Spinel ferrite a (nm) 𝜌 (g.cm -3 ) M 0 (emu.cm -3 ) M 𝑠 (emu.cm -3 ) K 𝑎 (J.m -3 ) T 𝐶 (°C) MnFe 2 O 4 0.85 5.00 560 400 -3.10 3 300 CoFe 2 O 4 0.838 5.29 475 425 2.10 5 520 NiFe 2 O 4 0.834 5.38 300 270 -5.10 3 585 Fe 3 O 4 0.839 5.24

General

Ferrofluids are colloidal suspensions of nanosized magnetic particles suspended in carrier liquids. 1,2 The intimate interaction between the magnetic nanoparticles and the liquid provide a unique system whose flow and properties can be precisely controlled using external magnetic field. One can imagine that the large range of possibilities that they offer make them attractive for a large range of applications. Indeed the research on ferrofluids falls into two types of domain. The first domain focusses on the rheologic properties of the ferrofluids and the ability to control their thermophysical properties. Applications range from mechanical engineering, 3 hyperthermia, 4 to even fine arts 5 . The second domain deals with the magnetic properties of the nanoparticles in the dried phase and takes advantage of the intense research activity in the ferrofluid synthesis to obtain magnetic nanoparticles whose magnetic behavior can be finely controlled by means of chemical processes. Magnetic nanoparticles of spinel ferrites are notably of particular scientific interest and are investigated for their electrical and magnetic properties. Nanospinels find applications in storage devices for computers, [START_REF] Frey | Magnetic nanoparticle for information storage applications[END_REF] in cancer therapy and medical diagnostics, [START_REF] Li | [END_REF] in microwave absorbers 8 and magneto-optical devices 9 .

The subject of this thesis focuses on the study of magnetic anisotropies and magnetic coupling of the nanospinels in ferrofluids. The characterization of magnetic anisotropies and magnetic couplings are provided by magnetometry measurements and X-ray magnetic X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD) are synchrotron radiation based techniques that provide unique tools for the study of electronic and magnetic systems. [10][11][12] These techniques present the advantages of element selectivity, and valence state and site symmetry sensitivity. On the DEIMOS beamline, XAS and XMCD are dedicated to the soft X-ray range which covers the L 2,3 (2p→3d) absorption edges of transitions metals (Mn, Fe, Co, Ni). The transition metals in the spinel structure may occupy multiple sites in possibly multiple valence states. Therefore, the techniques can be succesfully performed in these systems. 13,14 Soft XMCD can be seen as a local probe of the orbital and spin atomic moments and provide insights in the element-specific magnetic couplings and microscopic origin of the magnetic anisotropy.

Moreover, simulations performed in the Ligand Field Multiplet approach yield the spin and orbital part of the magnetic moments and the crystallographic distributions of the transitions metals in the nanoparticle structure. 15,16 The study of magnetic nanospinels in ferrofluids was motivated at different levels. The first one concerns our understanding of the correlation between the magnetic response and the fine structure and composition of the spinel ferrite nanoparticles. The finite size effects of magnetic nanoparticles confer them unique magnetic properties including superparamagnetism. The nanoparticles in the superparamagnetic state are essential for applications such as magnetic resonance imaging (MRI) or magnetic carriers for drug delivery. On the other hand, avoiding the superparamagnetic state is essential for maintaining the thermal stability of magnetic data bits in high-density storage. The superparamagnetic properties can be controlled via the magnetic anisotropy energy, the shape of the nanoparticles or the internal structure of the nanoparticle (core@shell nanoparticles for instance). The second motivation of this thesis is to extend XMCD to the in situ investigation of the nanospinels dispersed in the carrier liquid of ferrofluids. Indeed, several studies have shown that the magnetic properties of the ferrofluid can be significantly altered by the interactions between the nanoparticles arising from dipole-dipole interactions or exchange interactions.

Understanding the interparticle interactions is of fundamental interest and is also essential for certain applications of magnetic nanoparticles. However, XMCD experiments have been limited so far to the dried powder of nanoparticles because performing XMCD on liquid samples is still challenging from the instrumental point of view. In this context, I have developed several approaches in order to study liquid ferrofluids and I succeeded in recording photon inphoton out XMCD measurements thanks to a liquid cell that I have developed at the European Synchrotron Research Facility (ESRF).

This thesis presents my most prominent results that I could gather during the last three years. The results are structured on the basis of scientific papers that have today different status (published, submitted, not yet submitted). In addition, some other results are presented in a more traditional form and accompany the scientific papers. This thesis is organized in five chapters.

Chapter 1 gives a general overview of the magnetic and structural properties of ferrites nanospinels. Attention is paid to their synthesis and the properties of the various ferrofluids in which they can be incorporated. The theoretical basis and the scientific background of ferrofluids are presented and the main issues that have motivated this thesis are detailed.

Chapter 2 is an introduction to the experimental spectroscopic and magnetic methods that have been used to address the questions raised in chapter 1.

Chapter 3 is devoted to the description of the instrumental development implemented during this thesis. I have designed and developed two different types of liquid cells during my Ph.D. At ESRF I conceived and developed a liquid cell appropriate for the measurements of photon inphoton out spectroscopies on liquid and frozen ferrofluids. The liquid cell was successfully mounted on ID26 and the obtained scientific results are presented in chapter 5. At SOLEIL, I have developed a second liquid cell compatible with the soft X-rays environment of the DEIMOS beamline and that could be inserted in an electromagnet. This second development was not completely successful and we are still working on an upgraded version to be available soon.

In chapter 4, I have studied the relation that exists between the synthesis routes of the ferrofluids and the magnetic anisotropies of iron-cobalt nanospinels.

Firstly, we got interested in the most common synthesis process to obtain ferrofluids, refers as the coprecipitation synthesis. This synthesis was initially developed for the synthesis of maghemite and modified for the synthesis of CoFe 2 O 4 of different sizes.

Thanks to XMCD, we solve some puzzling questions regarding the relation between stoichiometry of the nanoparticles and their magnetic properties. The results of this study are presented in the paper entitled "Magnetic Anisotropies and Cationic Distribution in CoFe 2 O 4 nanoparticles prepared by the corecipitation route : influence of the particles size and stoichiometry". In this paper we establish the effect of the different steps of the synthesis on the magnetic properties of the different iron-cobalt nanospinels.

Secondly, the magnetic properties of 5 nm CoFe 2 O 4 nanoparticles prepared with the coprecipitation synthesis are compared to other 5 nm nanoparticles obtained with hightemperature decomposition processes, namely the "acac" process and the "polyol" process.

The results of this study are presented in the paper entitled "Small CoFe 2 O 4 Magnetic Nanoparticles in Ferrofluids, Influence of the Synthesis on the Magnetic Anisotropies".

The results obtained in these two papers are in good agreement with the literature of similar systems and validate the approach used to characterize these systems.

Thirdly, we present another chemical strategy to modulate the magnetic anisotropies of nanoparticles. The strategy consists in the functionnalization of maghemite nanoparticles with cobalt complexes. The cobalt complexes induced a magnetic anisotropy to the maghemite nanoparticles. This project was undertaken by Yoann Prado during a postdoctoral position at PHENIX and IPCM. I brought my knowledge of XMCD applied to nanospinels to precisely determine the origin of the increase of the coercive field. The results of this study are presented in the paper entitled "Enhancing the magnetic anisotropy of maghemite nanoparticles via the surface coordination of molecular complexes".

In chapter 5, we present two studies of nanospinels systems presenting new emerging properties. They are investigated in the liquid or the frozen ferrofluids with Resonant Inelastic X-ray Scattering-Magnetic Circular Dichroism spectroscopies (RIXS-MCD).

The first study concerns core@shell nanoparticles, where the core is a soft magnet of MnFe 2 O 4 and the shell a hard magnet of CoFe 2 O 4 . This study is presented in a paper untitled "Nanoscale Distribution of Magnetic Anisotropies within Bimagnetic Core@Shell Nanoparticles Dispersed in Ferrofluid". Thanks to the chemical selectivity of X-ray spectroscopies, we have disentangled the magnetic signature of the core and the shell of the core@shell structure. The RIXS-MCD detected magnetization curves show a clear evidence of the core being influenced by the shell and vice versa. In addition, the combination of soft and hard X-ray measurements provides an original and complete picture of the complex magnetic structure exhibited by these highly anisotropic core@shell nanospinels.

The second study concerns a physical mixture of MnFe

Introduction

My thesis concerns the investigation of the magnetic anisotropies and the magnetic couplings of ferrite nanospinels dispersed in ferrofluids. The magnetic anisotropies of these materials govern some of their magnetic response under an external magnetic field, that are of close interests for applications ranging from the fields of biomedical treatments to high-density data storage devices. There are three main reasons for that:

• nanoparticles have a reduced size,

• they present tunable magnetic properties that are not present in the bulk,

• they can be used in ferrofluids.

For a good understanding of the attractive features of nanoparticles, the presentation of the structural and magnetic properties of the associated bulk material is fundamental.

First of all, I describe the crystallographic structure of cubic spinel ferrites. The superexchange interactions in the spinel structure associated to the intrinsic properties of the atoms composing the structure induce a magnetic order which is further detailed. In a second section, we review the magnetic properties arising from the nanoscale range of the nanoparticles and that are not present in the bulk. In particular, we describe the different effects that can modify the magnetic anisotropies of nanoparticles.

The nanoparticles investigated in this thesis were obtained in the form of a stable colloidal suspension called ferrofluid. It is well-known that the synthesis method plays an important role on the final properties of the nanoparticles. A description of ferrofluids systems is given in a third section, with a special emphasis on their synthesis processes, field of applications and methods of characterization. Finally, the last part of this chapter is dedicated to a discussion on the current issues that have motivated this work.

Spinel ferrites 1.2.1 Crystallographic structure

The term ferrites refers to transition-metal oxides class of material bearing iron. Ferrites materials fall into two groups of different crystallographic structure:

• Cubic ferrites such as spinel ferries of general formula MFe 2 O 4 , where M 2+ is a divalent ion (M= Fe 2+ , Mn 2+ , Ni 2+ , Co 2+ , Zn 2+ ),

• Hexagonal ferrites such as barium ferrite of formula BaFe 12 O 19 .

In this thesis, only cubic ferrites have been studied. They crystallize in the spinel structure named after the mineral spinel MgAl 2 O 4 . 17 A convenient way to describe partially inverse structure is to use the inversion degree 𝛾 defined as the fraction of divalent cations in B-sites:

(𝑀 1-𝛾 𝐹 𝑒 𝛾 ) 𝐴 [𝑀 𝛾 𝐹 𝑒 2-𝛾 ] 𝐵 𝑂 4 (1.2.1)

Figure 1.2.1: Schematic of atomic positions in the crystal structure of spinel ferrites showing the rhombohedral unit cell of edge equals to the lattice parameter a. [START_REF] Chen | Superconductors -New Developments[END_REF] The cations distribution between Aand B-sites are determined by the affinity between the cation and the site considered that depends on the atomic radius of the ion, the size of the site and the stabilization energy induced by crystal field. [START_REF] Sickafus | [END_REF] However, the cations distribution predicted in bulk spinel ferrites can be altered at the nanoscale. Experimental measurements have shown that heat treatments present during the preparation process of the nanoparticles can be responsible for differences between the structures of the bulk and the nanoparticles. In particular, the rate of cooling from high temperature after synthesis (annealing treatment) was studied for CoFe 2 O 4 nanoparticles by Sawatzky et al. and indicates that quenched samples have a lower degree of inversion than slowly cooled samples. 20 Such rearrangement in the crystallographic structure may have direct consequences on the magnetic properties of the nanospinels.

Bulk magnetic properties

When a magnetic field H is applied to a material, the response of the material is called its magnetic induction B. B and H in SI units are related by the equation:

B = 𝜇 0 (H + M) Tesla. (1.2.2)
With 𝜇 0 the magnetic permeability of free space and M the magnetization of the material.

The magnetization is defined as the net magnetic moment 𝜇 per unit volume V:

M = 𝜇 𝑉 A.m 2 m 3 = A.m -1 (1.2.
3)

The process of magnetization, and in particular the variation of this quantity depends on the behavior of the individual magnetic moments of the elemental constituents of the material. Indeed, when a magnetic field is applied, the magnetic moment of each constituent, i.e ions, atoms or molecules, orientates in the direction of the field such as small magnetic dipole. The way they respond and interact with each others to the applied magnetic field is characterized by the magnetic susceptibility 𝜒 (the exact expression involves the derivative of M with H but for small magnetic fields, this is approximated by a simple ratio) :

𝜒 = M H (dimensionless) (1.2.4)
For one sample, the susceptibility is dimensionless but for convenience it can be expressed per unit volume of sample in cgs units (emu.cm -3 ). Depending on the sign of the susceptibility the samples can be classified as diamagnetic or paramagnetic systems. [START_REF] Cullity | Introduction to Magnetic Materials[END_REF] • diamagnetism: atoms have no net magnetic moments in the absence of unpaired electrons in the atomic orbitals. When a magnetic field is applied, the atoms gain a weak induced magnetic moment opposed to the external applied field. As a consequence, the susceptibility of a diamagnetic system is negative (∼ -10 -5 SI) and generally independent of the temperature.

• paramagnetism : atoms carry net magnetic moments randomly oriented. When a magnetic field is applied, the atomic moments tend to align in the direction of the field and can acquire a complete alignment depending on the relation between the thermal agitation and the intensity of the external magnetic induction. This results in a small susceptibility (∼ 10 -5 SI) for small inductions. The magnetization is generally temperature dependent: as the temperature increases, the thermal agitation tends to oppose to the alignment of atomic moments and the susceptibility decreases. This latter varies roughly as the inverse of the temperature according to the Curie law 𝜒 𝑚 =C/T with C the Curie constant.

For paramagnetic systems, when the temperature is lowered one may observe the building of a cooperative, magnetic order. There are three types of magnetic structures for which a long range magnetic order is observed: ferromagnetism, ferrimagnetism, and antiferromagnetism. [START_REF] Cullity | Introduction to Magnetic Materials[END_REF] • ferromagnetism: below a certain temperature, the Curie temperature (T C ), the Coulomb interactions between the electrons of the magnetic ions tend to align the magnetic moments (molecular field). This induces a spontaneous magnetization and a long range magnetic order. When a magnetic field is applied, a complete alignment can be reached, leading to the saturation of the magnetization. Above T C , the system remains in its paramagnetic phase.

• ferrimagnetism: in a ferrimagnetic material, the situation is quite similar to the one for ferromagnetism except that there are several magnetic networks with some of them pointing in different directions, as such that a net magnetic moment results from the sum of the various contributions from the different magnetic networks.

Similar to ferromagnets, the long range order of ferrimagnets appears only for temperatures below T C .

• antiferromagnetism: in an antiferromagnet, below a certain temperature, the Néel temperature T N , two or more sublattices with the same magnetic moment are pointing in opposed (or different) directions in such a way that the material has no net magnetic moment. When a moderate magnetic field is applied, the magnetization is usually similar to the ones measured for paramagnets so that the susceptibility is small and positive. At the difference of the ferrimagnets or the ferromagnets, there is a huge diversity of structures for antiferromagnets.

