances, monitoring the flux of deposited materials. One can be placed at the position of the sample for evaporator calibration, while the other two permanently monitor the flux emitted by the e-gun (one quartz crystal per set of crucibles) -Five other ports are available for new evaporators. On three of them, the evaporators can be mounted and baked independently, without venting the main chamber. Knudsen cells and Omicron EFM-type evaporators adapted to these ports are available for users On a beamline which is supposed to welcome users working in very different fields, it is fundamental to propose a versatile sample environment, able to handle as many materials as possible. In this prospect, we have developed (in collaboration with the SOLEIL Design Office) a three-position sample holder, for the preparation chamber. It is mounted horizontally, on a classical (X,Y,Z) table, a rotary feedthrough allowing to rotate the sample holder around its horizontal axis.

-On the first sample position, the sample can be heated by electronic bombardment. We can reach temperatures up to 1000 • C, suited for the preparation of most of the metals or oxides. The temperature can be measured either using a K-type thermocouple located close to the sample, or using a pyrometer placed on a viewport above the sample. On this first position, the sample can also rotate around an axis perpendicular to its surface (φ rotation) for RHEED measurements. -The second sample position allows to cool the sample down to 80 K, using a liquid nitrogen circulation. -The third sample position was designed to heat semiconductors by direct current.

In this case, the sample is mounted on a dedicated plate and a current, of the order of 1 to 10 A, circulates through the sample to heat it by Joule effect. This allows reaching very high temperatures (a temperature of 1200 • C is generally used to remove silicon oxide from a Si-wafer surface) in a very short time and a good vacuum. This complete Molecular Beam Epitaxy (MBE) system is a strong asset of the beamline. It made it possible to prepare quite sophisticated samples for ARPES or spin-resolved photoemission measurements like binary [START_REF] Bonell | Spin-polarized electron tunneling in bcc FeCo/MgO/FeCo(001) magnetic tunnel junctions[END_REF] or ternary [START_REF] Andrieu | Direct evidence for minority spin gap in the Co 2 MnSi heusler compound[END_REF] alloys for spintronics, thin films with metastable structure (like α-Sn [START_REF] Ohtsubo | Dirac cone with helical spin polarization in ultrathin α-Sn(001) films[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]), magnetic molecular films [START_REF] Djeghloul | Direct observation of a highly spin-polarized organic spinterface at room temperature[END_REF], quasi 1D-materials (either by metal deposition on a suitable surface [START_REF] Ohtsubo | Surface Tomonaga-Luttingerliquid state on Bi/InSb(001)[END_REF] or by polymerization of molecular chains [START_REF] Vasseur | Perepichka. Quasi onedimensional band dispersion and surface metallization in long-range ordered polymeric wires[END_REF])... In the following, I will present results about 2D electron gas at the surface of oxides. The ability to prepare those surfaces in UHV to obtain large and homogeneous samples (as compared to cleaved surfaces) as well as thin film deposition facilities was crucial for new breakthroughs.

Conclusion

Mounting a beamline is a team work. Throughout the design and building processes, the CASSIOPEE team took advantage of the help of many SOLEIL support groups : the Magnetic and Insertion Group, the SOLEIL Design Office, the Optics, Vacuum, Alignment, Detectors, Computing and Electronics Groups, the SOLEIL Workshop, not forgetting all the support from Administrative and Commercial Groups. It is a pleasure to acknowledge them all here for their help. Thanks to our joint efforts, the CASSIOPEE beamline has been working for already nearly 8 years, producing more than 90 publications since 2009.

In the following chapter, I will present an exemple of ARPES study on 2D electron gases at oxide surfaces.

CHAPITRE 5 2D-electron gases at the surface of oxides and their study by ARPES

The results presented in this section were obtained by T. Rödel during his PhD thesis entitled "Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission" [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF], defended on September the 8 th 2016 at Paris XI University (Orsay) and co-directed by Andres Santander-Syro (CSNSM, Orsay) and myself.

Introduction

Properties of transition metal oxides

Transition metal oxides (TMOs) show nearly all the known physical properties. They can be insulating or superconducting, ferromagnetic, ferroelectric... They show phase transitions with temperature or with applied magnetic/electric fields whose interpretation is often complex. These various physical behaviours are due to the numerous different degrees of freedom, like lattice, charge or spin. Indeed, e.g., in the case of 3d-element oxides, the cation can accomodate several oxidation states and the 3d-orbital degeneracy can be lifted by crystal fields of different symmetry depending on the crystallographic structure, not talking about the more or less localized character of the 3d electrons. The variety of physical properties found in 3d-oxides hence reflects the uncoutable configurations for all these parameters which interact to form different competing phases/states quite similar in energy. The introduction of defects (like oxygen vacancies in the lattice) or of doping by cation substitution can make the situation even more complicated.

Perovskites

A restricted view solely on the perovskite lattice already offers a variety of different properties ranging from insulators, metals to superconductors as well as ferroelectrics and ferromagnets. The perovskite lattice has the elemental formula ABO 3 , where A is often an alkali metal or an alkaline earth metal, B a transition metal and O oxygen. In this case, the oxidation states are : -II for oxygen, +I/+II for A and +IV/+V for B. A cubic perovskite lattice is shown in figure 5.1(a). The lattice is ionic and thus consists out of O 2-anions, B 4+/5+ cations and A +/2+ cations. Not only the oxidation state of the individual ions is of importance for the properties of perovskites, but also the charge state of alternating planes. As shown in figure 5.1(b), the lattice consists of alternating planes of AO and BO 2 along the 001 direction which can be either electrically neutral or charged based on the oxidation state of the ions. This potential polarity influences the lattice structure and the electronic structure at the surface and interface of oxides [START_REF] Noguera | Polar oxide surfaces[END_REF][START_REF] Nakagawa | Why some interfaces cannot be sharp[END_REF].

There are three common lattice distortions of the cubic perovskite lattice described above :

-An off-center displacement of the B cation in the oxygen octahedron (ferroelectric distortion) -Opposite rotations of the oxygen octahedra (antiferrodistortive distortions) -A deformation of the oxygen octahedron (Jahn-Teller distortions) Which one of the first two distortions is present depends on the ratio between the ionic radii of the A and B site cations and can be estimated by Goldschmidt's tolerance factor t [START_REF] Goldschmidt | Die Gesetze der Krystallochemie[END_REF] :

t = r A + r O √ 2(r B + r O ) .
A tolerance factor equal to one means that the ionic radii r A , r B and r O have values such that all the anions barely touch the cations ; the cubic phase is then stable. Some titanates (ATiO 3 ) show either ferroelectric distortions, rotations of the oxygen octahedra or none of the two depending on the size of the A site cation. In BaTiO 3 , the Ti 4+ cation is too small to fit well in the oxygen octahedron (t > 1) and tends to move off center, which is responsible for the ferroelectricity in this compound. For SrTiO 3 , the tolerance factor is close to one (t ≈ 1) and consequently, the lattice is perfectly cubic at room temperature. In CaTiO 3 , an antiferrodistortive ordering is observed as the oxygen octahedra are tilted to form a orthorhombic lattice (t < 1) (see short discussion in review by Zubko et al. [START_REF] Zubko | Interface physics in complex oxide heterostructures[END_REF]). Those distortions obviously influence the electronic structure in the concerned compound.

Perovskites heterostructures

This unique perovskite structure observed for a large number of compounds opened the way for the elaboration of oxide heterostructures. The elaboration of oxide thin films was developped since the mid-eighties, first by Molecular Beam Epitaxy (MBE) in the presence of an oxidant flux which can be molecular oxygen, purified ozone or oxygen plasma, depending on how hard to oxidise is the deposited material (see [START_REF] Schlom | Perspective : Oxide molecular-beam epitaxy rocks ! APL Mater[END_REF] for a review). The use of Pulsed Laser Deposition (PLD) in an oxygen pressure started a little bit later for oxides [START_REF] Dijkkamp | Preparation of YBaCu oxide superconductor thin films using pulsed laser evaporation from high T c bulk material[END_REF] but finaly also reached the same atomic layer precision as MBE [START_REF] Ho Nyung Lee | Strong polarization enhancement in asymmetric threecomponent ferroelectric superlattices[END_REF] and is now a widely (if not the main) used technique for the growth of oxide heterostructures. It turns out that ferroelectricity [START_REF] Ho Nyung Lee | Strong polarization enhancement in asymmetric threecomponent ferroelectric superlattices[END_REF][START_REF] Dawber | New developments in artificially layered ferroelectric oxide superlattices[END_REF], magnetism [START_REF] Coey | Magnetism at the edge : New phenomena at oxide interfaces[END_REF] or the transport [START_REF] Hilgenkamp | Novel transport phenomena at complex oxide interfaces[END_REF] and confinement [START_REF] Stemmer | Quantum confinement in oxide quantum wells[END_REF] properties observed in those systems really renewed the field of oxides study. 5.1.3.1 2D electron gas at the SrTiO 3 /LaAlO 3 interface Among all these results, one certainly drew attention more than the others. In 2004, Othomo and Wang made SrTiO 3 /LaAlO 3 heterostructures, SrTiO 3 and LaAlO 3 being both insulators, with respective gaps of 3.2 and 5.6 eV [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF]. Surprisingly, these authors evidenced the existence of a metallic 2D-electron gas (2DEG) at the interface between the two insulators. The existence of this 2DEG was shown by transport measurements. Several reviews discuss the particularity of this 2DEG from both a fundamental as well as device oriented point of view [START_REF] Mannhart | Twodimensional electron gases at oxide interfaces[END_REF][START_REF] Cheng Cen | Oxide nanoelectronics on demand[END_REF][START_REF] Mannhart | Oxide interfaces-an opportunity for electronics[END_REF]. Its electronic properties range from fieldeffect induced insulator-to-superconductor transitions [START_REF] Caviglia | Electric field control of the LaAlO 3 /SrTiO 3 interface ground state[END_REF] and magnetism [START_REF] Brinkman | Magnetic effects at the interface between non-magnetic oxides[END_REF] to the coexistence of magnetism and superconductivity [START_REF] Li | Coexistence of magnetic order and two-dimensional superconductivity at LaAlO 3 /SrTiO 3 interfaces[END_REF][START_REF] Bert | Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO 3 /SrTiO 3 interface[END_REF][START_REF] Dikin | Coexistence of superconductivity and ferromagnetism in two dimensions[END_REF].

The origin of this 2DEG is still debated, but the different ingredients to be considered have been certainly identified :

-Oxygen vacancies in the structure can play role. Taking out an O-atom from the SrTiO 3 crystallographic lattice would release 2 electrons in the system, which would likely fill the Ti-3d states at the bottom of the conduction band and form the 2DEG. This role of the Ti-ion as an electron provider is evidenced by the fact that the 2DEG only exists when LaAlO 3 is deposited on a TiO 2 -terminated SrTiO 3 substate, and is not observed for a deposition on a SrO-terminated SrTiO 3 . -In the (001) orientation, the LaAlO 3 layer deposited on the SrTiO 3 substrate is a piling of AlO - 2 -LaO + planes. Such a piling of alternatively plus or minus charged planes should lead to a potential increasing with the film thickness [START_REF] Harrison | Polar heterojunction interfaces[END_REF], the socalled polar catastrophe. The role of this potential induced by the polar LaAlO 3 atomic planes is outlined by the fact that at least 4 atomic layers of LaAlO 3 are necessary to observe the 2DEG at the LaAlO 3 /SrTiO 3 interface. A charge transfer from LaAlO 3 to SrTiO 3 could avoid a polar catastrophe [START_REF] Mannhart | Twodimensional electron gases at oxide interfaces[END_REF] (as for semiconductors [START_REF] Harrison | Polar heterojunction interfaces[END_REF]).

-The confinement of the electrons forming the 2DEG could be achieved inside the potential well created by the band-bending at the interface between LaAlO 3 and SrTiO 3 where the band structures of the two materials have to connect. The situation can be further complicated by other contributions to the total potential like the polar LaAlO 3 planes on top or charge transfers between the different cations of several atomic layers [START_REF] Mannhart | Oxide interfaces-an opportunity for electronics[END_REF]. Whatever is the origin of this 2DEG, the understanding of its physical properties requiers a precise study of its electronic structure. This is difficult to achieve on a buried interface. Fortunatly, this 2DEG was shown to exist also at the surface of cleaved oxide single crystals.