The theory of ferrimagnetism was developed by L. Néel in 1948 [START_REF] Smart | [END_REF] who named this type of magnetic ordering after the name of ferrites. Spinel ferrites are the most important material class of ferrimagnetic substances, although not all spinel ferrites are ferrimagnetic (e.g., ZnFe 2 O 4 is a complicated antiferromagnet). The interaction between the localized magnetic moment in spinel ferrites are due to superexchange interactions.

Superexchange is the interaction between neighboring magnetic atoms that is mediated by chemical bounding through an anion (chemists who are sensitive to the role played by the anions often give the name of "exchange interaction" to what physicists call "superexchange interaction", whereas physicists tend to limit the term of "exchange interactions"

to ferromagnetic coupling in metals). In ferrites, three different superexchange interactions have to be considered as the A and B sublattices are not equivalent either by the site symmetry and the nature of ions. One distinguishes the A-A interactions between two neighboring atoms in A-sites, the A-B interactions between neighboring atoms in Aand B-sites and the B-B exchange interaction between two B-sites. By extension of the definition of ferromagnetism, one says that two ions are ferromagnetically coupled when the Coulomb interactions tend to align the magnetic moments of the two ions. Similarly one says that two ions are antiferromagnetically coupled when the Coulomb interactions tend to oppose the magnetic moments of the two ions (there are other, more complex situations, such as the Dzyaloshinskii-Moriya interaction 23 , but that are of no interest for my thesis). The sign (ferromagnetic or antiferromagnetic) and intensity of the couplings depend on:

• the number of electrons on the 3d states,

• the 3d electronic states of the metal hybridization with the 2p state of O 2-.

For spinels, all the A-A, A-B, and B-B exchange interactions tends to be negative and in this case the magnetic structure cannot satisfy simultaneously the three interactions.

The length and angle of the chemical bonds metal-oxygen-metal define the dominant interaction. Strongest coupling are observed when the angle approach 180°and for the shortest bonds. Thus, the antiferromagnetic A-B exchange interactions are usually the strongest, so that the moments on the B sublattice are antiparallel to the moments on the A sublattice. The other antiferromagnetic interactions A-A and B-B play only a minor role (except in specific situations such as in surfaces where a lack of Asites can promote the B-B interaction).

The net magnetization 𝜇 of the structure results from the sum of the contributions of all the magnetic interactions between the cations. The different contributions are detailed hereafter for the bulk spinel ferrites studied in this thesis for which a rough estimation can be given by the spin only value of the different paramagnetic ions.

CoFe 2 O 4 . CoFe 2 O 4 has an inverse spinel structure. Fe 3+ are evenly divided between and Aand B-sites. The magnetic moments carried by Fe 3+ (≈ 5𝜇 𝐵 ) in Asites are aligned parallel with each other but are antiparallel to the magnetic moments carried by Fe 3+ in B-sites. Thus, the magnetic moment of Fe 3+ cations cancel due to the antiferromagnetic coupling between Aand B-sites. Co 2+ are in B-sites, and the A-B superexchange interaction is antiferromagnetic. This means that the net magnetization in CoFe 2 O 4 is equivalent to the magnetic moment of the Co 2+ ions, which is ≈ 3𝜇 𝐵 /f.u.. Fe 3+ have the same magnetic moment (≈ 5𝜇 𝐵 ). This means that the net magnetization of MnFe 2 O 4 is ≈ 5𝜇 𝐵 /f.u. whatever the cationic distribution among Aand B-sites.

One sees from Table 1.2.1 that the previous estimations for the magnetic moments per formula units roughly follow the measured ones at low temperature.

Magnetocrystalline Anisotropy

"Magnetic anisotropies" refer to the dependence of the magnetic properties on the direction in which they are measured. In particular, the magnetization in ferro-/ferrimagnetic crystals tends to align along preferred crystallographic directions that are called "easy axes". This phenomenon stems from the magnetocrystalline anisotropy and is mainly due to spin-orbit coupling. 24 For example, the magnetic moments in CoFe 2 O 4 align along the easy axis ⟨100⟩, while they are parallel to the ⟨111⟩ body diagonal of the cubic cell in all other ferrites. Magnetization along other crystallographic axes are possible (they are called "medium axis" or "hard axis"), but larger applied field are necessary to reach saturation than along the easy axis.

Magnetic domains

The magnetostatic energy in a bulk ferri-/ferromagnetic material is minimized with the formation of several magnetic domains in which the spontaneous magnetizations have different directions. Therefore, a bulk ferri-/ferromagnetic material has generally no net spontaneous magnetization. The boundaries between the domains in bulk ferromagnetic materials are called domain walls, or Bloch walls. When the magnetization by an external field occurs, the domains whose magnetization are close to the induction direction start to grow by domain wall motions at the expense of the other domains. Eventually, the applied field is sufficient to eliminate all domain walls from the material, leaving a single domain with its magnetization pointing along the easy axis most closely to the external magnetic field. When the magnetic field is removed, the magnetic moments rotate back to their easy axes and the magnetization decreases. However, domain walls are not able to fully reverse their motion back to their original positions due to the demagnetizing field.

Some magnetization remains, and the magnetization curve shows hysteresis. Domain walls displacement is very complex. In addition to the intrinsic factor of magnetocrystalline anisotropy, which comes from spin-orbit coupling in materials, domain wall displacement is greatly affected by many extrinsic factors including defects, lattice strains, and chemical impurities.

Magnetic properties of nanoparticles

At the nanoscale, materials can have different properties compared to the ones of the same materials with a larger size. As the size of spinels is reduced to nanometers, quantum size and disorder effects can begin to play a role, and these can significantly change the optical, magnetic or electrical properties.

Single domain behavior

Below a critical size that is connected to the size of the domain walls, the magnetic particles are not made of several magnetic domains anymore and a single-domain state is favored.

The critical size below which a specific system can be considered as a single domain varies but generally ends up as a function of E DW /M 2 𝑆 where E DW is the domain wall energy. For most magnetic materials, the critical diameter is in the range 10-100 nm. For instance, it was found to be ∼60 nm for Fe 3 O 4 . 25

Magnetic anisotropies

In the following, I will briefly present four contributions to the magnetic anisotropy.

Magnetocrystalline anisotropy

The symmetry of the magnetocrystalline anisotropy is always the same as that of the crystal structure. The magnetocrystalline anisotropy energy in a cubic crystal is:

𝐸 𝑐 = 𝐾 1 (𝛼 2 1 𝛼 2 2 + 𝛼 2 2 𝛼 3 3 + 𝛼 2 3 𝛼 2 1 ) + 𝐾 2 𝛼 2 1 𝛼 2 2 𝛼 2 3 + ... Joule. (1.3.1)
where K 𝑖 are the volumic anisotropy constants which depends on the material and the temperature, and the 𝛼 𝑖 's are the cosines of the angles between the saturation magnetization and the crystal axes. For single domain nanoparticle with a symmetry causing a uniaxial anisotropy energy, the angular dependence is only a function of 𝜃 that is the angle between the magnetization vector and the uniaxial symmetry axis. The magnetocrystalline energy is written as:

𝐸 𝑢 = 𝐾 𝑢 𝑠𝑖𝑛 2 𝜃 Joule (1.3.2)
with 𝐾 𝑢 the uniaxiale volumic anisotropy constant. According to Equation 1.3.2, the energy barrier 𝐾 𝑢 bounds two minima in energy for 𝜃=0 and 𝜃=𝜋.

Shape anisotropy

As a result of the demagnetizing field, [START_REF] Joseph | [END_REF] the magnetization of non spherical particle is easier along a long axis than along a short axis. This phenomenum induces a shape anisotropy expressed as:

𝐸 𝑠ℎ𝑎𝑝𝑒 = 1 2 𝜇 0 𝑉 (𝑁 𝑥 𝑀 2 𝑥 + 𝑁 𝑦 𝑀 2 𝑦 + 𝑁 𝑧 𝑀 2 𝑧 ) Joule (1.3.3)
where 𝑀 𝑥 , 𝑀 𝑦 and 𝑀 𝑧 the components of magnetic moment along the symmetry axes and 𝑁 𝑥 , 𝑁 𝑦 and 𝑁 𝑧 are the demagnetizing coefficients along these very symmetry axes. If the shape of the particle is spherical there is no shape anisotropy.

Surface anisotropy

The origin of the surface anisotropy is mainly due to local symmetry breaking which could originate from many different effects at the surface, such as the presence of structural defects (e.g., facets), broken exchange bonds, different number of neighbors, or different atomic distances with respect to the bulk (surface strain). These tend to align the moment in the plane, a phenomenon known as surface anisotropy. Due to their reduced size, the contribution of the surface anisotropy to the effective anisotropy can be dominant for nanoparticles.

Interparticle interactions

For an array of nanoparticles, interparticle interactions can affect the total anisotropy. Indeed, interparticle interactions that are mainly due to dipolar interactions will favor exchange interaction between the magnetic moments of the nanoparticles. Such interactions can be neglected in ferrofluids when the concentration of nanospinels is low enough.

Quasi-static magnetic properties

For a single domain particle with the anisotropy energy 𝐸 𝑎 , the amount of energy required to reverse the magnetization over the energy barrier from one stable magnetic configuration to the other is proportional to K 𝑒𝑓 𝑓 V, where V is the particle volume and K 𝑒𝑓 𝑓 the effective volumic constant anisotropy. If K 𝑒𝑓 𝑓 V becomes comparable to the thermal energy 𝑘 𝐵 𝑇 , then the thermal energy fluctuations can overcome the anisotropy energy barrier and spontaneously reverse the magnetization. For 𝑘 𝐵 𝑇 ≫ 𝐸 𝑎 , the nanoparticles are superparamagnetic. When a magnetic field is applied, the magnetic moments rotate from the easy axes to the direction of the magnetic field. The magnetization process is described by the Langevin function:

𝑀 = 𝜇𝜑ℒ(𝜉) 𝑎𝑛𝑑 𝜉 = 𝜇 0 𝜇H 𝑘 𝐵 𝑇 (1.3.4)
with ℒ(𝜉) = cothan(𝜉)-1 𝜉 the Langevin function, 𝜇 the net magnetic moment, 𝜑 the volume fraction, 𝜇 the magnetic moment per particle, 𝜇 0 the permeability of empty state, H the applied magnetic field, 𝑘 𝐵 the Boltzmann constant and T the temperature. In the superparamagnetic regime, the particle moments are easily saturated in the presence of a magnetic field to a value 𝑚 𝑠 𝜑 which corresponds to the magnetization at saturation M 𝑠 .

As the magnetic field is removed, the magnetic moments rotate back to their easy axes of magnetization, and the process is entirely reversible. A model of the magnetic curve is shown in Figure 1.3.2 (a).

For 𝑘 𝑏 𝑇 ≪ 𝐸 𝑎 , the thermal energy is not large enough to overcome the anisotropy energy. The magnetization of the nanoparticles is described by the Stöner-Wohlfarth model. The magnetization loop of an assembly of noninteracting particles results from the competition between magnetic anisotropies and the magnetic Zeeman energy. The hysteresis observed is characterized by a remnant magnetization 𝑀 𝑟 and a coercivity H c (Figure 1.3.2 (b)). The remnant magnetization corresponds to the residual magnetization of the material when the magnetic field is decreased to zero after the material has been saturated. The coercive field is the reverse field necessary to coerce the material back to zero magnetic moment.

In our case, the shape of the hysteresis is the sum of the contributions from the assembly of particles with their easy axes randomly oriented in space as such according to the Stoner-Wolhfarth model, at T=0 K :

𝐻 𝑐 ≃ 𝐾 𝑎 𝜇 0 𝑀 𝑠 (1.3.5)
This equation shows that the measurement of the coercive field is directly proportional to the anisotropy of the material. Magnetic materials can be divided into two groups, the magnetically soft and the magnetically hard materials. Magnetically soft materials are easy to magnetize and demagnetize, they possess weak anisotropy constant and thus, small H 𝑐 , e.g.

Dynamic magnetic properties

• The brownian relaxation is due to the rotation of the particles with brownian motions in the carrier liquid. The brownian relaxation is characterized by the relaxation time

𝜏 𝐵 : 𝜏 𝐵 = 3𝑉 𝐻 𝜂 𝑘 𝐵 𝑇 m 3 .kg.s 2 .K m 2 .kg.m.s.K = s (1.3.6)
with 𝜂 (kg.m -1 .s -1 ) the viscosity of the carrier liquid and 𝑉 𝐻 (m 3 ) the hydrodynamic volume.

• The Neel relaxation which corresponds to the rotation of the magnetic moment within the particle and characterized by the relaxation time 𝜏 𝑁 :

𝜏 𝑁 = 𝜏 0 𝑒𝑥𝑝 ( 𝐾𝑉 𝑚𝑎𝑔 𝑘 𝐵 𝑇 ) s (1.3.7)
with 𝜏 0 ∼10 -9 s and 𝑉 𝑚𝑎𝑔 (m 3 ) the magnetic volume. These two mechanisms occur in the ferrofluid, and the relaxation time 𝜏 of the magnetic moments is dominated by the shortest time since the total relaxation time is determined by the sum of relaxation probability :

𝜏 -1 = 𝜏 -1 𝑁 + 𝜏 -1 𝐵 (1.3.8)
Therefore, the "time of measurements" (the concept of "time of measurement" can be a concept difficult to define precisely) 𝜏 𝑚 is also determinant since:

• if 𝜏 ≪ 𝜏 𝑚 , the particles appears to relax with Brownian motions or Néel relaxation and show a superparamagnetic behavior,

• 𝜏 ≫ 𝜏 𝑚 , the particles appear in their blocked state and show hysteresis.

The limit between the regimes of superparamagnetic state or blocked state depends on the size of the nanoparticles (since 𝐸 𝑎 varies with the volume of the particles) and on the temperature (since the anisotropy constant is temperature dependent). For particle of constant size and for a given type of measurement, the blocking temperature T B is the temperature of the transition from the blocked state and to the superparamagnetic state.

For ferrofluids, the frozen point of the carrier liquid and its viscosity is also determinant.

As long as the colloidal ferrofluid remains in its liquid phase, the particle may rotate in the fluid. When the solvent freezes, the relaxation only occurs by rotation of the magnetic moment within the particle.

Ferrofluids

Definition

The melting point of magnetic materials is usually higher than its Curie temperature, above which it is paramagnetic. Therefore, the liquid state of most magnetic materials does not produce a magnetic liquid. On the contrary, a stable dispersion of ferro-/ferrimagnetic materials in a liquid carrier leads to a two-phase magnetic liquid that exhibits the unique combination of fluidity and ability to strongly interact with a magnetic field. This outstanding property makes them good candidates for various applications.

Two classes of fluids can be distinguished:

• Magnetorheological fluids which consist of dispersions of micron-sized (typically 1-5 𝜇m) magnetic particles in large amounts (up to 50% in volume). 27 • Ferrofluids that are stable colloidal suspensions of nano-sized (typically < 100 nm) ferro/ferrimagnetic particles in small amounts (below 10% in volume).

Magnetorheological fluids are similar to ferrofluids in the sense that there are both constituted of magnetic particles dispersed in a liquid medium. Their magnetic hydrodynamics (ferrohydrodynamics) 28 are comparable although there are only few applications where both can be found (e.g., dampers, physical sealers). The suspended particles in a ferrofluid are in the nanoscale range and present single domain, superparamagnetic behaviors while the particles in magnetorheological fluid are multi-domains, ferro-or ferrimagnetic particles. This strongly distinguishes the magnetorheological fluids from the ferrofluids and both have to be regarded as materials that belong to two different classes. In the following, I am only concerned by ferrofluids.

The name of "ferrofluid" was coined by Neuringer and Rosensweig. 29 The name conveys the concept of the magnetic response of the ferro-/ferrimagnetic nanoparticles and of the liquid state. It must be noted that the ferrofluids do not present ferromagnetic properties since the magnetic particles in the fluid are submitted to Brownian motions. Ferrofluids are then superparamagnetic in their liquid state, but when frozen, the Brownian motions are blocked and the ferrofluids can exhibit ferro/-ferrimagnetic behavior as long as the temperature is below the blocking temperature of the nanoparticles. In the literature, ferrofluids are also called "magnetic fluid" or "magnetic liquid". In this manuscript, I will only use the term of "ferrofluid".

The first stable ferrofluid synthesized is attributed to S.S Papell who worked for the National Aeronautics and Space Administration (NASA). In the early 60's, he invented a magnetic propellant for rocket engine usable in absence of gravity. The magnetized fuel was dragged into the engine by external magnetic forces. [START_REF] Papell | Low viscosity magnetic fluid obtained by the colloidal suspension of magnetic particles[END_REF] This ferrofluid propellant was finally never used because an alternative, valuable solution was found. In the mid 60's, ferrofluid technology was considered again in the space program of the NASA by R. Rosensweig, R. Kaiser and R. Moskowitz. They recognized the rich potential of ferrofluid technology that gathered magnetic and hydrodynamic properties. [START_REF] Kaiser | [END_REF] In 1968, R. Rosensweig and R.

Moskowitz launched the Ferrofluidics Corporation (now Ferrotec Company 1 ) in which first ferrofluid based devices were manufactured. In the 80's, ferrofluids were also involved in energy conversion devices 32 , viscous dampers 33 , seals [START_REF] Raj | [END_REF] , or gravity analyzers [START_REF] Kaiser | Method of separating materials of different density[END_REF] . Medical applications were also considered for sealing cranial aneuvrysms, for driving medium for heart assist pumps, or for transporting liquids within living bodies. [START_REF] Burton | [END_REF] In the 90's, numerous new applications of ferrofluids were developed in the biomedical field such as immune magnetic separation techniques of cells, proteins, DNA/RNA, bacteria or viruses, 37 or new contrast agents for diagnosis by Magnetic Resonnant Imaging (MRI), 38,[START_REF] Hasegawa | Water-soluble carboxypolysaccharide-magnetic iron oxide complex having a small particle diameter[END_REF] . In cancer therapy, the research group of Jordan in Berlin reported on the pioneer research of hyperthermia treatment. [START_REF] Jordan | [END_REF] When nanoparticles in ferrofluids are submitted to a high frequency, alternating magnetic field, a part of the magnetic energy is converted into thermal energy. 41 The treatment by hyperthermia induces the death of cancer cells by a moderate elevation of temperature. 4,[42][43][START_REF] Xie | In Advances in Nanotheranostics II[END_REF][45] Finally, drug delivery by magnetic nanoparticles was efficiently tested. 46,47 Nanoscale-fabricated magnetic materials also have applications in data storage. [START_REF] Weller | Advanced Magnetic Nanostructures[END_REF][START_REF] Spaldin | Magnetic Materials, Fundamentals and Applications[END_REF] Devices such as computer hard disks depend on the ability to magnetize small areas of a spinning disk to record information. If the area required to record one piece of information can be shrunk to the nanoscale (and can be written and read reliably), the storage capacity of the disk can be improved dramatically. Recent advances in novel magnetic materials and their nanofabrication are encouraging in this respect. Due to its enormous technological impact, the search for materials which may serve as magnetic media in future, high-density magnetic data storage has become a prominent issue in magnetism during the last years. One of the main challenges in this field is to push the blocking temperature to higher temperatures for the smaller particle sizes. [START_REF] Skumryev | [END_REF]51 One interest of ferrofluids reside from my point of view in their versatility. A ferrofluid is two phases system that originated from three different components:

• the dispersed, magnetic nanoparticles,

• the carrier liquid,

• the stabilizer necessary to ensure a stable colloidal dispersion.

Magnetic nanoparticles

Among the most often used materials dispersed in ferrofluids one can distinguish The choice of the magnetic material is in principle quite large. However, production of colloidal suspensions with sufficient stability requires a good compatibility of the nanoparticles with a stabilizer and a carrier liquid, and this greatly reduces the range of possibilities.

Carrier liquid

The carrier liquid provides the environment in which the particles are dispersed. It can be polar or non polar. The choice of the carrier liquid is often determined by the application.

It is chosen for its properties (boiling point, vapor pressure, freezing point, viscosity, toxicity) and its chemical inertia with the device. A wide spectrum of carrier liquids is exploited, e.g. water, alcohols, glycols, esters, organic solvent such as benzene, toluene, heptane, ethers, silicone oils, mineral oils, vegetable oils and more recently ionic liquids.

Stabilizer

Last but not least, the stability of the ferrofluid is ensured by a "stabilizer". I include in this term all the repulsive interactions introduced to prevent aggregations of the nanoparticles. Indeed, magnetic nanoparticles tend to aggregate due to magnetic dipolar and van

Synthesis of ferrofluids

The nature of the colloids, the carrier liquid and the stabilizers are conditionned by the synthesis of ferrofluids. Synthesis of iron oxide nanoparticles can be classified into chemical,

Experimental methods using Synchrotron radiation

Synchrotron radiation is based on the following physical phenomenon: every charged particle submitted to an acceleration loses energy by emitting an electromagnetic radiation.

Synchrotron facilities consist in circular ring where electrons are accelerated up to a relativistic speed. The ring is maintained in a Ultra High Vacuum (UHV) atmosphere of ∼10 -9 mbar. loses some energy in a form of electro-magnetic radiations. Three different devices with their very own merits are used in synchrotron to produce these magnetic fields, providing different forms of synchrotron radiation:

• bending magnets provide large photon flux with a broad spectrum, they are mandatory for storage rings,

• wigglers (4) provide higher photons energies than bending magnets, with very large photon flux in abroad energy range,

• undulators (6) provide a much brighter radiation with a small source size, accordable emission with narrow spectral range

The synchrotron radiations provided by the different sources are illustrated in Figure 2.1.2.

One of the major characteristics of synchrotron radiation resides in its high brilliance defines as radiated number of photons per time unit s, per source unit area (ΔA), per unit Synchrotron radiation is characterized by a very high brilliance, which is about 10 12 times brighter than X-ray sources that can be find in a laboratory. At ESRF the brilliance can be as large as 8.10 20 photons.s -1 .mm -2 .mrad -2 .0.1%(BW) whereas it amounts to 10 16 photons.s -1 .mm -2 .mrad -2 .0.1%(BW) at SOLEIL. The photons are emitted towards experimental stations called beamlines (7) surrounding the storage ring. A beamline is defined by the ensemble: source, optics and endstation. SOLEIL synchrotron hosts 27 beamlines and ESRF hosts 39 beamlines. Each beamline is dedicated to a specific technique. Indeed, the interaction of matter with electromagnetic waves is accompanied by many phenomena. The incoming wave can be partially or completely absorbed by the sample. It can also be diffracted, scattered elastically or inelastically, coherently or incoherently. Photons and electrons can also be emitted. Each beamline is equipped to study specifically one of those phenomena. They also provide a sample environment where the experimental conditions can be varied (X-ray polarization, temperature, magnetic field, pressure etc.). The synchrotron radiation covers very broad range of energies:

• hard X-rays, 4 keV < E < 100 keV

• tender X-rays, 1 < E < 4 keV

• soft X-rays 100 eV < E < 1.5 keV

• ultraviolet 3.3 < E < 100 eV • visible 1.7 eV < E < 3.3 eV • infrared 1.24 meV < E < 1.7 eV
The limits of each spectral range have no physical meanings, are somewhat arbitrary and mainly established by instrumental considerations. While the beamlines in SOLEIL synchrotron offer a large range of energies from the infrared to hard X-rays, all the ESRF beamlines but two (ID32 and ID12) are dedicated to hard X-rays. One can distinguish two families of experimental X-rays based techniques:

• spectroscopy techniques which allow to investigate the electronic and local structure of matter absorption (XAS, EXAFS, XANES)

emission (XES, HERFD)

inelastic scattering (IXS, RIXS, X-ray Raman)

• elastic scattering that probes the geometry of the microscopic structure diffraction for crystalline solids (XRD, GIXRD)

scattering for amorphous solids, liquids (XRS, WAXS, SAXS)

The separation between spectroscopy and scattering is also arbitrary as it is the case for DAFS (Diffraction Anomalous Fine Structure) that combines scattering and spectroscopy.

During my thesis, I have used spectroscopies involving both soft and hard X-rays produced by synchrotron radiation to investigate the electronic and magnetic properties of my systems. X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD) experiments were implemented using soft X-rays on the DEIMOS beamline at SOLEIL french synchrotron. I have also performed Resonant Inelastic X-ray Spectroscopy (RIXS) and RIXS-Magnetic Circular Dichroism (RIXS-MCD) using hard X-rays on the ID26 beamline at the ESRF European Synchrotron. XAS and XMCD are element specific techniques to study the local structure, the spin configuration, the oxidation state, or the site-symmetry. In the case of spinels ferrite nanoparticles, XAS and XMCD have been valuable in determining the details of the electronic and magnetic structures in nanoparticles. RIXS is a photon in -photon out element selective X-ray spectroscopy that provides for the absorbing atom a unique bi-dimensional mapping of its spectral signatures. In RIXS-MCD, we used the high sensitivity of RIXS coupled with XMCD to determine complex interfacial coupling in nanoparticles directly for ferrofluids in the liquid phase. XAS, XMCD, RIXS and RIXS-MCD techniques are described in the following section. Within this description, I do not pretend to give a complete overview of these techniques, but the target is to give a reasonable understanding of the techniques which should legitimate their

valuable application to answer the questions underlying my thesis. A special emphasis is brought to the experimental conditions implemented for the measurements.

X-ray Absorption Spectroscopy

In the X-ray absorption process, the absorption of a photon is accompanied by the promotion of a core electron into an empty state. XAS refers to the general name for the technique in which the empty states of the absorbing atom are probed. From visible light, it is well-known that the intensity of light 𝐼(𝜔) transmitted by an homogeneous isotropic material is proportional to its thickness d and is given by the Beer-Lambert law:

𝐼(𝜔, 𝑑) = 𝐼 0 (𝜔)𝑒𝑥𝑝 [-𝜇(𝜔)𝑑] (2.1.2)
where 𝐼 0 is the intensity of the incident light and 𝐼 the intensity of the transmitted beam.

The law introduces the photoabsorption coefficient 𝜇. When a X-ray photon with energy E = 𝜔 is absorbed, a core-level electron with 𝐸 𝑖 binding energy in the initial state |i⟩ is excited to an empty level |f⟩ above the Fermi level with energy 𝐸 𝑓 = 𝐸 𝑖 + E. Therefore, XAS probes the empty states of the absorbing atom. 𝜇 is proportional to the absorption cross section 𝜎 𝑖 , defines as the number of incident photons per unit area :

𝜇 = 1 𝑉 𝑛 ∑ 𝑖=1 𝜎 𝑎𝑏𝑠 (2.1.3)
where V is the volume of the unit cell of n elements. The absorption cross section is

𝜎 𝑎𝑏𝑠 = Γ 𝑖𝑓 𝐼 𝑝ℎ𝑜𝑡𝑜𝑛 (2.1.4)
with Γ 𝑖𝑓 the probability of the transitions from the ground state |𝑖⟩ towards the final state |𝑓 ⟩, and 𝐼 𝑝ℎ𝑜𝑡𝑜𝑛 the photon flux. The theoritical model describing X-ray absorption by matter is based on the Fermi Golden Rule that gives the probability Γ 𝑖𝑓 as:

Γ 𝑖𝑓 = 2𝜋 |⟨𝑓 |H 𝑖𝑛𝑡 |𝑖⟩| 2 𝛿(𝐸 𝑓 -𝐸 𝑖 -𝜔) (2.1.5)
where H 𝑖𝑛𝑡 is the interaction Hamiltonian describing the interaction of X-rays with electrons, 𝐸 𝑓 and 𝐸 𝑖 are respectively the final and ground state energies, |i⟩ and |f⟩ are the multielectronic wavefunctions for the initial and final configurations, and 𝜔 the incoming photon energy. The delta distribution (𝛿) takes care of the energy conservation which means that a transition takes place if the energy of the final state equals the energy of the ground state plus the X-ray energy. Electronic transitions consist in three components, namely the electric dipole transitions, the electric quadrupole transitions and the magnetic dipole term. Electric quadrupole transitions can be neglected in most cases except in the pre-edge region of 3d transition elements at K -edges. From the dipole approximation, Γ 𝑖𝑓 can be rewritten as:

Γ 𝑖𝑓 = 4𝜋 2 𝜔𝛼 0 |⟨𝑓 |⃗ 𝜀.⃗ 𝑟|𝑖⟩| 2 𝛿(𝐸 𝑓 -𝐸 𝑖 -𝜔) (2.1.6)
where 𝛼 0 is the fine structure constant 𝛼 0 = 𝑞 2 4𝜋𝜀 0 𝑐 , ⃗ 𝜀 the photonpolarization vector and ⃗ 𝑟 the integration variable. Hence, the absorption cross section is obtained by simply extending the sum of Γ 𝑖𝑓 over all the populated terms of the initial state and all the terms of the final state configuration as:

𝜎 𝑖𝑓 = 4𝜋 2 𝜔𝛼 0 ∑ 𝑖,𝑓 1 𝑑 𝑖 |⟨𝑓 |⃗ 𝜀.⃗ 𝑟|𝑖⟩| 2 𝛿(𝐸 𝑓 -𝐸 𝑖 -𝜔) (2.1.7)
with 𝑑 𝑖 the degeneracy of the multielectronic wave functions.

When the X-ray energy is close to the binding energy of a core-level, a sharp variation of the absorption coefficient is observed as a function of the x-ray energy, that is called an absorption edge. The characteristic edge jumps are the result of the consecutive excitation of core levels. The Fermi Golden Rule expresses the chemical and orbital selectivity of XAS. From equation 2.1.5, one sees that 𝜎 𝑖𝑓 depends on the energy with the 𝛿 distribution.

To give rise to the transition of an electron from a given core-level to an empty state, the incoming photon energy 𝜔 has to be at least equal or higher than the given corelevel energy 𝐸 𝑖 . The electron binding energy of a core-level corresponds therefore to the absorption edges energies. For linear polarized light the selection rule is Δ𝑚 𝑙 = 0, for left circularly polarized light it is Δ𝑚 𝑙 = +1, and for right circularly polarized light it is Δ𝑚 𝑙 = -1. In photoabsorption, effects such as chemical shift, splittings due to spin-orbit coupling, multiplet interactions due to Coulomb repulsions occur and leave their signatures on the XAS spectrum. Thus, valuable information about the electronic and magnetic structures or the site-symmetry can be extracted from XAS.In addition the selection rules for the electric quadrupole transitions write Δ𝑙 = ±2 or Δ𝑙 = 0. For 3𝑑 transition elements, the electric quadrupole transitions are negligible at the 𝐿 2,3 edges.