2D electron gas at the surface of SrTiO 3 (001)

This was demonstrated by Santander-Syro et al. at the (001) surface of SrTiO 3 [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF] (see also Meevasana et al. in a simultaneous paper [START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF]). A SrTiO 3 single crystal was cleaved in ultra-high vacuum and the clean surface was studied by Angle-Resolved Pho-toElectron Spectroscopy (ARPES). The spectra reveal metallic states (i.e. crossing the Fermi level), whose origin and behaviour is described in the paper. Even after the experimental discovery of a metallic 2DEG at the interface between two insulating oxides (see previous section), this finding is quite surprising as SrTiO 3 is an insulating oxide and the presence of a confined metallic state at the surface of this insulator is far from intuitive. Nevertheless, the attentive reader could recall how, in chapter 3 of this dissertation, insulating rutile-TiO 2 could be turned into a conductive material by creation of oxygen vacancies. ARPES measurements reveal three parabolic bands, two light ones and a heavy one (Figure 5.2). Their polarization dependence reveals different symmetries for these bands. The light bands are observed for linear vertical polarization (LV) of the incident photons which shows that they have a d xy nature, while the heavy band, which is observed for linear horizontal polarization (LH), has a d xz symmetry. The 2D nature of these bands is demonstrated by their photon energy dependance which shows no dispersion in k z (where z is the direction perpendicular to the surface).

This band structure is explained starting from the bulk expected electronic structure. In SrTiO 3 , the bottom of the conduction band is made of the Ti-3d states belonging to the t 2g manifold (d xy , d xz and d yz ). The electron dispersion along a given direction strongly depends on the overlap between these orbitals in the considered direction. Hence, for a d xy orbital with a large overlap in the (x, y) plane, a d xy -like band will appear as light when measured in the x or y directions, but as a heavy band in the z direction. Similarly, a d xz -like band will appear as light in the x or z directions, but as a heavy band in the y direction, and a d yz -like band will appear as light in the y or z directions, but as a heavy band in the x direction. At Γ, all those bands are degenerated.

This electronic structure is far from the observed one. To account for experimental observations and the 2D nature of the bands, one has to introduce a triangular potential well created by the oxygen vacancies confining the electrons along the z direction (see Figure 5.4(a)). The confinement of the electrons in this triangular potential well results in the quantization of the eigenenergies and produces an energy splitting between the different eigenstates that is inversely proportional to their effective masses along z (m * z ) direction, but light in the y-direction. It also gives an elliptical contour in the Fermi surface, perpendicular to the d xz contour. The expected electronic structure for a 2DEG is therefore a set of parabolic bands and subbands which can be either light or heavy depending on the considered dispersion direction.

Outline of this chapter

As described in this introduction, the study of 2DEG at the surface of insulating oxides is a very attractive research field, closely linked to the novel physics evidenced in oxide heterostructures. Recently, 2DEG have been also discovered at the ( 110) and ( 111) surfaces of SrTiO 3 [START_REF] Rödel | Orientational tuning of the Fermi sea of confined electrons at the SrTiO 3 (110) and (111) surfaces[END_REF] and at the (001) [START_REF] Santander-Syro | Orbital symmetry reconstruction and strong mass renormalization in the two-dimensional electron gas at the surface of KTaO 3[END_REF] and [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] [START_REF] Bareille | Two-dimensional electron gas with sixfold symmetry at the (111) surface of KTaO 3[END_REF] surfaces of KTaO 3 . ARPES has been also shown to be the adapted method to probe the band structure of these 2DEG. In this chapter, we will use this experimental technique for the study of 2DEG created at the surface of anatase-TiO 2 or at the interface between an Aluminum thin film and an oxide surface, thus illustrating two research lines : the discovery of 2DEG on different oxide surfaces on one hand, and progresses towards applications on the other hand.

5.2 2DEG at the surface of TiO 2 -anatase

Introduction

In its pure stoichiometric form, the TMO TiO 2 is a transparent insulator that crystallizes in mainly two different phases : rutile and anatase. Both phases have been studied extensively over the last decades due to their photocatalytic properties discussed in several reviews [START_REF] Diebold | The surface science of titanium dioxide[END_REF][START_REF] Henderson | A surface science perspective on TiO 2 photocatalysis[END_REF][START_REF] Fujishima | TiO 2 photocatalysis and related surface phenomena[END_REF]. On the other hand, the study of two-dimensional electron gases (2DEGs) in TMO surfaces/interfaces has becomed a very active field of research. The archetypal example, SrTiO 3 -based heterostructures, display many fundamentally interesting properties as described in the introduction of this section [START_REF] Mannhart | Oxide interfaces-an opportunity for electronics[END_REF][START_REF] Zubko | Interface physics in complex oxide heterostructures[END_REF][START_REF] Hilgenkamp | Novel transport phenomena at complex oxide interfaces[END_REF].

It is well established that the Ti-O atomic planes and their ability to accommodate chemical doping by oxygen vacancies at the surface region play a key role for the formation of the 2DEG at the surface of SrTiO 3 . Thus, as a step forward to understand the formation of 2DEGs in TMOs, it is natural to focus on pure TiO 2 crystals like rutile or anatase. But the chemical constitution of the crystal atomic planes is clearly not the only parameter to take into account. We will show later in this section that while 2DEGs can be readily obtained at various anatase surfaces (as it was previously published by Moser et al. [START_REF] Moser | Tunable polaronic conduction in anatase TiO 2[END_REF]), they cannot be observed on the cleaved or in situ prepared surfaces of rutile-TiO 2 (110), Adapted from references [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF] and [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF].

indicating that other factors are equally important. In fact, excess electrons in TiO 2 , due to oxygen vacancies at the surface, form polarons [START_REF] Moser | Tunable polaronic conduction in anatase TiO 2[END_REF] which behave quite differently for the rutile and anatase phases [START_REF] Setvin | Direct view at excess electrons in TiO 2 rutile and anatase[END_REF]. This demonstrates that structural factors, such as surface lattice distortions, can determine the fate of those electrons. Thus, to elucidate the origin and realization of 2DEGs in different oxides, it is essential to probe the surface electronic structure arising in different lattice configurations.

In this section, we report the observation of 2DEGs at the (001) and ( 101) surfaces of TiO 2 -anatase. Using angle resolved photoemission spectroscopy (ARPES), we found that, for both surfaces, the electronic structure consists of two light bands of d xy character. While the Fermi surface at the (001) surface is isotropic, the one at the (101) surface is highly anisotropic, reflecting the symmetry of the surface layer. Moreover, we use corelevel spectroscopy to evidence the role of the incident photons in the creation of oxygen vacancies and the consequences on the surface band bending allowing the confinement of some of the excess electrons to form the 2DEG.

Experimental conditions

The ARPES measurements were conducted at the Synchrotron Radiation Center (SRC, University of Wisconsin, Madison) and the CASSIOPEE beamline of Synchrotron SOLEIL (France) on surfaces cleaved at low temperatures under ultra-high vacuum. We used linearly polarized photons in the energy range 38 -103 eV and hemispherical electron analyzers with vertical slits. The total angle and energy resolutions were 0.25 • and 25 meV at SRC and 0.25 • and 15 meV at SOLEIL. The mean diameter of the incident photon beam was smaller than 100 µm. The results were reproduced for at least three different samples for each surface orientation.

O-vacancies created by light irradiation

As already discussed several times, electron doping via oxygen vacancies is one of the key elements to consider in the creation of a metallic 2DEG at the surface of oxides. The influence of light irradiation (in a photon energy range of hv=40 to 110 eV in synchroton facilites with sufficient photon density) on an anatase surface can be directly seen on a photoemission spectrum. Spectra recorded on a freshly-cleaved surface and after one-hour irradiation are compared on figure 5.5. The same comparisons for anatase-TiO 2 (001) and ( 101), CaTiO 3 (001) as well as SrTiO 3 [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] are presented on figure 5.6, showing the very general character of the observed changes in titanates.

Several modifications can be observed :

-A shoulder at the lower binding energy side of the Ti-3p peak appears due to the formation of Ti ions with lower valencies (e.g., 4 + to 3 + ) corresponding to the electron doping of the Ti ions. -The decrease in intensity of the O-2p valence band especially of the part close to the valence band maximum which consists mainly out of O-p π states showing either almost negligible hybridization with d-orbitals or are non-bonding [START_REF] Asahi | Electronic and optical properties of anatase TiO 2[END_REF]. -An in-gap state is created in the band gap of the doped insulator which was attributed to oxygen vacancies (See chapter 3 of this dissertation) and the subsequent filling of the Ti-3d states forming the bottom of the conduction band. -The disappearance of the small features 1 eV to 3 eV below the valence band minimum, on its high binding energy side. These features are more distinct for surfaces prepared in situ (e.g. SrTiO 3 [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF]) and thus, could be related either to carbonic contamination or to contamination due to the surface preparation. In any case, the light irradiation reduces the contamination. In principle, no contamination should be present at the cleaved surfaces, but low intensity features are still present in the first minutes of the light irradiation. Contrary, to this observations no (significant) spectral changes can be induced if the photon density or the photon energy is too low. A conventional laboratory source (e.g., He-lamp with photon energy of 21.2eV) does not induce changes in the electronic structure even after an UV irradiation of 12 hours. This is certainly due to the fact that this photon energy is too small to create a core-hole. Indeed, the relaxation of the system due to the presence of this core-hole results in a charge transfer of electrons from oxygen to the transition metal. The change in oxidation state of oxygen leads to the desorption of an oxygen ion, as proposed by Tanaka et al. [START_REF] Tanaka | Photostimulated ion desorption from the TiO 2 (110) and ZnO(1010) surfaces[END_REF]. Similary, the photon density at beamlines installed on first generation storage rings (like BL9 at the HISOR facility, Hiroshima, Japan) is too low to induce significant changes (i.e. no in-gap state). But, the in-gap state can be created using the much more intense irradiation of the 0 th -order of the monochromator grating (reflected, polychromatic beam). This indicates that there is threshold of photon density determining if the surface can be reduced sufficiently to create the 2DEG, certainly resulting from a balance between O-desorption from the surface and the (temperature-dependent) diffusion of O-atoms coming from the bulk filling these vacancies.

Coming back to anatase-TiO 2 , the presence of oxygen vacancies in the surface region of anatase can be identified using photoemission by probing the intensity of the in-gap state located around 1 eV below the Fermi level (E F ) and corresponding to electrons trapped near oxygen vacancies as well as the formation of a shoulder of the Ti-3p peak related to a lower valence of the Ti-cation. We fit the Ti-3p peak by one or two Voigt functions plus a Shirley background to determine the contribution of Ti 4+ and Ti 3+ states to the line shape. The ratio between the Ti 3+ and the total Ti-3p peak areas is used to calculate the concentration of O-vacancies x.

The intensities of the Ti 3+ component of the Ti-3p and of the in-gap state are plotted as a function of the irradiation time on figure 5.7. They both linearly increase showing the gradual creation of O-vacancies.

Figure 5.8(a) shows the binding energy of the Ti 4+ photoemission peak (determined by the same fitting procedure as for the intensity study above) measured at 100 eV photon energy as a function of the irradiation time for the anatase-TiO 2 (101) surface. Same procedure has been also applied to the (001) surface (not shown here). The peak position shifts to higher binding energies upon UV-irradiation, demonstrating the band bending (bb) at the surface (see figure 5.8(b)). This gives a shift of the Ti 4+ peak of E (001) bb = 110 meV for the (001) surface, and E (101) bb = 150 meV for the [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF] surface, which corresponds to the minimal band bending at the surface averaged over the photoemission probing depth at the used photon energy. The actual band bending might be larger, as oxygen vacancies might be already induced at the surface by the cleaving process or by the short beam exposure before the first measurement. Comparing figure 5.7 and figure 5.8 also shows that the band bending is not simply proportional to the amount of vacancies at the surface. It saturates at a rather low O-vacancy concentration. In fact, recent theoretical studies on the electronic structure of SrTiO 3 [START_REF] Jeschke | Localized versus itinerant states created by multiple oxygen vacancies in SrTiO 3[END_REF][START_REF] Hao | Coexistence of trapped and free excess electrons in SrTiO 3[END_REF] suggest that, for a high concentration of oxygen vacancies, excess electrons do not fill up the conduction band any longer, but form only localized states, and thus do not contribute to the rigid band shift. Since the core level are bent identically, the measurement of the Ti-3p binding energy gives an estimate of the depth of the created potential well, averaged on the depth probed by photoemission.

2DEG at the (101) and (001) anatase-TiO 2 surfaces

Let us now focus focus on the electronic structure of the 2DEG of delocalized electrons at the Fermi level, obtained once a stable band-bending has been attained after weak exposure to UV irradiation (typically ∼ 20 min). The Fermi surface at the (001) plane shown in figure 5.9(b) consists of two circles of d xy orbital character, confirmed by light polarization dependent measurements presented below (see Section 5.2.4.2), similar to the case of SrTiO 3 [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF][START_REF] Plumb | Mixed Dimensionality of Confined Conducting Electrons in the Surface Region of SrTiO 3[END_REF].