K pre-edge

In the K-edge spectroscopy process, a 1s electron is excited. At the K -edge, the electric dipole selection rules thus describe transitions from the 1s state to np states while electric quadrupole transitions correspond to transitions from the 1s state to 3d states. Their probability is much less than that of electric dipole transitions (about 10 to 100 times weaker). [START_REF] Stöhr | Magnetism: from fundamentals to nanoscale dynamics[END_REF] Thus, the most intense feature at the main K -edge is due to the electric dipole transitions (in the case of 3d elements) which does not allow probing the 3d shell of transitions metals. Nevertheless, quadrupole transitions can be detected at the 𝐾 preedge. They can be mixed with electric dipole transitions, depending on the symetry of the absorbing atom that allows or not hybridization of 3d orbitals with p orbitals. Such local 𝑝 -𝑑 mixing enhances the pre-edge peak intensity. 54 The possibility of hybridization depends on the metal ion symmetry and can be predicted from group symmetry arguments.

For

X-ray Magnetic Circular Dichroism

Dichroism usually refers to a variation of the absorption coefficient as a function of the polarization of the incoming X-Rays. The dichroism is called natural when it arises due to a charge anisotropy in the system, and magnetic when it is caused by a spin or orbit anisotropy. Four types of dichroism can be distinguished:

• X-ray Natural Linear Dichroism (XNLD) is due to an anisotropic charge distribution.

XNLD can be used to study the orientation of molecules for example. 55,56 The XNLD signal is even under both time reversal and spatial inversion.

• X-ray Magnetic Linear Dichroism (XMLD) occurs if the charge anisotropy is induced by an axial spin alignment. XMLD can be used to measure antiferromagnets which have no net total magnetic moment. The XMLD signal is also even under both time reversal and spatial inversion. 57,58 • X-ray Natural Circular Dichroism (XNCD) is caused by a charge anisotropy lacking a center of inversion. XNCD is even for time reversal and odd for spatial inversion.

• X-ray Magnetic Circular Dichroism (XMCD) is even under spatial inversion and odd for time reversal.

When a sample carries a net magnetic moment, the system is no more invariant by time reversal so that the absorption with left polarized X-rays is no more equal to the absorption with right polarized X-rays: this is the origin of XMCD. XMCD effect was predicted theoretically in 1975 by Erskin and Stern and observed experimentally at Fe K-edge in an Fe foil by Schütz et al. 59 At the Ni 𝐿 2,3 edges, a strong XMCD effect has first been reported in ferromagnetic nickel by Chen et al., 60 . The effect was ≈2 orders of magnitude larger than those at the 𝐾 edges of transition metals. 59 The principle of XMCD measurements is illustrated in figure 2.1.4. The quantization axis is defined in the ẑ direction that is usually the wave vector direction for the incident beam. When necessary, a magnetic induction is applied along ẑ to induce a net magnetic moment in the sample. The XMCD signal is the difference Δ𝜎 between the two absorption cross sections for left and right polarized X-ray beam defined as,

Δ𝜎 = 𝜎 -(𝐵) -𝜎 + (𝐵) = 𝜎 𝑟𝑖𝑔ℎ𝑡 (𝐵) -𝜎 𝑙𝑒𝑓 𝑡 (𝐵)
The signs "+" or "-" in 𝜎 + and 𝜎 -refer to x-ray helicity with "+" for left and "-"

for right polarized X-rays. The absorption cross section for a right circular polarized beam and for a magnetic induction B applied parallel (or antiparallel) to the propagation vector k is labelled 𝜎 ↓↑ (or 𝜎 ↓↓ respectively). Similarly, for left circularly polarized beam the corresponding absorption cross sections are represented by 𝜎 ↑↑ or 𝜎 ↑↓ respectively for B and k in parallel or antiparallel configuration. If all types of measurements can be performed, the XMCD signal is obtained by

𝜎 XMCD = (𝜎 ↑↓ +𝜎 ↓↑ ) 2 -(𝜎 ↓↓ +𝜎 ↑↑ ) 2
. With these definitions, a negative XMCD signal at the 𝐿 3 edge of 3𝑑 transition elements corresponds to a magnetic moment pointing in the same direction as the external magnetic induction.

In the electric dipole approximation, the isotropic absorption is the average of absorption measured for the three directions perpendicular to the polarization. The polarization vectors ε-, ε+ and ε|| are orthogonal and are defined by (to some phase conventions),

ε-= - 1 √ 2 ( ê𝑥 -𝑖ê 𝑦 ) ε+ = - 1 √ 2 ( ê𝑥 + 𝑖ê 𝑦 ) ε|| = ê𝑧
Then the isotropic cross section (i.e. the cross section that would be measured on a fully non oriented sample)

𝜎 iso = 1 3 ( 𝜎 + + 𝜎 -+ 𝜎 || )
In our specific case, for powder samples with negligible XMLD, the equation 𝜎 + +𝜎 -= 2𝜎 || holds and then the absorption cross section can be written as 𝜎 iso = 𝜎 + +𝜎 -

2

. The XAS and XMCD spectra at Fe 𝐿 2,3 edges are presented in Figure 2.1.4.

One of the important aspect of XMCD is the ability of measuring the element-specific magnetization curves. In this method, the intensity of dichroic signal is recorded by setting the monochromator at a given energy and the external magnetic induction is varied. When the XMCD signal is proportional to the magnetization of the absorbing atom, the XMCD detected magnetization curve is specific of the magnetization of the absorbing atom.

Multiplet calculations

Thanks to the magneto-optical sum rules applied to the XMCD spectra, spin and orbit contributions to the total magnetic moment carried by the 3𝑑 orbitals can be separated, and thus values of orbit and spin magnetic moments can be extracted.

ℋ = ℋ 0 + ℋ 𝐶𝐶 + ℋ 𝑍𝑒𝑒 (2.1.8)
ℋ 0 is the spherical part of the atomic Hamiltonian and takes into account the electron kinetic energy term,the electron-nucleus Coulomb attractions term, the whole electronelectron Coulomb repulsions between open shells, and the spin-orbit interaction on every shell of the absorbing ion. The radial integrals for interelectronic repulsions and spin-orbit coupling are calculated using an atomic Hartree-Fock code written by Cowan. [START_REF] Cowan | The Theory of Atomic Structure and Spectra[END_REF] For Fe(III) ions, the initial configuration is 2𝑝 6 3𝑑 5 and the final configuration is 2𝑝

Program TT-Multiplet

The program RCN was written by Cowan. [START_REF] Cowan | The Theory of Atomic Structure and Spectra[END_REF][START_REF] Cowan | s Atomic Structure Code[END_REF] (3). It is usually a point group symmetry that is consistent with the crystal-field symmetry, the presence of an external magnetic field and a possible exchange magnetic field. When the matrix elements are known, the cross section is simply obtained by applying Equation 2.1.7. The program PLOTTER yield a spectrum by convoluting the sum of Dirac distribution by a Lorentzian function and a Gaussian function.

Resonant Inelastic X-ray Scattering spectroscopy

This subsection is a brief description of Resonant Inelastic X-ray Scattering spectroscopy (RIXS). RIXS is a resonant two photons (one photon-in, one photon-out) spectroscopy that yields detailed information on the electronic structure of the absorbing atom and that is complementary to XAS. In this thesis I have used RIXS further combined with XMCD (namely, RIXS-MCD) to study the electronic and magnetic structure of the ferrite nanospinels in ferrofluids. Hence, after briefly introducing the principle of RIXS, I will mainly focus on RIXS-MCD spectroscopy. Readers interested in the applications of RIXS for the investigation of materials can refer to several detailed reviews [START_REF] Glatzel | [END_REF][69][70] and books [START_REF] De Groot | Core Level Spectroscopy of Solids[END_REF][START_REF] Winfried | Electron Dynamics by Inelastic X-Ray Scattering[END_REF][START_REF] Carra | Core Level Spectroscopies for Magnetic Phenomena[END_REF] on the subject.

Inelastic X-ray Scattering

Inelastic X-ray Scattering (IXS) is a spectroscopic probe of the electronic and dynamical properties. The pionneering experiments are attributed to Dorner and co-workers in 1986. 73,74 The rapid evolution of the technique is quite recent because energy resolved measurement of photons with inelastic scattering became feasible with high intensity Xrays delivered at third generation synchrotron sources. Although this spectroscopy has an involved theoretical and experimental management, it enables several interesting possibilities when using hard x-rays, amongst which:

• the measurement of phonons,

• the acquisition of soft X-ray like spectra, though using incoming high energy X-rays,

• the possibility to work with constrained sample environments (high pressure cells, liquids),

• the measurement of low energy excitations and their dispersions.

In the IXS spectroscopy process, an incident photon defined by its wave vector (𝑘 1 ), energy ( 𝜔 1 ) and polarization vector (𝜀 1 ) is scattered by the electron system. From the properties of the scattered photons (𝑘 2 , 𝜔 2 , 𝜀 2 ), the energy ( 𝜔) and momentum (𝑞) transferred to the electron are defined according to:

𝜔 = 𝜔 1 -𝜔 2
(2.1.9)

𝑞 = 𝑘 1 -𝑘 2 (2.1.10)
A scheme of the process is given in Figure 2.1.5. For high energy X-rays, the energy losses or gains during the scattering process is always much smaller than the energy of the incident photon ( 𝜔 ≪ 𝜔 1 ) so that q can be approximated as: In the IXS process, the probability of the transitions Γ 𝑖𝑓 is given by the Fermi Golden Rule applied to the interacting term of the Hamiltonian 𝐻 𝑖𝑛𝑡 developed to the second order of perturbation: 75

𝑞 ≈ 2𝑘 1 sin(𝜃/2) (2.1.11)
Γ 𝑖𝑓 = 2𝜋 ⃒ ⃒ ⃒ ⃒ ⃒ ⟨𝑓 |H 𝑖𝑛𝑡 |𝑖⟩ + ∑ 𝑛 ⟨𝑓 |H 𝑖𝑛𝑡 |𝑛⟩⟨𝑛|H 𝑖𝑛𝑡 |𝑖⟩ 𝐸 𝑛 -𝐸 𝑖 ⃒ ⃒ ⃒ ⃒ ⃒ 2 𝛿(𝐸 𝑓 -𝐸 𝑖 ) (2.1.12)
The sum ∑ 𝑛 extends over all the intermediate states |𝑛⟩ with |𝑖⟩ the ground state, |𝑓 ⟩ the final state, 𝐸 the energy and Δ is the Dirac distribution that ensures energy conservation.

The subsequent scattered photons is detected within a solid angle d𝜔 and with a resolution Δ 𝜔. The generic IXS process branches into the Non-Resonant IXS process (NIXS / NRIXS) and the Resonant IXS (RIXS) process.

Resonant Inelastic X-ray Scattering

In the RIXS spectroscopy process, the incident photon energy is tuned to an absorption edge of the sample. The RIXS cross section is then expressed by the Kramers-Heisenberg formula: 76 The general RIXS process is schematized on the left panel of Figure 2.1.6. We focused on the K absorption spectrum pre-edge feature (decribe above in XAS paragraph) and used the 𝐾𝛼 emission that describes the 2𝑝 → 1𝑠 transitions (𝐾𝛼 1 : 2𝑝 3/2 → 1𝑠, 𝐾𝛼 2 : 2𝑝 1/2 → 1𝑠). In the following this RIXS process is referred to as 1s2p RIXS. The total energy diagram representing the 1𝑠2𝑝 RIXS process for 3𝑑 ions, that we applied to study the transitions elements of our samples, is presented on the right panel of Figure 2.1.6.

𝐹 ( 𝜔 1 , 𝜔 2 ) = ∑ 𝑓 ( 𝑚 ) ⃒ ⃒ ⃒ ⃒ ⃒ ∑ 𝑛 ⟨𝑓 |𝑇 2 |𝑛⟩⟨𝑛|𝑇 1 |𝑖⟩ 𝐸 𝑖 -𝐸 𝑛 + 𝜔 1 -𝑖 Γ𝑛 2 ⃒ ⃒ ⃒ ⃒ ⃒ 2 × Γ 𝑓 2𝜋 (𝐸 𝑖 -𝐸 𝑓 + 𝜔) 2 + Γ 2 𝑓 4 (2.
One can observe that in 1s2p RIXS, the 2p 5 3d 𝑛+1 final state electronic configuration is identical to the 2p spin-orbit split final state configuration of XAS at the L 2,3 edges. RIXS measurements are drawn as 2D maps, where the recorded intensity is plotted as a function of the incident energy (horizontal line) and as the energy transfer (vertical line). The energy transfer is the difference between incident and emitted energies. An example of a RIXS plane recorded at the Mn K -edge is shown in Figure 2 • Diagonal cuts of RIXS plane yields to Constant Emission Energy (CEE) spectra.

They ressemble an absorption spectrum but with a reduced lifetime broadening, smaller than the core-hole lifetime broadening. CEE scans show a improved resolution smaller than XAS scans as such it is also referred as XAS in Partial Fluorescence Yield (PFY) or XAS in High Energy Resolution Fluorescence Detection (HERFD), depending on the detector used. CIE and CEE line plots of the RIXS plane are also shown in Figure 2.1.7. They allowed to study specific electronic excitations and enables an easier analysis as the rich multiplet structure arising from the RIXS planen is disentangled.

RIXS-MCD

RIXS-MCD is a newly developed spectroscopy that arises from the combination of 1s2p RIXS with XMCD. When performed at the K absorption pre-edge, it combines chemical, orbital selectivity with the bulk sensitivity of hard X-rays to probe the 3d transitions magnetic moments and their ordering. We have taken advantage of this technique to determine the local environment and magnetic anisotropies of ferrite nanospinels in liquid and frozen ferrofluids. The investigation of these systems using RIXS-MCD are presented in Chapter 5.