Band structure and Fermi surfaces

The quasi-2D character of these two electronic states is strictly demonstrated by the Fermi surface map in the 010 -001 plane, perpendicular to the surface plane, presented in figure 5.9(c). This Fermi surface shows that the bands are essentially non dispersing along k 001 over a bulk Brillouin zone, thereby confirming the confined character of the electrons close to the surface. Figure 5.9(d) presents the energy-momentum map close to the bulk Γ 102 point along the cut parallel to the 010 direction shown in panel (a). Two dispersive light bands are visible. Their bottoms are at -60 meV for the upper band, and -172 meV for the lower band. A parabolic fit yields an effective mass of approximately 0.5m e , which agrees well with theoretical [START_REF] Huy | Calculation of carrierconcentration-dependent effective mass in Nb-doped anatase crystals of TiO 2[END_REF][START_REF] Kamisaka | Density functional theory based first-principle calculation of Nb-doped anatase TiO 2 and its interactions with oxygen vacancies and interstitial oxygen[END_REF] and experimental [START_REF] Hirose | Large electron mass anisotropy in a d-electron-based transparent conducting oxide : Nbdoped anatase TiO 2 epitaxial films[END_REF] results on bulk Nb-doped anatase. The corresponding Fermi momenta are 0.09 Å-1 and 0.16 Å-1 . identical orbital character directly implies that the probed electronic structure is not simply the one expected for bulk anatase. For SrTiO 3 , the existence of different subbands has been related to the confinement of the electronic states in a quantum well at the surface [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF]. As shown in the Supplemental Material of reference [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF], the spatial extent of the 2DEGs in anatase is similar to the ones at the surfaces of SrTiO 3 and KTaO 3 , namely about 2 nm.

In contrast to the 2DEGs at the surface of SrTiO 3 and KTaO 3 , our ARPES data in TiO 2 -anatase do not show any heavy (d zx or d yz ) subbands -which we confirmed by complementary measurements as a function of photon polarisation and energy. The degeneracy of the three t 2g -orbitals is lifted in bulk anatase [START_REF] Asahi | Electronic and optical properties of anatase TiO 2[END_REF] due to its tetragonal crystal structure and the inequivalent Ti-O bonding in the x -y plane compared to the z direction. Consequently, the electron gases confined at the surfaces of TiO 2 anatase are only composed of electrons of d xy -orbital character.

We also showed [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF] that exposure to a large UV irradiation dose leads to the local destruction of the 2DEG. On the studied surfaces, it is observable on freshly-cleaved surfaces after only a few minutes of UV-irradiation. However, the spectral weight of the dispersing features essentially disappears after 1-2 hours of exposure to UV light, leaving almost no intensity at the Fermi level. The 2DEG is fully recovered after moving the UV spot to a neighboring region in the sample, not irradiated before, and illuminating for a few minutes. Hence, a high concentration of oxygen vacancies induced by the UV irradiation also destroys the crystallinity at the surface, which might in turn lead to the localization of the itinerant electrons forming the 2DEG. As the size of the beam spot is only ≈ 50 × 50 µm 2 , the strong reduction of the surface is local.

Polarisation dependence

The study of 2DEGs gives a nice illustration of the capability of ARPES to reveal the symmetry of the measured orbitals. The polarisation dependence of the t 2g orbitals (d xy , d xz , d yz ) forming the 2DEG at the (001) surface of SrTiO 3 was discussed in previous works [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Yukawa | Electronic structure of the hydrogen-adsorbed SrTiO 3 (001) surface studied by polarization-dependent photoemission spectroscopy[END_REF] and can be directly applied to the (001) surface of anatase.

To understand the photoemission selection rules, the geometry of the experimental setup is essential and shown in figure 5.11(a). We used light polarised horizontally (LH, in the x -z plane) and vertically (LV, along the y-direction). The slits of the analyzer are aligned vertically along the y-direction and the sample was rotated around the x axis. In this geometry, the measurement plane containing the electrons ejected from the surface and entering the detector through the vertical slits, coincides with the yz plane (see figure 5.11(a)).

The measurements were conducted at a photon energy of hν=47 eV both at normal emission and tilted by 26 • around the x-axis. The corresponding positions in reciprocal space of bulk anatase, labelled A and B, are shown in figure 5.11(b).

The sample being oriented with its [010] axis parallel to the analyzer slit, the y -z plane is a symmetry plane for the (001) surface. To measure a non-zero intensity, the final state needs to be even with respect to the y -z measurement plane, since a odd final state would cancel in a symmetry plane. As LV polarisation is even with respect to this plane, the simple rule given in section 4.2.2 (chapter 4) says that only states with the same parity as can be observed, i.e. orbital with even character to the y -z plane. Among the three t 2g orbitals (d xy , d xz and d yz ), this is the case only for d yz states, which are therefore the only ones which can be detected in this polarisation condition.

The LH polarisation has even as well as odd components with respect to the y -z plane and states of all t 2g orbitals have non-zero matrix elements using this polarisation.

The ARPES spectra in figures 5.11(c, d) show the measured intensities at the point B in reciprocal space for LH and LV polarisations, respectively. The almost zero intensity in LV polarisation demonstrates that the orbital character is not d yz .

To exclude one more orbital character we turn to the measured intensities at normal emission (point A) in figure 5.11(e). To have a non-zero matrix element at the Γ point in normal emission, the final state has to be even with respect to both the x -z and y -z planes. Hence, as the LH polarisation is even with respect to the x -z plane, only states with an orbital character even to the x -z plane (d xz ) can be detected. The measured intensity at and close to normal emission in figure 5.11(e), i.e. around k = 0, is zero and thus, the bands are not of d xz character.

Consequently, the orbital character of the bands is d xy . We verified the matrix elements at a different photon energy to affirm that the matrix elements are due to orbital character and not photon energy.

Comparison between rutile and anatase

The different behavior of excess electrons induced by oxygen vacancies in rutile and anatase was already discussed previoulsy in the introduction of this section dedicated to 2DEG in anatase. Our first try to create a 2DEG at the surface of a TiO 2 crystal was actually on rutile. In contrast to anatase, it turned out that the excess electrons in rutile do not fill up the conduction band (forming the 2DEG), but are localized at lattice Ti sites [START_REF] Lee | Creation and control of twodimensional electron gas using Al-based amorphous oxides/SrTiO 3 heterostructures grown by atomic layer deposition[END_REF]. Accordingly, we did not detect any dispersing features at the Fermi level at the surface of rutile [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF], neither for cleaved nor for in situ prepared surfaces under various measurement conditions (photon energy, emission angle, light polarisation) at T =7 K.

To illustrate the difference between the two systems, figure 5.12(a,b) shows the valence band, the in-gap state corresponding to the localized electrons and, in the case of anatase, the 2DEG measured at normal emission at hν = 100 eV. The angle-integrated data in figure 5.12(c) demonstrates that the concentration of oxygen vacancies is similar in the two cases, as the in-gap states have similar intensities. The failure to observe dispersing features at the Fermi level of rutile shows that oxygen vacancies at the surface are not sufficient to create a 2DEG, and that structural factors play a crucial role regarding the localization/delocalization of excess electrons.

Conclusions

In conclusion, we demonstrated the existence of 2DEGs at the (001) and ( 101) surface of TiO 2 -anatase. The two d xy subbands composing the 2DEGs form concentric circular Fermi surfaces at the (001) termination and ellipsoidal Fermi surfaces at the (101) termination. Such orientational tuning of the Fermi sea symmetries is wholly analogous to the one found at different surfaces of SrTiO 3 [START_REF] Rödel | Orientational tuning of the Fermi sea of confined electrons at the SrTiO 3 (110) and (111) surfaces[END_REF]. Furthermore, we found that light irradiation locally dopes the anatase surfaces, while the behavior of the excess electrons, i.e. delocalized or localized, depends on the concentration of oxygen vacancies at the surface, eventually resulting in the local destruction of the 2DEG after a high UV irradiation dose. This effect shows that UV light can be used to tailor locally the surface order/disorder in anatase and thus engineer nano-patches of metallic 2DEG alongside patches of disordered insulating material.

All the results presented in this section were published in reference [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF].

5.3 2DEG at the interface between an Aluminum thin film and an oxide surface

Introduction

Oxides and oxide heterostructures are an infinite playground for scientists for their fundamental interests. But another goal is to go towards applications and, possibly, to design a whole new electronics based on oxides, going beyond what can be achieved with semiconductors mainly in terms of functionalization [START_REF] Mannhart | Oxide interfaces-an opportunity for electronics[END_REF][START_REF] Cheng Cen | Oxide nanoelectronics on demand[END_REF].

Semiconductor-based electronics shaped the world we live in. It revolutionized domains like telecommunications or computer industry which are now ubiquitous in our everyday's life. As for oxides, the device is not only the semiconductor itself, but also the interfaces between different (or differently doped) semiconductors. High mobility 2Delectron gases, confined in the potential well created by band bending at the interface between semiconductors, are also a key ingredient for high efficiency transistors [START_REF] Delagebeaudeuf | Two-dimensional electron gas m.e.s.f.e[END_REF] or optoelectronic devices. As in an atomic construction set, scientists and engineers took advantage of the common crystallographic structure of the semiconductors family, the zinc-blende structure, to stack different pure or alloyed compounds thus triggering new developments for elaboration techniques like Molecular Beam Epitaxy.

It is striking to notice the similarities between semiconductors and the oxide family. Many oxides stabilizes in the perovskite (or perovskite-like) structure. It is thus very tempting to grow oxide superlattices. As described above, the event that gave birth to the idea of an oxide-based electronic was the discovery of a high mobility metallic 2Delectron gas (2DEG) at the LaAlO 3 /SrTiO 3 interface by Ohtomo and Hwang [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface[END_REF], two insulating oxides. As compared to semiconductors, the new exciting open field will be to take advantage of the unique panel of physical properties which can be found in oxides, like superconductivity, ferroelectricity or magnetism to develop highly fonctional devices.

Fundamental studies are eminently useful to understand the reasons for the existence of this 2DEG as well as to learn how to control it. But as in semiconductor devices, it is also of great interest to proceed towards applications. However, the fabrication of 2DEGs in oxide hetero-structures, like LaAlO 3 /SrTiO 3 , requires the growth of at least 20 Å of the top layer using evolved deposition techniques to elaborate binary or ternary oxides. On the other hand, 2DEGs at the surface of SrTiO 3 or other oxides created by oxygen vacancies near the surface can only exist in ultra-high vacuum and are obviously not suited for experiments or applications at ambient conditions. There must be a step forward in the preparation of these 2DEGs to make them easily available both for fundamental studies and/or for future technological applications.

In this prospect, we show here that one can generate 2DEGs at various surfaces of different transition-metal oxides by simple deposition, at room temperature and in UHV, of an amorphous ultra-thin film (2 Å) of pure Aluminum (Al). Due to an efficient redox reaction, the Al-film pumps oxygen from the substrate, oxidises into insulating AlO x , and forms a pristine, homogeneous 2DEG in the first atomic planes of the underlying oxide. Furthermore, the 2DEGs generated in this way are naturally capped with an ultra-thin, highly insulating protective layer and are thus unaffected by exposure to ambient conditions or to strong UV irradiation. We also show here and in that this new, simpler and cheaper fabrication route for 2DEGs is adaptable to numerous oxides, scalable to industrial production, and ideally suited for the top-gating control of the confined electrons and for the realization of mesoscopic devices.

Results

Local, high concentrations of oxygen vacancies can be created through redox reactions at the interface of SrTiO 3 and some metals or metal oxides [START_REF] Fu | Interaction of nanostructured metal overlayers with oxide surfaces[END_REF], such as amorphous LaAlO 3 [START_REF] Chen | Metallic and insulating interfaces of amorphous SrTiO 3 -based oxide heterostructures[END_REF] or Al 2 O 3 [START_REF] Lee | Creation and control of twodimensional electron gas using Al-based amorphous oxides/SrTiO 3 heterostructures grown by atomic layer deposition[END_REF]. In fact, for early transition metals, the redox reaction at the interface with SrTiO 3 is thermodynamically favored, and in the case of Al/SrTiO 3 the oxidation of Al occurs even at room temperature [START_REF] Fu | Metal/oxide interfacial reactions : Oxidation of metals on SrTiO 3 (100) and TiO 2 (110)[END_REF]. This is the route we follow in the present work. We tested this method on different oxide surfaces like SrTiO 3 (001) and ( 111) and TiO 2 -anatase(001) but it was shown to work also on other oxides like BaTiO 3 (001) [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF], CaTiO 3 (001) [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF] or ZnO(0001) [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF].

Experimental conditions

The non-doped, polished crystals of SrTiO 3 were supplied by CrysTec GmbH and the TiO 2 -anatase crystals by SurfaceNet GmbH. To prepare the SrTiO 3 surfaces, the samples were ultrasonically agitated in deionized water, subsequently etched in buffered HF and annealed at 950 • C for three hours in oxygen flow. This results in Ti-terminated (001) or [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] surfaces with terraces of width 50 to 200 nm separated by steps, as verified by atomic-force microscopy (AFM) in contact mode.

To clean the surfaces in UHV, the SrTiO 3 samples were annealed at a temperature T = 550-650 • C for t=10-90 min at pressures lower than 2×10 -8 mbar. The anatase crystals were prepared by Ar + sputtering (U=1 kV, t=10 mn) and annealing cycles (T=550-600 • C, t=30 mn) similar to the procedure described by Setvin et al. [START_REF] Setvin | Direct view at excess electrons in TiO 2 rutile and anatase[END_REF].