As the application of the technique in the hard x-ray range is quite recent, very few 1s2p RIXS-MCD studies are reported in litterature. [77][78][79] The first combined experiments of RIXS with XMCD were reported at the 𝐿 2,3 edges. The first experimental study is reported by Braicovich et al. who observed low energy transfer excitations (2𝑝 → 3𝑑 and 3𝑠 → 2𝑝 excitations) in transitions metals. 80,81 Using hard X-rays, the technique has also been applied to reveal 2𝑝 → 4𝑓 quadrupole transitions in lanthanides 69,82 . In 2010, Sikora and co-workers observed that the XMCD signal of Fe in magnetite is about one order of magnitude larger when it is measured at the maximum of the 𝐾𝛼1 emission than when using Total Fluorescence Yield detection. 77 The study highlights a dichroic amplitude measured in 1s2p RIXS-MCD as large as 16% (peak-to-peak) of the pre-edge maximum, similar to what has been reported at the Fe 𝐿 3 edge in magnetite. Hard x-ray RIXS-MCD experiments thus can be adopted as an element and site-selective magnetic probe that present unique advantages over the L 2,3 and K -edges XMCD spectroscopies. Compare to L 2,3 XMCD spectroscopy often recorded in Total Electron Yield mode of detection (see Section 2.2), 1s2p RIXS-MCD is a bulk sensitive method using penetrating hard X-rays, which allows working with absorbing sample environment such as diamond anvil cells or liquids. Self-absorption effects that influence the shape and dichroism of the main K -edge can be avoided by focusing in the pre-edge where these effects can be neglected. Moreover, at the K -edge, XMCD spectroscopy gives a weak magnetic signal (0.1 to 1 percent with respect to the edge jump) and the absence of spin-orbit split edges makes the quantitative interpretation of the results much more challenging than at the 𝐿 2,3 edges. But in the 1s2p RIXS-MCD spectroscopy, the final state of the process 2𝑝 5 3𝑑 𝑛+1 is identical to that of the 2p spin-orbit split 𝐿 2,3 absorptions edges. Using theoretical spectra calculated within the LFM approach, Sikora et al. were able to explain the RIXS-MCD process in the case of Fe 3+ . In the process, a 1𝑠 photon is excited to a 3d unoccupied level such as the 1𝑠 with 2p spin-orbit interaction. As a consequence, a energy shift between left and right polarization along both the incident energy and energy transfer directions is observed in the RIXS-MCD plane, which yields a non-zero MCD signal.

In order to define the RIXS-MCD signal, we use the same phase convention as to define XMCD. A RIXS-MCD plane is obtained by taking the difference of two RIXS planes measured for two different circular polarization states (right and left) in the presence of a magnetic induction B. The RIXS-MCD cross section is then expressed from the direct difference of those obtained for RIXS for left and right photons helicities:

Δ𝐹 𝑅𝐼𝑋𝑆-𝑀 𝐶𝐷 ( 𝜔 1 , 𝜔 2 ) = 𝐹 𝑙𝑒𝑓 𝑡 ( 𝜔 1 , 𝜔 2 ) (B) -𝐹 𝑟𝑖𝑔ℎ𝑡 ( 𝜔 1 , 𝜔 2 ) (B) (2.1.14)
Note that, if one integrates the RIXS-MCD plane over the pre-edge range along the incident energy direction, one obtains a spectrum that is, in a very crude approximation, similar to a 𝐿 2,3 XMCD spectrum. Despite obvious differences in intensity and spectral shape, one can use this to quickly check that the phase convention is correct (such that, for a Fe 3+ ion with a magnetic moment parallel to the induction, the XMCD signal at the 𝐿 3 edge is negative). Similarly to XMCD, one can perform magnetometry measurements using RIXS-MCD by fixing the incident energy and the emission energy to values of interest in the RIXS-MCD plane, and by changing the value of the induction.

Experimental aspects of Synchrotron experiments 2.2.1 Detection modes for absorption measurements

During my thesis, I have used three common ways to record the absorption signal:

• Total Electron Yield (TEY)

• Transmission

• Total Fluorescence Yield (TFY)

• High Energy Resolution Fluorescence Detection (HERFD)

Whatever the mode of detection, the goal is to determine the absorption cross section as a function of the energy of the incoming photons.

The Total Electron Yield

In TEY mode, the absorption cross section is determined from the detection of all electrons that emerge from the sample surface. The current intensity of the electrons recorded is then proportional to the absorption cross section. These electrons have a low kinetic energy (secondary electrons) because electrons interact stronger with the sample than Xrays which implies that they originate mainly from the surface. Therefore, the probing depth of TEY in the soft X-ray range is around 5 nm, and 80% of the signal recorded in TEY arises from the top 2 nm making this mode of detection much sensitive to the surface. Except for samples that have been prepared with the liquid cell setups (see Chapter 3), all the measurements in soft X-rays presented in this thesis have been recorded in TEY mode. On the DEIMOS beamline, the electrons are collected using the "sample current" technique. In this technique, the current from the electrons ensuring the electric neutrality of the sample is measured with an electrometer connected to the electrically isolated sample.

Transmission mode

Transmission is the most direct detection mode as it is a direct measurement of the absorption cross section. The absorption is simply obtained comparing the incoming photon intensity (I 0 ) with the intensity transmitted by the sample (I 𝑡 ). Hard X-rays have a large attenuation depth so that Transmission experiments are standard in this environment.

However, detection in Transmission in Soft X-rays are limited the difficulties it implies in sample preparation. Due to the low attenuation depth of soft X-rays, the sample has to be extremely thin (about hundred nanometers), free from inhomogeneities and thickness variation. Measurements recorded in transmission mode of detection are presented in Chapter 3, using the liquid cell setup implemented on the DEIMOS beamline. The outgoing photons are detected with a removable photodiode working in integration mode.

Total Fluorescence Yield

The emission of X-ray fluorescence is indirectly proportional to the absorption. The corehole created after the excitation of an electron can be filled by two processes, which correspond to the transition of another electron from a higher energy level down to the hole left behind. The resulting energy gain results either as the emission of a photon (X-ray fluorescence) or of an electron (Auger electron). The photon created in the fluorescence decay has a mean free path of the same order of magnitude as the incoming X-rays.

Therefore, TFY is a bulk sensitive technique. However, the analysis of the experimental spectra recorded in TFY can be difficult due to self-absorption effects which severely distort the absorption spectrum. At the 𝐾 edge, this affects in particular the relative intensity of the pre-edge with respect to the edge, and the intensity of the white line and of the features above the edge. In the 1𝑠2𝑝 RIXS and RIXS-MCD experiments, complementary to the RIXS detection using the spectrometer, we have also collected TFY spectra usign a diode in order to compare our TFY-XAS data to spectra from literature, which is always useful.

High Energy Resolution Fluorescence Detection

"Absorption-like" spectra can be measured on a RIXS endstation using a spectrometer, by fixing the emission energy to a given value (for example, the maximum of the 𝐾𝛼 line).

Such spectra are called HERFD-XAS and correspond to a diagonal cut through the RIXS plane. HERFD XAS offers the best possible signal-to-background ratio because the energy resolution is of the order of the core hole lifetime broadening, which results in a significantly shaperned spectral features. The K absorption pre-edges in 3d transition metals can thus be better separated from the main edge. Another consequence is the suppression of diffraction peaks in XAS measurements of polycrystalline samples. However, there can be significant differences between standard XAS and HERFD-XAS spectra, as was discussed by Carra et al. HERFD-XAS cannot be considered as a true absorption spectrum, and it can be understood only within the framework of the Kramers-Heisenberg equation. 83

Detection mode in RIXS experiments

In a RIXS experiment, detection of the scattered photons is achieved using a spectrometer composed of one or several analyzer crystals (Figure 2.2.1). The principle is based on Bragg's law: the spectrometer analyses the fluorescence from the sample by selecting only photons having a particular energy, such that they are in Bragg condition for the incident angle on the crystal. These selected photons are reflected on a photon counter (Avalanche Photo Diode, APD). The emission energy can then be tuned to a different value by moving the spectrometer, and the RIXS plane can be acquired step by step. The sample, the analyzer crystal(s) and the APD are set in a Rowland geometry on ID26 beamline. The choice of the analyzer crystals depends on the energy of the fluorescence line that has to be selected. An helium bag is put between the sample, the analyzers and the detector so that the X-ray photons are not absorbed by air.

DEIMOS CROMAG endstation

Beamline

Soft-XAS and XMCD experiments were performed on the DEIMOS (Dichroism Experimental Installation for Magneto-Optical Spectroscopy) beamline at SOLEIL at the Mn and Co L 2,3 edges. 85 The beamline is fully dedicated to the study of magnetic and electronic states of nanoscale structures with XAS and XMCD in the range of soft X-rays (the beamline also provides the environment for XLD measurements). Indeed, the beamline has been optimized to for the requirements of the dichroism technique that are: 86

• the source has to be optimized for polarization

• the stability and reproducibility in terms of photon flux and photon energy have to be optimal

The main end-station (CROMAG endstation) consists of a superconducting cryo-magnet providing an induction of ±7 T along the X-rays beam or ± 2 T perpendicular to the beam and a temperature on the sample ranging from 1.5 K to 370 K. The chamber is maintained in UHV (10 -10 mbar) continously as sample transfers do not require to break the vacuum.

The incident photons energy on the sample is selected with a monochromator optimized for the energy domain 240-2500 eV. The beamline is equipped with two undulators. The Apple-II helical undulator with a period of 52.4 mm provides circularly polarized light over the full energy range (240-2500 eV) and horizontal and vertical linearly polarized light from 350 eV to 2500 eV. The second undulator is an hybrid electromagnet/permanent magnet helical undulator (EMPHU65) with a period of 65.0 mm optimized for a fast switching ( 5Hz) of the circular polarized light.

Experiments

Two or three drops of ferrofluid are deposited on gold plated silicon wafer using a Pasteur pipette. When dried, a thin uniform layer of nanoparticles is formed. The Si wafer is then mounted on a sample holder made of copper that can hold six different samples in the same time (see Figure 2.2.2). The sample holder is transferred in the CroMag chamber through a load lock. All the measurements were made in TEY detection mode at 4 K under ultra high vaccuum (10 10 mbar). We have recorded left and right circulary polarized X-ray absorption spectra in the TurboScan mode 87 (continuous energy scan with the synchronization of the monochromater and the undulator) with the Apple-II HU52 helical undulator in a magnetic induction operating between 6.4 and 6.8 T (depending on instrumental specifications during the beamtime). XAS spectra are recorded by both flipping the circular polarization (either left or right helicity) and the external magnetic

ID26 endstation implemented for RIXS-MCD

Ferrofluid samples measured in RIXS and RIXS-MCD were investigated using an original sample cell developed on purpose in collaboration with the staff of ID26 beamline (M.

Rovezzi) and the ESRF Sample Environment group (H. Vitoux). In brief, it consists in a sample holder in which a square cavity for liquid has been machined. The sample holder is attached to a cold plate cooled with a mini-cryostat. The description and a photograph of this custom made sample holder can be found in Chapter 3. In June 2014, I participated to the tests of the sample cell : I have assembled the liquid cell prototype, tested it was leak free, checked the temperature range that was available and exercised on how to fill and purge the liquid cell. These tests lay the foundation for an experimental protocol to use the liquid cell.

Two weeks of beamtime dedicated to the measurements of ferrofluids were carried out during my thesis. Measurements were performed on the ID26 beamline at ESRF at the Mn and Co K -edges. The incident energy was selected using an Si(311) monochromator with a resolving power of Δ𝐸/𝐸 ≈ 35000 (∼0.2 eV at 7000 eV). The inelastically scat-tered beam was analyzed using a set of four spherically bent Ge(111) (to record the Mn 𝐾𝛼 emission) and Si(531) (to record the Co K𝛼 emission) crystals. In the present experimental configuration (Ge(111) at ∼74°and Si(531) at ∼77°), the energy resolutions of the crystals are approximately 0.9 eV FWHM for Ge (111) and 0.6 eV FWHM for Si(531).

The scattering angle was set to 90°with sample surface at 45°to the incident beam. 1𝑠2𝑝 RIXS planes were recorded as a set of CET scans over the energy of the 𝐾𝛼1 line and of the 𝐾 pre-edge. HERFD-XAS have been measured by setting the emission energy to the maximum of the 𝐾𝛼 line.

To record MCD measurements, the circular polarization of the incident X-rays was set by a 500 𝜇m thick diamond (111) quarter wave plate downstream the monochromator with a circular polarization degree estimated to 75%. The magnetic induction was provided by an electromagnet that allows to reach a magnetic induction of 1.5 T. The calibration curve of the electromagnet was carefully measured using a hall probe, at the beginning and at the end of the beamtime. RIXS-MCD planes were recorded by switching photon helicity at each incidence point for +1.5 T magnetic induction and same measurements were repeated for -1.5 T magnetic induction. HERFD-XAS and HERFD-MCD scans were also collected by setting the emission energy to the maximum of the 𝐾𝛼 line.

RIXS-MCD detected magnetization curves were measured by setting the incident energy and the emission energy to the maximum value of RIXS-MCD intensity (over the RIXS-MCD plane) and by sweeping the magnetic field from -1.5 T to 1.5 T for each polarization.

Magnetometry

The static magnetic properties of the samples studied in this thesis have been investigated using magnetometer devices. The measurements were made at the Plateforme de mesures physiques à basse température (UPMC) using Super Quantum Interference Device (SQUID) and Physical Property Measurement System (PPMS) commercial devices (Quantum Design). In this section, the measurements implemented in magnetometry are detailed.

The SQUID magnetometer is based on a superconducting Josephson device used with a superconducting magnet. [START_REF] Clarke | The New Superconducting Electronics[END_REF] SQUID magnetometer acts as a very high-sensitivity fluxmeter. The method consists in recording a value proportional to the flux change in a pick-up coil when the sample moved along the direction of the magnetic field. SQUID magnetometry is a highly sensitive methods, allowing measurements up to 10 -10 A.m 2 . The PPMS is a commercial Vibrating Sample Magnetometer (VSM). 89 The principle of VSM is based on the measure of the flux change in a coil when a sample is vibrated near it. Sensitivity of 10 -8 A.m 2 can be achieved with the PPMS.

The direct experimental result of SQUID and PPMS measurements is a plot of the sample magnetization vs the applied field for a given temperature or the magnetization vs. the applied temperature for a given external field.

Magnetization vs. applied field

Nanopowders Measurements of magnetization vs. applied field were performed at 300 K on the samples to determine the saturation magnetization. The dried powder nanoparticles are obtained from the ferrofluids whose carrier liquid is evaporated at room conditions.

The thermal energy being high, the nanoparticles are mainly in the superparamagnetic state. The magnetic curve is reversible and can be described according to the Langevin function (see section 1.1):

𝑀 = 𝜇𝜑 ( 𝑐𝑜𝑡ℎ𝑎𝑛 ( 𝜂 0 𝜂𝐻 𝑘 𝐵 𝑇 ) - 𝑘 𝐵 𝑇 𝜂 0 𝜂𝐻 ) (2.3.1)
Then for very high field, 𝜂 0 𝜂𝐻 ≫ 𝑘 𝐵 𝑇 and equation 2.3.1 can be written:

𝑀 𝜑 = 𝜇 ( 1 - 6𝑘𝑇 𝑑 3 𝜂 0 𝜋 1 𝐻 ) (2.3.2) Plotting 𝑀 𝜑 = [ 𝑓 ( 1 𝐻 )]
, M s =𝜇𝜑 is determined from the extrapolation to zero to the linear curve, i.e. y-axis intercept. In order to cancel the mass contributions of surfactants and other organic substances remaining from the synthesis to the total mass of the sample, thermogravimetric analysis measurements (TGA) have been performed on the dried powder nanoparticles. The sample is placed in a small furnace electrically heated in a purged chamber. While heating the sample up to 1000°C, the mass change and the temperature change are recorded. One may thus obtain the mass losses due to the decomposition of organic substances that are liberated during heating. Knowing the mass of the starting sample and percent mass losses, we obtain the mass ratio contribution of the magnetic nanoparticles. The M s values are then corrected with the TGA measurements.