The surface quality and the possible existence of surface reconstructions was probed by low-energy electron diffraction. The SrTiO 3 (001) surface is unreconstructed, whereas the [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] surface shows a 3×3 reconstruction, and the anatase (001) surface shows a twodomain 1×4 reconstruction. To create a local, high concentration of oxygen vacancies in the surface region of SrTiO 3 or TiO 2 -anatase, amorphous Al-films with thicknesses between d=2-10 Å were deposited on the prepared surface of the crystals. Aluminium was evaporated from a Knudsen cell using an alumina crucible. The growth rate was approximately 0.3 Å/min, corresponding to a temperature of about 925 • C of the crucible. The Al-flux was calibrated prior to the evaporation using a quartz microbalance. The cleanliness of the deposit was checked by evaporating a thin Al-film on a Cu substrate where no oxidation could be detected by Auger spectroscopy. The temperature of the crystals ranged between T =25-100 • C during the Al-deposition.

The ARPES measurements were all conducted at the CASSIOPEE beamline of Synchrotron SOLEIL. We used linearly polarised photons in the 30-110 eV energy range and a hemispherical electron analyzer with vertical slits. The angular and energy resolutions were 0.25 • and 15 meV, respectively. The mean diameter of the incident photon beam was smaller than 50 µm. The samples were cooled down to T=8 K before measuring. The results have been reproduced on more than 10 samples for SrTiO 3 (001) and on at least two samples for other surface orientations and for TiO 2 -anatase. All through this section, reciprocal-space directions hkl and planes (hkl) are defined in the conventional cell of each material (cubic for SrTiO 3 and simple tetragonal for anatase). The indices h, k and l of Γ hkl correspond to the reciprocal lattice vectors of the cubic (SrTiO 3 ) or body-centered tetragonal (anatase) unit cell.

For simplicity, and to recall that we are simply depositing pure Al (not Aluminum oxide) on top of the oxide surfaces, all throughout this section we note the resulting oxidised Al capping layer simply as Al, specifying in parenthesis the evaporated thickness.

ARPES results

The existence of a 2DEG at the interface between the oxidised Al layer and SrTiO 3 (001), SrTiO 3 [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] and anatase-TiO 2 (001) is evidenced by our angle-resolved photoemission spectroscopy (ARPES) data presented in figure 5.13. The energy-momentum and Fermi surface maps formed by the t 2g orbitals, shown in figure 5.13, agree with previous ARPES studies at the reduced surface of these materials demonstrating that, in both cases, the same 2DEGs are observed [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF][START_REF] Plumb | Mixed Dimensionality of Confined Conducting Electrons in the Surface Region of SrTiO 3[END_REF][START_REF] Rödel | Orientational tuning of the Fermi sea of confined electrons at the SrTiO 3 (110) and (111) surfaces[END_REF][START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF]. Note that, instead of the local creation of oxygen vacancies using an intense UV beam, the evaporated Al reduces the whole surface homogeneously. As a consequence, the data quality, evidenced by the line widths, is also much better than in previous studies. Thus, as shown in Figure 5.13(a), a kink and change in intensity in the dispersion of the light bands at E≈-30 meV, attributed to electron-phonon coupling [START_REF] King | Quasiparticle dynamics and spin-orbital texture of the SrTiO 3 two-dimensional electron gas[END_REF][START_REF] Walker | Control of a Two-Dimensional Electron Gas on SrTiO 3 (111) by Atomic Oxygen[END_REF], can be very clearly distinguished. The Fermi-surface areas and, hence, the charge carrier densities of the 2DEGs at the Al/SrTiO 3 [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] and Al/TiO 2 (001) interfaces are about 1.3 and 2 times larger than their counterparts at the surfaces reduced by photons, probably due to a higher and more homogeneous concentration of oxygen vacancies.

The Al-deposit

To understand the redox reaction at the Al/oxide interface, we probed the oxidation state of Al by measuring the Al-2p core levels, whose binding energies are very different for metallic and oxidised Al. As shown in figure 5.14, the two contributions can be distinguished in the Al(6 Å)/SrTiO 3 spectrum (blue curve), with the metallic component around 72.5 eV binding energy and the oxidised part around 75 eV binding energy. In contrast, the metallic Al component decreases for a thinner 4 Å film (black curve), and the deposition of only 2 Å of pure Al results in a nearly fully oxidised Al-film (red curves). In other words, an ultra-thin layer of 2 Å of pure Al is sufficient to pump the oxygen from the surface region of all the oxides studied in this work.

To determine if the thickness of the Al-layer has an influence on the electron density of the 2DEG, we turn to the momentum distribution curves (MDCs) at the Fermi level as shown in figure 5.14(a). As can be seen in 5.14(b), the Fermi momenta are essentially the same, within 0.01 Å-1 for the 2 Å (red MDC), 4 Å (black) and 6 Å (blue) thick Al-films. As the 2D density of electrons depends solely on the Fermi momenta, it is clear that this electron density already saturates at an Al-film thickness of 2 Å. Thus, our method overcomes the necessity of a "critical thickness" of capping layer to generate a 2DEG in heterostructures. Previous studies on the bare surface of SrTiO 3 prepared in situ showed that synchrotron UV-irradiation was necessary to create the oxygen vacancies responsible for the 2DEG. This is again demonstrated in the lower panel of figure 5.14(c), which shows the evolution with time of the MDC at E F upon UV-irradiation on a bare SrTiO 3 (001) surface. While the 2DEG is absent at t=0 h (black MDC), its carrier density increases up to saturation upon UV irradiation (blue and red MDCs), as denoted by the increase of k F for increasing exposure times. Contrary to the bare surface, there is no measurable influence of the UV irradiation on the electronic structure of the Al/SrTiO 3 system, neither on the charge carrier density nor on the lineshapes or spectral weight of the 2DEG, as demonstrated in the top panel of figure 5.14(c) : the MDCs at E F show a stable subband structure and a maximum electron density from the very beginning of the measurements. This indicates that the oxygen vacancy concentration and distribution, due the redox reaction at the interface between Al and SrTiO 3 , is already saturated and stable upon irradiation.

Conclusion

As presented above, we developed a new and versatile method to create a 2DEG at the interface between an oxide and a AlO x capping. This method produces, in a simple way, an homogeneous 2DEG on the whole sample surface. The Al-deposit also acts as a protective layer making it possible to take the sample out from vacuum for, e.g., transport measurements [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF]. In addition to SrTiO 3 (001) and [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] or anatase-TiO 2 (001), we showed that this method also works with BaTiO 3 (001), CaTiO 3 or ZnO(0001) [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF].

The preparation of a 2D metallic state at the surface of the room-temperature ferroelectric insulator BaTiO 3 is particularly interesting. Such hitherto unobserved coexistence of ferroelectricity and 2D conductivity in the same material is promising for functional devices using ferroelectric resistive switching or for ultra-sensitive strain or pressure detectors. More generaly, we believe that the method presented here is very promissing both for further fundamental studies and for technological purposes.

The results presented in this section are further detailed in reference [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF].

Conclusions

The study of two-dimensional electron gases at the surface of oxides by ARPES to better understand the striking properties of oxide heterostructures started on the oxygendeficient surface of fractured SrTiO 3 by ARPES. [START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF]. This unexpected finding together with the interest in 2DEGs at SrTiO 3 -based interfaces (e.g. LaAlO 3 /SrTiO 3 ) make this field one of the most active areas of research in modern condensed matter physics. Our major contribution is the generalization of this finding to many other oxygen-deficient surfaces (including different surface orientations) of transition metal oxides (TiO 2 -anatase, CaTiO 3 (see [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF]), BaTiO 3 [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF] or ZnO [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF]). A comparison of the results obtained on those different compounds enlightens the role of slight changes in the crystallographic structure. Hence, the tilt of the O-octahedra surrounding the Ti-atoms in CaTiO 3 notably changes the Fermi surface due to hybridization between the light and the heavy bands [START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF].

Such a general study, mainly led by T. C. Rödel during his PhD, allowed to shed some light on the mechanisms responsible for the creation of oxygen vacancies, either by UV-irradiation or by a redox reaction at the interface between the considered oxide and a highly reducing coating like Aluminum. The behavior of the excess electrons introduced by these oxygen vacancies is not easily predictible. In electron-doped d 0 transition metal oxides, both localized and itinerant electrons can exist. Which of the two cases is energetically favorable can depend on subtle differences as demonstrated above by studying two polymorphs of the same material, TiO 2 in the anatase or rutile structure.

If one makes the comparison with two dimensional electron gases (2DEGs) in semiconductors, transition metal oxides show a variety of properties usually not observed in semiconductors, like ferroelectricity, ferromagnetism, superconductivity and strong electron correlations. This opens the prospect of highly functional devices. The deposition of a thin pure Aluminum film at the surface of various transition metal oxides appears to be an easy and versatile method to stabilize oxide 2DEGs and makes them suitable for in air purposes.

ARPES turned out to be a very adapted technique for the study of 2DEGs and brought many new pieces of information on their electronic band structure to the community. The CASSIOPEE setup and its very complete MBE system was a crucial tool to go from the cleaved surfaces studied in 2011 to the large, homogeneous and highly reproducible samples made from UHV-prepared oxide surfaces capped with Aluminum.

CHAPITRE 6

Conclusions and perspectives

Conclusions

Throughout this dissertation, I described results obtained using synchrotron radiation on various materials like metals or rare earth compounds but mainly on oxides. X-ray absorption spectroscopy allowed to precisely characterise the distorted structure of epitaxial thin magnetic films which is mandatory to fully understand their magnetic properties. X-ray absorption is also a probe of the first empty electronic states just above the Fermi level and can therefore give an insight into the electronic structure. Hence, the absorption edge profiles provide a valuable information on, e.g., magnetism (using X-ray Magnetic Circular Dichroism, XMCD), on the nature of these first empty states, on their symmetry... We developped new applications of resonant electronic spectroscopies (resonant photoemission and resonant Auger) for the interpretation of absorption edge profiles. We were able to detect quadrupolar transitions in the Ti-K-edge in TiO 2 -rutile by resonant Auger thanks to spectator lines due to these transitions towards localized d-states. It was at this time, to my knowledge, the first observation of spectator Auger lines in solids. Resonant 3d-photoemission was also used to unravel the contributions of different final states at the Ce-L 3 -edge in mixed-valent Ce-compounds. For these two studies, we worked with photon energies between 5 and 6 keV for two of the first significant publications using hard X-ray photoemission. The data were collected at the ID32 (ESRF, Grenoble-France) and BW2 (HASYLAB, Hamburg-Germany) beamlines which were both pioneering in this field, triggering the broad interest that we nowadays observe with numerous X-ray beamlines dedicated to photoemission in the United States of America, in Germany, in France or in Japan.

Resonant measurements in the soft X-rays or VUV-range are still easier. The crosssection and the resonant effects are much larger although the interpretation of the results can be more complicated. I also presented results obtained at the Ti-L 2,3 -edges for the interpretation of Auger line profiles or for the caracterization of defects (O-vacancies in this case) in oxides. This latest work is of new interest with all the scientific activity around oxide heterostructures and 2D-electron gas where O-vacancies play a crucial role. Up to now, the resonant photodiffraction technique that we used is still the only experimental technique able to locate these defects in the crystal structure, not only in the surface layer (which is possible by Scanning Tunneling Microscopy, STM), but on the last 3-4 atomic planes.

Going further into soft X-ray and VUV resonant electronic spectroscopies was the goal when I joined the CASSIOPEE team. We built a state-of-the-art beamline dedicated to angle-resolved and spin-resolved photoemission which welcomes users from all around the world and produces every year many high-level publications.

The most important results I had on CASSIOPEE were finaly ARPES results obtained on 2D electron gas at the surface of oxides during Tobias Rödel's PhD, co-directed with Andres Santander-Syro. The main achievements of this thesis were to detect this 2D electron gas on various oxide surfaces (so far, it had been only observed at the cleavedsurfaces of SrTiO 3 or KTaO 3 ) and also to take advantage of surface science techniques to create it on prepared surfaces. We first used (local) UV-irradiation and then deposition of a reducing layer, making it possible to stabilize a homogeneous electron gas on the whole sample surface. These experimental progresses were made thanks to a good understanding of the involved mechanisms.

Perspectives

Experimental perspectives

As a good experimentalist, I start this section with the perspectives of new experimental developments.

In the international context, CASSIOPEE is among the best beamlines dedicated to photoemission, every beamline having its strengths and its weaknesses. Some have better ultimate energy resolution and very low temperatures (like the 1 3 -beamline on BESSY II, in Berlin, Germany), some have better sample holders (like SIS on the SLS, in Villigen, Switzerland). CASSIOPEE offers a good balance between energy resolution (with a routinely accessible energy resolution of the order of 5-8 meV) and a cryostat allowing to cool the sample down to 5-6 K with only one rotation. On the other hand, the very large accessible photon energy range (from 8 to 1500 eV) is a strong asset. It is ideal for both VUV and soft X-ray ARPES, resonant spectroscopy at many absorption edges and core-level photoemission.