Ferrofluids Magnetization vs. applied field were recorded on the ferrofluids sample at low enough temperature to freeze the carrier liquid. The nanoparticles are blocked in the frozen matrix, and reveal their intrinsic magnetic properties. Hysteresis appears, evidenced by non-zero coercivity.

Magnetization vs. temperature

Magnetization vs. temperature measurements were performed to determine the blocking temperature T B of the nanoparticles. T B is reached as 𝜏 𝑚 =𝜏 𝑛 (see Chapter 1). Above T B , the nanoparticles have enough thermal energy to be superparamagnetic (𝜏 𝑚 ≫ 𝜏 𝑛 ), while below T B , they are blocked and show hysteresis (𝜏 𝑚 ≪ 𝜏 𝑛 ). T B is usually determined from Zero-Field-Cooled (ZFC) and Field-cooled (FC) combined measurements.

The experimental protocol for the ZFC-FC measurements presented in ZFC-FC curves were recorded on the ferrofluids samples when they are dispersed in aqueous medium. However, nanoparticles may be dispersed in heptane for some of the ferrofluids studied (ferrofluids obtained with acac synthesis). In order to avoid the critical fusion point of heptane, nanoparticles obtained in heptane were redispersed in Paraffin.

ZFC-FC temperature dependence of magnetization were then carried on nanoparticles dispersed in Paraffin.

Chapter 3

Instrumentation: Liquid Cells

Introduction

Investigations of liquids by X-ray magnetic spectroscopy is scarce compared to what has been developed for the solid state phase. The study of magnetic materials in the liquid phase is mainly performed by using Mössbauer spectroscopy, 91,92 conventional magnetometry 93,94 or neutrons scattering 95,96 . Synchrotron based magnetic spectroscopy such as X-ray Magnetic Circular Dichroism (XMCD) or Resonant Inelastic X-ray Spectroscopy for Magnetic Circular Dichroism (RIXS-MCD) are unique tools to gain information on complicated magnetic systems by recording magnetic signatures that are chemically selective. Up to now, none of these techniques have ever been employed to answer question dealing with magnetic liquids such as ferrofluids or magnetic molecular systems in the mother solvent. 97 Most synchrotron beamlines require good vacuum conditions and in the soft X-ray range UHV conditions are often mandatory. At the difference of the hard X-ray range where the penetration depth is rather large (i.e. in the 10 𝜇m range), the penetration depth in the soft X-ray range is close to 100 nm and when the detection mode is the Total Electron Yield (TEY), the escape depth of the electrons is not larger than 5 nm.

These constraints make investigations of magnetic liquids with X-rays quite challenging.

These past years, the ferrofluid community has shown an increasing interest for interparticle dipolar interactions in ferrofluids. It was found that such interactions can induce self-assembly of nanoparticles in external magnetic fields in chains, monolayers, rings or even 3D geometry. [98][99][100] The magnetic interactions between nanoparticles were found to govern the magnetic properties for bidisperse ferrofluids 101 (i.e. a ferrofluid with magnetic nanoparticles that have two distinct sizes), or for binary ferrofluids 102 (i.e. a ferrofluid with nanoparticles of two distinct magnetic nature). In either bidisperse or binary ferrofluids, the liquid environment of ferrofluids must be preserved if the target is to understand the magnetic interactions in the ferrofluid as they are. Our knowledges of these complex systems would gain a lot from in situ XMCD experiments that could be selectively sensitive to the individual components of a binary ferrofluid. Recently, such experiments have become feasible owing to recent achievements in synchrotron radiation instrumentation and in experimental techniques. Three main instrumental approaches are currently being developed for the investigation of liquids:

• liquid microjets,

• static liquid cells,

• flow-through liquid cells.

Liquid microjets technology is applied in environment as diverse as electron-yield or ionyield XAS or photoelectron spectroscopy. [103][104][105][106][107][108][109] It basically consists in a liquid micro jet that is directly injected into the vacuum of the experimental setup. It requires a whole dedicated custom-made chamber. Besides the technical difficulties to maintain the analysis chamber at low enough pressure, the liquid in such a jet is far from its thermodynamic equilibrium and this may complicate the interpretation of the data, especially in the case of liquids. In addition, this method adds to the detected signal a considerable contribution from the vapor surrounding the liquid jet that can make the interpretation of the results even more complicated. These considerations led us to the conclusion that liquid microjets technology is unlikely appropriate to XMCD measurements. Hence, the instrumental developments that I am presenting hereafter focused on the two others instrumental approaches, the static liquid cells [110][111][112][113] and the flow-through liquid cell [114][115][116][117][118][119] . For both options, no commercial solutions are available as it is often the case for advanced instrumental setups related to synchrotron facilities. Since each beamline endstation has its own specific environment (geometry of the endstation, available space around the sample, transfer mode for the sample from the preparation chambers, detection mode, vacuum quality etc.) the liquid cell has to be custom-made.

In the following of this chapter, I shall present the two types of liquid cells that I have been developing during my Ph.D. thesis in order to answer the questions that I wanted to solve. The first one is a flow-through liquid cell developed for the DEIMOS beamline at SOLEIL, the second one is a static liquid cell developed for ID26 beamline at ESRF. In the first section, the development of the liquid flow-through cell on the DEIMOS beamline is described after a small review of the literature. The liquid cell design has been elaborated to be compatible with the soft X-ray MCD environment and constituted a real, innovative challenge. The conception, drawings of the blue prints, the realization and the first feasibility tests took quite a long period and extended over the whole time of my Ph.D.

thesis. The work is still an ongoing task and it is now in the hands of Fadi Choueikani, one of the scientists of the DEIMOS beamline. To answer the questions raised by my thesis, it was important to find another approach that would enable the investigation of the magnetic anisotropies of nanoparticles in the ferrofluids. A valuable solution was found in RIXS-MCD, which benefits from the advantages of hard X-rays (bulk sensitivity, low absorption effects) with the high resolution of RIXS. RIXS-MCD experiments had to be performed with samples attached to a variable temperature insert so that the liquid cell had to be compatible with secondary vacuum and cryogenic cooling. In the second section, I review the design of the liquid cell. Both developments of liquid cells have been tested during real experimental sessions and the obtained results are summarized at the end of the present chapter with connection to other experimental findings that can be found in Chapter 5. The present chapter closes on a summary and a brief out-look of the future instrumental developments.

Liquid Cell for soft X-ray MCD environment

Literature review

Developing a cell for liquids that would allow the measurement of XMCD on a soft X-ray beamline is a challenging adventure since most soft X-ray beamlines are in the vacuum of the synchrotron ring and often require ultra high vacuum conditions. Most liquids have high vapor pressure (∼3.5 kPa for water 120 and ∼6.7 kPa for heptane 121 at 300 K) so that the liquid phase is not compatible with any vacuum conditions and specially devised liquid cells compatible with UHV conditions have to be developed. While samples in the solid state phase have been extensively studied with soft X-rays, the first investigation of liquids had to wait 1987. In the pioneering investigation of XAS on liquid, Yang & Kirz reported experimental studies of liquid water achieved with Extended X-ray-Absorption Fine Structure (EXAFS) measured at the O K -edge (the creation of a 1s occurs at ≈540 eV for Oxygen). 110 In this study, a water film was investigated by squeezing a small amount of liquid water between two 150 nm thick Silicon Nitride (Si 3 N 4 ) membranes. This static liquid cell was the simplest conceivable one, in which very thin membranes encapsulated a tiny amount of liquid. The key features of the liquid cell conceived by Yang & Kirz are the two membranes that are transparent to soft X-ray and that can hold a pressure difference as large as 1 bar. This system has been reproduced by many other authors with membranes made of either Si 3 N 4 or Silicon Carbide (SiC) membranes. The signal was collected in the transmission mode so that the requirements for such a cell were two highly transparent membranes and very thin sample (≈500 nm at the O K -edge). One can imagine that sample preparation can be quite challenging with such thin thickness.

However, the XAS in transmission mode is a truly bulk sensitive probe. The experimental setups developed to record XAS or XES spectra on liquids is highly conditioned by the detection mode that is selected for the experiment. Each detection mode has its quality and its drawback. Total Electron Yield is only a surface method and can hardly be implemented for liquid cells. Total Fluorescence Yield is a bulk sensitive technique at least in the micron range but possible self-absorption effects have to be overcome. 122 The transmission mode is highly sensitive to inhomogeneities and to thickness variations that may completely hamper the measurements but the technique is a direct measurement of the absorption cross section. Thus a few designs of liquid cells for measurements in transmission mode can be found in the literature despite the challenging manufacturing that relies on various types of membranes. 110,119,[123][124][125][126][127] Other designs for static liquid cells have also been reported in literature for which the measurements were made by collecting the Total Fluorescence Yield (TFY) in order to record XAS or XES spectra. 112,113 TFY measurements do not require thin samples. They only require a thin entrance membranes so that the design of such liquid cells is much simpler than the one for liquid cells where the signal is collected in transmission. The electronic structure of cobalt nanocrystals suspended in liquid, for instance, have been investigated with XAS and XES by Liu et al. using such TFY compatible liquid cell. 128 Another solution was the one developed on beamline 8.0 at the Advanced Light Source (Berkeley) dedicated to the study of aqueous samples for environmental sciences. The sample chamber can be maintained at 1 bar thanks to a 160 nm thick Si 3 N 4 membrane placed between the sample chamber and the upstream part of the beamline that is in UHV. Several liquid systems have been successfully investigated using this endstation. Myneni et al. studied the electronic structure of liquid water at the O K -edge. 129 Edwards & Myneni collected Near Edge X-ray Absorption Fine Structure (NEXAFS) spectra at the carbon (∼280 eV) , nitrogen (∼410 eV) and oxygen K -edge of bacterial macromolecules in aqueous solutions. 130 Static liquid cells have proved to be efficient in soft X-ray environments but they also have some limitations. The heating can produce gas bubbles that could displace the liquid. But in the case of organic solutions, it can also cause the decomposition of the liquid producing thin layers of dissociation products that can dominate the spectra. Moreover, the temperature measured can be far from the effective temperature of the sample. The authors report on a liquid flow-through cell where the probing volume of liquid can be refresh with high flow rate to obtain the desired sample temperature. They also have reported a new improved version of this liquid flow-through cell. 117 Finally, Schreck et al. conceived a liquid cell for soft XAS measurements that combines the two more challenging aspects mentionned before:

the liquid flow and the transmission mode of detection. Their liquid flow-through cell consists in a sample holder for connecting the tubings and a very thin sample cell placed in the sample holder. 118 The design of our liquid cell is based on their approach.

Starting from a literature monitoring summarized below, we have developed a liquid flow-through cell design adapted to the beamline endstation environment of DEIMOS.

The 2D blue prints for the fabrication of the setup were drawn by the Bureau d étude from SOLEIL in accordance with our specifications that resulted from many meetings and discussions.

Specification and needs

The technical specifications of the setup are detailed in this section. The material components are required by the XMCD environment while the liquid flow and the detection mode were strategic choices detailed hereafter.

Transparent soft X-rays windows

Membranes almost transparent to soft X-rays are necessary to acquire spectra with good signal-to-noise ratio. Examples of successful use of Si 3 N 4 membranes for liquid investigations have been presented in the short literature review. Si 3 N 4 membranes can be made extra thin so that they would allow measurements between 200 eV and 1000 eV. The main drawbacks from Si 3 N 4 membranes come from the various edges of the silicon and nitrogen atoms: the Si L 2,3 edges (∼100 eV), Si L 1 edge (∼150 eV), and the N K -edge (∼400 eV).

SiC membranes are another possible match with low absorption of soft X-rays that allow measurements at the N K -edge at the expense of the C K -edge (∼280 eV). Both membrane types are compatible with the study of ferrofluids with the difference that Si 3 N 4 membranes exhibit a slightly better fracture resistance than SiC membranes. 131 We hence made the choice of Si

Detection mode

To realize bulk sensitive measurements, we wanted to perform the measurements in the transmission mode that implies that the X-rays have to go through the two membranes encapsulating the liquid sample before reaching the detector. The sample has to be also thin enough to transmit enough so that spectra with a high signal-to-noise ratio are recorded.

From the instrumental point of view, the X-ray attenuation length is the limited factor and the two features to consider are :

• the absorption of the membranes,

• the absorption of the liquid sample.

The photons transmission is calculated for different thickness of Si 3 N 4 using the X-ray database of the Center for X-Ray Optics (CXRO) The second criterion would be the ferrofluid absorption which can be controlled by three features: the liquid thickness, the nanospinels concentration in the ferrofluid, the nature of the liquid carrier. The nature of the liquid carrier is determined by the synthesis and cannot be easily changed. In the following we shall consider that the liquid carrier is water. Similar results are obtained for heptane. In order to evaluate the sample thickness, we consider a ferrofluid consisting in CoFe 2 O 4 nanoparticles in water with concentration range between 0.1% and 1% by volume where 1% is the maximum working concentration that we can use (the concentration of the sample is discussed in section 5.4). The density of CoFe 2 O 4 is 5.29 g.cm -3 (against 1 g.cm -3 for water). The total density of the slurry for 1% concentration is close to that of water and is approximately constant if the CoFe 2 O 4 concentration varies between 0.1% and 1%. Therefore, the variation of transmission through the sample thickness can be only followed as a function of the sample thickness. The absorption at Mn, Fe and Co edges depends on the volume fraction and the values reported hereafter are for 1% volume concentration. We have plotted the transmission as a function of the sample thickness in Figure 3.2.2. For a 500 nm thick ferrofluid sample, the transmission is larger than 50% on the whole energy range so that the total transmission with the two membranes is larger than 25% at 600 eV and larger than 50% at 800 eV. Thus, we have determined that a sample thickness of 500 nm encapsulated by two 100 nm Si 3 N 4 membranes should allow measurements with a good signal-to-noise ratio. Besides the transmission mode, the design of the liquid cell is also compatible with the Fluorescence Yield detection mode that is slightly less demanding.

Materials

The presence of high magnetic induction during XMCD measurements imposes constraints on the materials for the liquid cell that has to be amagnetic. Among the available materials, we considered the copper, polyetheretherketone (PEEK), and amagnetic stainless steels. We decided to use 316 LN stainless steel because copper is difficult to machine and PEEK gets damaged easily.

Temperature control

In order to study magnetic anisotropies, one would need to investigate the magnetic nanoparticles in the ferrofluid for a varying set of temperatures, down to the freezing temperature of the liquid carrier. Cryogenic implementation for a liquid cell is quite challenging and for a first design, we chose to only work at room temperature. In a near future, we plan to upgrade the liquid cell so that it can be mounted inside a cryostat for variable temperature measurements.