These last 4 years, we've been working in collaboration with the SOLEIL Design Office on the study and manufacturing of a new cryogenic sample holder with six-degrees of freedom, three X, Y and Z translations and three rotations (θ, φ and Tilt) (see figure 6.1). The large angular ranges will allow to reach regions of the reciprocal space up to now not accessible on CASSIOPEE. This new sample holder is now in the commissioning phase. First cryogenic tests demonstrated a temperature around 10 K for the sample. We still have to characterise precisely the three rotations and it should be ready for operation by the end of 2017 to open new possibilities for the CASSIOPEE ARPES endstation.

One of the assets of the CASSIOPEE beamline, as described in chapter 4, is certainly its complete MBE system coupled to the measurement chambers. Complex materials, like binary or ternary alloys, 1D epitaxial systems or molecular films can be prepared and characterised. We plan to implement a plasma source, able to produce atomic oxygen or nitrogen. The goal is to be able to grow oxides (or nitrides) as thin films but also to clean oxide samples grown elsewhere by O-plasma exposure. Simultaneously, we (and in particular, Julien Rault) also develop a UHV-suitcase compatible with the growth chambers of our favorite collaborators.

Metastable epitaxial materials for ARPES

Since we collect electrons with a very small mean free path, ARPES is a very surface sensitive technique. This is not a problem and even an asset for surface science. But for the solid state physicist, the first challenge to tackle prior to any measurements is always to prepare a clean single-crystal surface. For some samples like "2D-systems", e.g. made of "solid" crystallographic atomic planes weakly bonded in a direction perpendicular to those planes (cobaltates, sulphides, selenides...), cleaving is an easy way to prepare such clean surfaces. For "3D-materials", like the perovskites we studied in chapter 5 or semiconductors, cleaving can also be a solution even if those crystals are more difficult to break. Cleaving often results in a small clean area of the order of some tens of µm 2 , i.e. of the order of the size of the beam, which makes the measurements quite delicate.

For metallic samples, or materials which are difficult to find as single crystals, or simply if one wants to do a systematic study as a function of composition, doping or stoechiometry, an elegant way to obtain good samples, suitable for ARPES study, is to make them in situ, as thin films deposited on an adapted substrate. In addition, the epitaxy opens the possibility to stabilize metastable phases which could show new physical properties. In other words, the ability to grow samples in situ, in a MBE facility coupled to the measurement chamber opens wide prospects that I intend to use. I give here some exemples (see also next section) of studies of new, or metastable or "artificial" materials.

A way to create new materials with original physical properties is to take advantage of the epitaxy on a substrate to stabilize metastable structures. In a recent paper, it was shown that one could stabilize FeSi 2 [START_REF] Kaindl | Surface and bulk electronic structure of metallic cerium systems[END_REF] in the α-phase by epitaxy on Si(001), a phase which normaly only exists above 950 • C [START_REF] Guixin Cao | Ferromagnetism and nonmetallic transport of thin-film α-FeSi 2 : A stabilized metastable material[END_REF]. Surprisingly, these α-FeSi 2 films are semiconducting and ferromagnetic (with a Curie temperature of 50 K) while they were expected to be metallic and nonmagnetic. The strains of the structure had to be taken into account in a band structure calculation to explain the material properties. Obviously, ARPES combined with spin-resolved photoemission measurements could give a complete description of the band structure and CASSIOPEE would be the perfect place for that. We already tried the growth of α-FeSi 2 (111) films on Si(001), but, up to now, we've never been able to have a single-phase film. A monitoring by RHEED during the growth could help us to find the optimal growth conditions.

More than a unique perspective, this study of metastable α-FeSi 2 films is just an illustration of the interest of epitaxial materials for photoemission study.

Oxides

For more than 15 years, oxides have been my "bread and butter". Perspectives are still numerous in this field.

Spinels

So far, oxide heterostructures have been very mainly made from perovskites. On the other hand, as we saw it in chapter 5 of this dissertation, 2D-electron gas can be stabilised at the surface of other structures like the teragonal structure of anatase or the wurtzite structure of ZnO. The CASSIOPEE team is a partner of the SPoTEleSS ANRproject, led by Rémi Arras (Centre d'Elaboration des Matériaux et d'Etudes Structurales, Toulouse) whose goal is to study both theoreticaly and experimentaly spinel/spinel heterostructures. The idea is to focus on magnetic materials, such as CoFe 2 O 4 in the CoFe 2 O 4 /MgAl 2 O 4 (001) system, to create a spin-polarized 2D-electron gas (SP2DEG), as predicted in reference [START_REF] Arras | Fully spin-polarized two-dimensional electron gas at the CoFe 2 O 4 /MgAl 2 O 4 (001) polar interface[END_REF].

One could think about different inputs from the CASSIOPEE beamline on this project.

First, if the capping layer is not too thick (reference [START_REF] Arras | Fully spin-polarized two-dimensional electron gas at the CoFe 2 O 4 /MgAl 2 O 4 (001) polar interface[END_REF] gives a critical thickness of 19 Å of CoFe 2 O 4 for a possible existence of a SP2DEG), a resonant measurement at the Fe-L 3 -edge could allow to detect metallic states at the interface. Figure 6.3 shows such a measurement at the Ti-L 3 -edge (459 eV) on a 10 Å-Al/SrTiO 3 (001). We clearly see the contribution of metallic states to the Fermi surface due to the 2DEG at the interface, buried under the nominal 10 Å of Aluminum. As the mass density of Al is 2.7 g/cm 3 and the one of amorphous Al 2 O 3 is about 4 g/cm 3 , the deposition of 10 Å of Al yields an oxidized Al-film of around 13 Å. At the Fe-L 3 -edge (around 707 eV), it should be possible to probe the ferrite-based spinel/spinel interfaces made to produce this SP2DEG. More generaly, the soft X-ray range of the beamline for angle-resolved photoemission measurement is to be explored. This has been already started, mainly by Julien Rault (beamline scientist on CASSIOPEE) for the study of SrRuO 3 /BaTiO 3 or La 0.7 Sr 0.3 MnO 3 /SrTiO 3 and SrTiO 3 /La 0.7 Sr 0.3 MnO 3 /SrTiO 3 systems.

Second, the study of bare spinel ferrite surfaces at low photon energy, similar to what we did on other various oxides, could give the band structure of the 2DEG. The process for the creation of the 2DEG as described in the calculation of reference [START_REF] Arras | Fully spin-polarized two-dimensional electron gas at the CoFe 2 O 4 /MgAl 2 O 4 (001) polar interface[END_REF] is based on an internal electric field appearing due to the charge discontinuities at the interfaces, but, similarly to SrTiO 3 , the same result could maybe be obtained by creation of oxygen vacancies. This could be done on thin films elaborated ex situ and cleaned in our setup by O-plasma exposure, or on films grown in situ. O-vacancies could then be created either by UV-irradiation or by an Aluminium capping [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF]. Last, for these systems supposed to be magnetic, the combination of ARPES and spin-resolved photoemission available on the beamline would provide a complete characterisation.

This topics is a collaboration with Rémi Arras and Lionel Calmels (CEMES, Toulouse) and Jean-Baptiste Moussy and Antoine Barbier (SPEC, CEA-Saclay).

Water photoelectrolysis

Producing hydrogen through solar water splitting is very appealing as it is an energy source of choice which does not lead to any greenhouse gas production when produced with solar light. During the process, electron-hole pairs photogenerated in semiconductors in contact with an aqueous solution participate to the water oxidation and reduction reactions (oxygen and hydrogen production respectively). Since the pioneering discovery of water photo-assisted electrolysis using TiO 2 [START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF], several materials were investigated as photoanodes. Unfortunately, there are no simple semiconductors fulfilling all requirements and new routes need to be explored. Combining materials in heterojunctions, hence trying to take advantage of their individual properties, appears as a very promising way to improve the photoanode performances. Doped oxides (like Ti-doped hematite α-Fe 2 O 3 [START_REF] Magnan | Enhanced photoanode properties of epitaxial Ti doped α-Fe 2 O 3 (0001) thin films[END_REF][START_REF] Rioult | Single Crystalline Hematite Films for Solar Water Splitting : Ti-Doping and Thickness Effects[END_REF]) are also promising candidates as photoanodes for solar water splitting devices. The main advantage of hematite is its low band gap of ∼2.1 eV, well-adapted for the visible light absorption. Ti-doping greatly enhances the performances through an increase of the carriers diffusion length while conserving the corundum structure.

We study these materials in collaboration with Hélène Magnan (SPEC, CEA-Saclay) for their characterisation by photoemission. In particular, for doped samples, resonant photoemission at one of the dopant's absorption edge can be used to enhance the dopant contribution to the valence states.

Sophisticated oxides

The growth on adapted substrate is also a way to stabilize new materials as singlecrystal with a clean surface in a known crystallographic orientation. The development of oxide deposition by MBE or PLD opened the way for the elaboration of simple interfaces between two oxides but also to the making of more sophisticated artificial materials like oxide "multilayers", where a layer can be as thin as 1 atomic plane. This was achieved, e.g. by alternating LaNiO 3 , LaAlO 3 and LaTiO 3 layers [START_REF] Ankit | Orbital engineering in symmetry-breaking polar heterostructures[END_REF]. The charge transfers occuring at interfaces change the orbital occupation and allow to tailor the electronic structure. In reference [START_REF] Ankit | Orbital engineering in symmetry-breaking polar heterostructures[END_REF], the only characterisation method used is X-ray absorption at the Ti-L 2,3edges (and Ni-K-edge), which is very sensitive to the Ti valence. Photoemission could also give a quantitative evaluation of charge transfer for each species by measuring corelevel shifts for, e.g., Ti and Ni 3p and 2p lines and Al-2p. More interestingly, it will give a direct image of the resulting band structure. This kind of "layered", three component-compounds has already been made in the CASSIOPEE MBE using evaporation sources with computer-controlled motorised shutters. In this experiment, the sample was a Heusler-alloy made of 10 times the piling made of 1.5 ML of Co 2 MnAl and 1.5 ML of Fe 2 MnAl (Tobias Brown-Heft et al., Palmstrøm Research Group, University of California-Santa Barbara). With the installation of an O-plasma source, one could think about making artificial oxide compounds of the same kind as those described in reference [START_REF] Ankit | Orbital engineering in symmetry-breaking polar heterostructures[END_REF] to study them by photoemission.

Defects in oxides

Defects at the surface of oxides have been a central concern for chemists since they create new electronic states, in particular in the gap, and perturb the reactivity. These last 10 years, their study also became a real priority for physicists interested in oxide heterostructures and their associated properties. Indeed, defects like O-vacancies can release electrons in the structure whose behaviour is of key importance for physical properties. Are they localized or delocalized ? Can they be simply described or do they form quasiparticles like polarons ? ARPES measurements brought answers to these questions in some compounds but the modelisation of the electronic structure requires a precise description of the surface crystallography, including possible reconstructions [START_REF] Dupont | Structure of TiO 2 (011) revealed by photoelectron diffraction[END_REF] and the preferential atomic sites for the nucleation of defects. Apart from STM measurements (probing only the surface plane) and predictive calculations, it is hard to obtain an information about the defect localization on the last 3-4 atomic planes, those which host, e.g., the 2DEG evidenced on SrTiO 3 and many other oxides.

Our resonant photoelectron diffraction study presented in chapter 3 gave access to the excess charge localization by studying a (resonantly enhanced) spectroscopic signature of these defects, i.e. the intensity variations of the electronic states appearing in the gap. This study was carried out using soft X-rays (around the Ti-L 2 -edge) which made the data interpretation easier since forward scattering is dominant for high kinetic energy electrons [START_REF] Krüger | Defect states at the TiO 2 (110) surface probed by resonant photoelectron diffraction[END_REF].

Recently, on CASSIOPEE, we investigated again the intensity behaviour of the ingap state in TiO 2 -rutile(110) as a function of the collection angle, the photon energy and also the light polarization. On very well-ordered surfaces (heated above 1100 • ), the in-gap state peak intensity shows very strong variations, giving nice patterns which can certainly bring information on the defects locations and the nature of the involved electronic states. Once the results understood, this study on rutile could be extended to other oxides.

L 3 -

 3 edge in mixed-valent compounds . . . . . . . . . . . . . . . . . . . . . 3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Mixed-valent Ce-compounds . . . . . . . . . . . . . . . . . . . . . 3.4.3 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Interpretation of the Ce-L 3 absorption edge using high-energy resonant 3d-photoemission . . . . . . . . . . . . . . . . . . . . . . . 3.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Other applications of resonant measurements . . . . . . . . . . . . . . . . 3.5.1 Ti-LM V Auger lineshape in rutile . . . . . . . . . . . . . . . . . . 3.5.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1.2 Experimental conditions . . . . . . . . . . . . . . . . . . 3.5.1.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Resonant photoelectron diffraction : defect sites in rutile . . . . . 3.5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2.2 Experimental conditions . . . . . . . . . . . . . . . . . . 3.5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 1 -

 11 Figure 1.1 -Schematic view of a LaAlO 3 /SrTiO 3 heterostructure. After reference [3].

Figure 2 .