Experimental setup

In this section, we describe the design of the liquid cell setup. On DEIMOS beamline, there are two endstations for XMCD, the CroMag setup for high magnetic field measurements (see section 2.2) and the 2 Tesla electro-magnet endstation (MK2T) for high temperature measurements. We chose to install the liquid cell in the MK2T endstation. A schematic drawing of the MK2T endstation is shown in Figure 3.2.3. The experimental chamber consists in two electromagnetic coils providing an induction of ± 2 Tesla. The liquid cell is inserted on the port side of the MK2T chamber (see Figure 3.2.3). The vacuum of the MK2T chamber ranges in the 10 -8 mbar with no prior baking. Upstream, an aluminum foil is mounted on a valve to protect the CroMag endstation from any sudden rupture of the vacuum due to breaking of any membrane from the liquid cell. The liquid cell is built out of three main parts:

• the sample cell (also referred as the chip),

• the sample holder (also referred as the head) that holds the sample cell,

• the horizontal insert on which the sample holder is mounted.

Horizontal insert

The horizontal insert has several main functions:

• it enables the transfer of the cell header to the electromagnet coils,

• it contains the electrical wires for detection,

• it contains the liquid channels for the cell filling.

Liquid cell filling

The liquid cell is filled using a microfluidic montage with a syringe pump. Several tests have been performed while varying the liquid flow between 60 nL.min -1 and 900 nL.min -1 . The maximum flow rate of 900 nL.min -1 in the tubing corresponds to a flow speed of 1 cm.min -1 in the volume of the sample cell. Higher flow rates were avoided to prevent membrane rupture during the filling.

We also tried different strategies to pump the liquid through the tubings by connecting the syringe pump either to the outlet tubes, or to the inlet tubes. We found that the best strategy is to connect two syringes, one pumping from the oulet and one pushing into the inlet with flow rates that are synchronized.

None of our filling attempts made with water-based ferrofluid worked out. But by changing the solvent with heptane, we succeeded several times in filling the membrane.

However, very few fillings were homogeneous, and the sample cell often contained bubbles. Moreover, it was found very difficult to preserve the liquid when the tubing system was disconnected even with closed valves. The disconnection of the syringes creates a depressurization which highly perturbs the sample cell filling.

Results and errors analysis

Results

In a first step, we filled the sample cell with a ferrofluid. As explained in the previous section, the filling could only be performed after quite a large number of tries. During the filling procedure, the sample cell is mounted in the sample holder that is connected to the horizontal insert and the whole setup is in the air. Once the sample cell is filled, we have introduced the whole setup (horizontal insert + sample holder + sample cell) in the introduction chamber of the MK2T endstation (see Figure 3.2.3). The introduction chamber is pumped down to 10 -5 mbar with a turbo pump and then to 10 -8 mbar with an ionic pump. The whole setup is then introduced in the measurement chamber of the MK2T endstation and the horizontal insert is translated until the center of the sample cell is aligned with the X-ray beam.

The absorption signal was recorded in the transmission mode and in the fluorescence yield mode. However, the position of the diode for the fluorescence mode was not optimized and only very noisy fluorescence signals could be recorded. In the following I will not present the fluorescence results and I will only focus on the ones obtained in the transmission mode. For the transmission mode, the transmitted signal is measured by Silicon diode, working in the integration mode, that is connected to a low noise pre-amplifier and a Voltage-to-Frequency converter integrated in a Novelec electrometer coupled to a National Instruments counting card (NI-6602). The measurements were performed using the large spot size (800×800 𝜇m) which corresponds approximately to the size of the sample window. We performed three different types of measurements on the photodiode:

• the horizontal insert is removed so that there is no absorption from the sample, nor the sample cell,

• the horizontal insert is in position and the sample cell is empty,

• the horizontal insert is in position and the sample cell is filled with ferrofluid.

The different results of the transmitted signal are presented in Table 3 The results presented below have been measured with a ferrofluid for which the nanoparticles were large CoFe 2 O 4 nanospinels. The particles were synthesized using the hightemperature decomposition process of acetylacetonate precursors (acac process). With a seeded-growth approach, we obtained nanoparticles of ∼18 nm, as determined by TEM size, and dispersed in heptane. This ferrofluid has been specifically selected because such large particles possess a blocking temperature T B above room temperature. Therefore, the dry nanoparticles where heptane would have evaporated exhibit a magnetic hysteresis at room temperature at the difference of the ferrofluid in its liquid phase for which the magnetization curve is closed. Hence magnetization curves measured in this sample is a direct indication on the presence of the liquid ferrofluid.

The X-ray intensity transmitted through the sample is calculated using the Beer-Lambert law as: The magnetization curves exhibit an opening of 0.11 T that clearly indicates that the probed nanoparticles are in their dried solid phase.

𝜇( 𝜔) × d = -𝑙𝑛[𝐼( 𝜔)/𝐼 0 ( 𝜔)] (3.

Errors analysis and undertaken corrections

The magnetization curves measurements have shown that the liquid carrier evaporated before it can be measured. I believe that the evaporation occurs when the introduction chamber is pumped. The evaporation is not the consequence of a membrane rupture because no abrupt increase of pressure was observed so that membrane leaks were not detected. Actually, the conception of the membranes proved to be appropriate since the membrane mechanical strength was large enough for Ultra High Vacuum. The evaporation of heptane is very likely due to some tiny leaks at the connection between the sample cell and the sample holder. The connection is ensured by small Viton O-rings and we are presently working on finding new types of connections.

However, we quickly realized that the filling of the liquid cell is the most challenging step of the experimental process. At first there were severe problems during the filling of the sample cell with water-base ferrofluid. This was alleviated by using heptane-based ferrofluid. The lower viscosity of heptane could explained this result. However the filling process was still not an easy and straightforward process. Several attempts were sometimes needed to fill a sample cell. This step involves several issues that belong to the microfluidic domain. As our group does not have much expertise in this domain, the design of the liquid cell was far from perfect. Two major but also independent issues have been identified:

• The microfluidic setup for the liquid flow was not optimized for a straightforward and easy filling of the cell,

• The connections between the membrane chips and the liquid flow ports were not sealed enough.

For the microfluidic setup, we have begun a collaboration with Gabriel David from SOLEIL who is an expert in microfluidic experiences for biomedical applications. We have presently reviewing the whole design of the liquid cell with a special attention to a more efficient filling and to removing all possible sources of leaks. For this new prototype, the sample cell would include microchannels that could be directly plugged to the sample holder for a easy and straighforward connection with the liquid flow circuit. A schematic, tentative model of the sample cell <and its plugging setup is shown Figure 3.2.13.

Liquid Cell for hard X-ray MCD environment

Introduction

In the hard X-ray range, the development of a cell available for liquids and that would allow the measurement of XAS or RIXS is favored thanks to the large penetration depth of the hard X-rays. This makes the development of such cells much easier than in the case of the soft X-rays so that liquid cells have been combined with high pressure experimental setups, with cryostats or with built-in electrodes for electrochemistry. [133][134][135] As they do not present serious experimental issues, cell designs (for hard X-rays environment) to study liquid at room conditions have rarely been the subject of publication. 133 Publications reporting on the detailed construction are often related to setup requiring the application of high pressure or temperature. 135 However, many groups have reported hard X-ray measurements of liquids suggesting that liquid cells compatible with the experiment were implemented. ID26 is a ESRF beamline dedicated to RIXS experiments in the hard X-ray range where the RIXS-MCD experiments have first been recorded. In this photon inphoton out magnetic spectroscopy, the magnetic field is delivered by a 1.5 T electromagnet delivering a magnetic induction parallel to the propagation vector of the incoming photons.

We wanted to measure RIXS-MCD for ferrofluids in their liquid phase or in their frozen phase so that a customized liquid cell had to be developed. The different experimental constraints for RIXS-MCD measurements are as follow:

• the cell has to be compatible with the ferrofluids and their solvent,

• the air gap between the coils of the electromagnet is less than 2 cm,

• any temperature between 300 K and 4 K should be available,

• incoming and outgoing X-rays make an angle of 90°so that the head of the liquid cell has to provide a wide access.

The design of the liquid cell has been developed at the ESRF under the joint impulse from ID26 staff and our group. The liquid cell has been machined by the Sample Environment group which is expert in cryogenic inserts. In close collaboration with Mauro Rovezzi from ESRF, I have assembled the liquid cell prototype, tested it was leak free, checked the temperature range that was available and exercised on how to fill and purge the liquid cell. After several tries and errors, I finally developed a robust experimental protocol that has been widely applied by any other team desirous to use the liquid cell.

Experimental setup

Sample holder

The liquid cell is at the extremity of a copper sample holder that is mounted on a cryostat.

A parallelepiped cavity is machined into the copper sample holder. The upper side of the cavity is hermetically sealed by a 50 𝜇m Kapton foil. The Kapton foil is glued by an epoxy glue activated at 80 °C and during the gluing process, we take care to avoid any air bubbles formation within the glue. The sample holder parallelepiped cavity is filled by injecting ferrofluids with a syringe through a side hole (see Figure 3.

Sample preparation

Each sample was prepared by injecting a small amount of ferrofluid (∼0.1 mL) using 1 mL syringes with 0.8 mm needle diameter. The injection of the liquid is a tricky part where two conditions have to be fulfilled to obtain an homogeneous sample with no bubbles :

• it has to be a one-step filling procedure,

• the needle has to enter the square cavity and inject at less than 1 mm from the Kapton layer.

Thus any bad move with the needle damages the thin Kapton window and the lengthy sample preparation has to be re-started from scratch.

Cold Finger

The sample holder is screwed to the cold finger of a cryostat that works with a continuous flow of liquid helium. The cryostat consists of two heat exchangers. The main heat exchanger (the cold plate) cools the copper sample holder and a secondary heat exchanger recovers the remaining enthalpy of the returning helium gas for cooling the head shield.

The cryostat and the sample are protected from the outside by a hood that allows to maintain the cryostat head and the sample in a secondary vacuum, 10 -7 mbar. The hood is at 300 K and the thermal shield protects the main exchanger but not the sample itself from the thermal radiation from the surrounding. The temperature is set by controlling the helium flow rate of the cryostat through the helium needle valve. The exhaust helium is pumped by a turbo pump and the exhaust pressure is maintained in the 30 mbar range.

The measurement of temperature is made by two platinum probes, T A that is located in the main exchanger and T B that is embedded in a grove very near the liquid cavity.

Experimental results

RIXS and RIXS-MCD measurements at the Mn and Co K -edges were successfully performed on seven different ferrofluids in total. The incident energy was selected using a pair of Si(311) crystals. The intensity of Mn and Co K𝛼 emission lines (of the inelastically scattered beam) was analyzed using a set of four or five spherically bent Ge (111) and Si (531) crystals, respectively. The diffracted emission was detected by an Silicon Avalanche

Photo Diode where the sample, the analyzers and the APD detector are mounted in the

Conclusion

In order to investigate ferrites nanospinels present in ferrofluids, I have contributed to the development of two original setups. On DEIMOS beamline at SOLEIL, we wanted to develop a flow-through liquid cell compatible with soft X-ray MCD environment, i.e. UHV conditions and limited soft X-rays penetration depth. The design of the liquid cell has been implemented with the support of the Bureau d étude from SOLEIL. The liquid flowthrough cell was designed to detect the transmitted X-rays and the Total Fluorescence

Yield for experiments at 300 K. The thickness of the liquid sample was limited to 500 nm and the liquid could be circulated in the measuring position allowing possible in situ changes. The transmission mode was successfully validated. However we were not able to preserve the liquid phase in the sample cell due to a misconception of the membrane sealing. By working with a microfluidic expert, we gained better insights on the drawbacks of the first design and a new prototype is under construction for future experiments.

On the ID26 beamline at ESRF, I developed a static liquid cell in collaboration with Mauro Rovezzi. The liquid cell was implemented to be compatible with RIXS-MCD measurements in the fluorescence mode and adapted to the specific geometry of the beamline.

In addition, the sample holder could be mounted on a cold finger developed by the Sample Environment group from ESRF for experiments between 25 K and 300 K. We have been using this liquid cell for three different beamtimes and we could record successful measurements on different systems that are presented in Chapter 5. For those measurements, probing the nanoparticles in the ferrofluids allowed to preserve the magnetic interactions occurring between the nanoparticles. This aspect is crucial in binary systems for example (see Section 5.4). The liquid cell setup for RIXS-MCD measurements is currently available on ID26 beamline and open to other users. Indeed, magnetic X-ray spectroscopy measurements in liquids can open new exciting perspectives to a large community. For example, magnetic complexes based on organic species that are not always stable in the air could benefit from measurements in liquid environment. 136,137 Chapter 4

Magnetic Anisotropy

Controlled by Synthesis Routes

Introduction

In the present chapter, we aim at tailoring nanoparticles so that they present interesting magnetic properties such as large magnetic anisotropy inducing large coercive fields or large remnant magnetizations. The nanoparticles are iron bearing spinels of chemical formula MFe 2 O 4 and they are known to be soft magnets when M=Fe. Divalent cobalt ions in octahedral symmetry are true makers of magnetic anisotropy, so that cobalt ions have been introduced into or grafted at the surface of the nanospinels. In the present chapter, we have investigated the effects of divalent cobalt ions on the nanoparticle magnetic anisotropies via two different approaches :

(i) cobalt ions are introduced into the spinel structure of the nanoparticles and the magnetic anisotropy can be modulated by a rationalized approach of various synthesis routes.

(ii) cobalt ions present in molecular complexes can be grafted at the surface of soft magnetic nanoparticles in order to increase the magnetic anisotropy.

Coprecipitation synthesis

Early ferrofluids of magnetite (Fe 3 O 4 ) were obtained by grinding or ball milling bulk magnetite. [START_REF] Papell | Low viscosity magnetic fluid obtained by the colloidal suspension of magnetic particles[END_REF][START_REF] Rosensweig | Ferrofluid compositions and process of making same[END_REF][START_REF] Berkowitz | [END_REF] These top-down methods offer challenges to have real control of the nanoparticles size, morphology or stoichiometry. Although many potential applications of ferrofluids could be foreseen, such a synthesis route did not allow any adjustment of the fine properties of the particles to be tuned to the requirement of specific systems.

During the 80's, R. Massart developed the so-called coprecipitation synthesis which allows the production of ionic magnetic fluids constituted of nanoparticles stabilized in alkaline or acidic medium with long-term stability. 140 Indeed, the stabilization of particles in the fluid is obtained by introducing electrostatic repulsions at the surface of the nanoparticles.

The chemical process rely on the wet chemical precipitation of precursors of metallic salts by means of alkaline solutions (NaOH or NH 4 OH for example). The synthesis of spinel ferrites nanoparticles can be thus described by the reaction from equation 4.1.1:

M 2+ + 2Fe 3+ + 8OH --→ MFe 2 O 4 + 4H 2 O (4.1.1)
The synthesis of cobalt ferrites is carried out following the same principle, but the reagent have to be brought to the boil as such:

Co 2+ + 2Fe 3+ + 8OH -ΔT --→ CoFe 2 O 4 + 4H 2 O (4.1.2)
The coprecipitation synthesis developed by R. Massart is a soft chemical (the highest temperature reached during the synthesis is 100°C at atmospheric pressure for the synthesis of cobalt ferrite nanoparticles) and low-cost process that allows the efficient production of large amount of ferrofluids. The quality of the coprecipitation procedure contributed to its rapid adoption by the chemists for the ferrofluids synthesis. [141][142][143][144] However, particle were limited to size ranging from 8 to 11 nm with this method and the stabilization strat-egy leads to the dispersions of nanoparticles in aqueous media in only alkaline or acidic pH. 145 Then several authors brought modifications and improvements of the synthesis to obtain a larger range of nanoparticles sizes (from ≈2 nm up to ≈40 nm) 141,[146][147][148] and their dispersion in water at neutral pH [149][150][151] . This latter improvement had a significant impact since it opened the biomedical field to ferrofluid applications. [152][153][154] The control of the nanoparticles size allowed a first-order tailoring of the magnetic properties since it was observed a fine dependence of nanoparticles diameter with the coercive field and the magnetization at saturation. [155][156][157] Indeed, numerous publications showed the variations of the magnetization properties of the nanoparticles as a function of their sizes, their morphologies or their chemical compositions. [158][159][160][161] The effect of magnetic disorder at the surface or inside the nanoparticles could be related to the parameters controlled via the synthesis route. [162][163][164] Despite an abundant literature, the impact of one single parameter is often difficult to determine because it generally cannot be tuned independently from the others.