 2 Figure 2.2 -X-ray absorption spectrum recorded at the Cu K-edge (Top part). Schematization of the photoelectric effect for the different region of the spectrum (Bottom part).

Figure 2 . 3 -

 23 Figure 2.3 -Schematic view of the electronic wave leaving the photoexcited atom. The figure shows the interferences between this outgoing wave and its scattered parts by the surrounding atoms.

Figure 2 . 4 -

 24 Figure 2.4 -The first steps for the data analysis of EXAFS data. (a) A raw absorption spectrum. (b) Determination of the threshold energy. (c) Determination of the edge jump J. (d) Determination of the atomic absorption µ 0 . (e) Calculation of χ(E), where E is the electron kinetic energy. (d) Calculation of χ(k), where k is the electron wave vector calculated from E using E = 2 k 2 /2m.

Figure 2 . 5 -

 25 Figure 2.5 -(a) χ(k) and the limits chosen for the Fourier transform. (b) Modulus of the Fourier transfom of χ(k), showing a series of peaks roughly centered at the position of the different neighbour shells.

Figure 2 . 6 -

 26 Figure 2.6 -Top part : Modulus of the Fourier transform and the limits chosen for the inverse Fourier transform. Bottom part : Inverse Fourier transform of the first peak of the Fourier transform.

Figure 2 . 7 -

 27 Figure 2.7 -Top part : χ 1 (k) recorded at 77 K (solid line) and at 300 K (dashed line). Middle part : Amplitude A (k) extracted for both temperatures. Bottom part : Experimental ratio of the two amplitudes (solid line) and fit by a straight line (dotted line).

Figure 2 . 8 -

 28 Figure 2.8 -Two possible scattering paths for the electronic wave. The 1-4-1 path is a single-scattering path, whereas the 1-2-3-1 path involves two scattering processes. Since both paths have roughly the same total length, their respective contribution will appear at the same location in R in the Fourier transform.

Figure 2 . 10 -

 210 Figure 2.10 -Fourier transforms of EXAFS spectra recorded on fcc copper, bcc iron and hcp cobalt. For hcp cobalt, the spectra were recorded on a single crystal with the linear polarisation of the X-rays either in the (0001) plane (Normal, solid line) or perpendicular to it (Grazing, dashed line).

Figure 2 .

 2 Figure 2.11 -Schematic representation of the (001) planes in a fcc crystal. Open circle : central atom. Closed circles : "in-plane" (intralayer) first nearest neighbours of the central atom. Cross-hatched circles : "out-of-plane" (interlayer) first nearest neighbours of the central atom.

Figure 2 .

 2 Figure 2.12 -EXAFS spectra recorded at 77 K at the cobalt K-edge (a) for 3 ML Co/Cu(001) grown at 300 K in normal and in grazing incidence. (b) for 3 ML Co/Cu(001) and 8 ML Co/Cu(001) grown at 300 K in normal incidence.

Figure 2 . 13 -

 213 Figure 2.13 -Fourier transforms of EXAFS spectra recorded at 77 K (full line) and 300 K (dotted line), in normal and grazing incidence, for 3 and 15 ML Co/Cu(001) grown at 300 K.

Figure 2 . 14 -

 214 Figure 2.14 -Simulations of the inverse Fourier transforms of the first nn shell for the 15 ML Co/Cu(001) grown at 300 K, in normal and in grazing incidence. The EXAFS spectra were recorded at 77 K. Open circles : Experimental data. Full line : Simulation.

Figure 2 . 15 -

 215 Figure 2.15 -Fourier transforms of k.χ(k) in normal and in grazing incidence for : (solid line) Experimental EXAFS spectra recorded at 300 K of a single crystal of cobalt (0001) ; (dotted line) Simulation with the FEFF code of an EXAFS spectrum of a hcp cobalt (0001) at 300 K, with a=2.51 Å and c=4.07 Å as lattice parameters, using S 2 0 =0.81 and T Debye =385 K.

Figure 2 . 16 -

 216 Figure 2.16 -Fourier transforms of k.χ(k) in normal (left) and in grazing (right) incidence for : (top part) Simulations with the FEFF code of EXAFS spectra calculated on the different t1, t2 and t3 fct structures (see text). (bottom part) Comparison of the t2 structure (dotted line) with experimental EXAFS spectra recorded on a 15 ML Co/Cu(001) film (solid line).

Figure 2 . 17 -

 217 Figure 2.17 -Perspective view (top) and top view (bottom) of the first nearest neighbour shell in a fcc structure (left) and in a hcp structure (right).

Figure 2 .

 2 Figure 2.18 -Top : Perspective views of a fcc (left) and a hcp structure (right). Bottom : Cut along the 11 2 direction evidencing the atomic alignements in the fcc structure which disappear in the hcp structure.

Figure 2 .

 2 Figure 2.19 -EXAFS spectra recorded at 77 K at the cobalt K-edge (a) for 3 ML Co/Cu(111) grown at 300 K in normal (solid line) and in grazing (dashed line) incidence.

Figure 2 .

 2 Figure 2.20 -FT of experimental EXAFS data recorded in grazing incidence on a 8 ML Co/Cu(111) (solid line) compared with simulations done on a distorted fcc (right) or a distorted hcp (left) structure (dashed line).

Figure 2 .

 2 Figure 2.21 -XANES spectra in GI (solid line) and NI (dotted line). (a) Experiment on an hcp Co(0001) single crystal, 8 ML, 3 ML, and 1.5 ML Co/Cu(111) and fcc bulk Cu. (b) FEFF6 simulations for hcp Co(0001), 3 ML Co/Cu(111) (ABCaba and ABCaba stackings) and fcc Cu. The abscissa is the photon energy relative to the threshold (7710 eV for Co and 8980 eV for Cu).

Figure 2 .

 2 Figure 2.22 -FT of experimental EXAFS data recorded in grazing incidence on a 0.5 ML Co/Cu(111) (solid line) compared with simulations done for 1 ML of Co deposited on an ABC terminated Cu(111) either on A sites (a) or on B sites (b).

Figure 2 .

 2 Figure 2.23 -FT of EXAFS data recorded on a 3 ML Co/Cu(111) film : experiment (solid line) and FEFF6 simulations (dotted line) for the indicated stackings.

Figure 3 . 1 -

 31 Figure 3.1 -Schematic view of the two possible decay processes for a core-hole. Left part : Auger decay. Right part : Fluorescence decay.

Figure 3 . 2 -

 32 Figure 3.2 -Two-step picture of the Raman regime. The excitative photon energy increases from left to right. The energy of the emitted photon (symbolized by the width of the wiggling arrow) increases to finaly reach the normal fluorescence energy.

Figure 3 . 3 -

 33 Figure 3.3 -The correct one-step picture of resonant fluorescence (right part) is similar to the Raman process (left part), where part of the photon is absorbed.

Figure 3 . 4 -

 34 Figure 3.4 -Normal Kα fluorescence line (black curve), and the part of it revealed when the incident photon energy is below the edge from E exc (red-hatched part).

Figure 3 .

 3 Figure 3.5 -A simple picture explaining the dispersive behaviour of a spectator line.

Figure 3 . 6 -

 36 Figure 3.6 -Dispersive behaviour of the Raman line (black curve) and of a spectator line (red curve).

  Figure 3.7 -RIXS measurement at the Cu-K-edge in CuO. Left : XAS measurement at the Cu-K-edge. Right : RIXS spectra recorded for various photon energies across the Cu-K-edge. In the pre-edge region (red zone in left panel), a spectator line (labeled C on the right panel) appears, due to 1s → 3d transitions . In the green region, another spectator line labeled B (due to 1s → 4p transitions) appears. After reference [59].

Figure 3 . 8 -

 38 Figure 3.8 -RIXS measurement at the Gd-L 3 -edge in Gd 3 Ga 5 O 12 . (a) XAS measurement at the Gd-L 3 -edge. (b) RIXS spectra recorded for various photon energies (indicated by vertical lines in (a)) across the Gd-L 3 -edge. In the pre-edge region, a spectator line (labeled A) appears, due to 2p → 4f quadrupolar transitions. (c) Intensities of lines A, B and C as a function of the incident photon energy. After reference [60].

Figure 3 . 9 -

 39 Figure 3.9 -Two-step picture of the Raman-Auger regime.

Figure 3 .

 3 Figure 3.10 -Left : Direct photoemission process. Right : Autoionization process. The two processes produce electrons with the same kinetic energy (top part).

Figure 3 .

 3 Figure 3.11 -Fano profiles for different values of q [65].

  and D whose intensities strongly vary with the photon energy. Both Q 1 and Q 2 always appear at constant binding energy (959.1 and 961.1 eV, respectively), while D has a different behaviour. It first appears at a constant binding energy of 963.2 eV, until it reaches the

Figure 3 .

 3 Figure 3.12 -A 1 , A 2 , and A 3 prepeaks of the Ti K-absorption edge in rutile. The X-ray wave vector is perpendicular to the c axis and either parallel to (0 • ) or at 45 • (45 • ) from the (110) surface normal. The bottom curve is the difference between the two absorption spectra. Inset : Total absorption threshold at 0 • .

Figure 3 .

 3 Figure 3.13 -Ti KL 2 L 3 ( 1 D 2 ) Auger line for the indicated different photon energies recorded in the 0 • (left panel) and the 45 • (right panel) geometries.

Figure 3 .

 3 Figure 3.14 -(a) The three A 1 , A 2 , and A 3 prepeaks observed before the main Ti Kabsorption edge in rutile-TiO 2 for the 0 • , and the 45 • geometries. Bottom part : Difference between the XAS spectra recorded at 0 and 45 • . Intensities of the three peaks Q 1 (b), Q 2 (c) and D (d) for the two incident angles of the X-rays for 0 • (open circles) and 45 • (closed circles).

Figure 3 . 15 -

 315 Figure 3.15 -Ce 3d photoemission spectrum in CeNi 5 and peak assignement. After reference [79].

Figure 3 .

 3 Figure 3.16 -Ce-L 3 absorption edge in the trivalent Ce 7 Rh 3 (left) and mixed-valent CeRh 3 compounds (right).

Figure 3 .

 3 Figure 3.17 -(a) Photoemission spectra for Ce 7 Rh 3 , CeRh 2 , and CeRh 3 at a photon energy of 5734 eV. (b) Ce-L 3 absorption edge (top part), and different CIS spectra recorded on CeRh 3 for three photoemission lines corresponding to the 3d 5/2 -4f 2 (triangles), 3d 5/2 -4f 1 (circles), and 3d 3/2 -4f 0 (squares) configurations. The solid lines are fits with the Fano function, and the vertical dotted lines show the positions of the resonance energies E 0 determined from the fits, respectively, 5725±1, 5728±1, and 5737±1 eV.

3. 5 . 1

 51 Ti-LM V Auger lineshape in rutile 3.5.1.1 Introduction

Figure 3 .

 3 Figure 3.18 -Ti-LM V Auger spectra recorded off-resonance in stoichiometric rutile-TiO 2 (bottom), reduced-TiO 2 (TiO 2-x , middle), and metallic titanium (top). The TiO 2and TiO 2-x spectra were recorded at 542 eV photon energy. On metallic titanium, the spectrum was recorded at 465.6 eV. The feature seen at 407 eV kinetic energy in metallic titanium spectrum is the Ti-3s photoemission. The two other Auger spectra, which were recorded at higher photon energies are not contaminated by this photoemission peak.

Figure 3 . 19 -

 319 Figure 3.19 -Schematization of the Auger LM 2,3 V process.

Figure 3 . 20 -

 320 Figure 3.20 -Experimental resonant electron spectra obtained on stoichiometric TiO 2rutile (left part), TiO 2-x (middle part) and metallic titanium (right part). The absorption spectrum (top), the resonant Ti-L 2,3 M 2,3 V Auger spectra (bottom left), and the resonant valence-band spectra (bottom right), both recorded at the Ti-L 2,3 edges, are presented for each sample. For the resonant spectra, the excitative photon energy is given on the left of the spectrum. The slanting lines in the Auger panel indicate the position of the Ti-3p photoemission lines, whose kinetic energy varies with photon energy. The strongly dispersive line observed in the valence-band spectra recorded on TiO 2 , marked by a vertical stroke between 455 and 459.1 eV photon energy, is the Ti-2p 1/2 photoemission excited by the monochromator second-order reflection. The spectra recorded on metallic Ti, for photon energies above the Ti-L 2 edge show some contamination effects through the presence of carbon or oxygen valence states.

Figure 3 . 21 -

 321 Figure 3.21 -Ball and stick model of the TiO 2 (110) surface. Big red (small blue) balls are O (Ti) atoms. V indicates a bridging oxygen (O1) vacancy.

3. 5 . 2

 52 Resonant photoelectron diffraction : defect sites in rutile 3.5.2.

Figure 3 . 22 -

 322 Figure 3.22 -Principle of a PhotoElectron Diffraction (PED) experiment. An X-ray beam excites photoelectrons and the intensity of a selected line is measured as a function of the polar angle θ and the azimuthal angle φ. This PED pattern can be projected in a (θ,φ) plane (right).

Figure 3 . 23 -

 323 Figure 3.23 -Experimental photoelectron diffraction (PED) patterns. Left : Standard PED from the Ti-2p 3/2 core level. Right : Resonant PED from the defect state. The projection is linear in θ with the surface normal (θ=0) in the center. Ticks are drawn at every 10 • . φ=0 (φ=90) is found at 3 o'clock (12 o'clock) and corresponds to the [110] ([001]) direction.

Figure 3 . 24 -

 324 Figure 3.24 -Calculated photoelectron diffraction patterns from the defect level along with the experimental one ("exp"). Pattern "n" (n=1...4) corresponds to emission from Ti(n) atom alone. Pattern "1-n" corresponds to a weighted sum over the emission intensities of Ti(1) to Ti(n). The weights are obtained through R-factor minimization.

Figure 4 . 1 -

 41 Figure 4.1 -A photoemission experiment. Adapted from the Wikipedia article on photoemission.

Figure 4 . 2 -

 42 Figure 4.2 -Schematic view of the photoemission process. On the left side, a strongly simplified band structure of a sample is shown. It consists only of one core level and the valence band. The electron states are occupied up to the Fermi energy E F which is defined as the zero binding energy E F = 0. Electrons with the binding energy E B are excited by photons with energy hν to a final state with energy E f with a kinetic energy E kin . The work function Φ is the energy between the Fermi energy E F and the vacuum level E vac . The final state of the photoexcited electron is modeled as a band of a free electron. The energy of the valence band bottom E 0 corresponds to the bottom of the free-electron parabola of the final state.Together with the vacuum level E vac , E 0 defines the inner potential V 0 . On the right side, the detected spectrum is shown. Taken from reference[START_REF] Reinert | Photoemission spectroscopy -from early days to recent applications[END_REF].

Figure 4 . 3 -

 43 Figure 4.3 -Principle of an ARPES experiment.

Figure 4 . 4 -

 44 Figure 4.4 -The different steps of the photoemission process.In its initial state, defined by its binding energy E B and its wave vector k, the electron belongs to the occupied states of the solid band structure (black solid line), below the Fermi level. The excitation by the photon promotes it to an empty state of the band structure inside the solid, whose energy is E f but with the same wave vector k. This final state is approximated

Figure 4 . 5 -

 45 Figure 4.5 -Electron refraction at the interface between the solid and vacuum. The component of the electron wave vector perpendicular to the surface k ⊥ is reduced, while the component parallel to the surface k || is conserved.

Figure 4 . 6 -

 46 Figure 4.6 -Top : Raw ARPES spectrum measured using 100 eV photons on a TiO 2rutile(110) single crystal along the [001] direction (T=5 K). The result is an image whose axis are kinetic energy (in eV) and emission angle θ (in degrees). Bottom : Same ARPES spectrum after a mathematical treatment to display k || as a function of the binding energy.

Figure 4 .

 4 Figure 4.7 -A simple experimental geometry where the green horizontal plane is a mirror plane for the sample and also the incidence plane, i.e. the plane containing both the incident photons and the collected electrons.

Figure 4 . 8 -

 48 Figure 4.8 -3D-view of the CASSIOPEE beamline from the front end (right) to the endstations (left).

Figure 4 . 9 -

 49 Figure 4.9 -The HU256 undulator at the BINP (Novosibirsk, Russia).

Figure 4 .

 4 Figure 4.10 -Top : Working principle of an APPLE II-type undulator. Depending on the position of the rows of magnets, it can produce linear horizontal, linear vertical or elliptical polarisations. Bottom : A picture of the CASSIOPEE HU60 undulator.

Figure 4 .

 4 Figure 4.11 -The two configurations for the CASSIOPEE entrance optics. (a) Low photon energy configuration with a 5.02 • incidence on the first mirror. (b) High photon energy configuration with a 2.44 • incidence on the first mirror.

Figure 4 .

 4 Figure 4.12 -The CASSIOPEE entrance optics.

Figure 4 . 13 -

 413 Figure 4.13 -Schematic side view of the CASSIOPEE monochromator. The incident angles on the grating (α) and on the mirror (D/2) can be both changed.

Figure 4 . 14 -

 414 Figure 4.14 -Top view inside the CASSIOPEE monochromator.

Figure 4 .

 4 Figure 4.15 -Calculated resolving power for the CASSIOPEE monochromator as a function of the photon energy and for different values of c. G1, G2 and G3 are the 400, 800 and 1600 l/mm gratings, respectively.

Figure 4 .

 4 Figure 4.16 -K-edge absorption at the 1s → π * resonance of N 2 molecules. The experimental data (red crosses) have been adjusted by seven Voigt functions (blue line).The natural linewidth of the lines due to the core-hole lifetime being usually estimated to 115 meV, we adjusted the experimental spectrum with seven Voigt functions, combining a 115 meV wide lorentzian and a resolution gaussian. The best adjustment of the experimental spectrum is obtained for an experimental resolution of 10 meV. This value corresponds to a resolving power of 40000, which is the value expected from the Optics Group calculations.

Figure 4 . 17 -

 417 Figure 4.17 -Top view of the four CASSIOPEE experimental chambers.

Figure 4 .

 4 Figure 4.18 -(a) The ARPES experiment focusing optics consists in two spherical and toroidal mirrors in the so-called pseudo-Wolter configuration. (b) Calculations of the beam size in the ARPES chamber done by the SOLEIL Optics Group for 9, 25 and 100 eV photons.

  single crystal, as shown on figure 4.20. The measurement has been performed with 30 eV photons on a sample fixed on the cold cryostat (T=4.8 K). The temperature of the sample surface is nevertheless difficult to estimate. The experimental data were adjusted by the Fermi function calculated at 6 K (figure 4.20(a)) and 19 K (figure 4.20(b)) convoluted with a gaussian function whose width (used as one of the fit parameters) accounts for the broadening due to the energy resolution. For a realistic temperature of 6 K at the surface of the Ag(110) sample, the fit result gives an overall resolution of 6.5 meV, coherent with what we routinely observe (4.20(a)).

Figure 4 .

 4 Figure 4.19 -(a) Left : View inside the ARPES chamber, with the cryostat shield and the nose of the Scienta R4000 electron analyzer on the left. Right : 3D-image of the sample holder. The rear door is open and one can see the cold finger, with the Omicron plate (in red, on which the sample is attached) on it. This cold finger rotates inside the cryogenic shield. (b) The angular range accessible on the CASSIOPEE ARPES setup. The angular resolution in the vertical direction is ensured by the analyzer over ±15 • around normal emission. The collection angle can be varied in the horizontal direction by rotating the sample thanks to a differentially pumped rotary feedthrough (θ rotation). The accessible emission angles are materialized by the red rectangle.

Figure 4 .

 4 Figure 4.20 -(a) Fermi step recorded on a Ag(110) single crystal fixed on the cryostat at 4.8 K (red crosses) and a fit by a Fermi function calculated for a 6 K temperature convoluted with a gaussian function. The fit gives a full width at half maximum (FWHM) of 6.5 meV for the gaussian function. The top curve is the difference between the experimental spectrum and the fit. (b) Same as (a) but for a Fermi function calculated for a 19 K temperature. In this case, the fit gives a FWHM of 2.7 meV for the gaussian function. Measurements by P. de Padova et al..

Figure 4 .

 4 Figure 4.21 -The CASSIOPEE preparation chamber sample holder with its three positions for the sample. Top : Without the protecting shield. Bottom : With the protecting shield, as it is mounted in the preparation chamber.

Figure 5 . 1 -

 51 Figure 5.1 -(a) Cubic perovskite unit cell. The oxygen anions (yellow spheres) form an octahedron (gray lines) around the transition metal cation (red sphere). The alkali metal/earth alkaline metal cations (black spheres) are situated in the corners of the unit cell. (b) Along the 001 direction, the perovskite structure can be represented by the alternating stacking of AO and BO 2 planes. Depending on the oxidation state of the metal cations, the planes can be either neutral or single charged. (c) Lifting of the degeneracy of d orbitals in an atom due to a crystal field of octahedral symmetry as for the transition metal cation in the perovskite structure shown in (a). The eigenenergies of the d states split in t 2g and e g states. After T. Rödel, PhD thesis [127].

Figure 5 . 2 -

 52 Figure 5.2 -Electronic bands observed at the cleaved surface of SrTiO 3 (001). Two light bands are observed around the Γ 102 point of the reciprocal space for linear vertical polarization of the incident photons and a heavy one around Γ 112 for linear horizontal polarization. This electronic structure is the same, whatever is the electron doping in the bulk. The top pictures show different SrTiO 3 single crystals for different electron dopings : the darker the crystal, the larger the doping. Adapted from reference [148].

Figure 5 . 3 -

 53 Figure 5.3 -(a) Expected band structure of the conduction band in bulk SrTiO 3 . (b) d xy orbitals : because of the large overlap in the(x, y) plane, a d xy -like band will appear as light when measured in the x or y directions. The small overlap in the z direction will make it appear as heavy when measured in this direction. (c) The expected Fermi surface for those bands in the (k x , k y ) plane, providing the Fermi level is lifted up in (a) to partially fill the conduction band. A d xy -like band, light in both the x and y directions will give a small circular sheet. The d xz -like band (respectively, d yz -like band) will give an elliptical sheet, with its major axis in the y (x) heavy direction, and its minor axis in the x (y) light direction. Adapted from reference[START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF].

Figure 5 . 4 -

 54 Figure 5.4 -(a) Triangular potential resulting from an homogeneous charge distribution over a depth of the order of L. F is the electric field generated by the charges, from which the potential is derived. (b) Expected band structure of the conduction band in bulk SrTiO 3 . (c)Modification of the bulk SrTiO 3 band structure when confined in the potential well decribed in (a) (dotted lines). The expected bands are superimposed on a compilation of the experimental measurements (bands measured around Γ 102 in LV and around Γ 112 in LH) (Left). The corresponding Fermi surface is shown on the right.Adapted from references[START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF] and[START_REF] Rödel | Two-dimensional electron gases (2DEGs) in transition metal oxides studied by photoemission[END_REF].

Figure 5 . 5 -

 55 Figure 5.5 -Photoemission spectra recorded at 100 eV photon energy and at 6 K on a freshly-cleaved anatase-TiO 2 (101) surface (black curve) and after one-hour irradiation (red curve).

Figure 5 . 6 -

 56 Figure 5.6 -Photoemission spectra recorded at 100 eV photon energy and at 6 K on freshly-cleaved (dark colours) and VUV-reduced (light colours) surfaces of various oxide (From reference [127]).

Figure 5 . 7 -

 57 Figure 5.7 -Concentration of oxygen vacancies (ratio between the Ti 3+ and total Ti-3p peak area measured at 100 eV photon energy and at 6 K) for different durations of irradiation exposure of the anatase-TiO 2 (101) surface (left). Intensity of the in-gap state measured at 100 eV photon energy and at 6 K for different durations of irradiation exposure (right).

Figure 5 .

 5 Figure 5.8 -(a) Binding energy of the Ti 4+ photoemission peak measured at 100 eV photon energy and at 6 K as a function of the irradiation time for the anatase-TiO 2 (101) surface. (b) Schematic view of the band structure close to the surface. O-vacancies due to irradiation are located close to the surface and create a potential which bends the bands.Since the core level are bent identically, the measurement of the Ti-3p binding energy gives an estimate of the depth of the created potential well, averaged on the depth probed by photoemission.

Figure 5 .

 5 Figure 5.9(a) shows the bulk Brillouin zone of anatase, its high symmetry directions, and the planes containing the measured Fermi surfaces when the cleaved surface is (001).The Fermi surface at the (001) plane shown in figure5.9(b) consists of two circles of d xy orbital character, confirmed by light polarization dependent measurements presented below (see Section 5.2.4.2), similar to the case of SrTiO 3[START_REF] Santander-Syro | Twodimensional electron gas with universal subbands at the surface of SrTiO 3[END_REF][START_REF] Meevasana | Creation and control of a two-dimensional electron liquid at the bare SrTiO 3 surface[END_REF][START_REF] Plumb | Mixed Dimensionality of Confined Conducting Electrons in the Surface Region of SrTiO 3[END_REF].The quasi-2D character of these two electronic states is strictly demonstrated by the Fermi surface map in the 010 -001 plane, perpendicular to the surface plane, presented in figure5.9(c). This Fermi surface shows that the bands are essentially non dispersing along k 001 over a bulk Brillouin zone, thereby confirming the confined character of the electrons close to the surface. Figure5.9(d) presents the energy-momentum map close to the bulk Γ 102 point along the cut parallel to the 010 direction shown in panel (a). Two dispersive light bands are visible. Their bottoms are at -60 meV for the upper band, and -172 meV for the lower band. A parabolic fit yields an effective mass of approximately 0.5m e , which agrees well with theoretical[START_REF] Huy | Calculation of carrierconcentration-dependent effective mass in Nb-doped anatase crystals of TiO 2[END_REF][START_REF] Kamisaka | Density functional theory based first-principle calculation of Nb-doped anatase TiO 2 and its interactions with oxygen vacancies and interstitial oxygen[END_REF] and experimental[START_REF] Hirose | Large electron mass anisotropy in a d-electron-based transparent conducting oxide : Nbdoped anatase TiO 2 epitaxial films[END_REF] results on bulk Nb-doped anatase. The corresponding Fermi momenta are 0.09 Å-1 and 0.16 Å-1 .

Figure 5 . 9 -

 59 Figure 5.9 -(a) Bulk Brillouin zone of anatase, showing the relevant high symmetry directions (green) and planes (red and blue) of the Fermi surfaces and band dispersion at the (001) surface. (b) Fermi surface map (second derivative of ARPES intensity, negative values) measured at hν = 47 eV on a cleaved, bulk insulating TiO 2 -anatase (001) surface. The red lines indicate the edges of the bulk Brillouin zones in the (001) plane around Γ 102 . (c) Fermi surface map (second derivative of ARPES intensity, negative values) in the k 001 -k 010 , or (100) plane, acquired by varying the photon energy by 1 eV steps between hν 1 = 38 eV and hν 2 = 85 eV. To calculate the momentum perpendicular to the surface, we set the inner potential to V 0 =13 eV. The blue lines are the bulk Brillouin zones containing Γ 102 and Γ 103 . (d) Energy-momentum map measured at hν = 74 eV along the 010 direction on the (001) surface. Dashed red lines are parabolic fits to the dispersing light bands. Red arrows show a kink attributed to electron-phonon coupling [156]. (e-h) Same as (a-d) on the anatase (101) surface. Data in panels (f) and (h) were measured at hν = 47 eV. The green dashed arrow in (f) indicates the direction of measurements along k y in (g-h), which is slightly off 010 . The out-of-plane Fermi surface map (second derivative of ARPES intensity, negative values) in (g) was measured by varying the photon energy by 1 eV steps between hν 1 = 33 eV and hν 2 = 51 eV and between hν 3 = 76 eV and hν 4 = 103 eV.

Figure 5 .

 5 Figure 5.10 -Some of the results published by Moser et al.. (a) Energy-momentum map measured at hν = 85 eV along the 100 direction (of figure 5.9(a)) on a (001) anatase surface. (b) Corresponding Fermi surface map in the k 100 -k 010 plane and (c) in the k 100 -k 001 plane. After reference [156].

Figure 5 .

 5 Figure 5.11 -(a) Sketch of the experimental ARPES setup.(b) Schematic representation of the reciprocal space of bulk TiO 2 anatase over several Brillouin zones in the (100) plane. (c) Energy momentum map measured at hν = 47 eV with linear horizontal light polarisation (LH) at the surface of a tilted sample corresponding to position B in reciprocal space in (b). (d) Same as (c) but with linear vertical light polarisation (LV). (e) Same as (c) but at normal emission, position A in (b).

Figure 5 .

 5 Figure 5.12 -(a,b) Energy-momentum maps measured at hν = 100 eV along the 010 or the 001 direction at the anatase (101) and rutile (110) surfaces. The intensities in different energy intervals (valence band, in-gap, 2DEG) were normalized to make all the features visible. (c) Angle-integrated, raw spectra of the two energy-momentum maps in (a,b). The inset shows a zoom of the angle-integrated spectra (log scale) for angles close to normal emission. The spectral weight at the Fermi level in the case of the anatase (101) surface corresponds to the 2DEG.

Figure 5 .

 5 Figure 5.13 -(a,b) ARPES energy-momentum intensity maps measured at the Al(2 Å)/SrTiO 3 (001) interface prepared in-situ, using respectively 47 eV LV and 90 eV LH photons. (c,d) Corresponding Fermi surface maps. Data at hν = 47 eV were measured around the Γ 102 point, while data at hν = 90 eV were measured around Γ 103 . (e,f) Fermi surface maps measured at the Al/SrTiO 3 (111) and Al/TiO 2 (001) anatase interfaces prepared in-situ. All spectra were measured at T = 8 K.

Figure 5 .

 5 Figure 5.14 -(a) Angle-integrated spectra of the Al-2p peak of the Al/SrTiO 3 (001), (111), Al/TiO 2 -anatase(001) and Al/BaTiO 3 (001) interfaces measured at a photon energy of hν = 100 eV. The curves in different colors correspond to different thicknesses of Al (red 2 Å, black 4 Å, blue 6 Å) and the dashed curve to the 4 Å Al sample after an annealing at T=350 • C. The peak shape of the Al-2p peak indicates if the Al-layer is oxidised or metallic. (b) Momentum distribution curves (MDCs) at the Fermi level E F measured at the Al/SrTiO 3 (001) interface at a photon energy of hv = 47 eV for different Al thicknesses. The Fermi momenta are very similar for the different thicknesses indicating similar charge carrier densities. The decrease in intensity of the peaks in the MDCs is merely due to a damping of the photoemission signal when the Al-thickness increases. (c) Top : MDCs integrated over E F ±5 meV for increasing UV exposure times on the Al/SrTiO 3 (001) interface and the bare SrTiO 3 surface measured under identical conditions. The similarity of the two MCDs at the interface is in strong contrast to the evolution under light irradiation of the MDCs at the bare surface (bottom part).

Figure 6 . 1 -

 61 Figure 6.1 -The new six-degrees of freedom sample holder for the ARPES endstation of CASSIOPEE. (a) Left : The sample holder mounted on a test chamber equipped with a SES100 electron analyzer. Right : A zoom on the sample environment. The sample position is indicated by an arrow. A liquid helium circulation cryostat is connected to the sample by a copper-bread, allowing to cool down the sample without preventing the Tilt and φ rotations. (b) The accessible angular range is -10 • to +60 • for the Tilt (with respect to a vertical position). (c) The accessible angular range is -25 • to +95 • for the φ (with respect to the transfer position).

Figure 6 . 2 -

 62 Figure 6.2 -The AB 2 O 4 spinel structure. It is a cubic lattice where the A and B cations are surrounded by oxygen atoms (red balls) in tetrahedral and octahedral environments, respectively.

Figure 6 . 3 -

 63 Figure 6.3 -Fermi surface recorded at the Ti-L 3 edge (459 eV) on a 10 Å Al/SrTiO 3 (001) system exposed to air for 20 mn. The red dashed circles and ellipses illustrate the Fermi surface as measured with UV-photons (See chapter 5 of this dissertation). The thick red lines correspond to the borders of the bulk Brillioun zones (Adapted from reference [172]).

Table des matières

 des Outline of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . Thin cobalt films on Cu(001) . . . . . . . . . . . . . . . . . . . . . . . . Multiple scattering simulations . . . . . . . . . . . . . . . . . . . 2.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Adsorption site, growth and structure of thin cobalt films on Cu(111) . . 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Analysis of the first-nearest neighbour shell . . . . . . . . . . . . . 2.4.4 Adsorption site and stacking period determined by multiple scattering calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i 3 Interpretation of X-ray absorption edges by high-energy resonant electronic spectroscopies 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Resonant spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Decay processes-Principle of a resonant experiment . . . . . . . . 3.2.3 Resonant fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3.1 Experimental observation . . . . . . . . . . . . . . . . . 3.2.3.2 A simple picture . . . . . . . . . . . . . . . . . . . . . . 3.2.3.3 A correct picture . . . . . . . . . . . . . . . . . . . . . . 3.2.3.4 Dispersion and energy width . . . . . . . . . . . . . . . 3.2.3.5 Spectator lines . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Resonant Auger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Resonant photoemission . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Quadrupolar transitions at the Ti-K-edge in TiO 2 -rutile evidenced by resonant Auger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction 1.1 Electronic properties of materials . . . . . . . . . . . . . . . . . . . . . . 1.2 Surfaces and thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Synchrotron radiation for the study of structural and electronic properties of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 2 Structure of magnetic thin films by X-ray absorption spectroscopy 2.1 Magnetism of thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 EXAFS and Surface EXAFS . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 X-ray Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . 2.2.2 The EXAFS oscillations . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Data analysis -Which information in the EXAFS oscillations ? . 2.2.4 Single scattering and multiple scattering . . . . . . . . . . . . . . 2.2.5 Surface EXAFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Analysis of the first nearest neighbour shell . . . . . . . . . . . . . 2.3.4 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Angular dependence of XAS spectra . . . . . . . . . . . . . . . . 3.3.4 Resonant Auger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 High-energy resonant photoemission in CeRh 3 -Interpretation of the Ce

& &

Assuming two spin orientations per band, this gives an electron concentration of n (001) 2D ≈ 5.4 × 10 13 cm -2 , or about 0.08 electrons per a 2 , where a is the short lattice constant of the tetragonal lattice and a 2 the cross section of the unit cell in the (001) plane.

Note that a kink in the dispersion at a binding energy of about 70 meV is visible (red arrows). Such a kink has been attributed to electron-phonon coupling and studied in detail by Moser et al. [START_REF] Moser | Tunable polaronic conduction in anatase TiO 2[END_REF]. They characterised the polaronic conduction for different charge carrier densities (controlled by the oxygen partial pressure in the sample chamber) at the anatase-TiO 2 (001) surface using ARPES. Contrary to our results, they observed only one dispersing subband, also showing a dispersion perpendicular to the surface. The authors assigned it to a 3D character of these states, not strongly confined at the surface at low charge carrier densities. For a low concentration of oxygen vacancies and charge carriers, the potential well at the surface is rather shallow and the electrons are thus barely confined. But, even for charge carrier densities comparable to our results (n 3D,Moser ≈ 2 × 10 20 cm -3 to n 3D ≈ (n

), Moser et al. observed only one dispersing band. One possible explanation is a difference in photon energies used to probe the electronic structure. As can be seen in the Fermi surface map in figure 5.9, the outer parabolic band is not visible at all photon energies due to matrix elements governing the photoemission process. Finaly, the bands in Moser et al. spectra are much more diffuse than in our measurements and they may have, on one hand, missed the outer band, and, on the other hand, overinterpreted their dispersion measurements perpendicular to the surface (see figure 5.10).

Next, we present the ARPES measurements on the (101) surface of anatase. The bulk Brillouin zone is shown again for clarity in figure 5.9(e), together with relevant directions for the [START_REF] Rödel | Engineering two-dimensional electron gases at the (001) and (101) surfaces of TiO 2 anatase using light[END_REF] surface and the planes of the measured Fermi surfaces. Figure 5.9(f) shows the Fermi surface on the (101) plane. It consists of two ellipses of identical shape, corresponding again to d xy orbitals, similar to the d xy derived ellipses observed for the 2DEG at the SrTiO 3 [START_REF] Wieliczka | Photoemission studies of the γ -α phase transition in Ce : Changes in 4f character[END_REF] surface [START_REF] Wang | Anisotropic two-dimensional electron gas at SrTiO 3 (110)[END_REF][START_REF] Rödel | Orientational tuning of the Fermi sea of confined electrons at the SrTiO 3 (110) and (111) surfaces[END_REF].

The Fermi surface map in the k y -k z plane, perpendicular to the cleaved surface, is shown in figure 5.9(g). The bands are essentially not dispersing along k z , indicating their 2D character. Note that, in contrast to the (001) surface, the intensity of the 2DEG states in the k z -k y plane at the (101) surface drops quickly far from bulk Γ points, due to finalstate effects in the photoemission cross-section (see the discussion in the Supplemental Material of [START_REF] Rödel | Orientational tuning of the Fermi sea of confined electrons at the SrTiO 3 (110) and (111) surfaces[END_REF]).

Figure 5.9(h) shows the energy-momentum map close to the bulk Γ 210 point along the k y direction. As on the (001) surface, two light bands, upper and lower, are also observed in this case. Their bottoms are located at -60 meV and -130 meV, respectively. The Fermi momenta taken from the Fermi surface in figure 5.9(f) are 0.41 Å-1 and ∼ 0.33 Å-1 in the 101 direction and 0.15 Å-1 and ∼ 0.10 Å-1 in the 010 direction. A parabolic fit based on the experimental Fermi momenta and band bottom energies yields an effective mass of m 010 (101) = 0.6m e along the 010 direction, very close to the one measured at the (001) surface along the same direction. Assuming again 2 spins per band, this gives an electron concentration of n (101) 2D ≈ 1.5 × 10 14 cm -2 , three times larger than the one at the (001) surface, which is probably related to the higher concentration of oxygen vacancies at the (101) surface [START_REF] Thomas | Comparison of the electronic structure of anatase and rutile TiO 2 single-crystal surfaces using resonant photoemission and x-ray absorption spectroscopy[END_REF].

On both the (001) and ( 101) surfaces, the presence of two non-degenerate bands of