Influence of the synthesis process

Starting from the coprecipitation synthesis, we studied the influence of the synthesis route on the crystallographic structure of cobalt ferrites by means of XMCD that is a local probe of the magnetic order. PHENIX laboratory has a long-standing expertise in the synthesis of ferrofluids and particularly in the coprecipitation route. We have synthesized a set of six cobalt ferrites nanoparticles with stoichiometry close to CoFe 2 O 4 and with sizes ranging from 7 nm to 21 nm. For the systems under study, we wanted to answer the following questions :

(i) where are located the Fe and Co ions inside the spinel structure (i.e. Tetrahedral vs Octahedral sites)?

(ii) what is the nature of the magnetic couplings between the various ions in the nanoparticles?

(iii) do we have access to the magnetic disorder that might be present inside the nanoparticles or at the surface?

(iv) can we ascribe the magnetic properties of CoFe 2 O 4 to a single parameter that could be modulated by the synthesis process?

In Paper I, entitled "Magnetic Anisotropies and Cationic distribution in CoFe 2 O 4 nanoparticles prepared by coprecipitation route : influence of particles size and stoichiometry", we aim to establish the effect of the different steps of the coprecipitation synthesis on the resulting magnetic properties of the nanoparticles with a special attention to the crystallographic sites occupied by cobalt ions.

In Paper II, entitled "Small CoFe 2 O 4 magnetic nanoparticles in ferrofluids, influence of the synthesis on the magnetic properties", we have studied the effects of three different synthesis routes on the magnetic anisotropies of the nanoparticles. Indeed, despite the advantages offered by the coprecipitation route, the obtained nanoparticles are in a metastable state and this limits the possibility to improve their magnetic properties.

More recently, two other syntheses at higher temperature have been developed and be-came widespread processes (see section 1.4):

(i) the so-called "polyol process" which consists in a forced hydrolysis of M 2+ and Fe 3+ salts dissolved in a polyol medium, 165 (ii) the so-called "acac synthesis" which consists in the high-temperature decomposition of complexes of metallic precursors with acetylacetonate ligands. 166 In Paper II, we compare the three routes (i.e. coprecipitation, polyol or acac syntheses) and their impact on the magnetic properties of small nanoparticles with similar sizes. My results confirm the conclusions obtained by others in previous pieces of work.

Nanoparticles functionnalization

Paper III, entitled "Enhancing the magnetic anisotropy of maghemite nanoparticles via the surface coordination of molecular complexes" presents another strategy to modulate the magnetic anisotropies of nanoparticles. Cobalt complexes are grafted at the surface of maghemite nanoparticles (𝛾-Fe 2 O 3 ). The maghemite nanoparticles are synthesized following the coprecipitation process described in Section 4.2. The bare particles do not present any large magnetic anisotropy as can be expected for nanoparticles containing only Fe 3+ ions in high spin configuration. The Co complexes have divalent cobalt ions in 6-fold coordination so that one expects a large magnetic anisotropy stemming from spinorbit coupling acting at first order accompanied by a substantial orbital magnetic moment.

The synthesis strategy was developed by Yoann Prado, Laurent Lisnard, Benoît Fleury, Vincent Dupuis and Jérôme Fresnais from UPMC. In collaboration with them, I have performed XAS and XMCD measurements at the Co and Fe L 2,3 edges on the bare and the decorated maghemite nanoparticles. This piece of work is not at the center of my thesis and my contribution was to bring my expertise in the analysis of XAS and XMCD signals of nanospinels. Our measurements revealed the nature of the magnetic coupling between Co 2+ ions and Fe 3+ ions. Paper III, has been published in Nature Communications. 167

Introduction

Ferro/ferri magnetic materials present attractive properties for modern applications due to the magnetic anisotropies that arise from the system. Even more enhanced magnetic properties, not shown in the bulk, appear in the nanoscale of ferro/ferri magnetic materials. Such enhanced magnetic properties associated to the nanoscale range make them good candidates for applications in the biomedical field or for magnetic devices. 168 Approaches to use magnetic nanoparticles in biomedical applications rely on the large magnetization at saturation and on the large remanent magnetization of ferromagnetic materials that are mandatory for Magnetic Resonnance Imaging (MRI) 169 while advances in anticancer treatment take the advantage on the specific loss power of magnetic nanoparticles at radiofrequencies 42 . In the field of magneto-optical devices, integrated optics 170 , core optical fibers 9 or tunable beam splitter 171 incorporate magnetic nanoparticles for their tunable magneto-optical properties. For such applications, ferrites with a spinel structure MFe 2 O 4 (with M = Fe, Co, Mn, Ni, Zn...) present appealing properties. 172 Among them cobalt ferrite (CoFe 2 O 4 ) is a promising magnetic material for high-storage devices 173 taking advantage of its large magneto-cristalline anisotropy energy 174 , associated with a large coercive field H 𝑐 , and a moderate magnetization at saturation M S . However the magnetic properties of CoFe 2 O 4 nanoparticles can be strongly influence by the morphology, the size, the chemical composition and the crystallographic structure. Ultimately, processes used to synthesize nanoparticles can be adjusted to the requirement of the application. In particular, chemical processes offer to tune a quasi-infinite number of parameters (chemical agents, pH, temperature, atmosphere and so on). During the last decades, various preparation modes of magnetic nanoparticles in fluids have been adopted. [175][176][177][178][179] Among them, the coprecipitation route 140 developed by R. Massart is a highly reliable, very convenient and cost-effective process to obtain well-crystallized and long term stable spinel nanoparticles dispersed in aqueous media. It is already known that the acidity of the medium or the process temperature can influence the crystallographic order, the size, the shape and the stoichiometry of the nanocrystals, as well as the valence states of the cations. 180,181 However, so far we know, it does not exist any systematic study linking the synthesis conditions of coprecipitation to the different magnetic properties of the nanospinels obtained.

To obtain a clear picture of the relations existing between the coprecipitation synthesis conditions of iron-cobalt nanospinels and their magnetic properties, we have investigated six different sets of iron-cobalt nanospinels with different size and stoichiometry. The present study focuses on Co 𝑥 Fe 𝑦 O 4 nanoparticles with sizes ranging from 7 to 21 nm and with molar ratios X M equal to either 25% or to 33%. The cobalt molar ratio X M is defined as follow : The inversion degree illustrates the crystallographic disorder. In the case of cubic spinels structure, the crystallographic order is deeply related to the magnetic anisotropies arising from the system. The crystallographic order of the nanoparticles have been investigated in various studies where the different cations distribution among T 𝑑 and O ℎ sites can be associated to different synthetic processes. Depending on the preparation mode of CoFe 2 O 4 nanoparticles, inversion paramaters from 0.20 to 0.96 have been obtained. 20,[182][183][184][185] In parallel, Peddis and co-workers also established the major role played by surface spin-canting in the magnetic properties of small nanoparticles. 162,182 . Among the technics used to characterized the cationic distributions in the spinels structure, if

𝑋 𝑀 = [𝐶𝑜] [𝐶𝑜] + [𝐹 𝑒] ( 4
Mössbauer provides good results, more recently the composition and structure of Co-doped maghemite 𝛾-Fe 2 O 3 nanoparticles have been studied by Extended X-ray Absorption Fine

Structure at the Fe and Co K-edge 186 and X-ray Absorption Near-Edges Spectra was used to study nanoparticles with different sizes prepared in a polyol medium 156 . In the present study, we investigate iron-cobalt nanospinels with X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD). These element selective spectroscopies have already been applied to investigate magnetic and cationic structure of such system. 14,163,[187][188][189][190][191][192][193][194][195][196][197][198][199][200][201][202] As local probes of the electronic and magnetic properties, XAS and XMCD allows to solve the crystallographic structure and disentangle the magnetic signature of Co 2+ and Fe 3+ in CoFe 2 O 4 nanoparticles. In the following, we first describe the various coprecipitation synthesis routes that allowed to obtain the nanoparticles with variable sizes and X M ratios, and then the characterization methods are detailed. Magnetometry measurements and XAS and XMCD results are presented and show that the magnetic properties of the nanospinels are not simply given by their composition and their size but are also governed by the organization on the cationic sublattices.

Experimental

Synthesis The coprecipitation synthesis yields nano-clusters dispersed in aqueous media with sizes ranging between 5 to 25 nm and different stoichiometries. We investigate here synthesis routes benefiting from significant improvements and new added treatments.

In the following, the samples are named CoFeX_Y where X is the value of the molar ratio X M and Y is the diameter in nm of the iron-cobalt nanospinels. The list of the six nanospinels under study is reported in Table 4.2.1.

The synthesis described in this paragraph leads to nanoparticles with a mean size of 9 nm and a molar ratio X M =25 %, named CoFe25_9. The process is detailed in 5 steps.

Initially, precipitation of hydroxides were made at 100˚C as described by Tourinho et al.. 203 We modified this one-step procedure into two steps further described (Step 1 and

Step 2).

Step Step 3-Dispersion in acidic medium. To eliminate spurious non magnetic and amorphous hydroxydes, nitric acid (200 mL, 2 mol.L -1 , pH 2) is added to the suspension.

This step favors the dispersions of cobalt ferrites, as (-O -) anions initially at the surface after Step 1 are protonated and give (-OH + 2 ) species. Successive washing of the precipitate with acetone are used to remove the excess of acid. As cobalt ferrites are not necessary stable in acidic media, further treatments are used to prevent their degradation. 143 Step 4-Stabilization. Following the Massart process, ferric nitrate (200 mL, 0.3 mol.L -1 ) is added and the solution is kept boiling during 30 min. The nitrate treatment allows the stable dispersion of cobalt ferrites nanoparticles in acidic medium but leads to the molar ratio X M =25 %. 145 Step 5-Dispersion in aqueous solvent. The nanoparticles obtained are washed several times with acetone and ether and dispersed in the aqueous solvent, which yields a colloidal solutions of cobalt ferrites nanoparticles.

Steps 1, 2 and 4 are modified in order to produce the five other nanospinels than CoFe25_9. A scheme that details the steps followed to obtain the six samples is given in Supplementary Informations (Figure 4.3.1).

Step 1 ′ . In order to obtain smaller cobalt ferrites nanoparticles, hydroxides precipitation is performed in the presence of complexing species. 149 Step 1 is modified by adding tartrate ions to the mixture of Co(NO 3 ) 2 .6H 2 O and Fe(NO 3 ) 3 .6H 2 O before the addition of sodium hydroxide. Step 1 ′ is used instead of Step 1 to obtain CoFe25_7 ferrofluid.

Step 2 ′ . From the litterature, larger size of nanoparticles can be obtained with hydrothermal treatment. 147 After Step 1, the mixture is transferred into an autoclave reactor set at 200˚C for 1 hour. Step 2 ′ is used instead of Step 2 to obtain CoFe33_13 ferrofluid.

Step 2 ′′ . The duration of the hydrothermal treatment influences the size of the nanoparticles. 148 In Step 2 ′′ , the hydrothermal treatment at 200˚C is performed during 24 hours in order to obtain larger particles. Step 2 ′′ is used instead of Step 2 to obtain CoFe33_21 ferrofluid.

Step 4 ′ . Chemical composition of X M =33 % can be obtain for nanoparticles further dispersed in acidic medium with a cobalt nitrate treatment. 204 Step 4 is modified by adding a solution of Co 2+ nitrate (200 mL, 0.3 mol.L -1 ) and the mixture is boiled for 30 minutes. Step 4 ′ is used in a fraction of the synthesis batch of CoFe25_9 after Step 3 to obtain CoFe33_9.

Step 4 ′′ . To obtain a stable ferrofluid at neutral pH, hydroxyl groups at the surface of the particles are exchanged with ligands that ensure long-term stability of ferrofluids combining steric and electrostatic repulsions. 149 X-ray Magnetic Circular Dichroism. XMCD has first been observed by G. Schütz at the K -edge of iron. 59 Since then, XMCD at L 2,3 edges has become a powerful method to probe the 3d magnetic orbitals of transition metal ions. XMCD possesses the chemical and orbital selectivities of XAS and is sensitive to the site symmetry and the valence of the absorbing atom. XMCD is a magnetic technique that can mostly be explained in the electric dipole approximation so that it chiefly yields information on the orbital magnetic moment of the absorbing atom. When spin-orbit is large enough as it is the case for spin-orbit coupling acting on the 2𝑝 core-hole, one can also gather information on the spin magnetic moment. As a consequence, it is a unique tool to separate contributions from the different magnetic ions in a ferrimagnetic system such as iron-cobalt nanospinels. the DEIMOS cryo-magnet. 85 Measurements are performed on dried magnetic nanoparticles. For XAS the isotropic absorption cross-section is taken as

𝜎 𝐼𝑠𝑜 = 𝜎 -+ 𝜎 + 2 .
This assumption is fully satisfied for powders of nanoparticles with a cubic crystallographic structure.

By following the variation XMCD intensity as a function of the external magnetic induction, one can measure element-specific magnetization curves. One can select energies that correspond to specific spinel sites such as 707. 98 XAS and XMCD spectra. In Figure 4 in O ℎ symmetry . All XAS spectra have been normalized to 1 at the maximum of the L 3 edge and the XMCD spectra have been plotted with respect to the maximum of the isotropic XAS signal. The assignment of the spectral features for Fe and Co L 2,3 edges is confirmed by Ligand Field Multiplet calculations that have been performed following procedures detailed in previous papers. 14,207 The calculated XAS and XMCD signals can be found in Supplementary Informations (Figures 4.3 4.3.1). In iron-cobalt nanospinels, the magnetic anisotropy mainly arises from the Co ions. 209 For the four different samples with X M =33%, the proportion between iron and cobalt ions is constant so that an increase of coercivity cannot be attributed to an increase of Co ions concentration. The Co anisotropy depends on the sites it occupies.

Results and discussion

The origin of the coercivity for Co ions comes from a strong interplay between spin-orbit coupling and crystal field in O ℎ symmetry. Indeed the electronic configuration for Co 2+

ions is 3d [START_REF] Li | [END_REF] .When the Co 2+ ion is in a 𝑇 𝑑 site, its configuration is 𝑒 4 𝑡 3 2 in the ground state where the 𝑒 orbitals are at lower energy than the 𝑡 2 ones. The corresponding spectroscopic term is 4 𝐴 2 with no orbital degeneracy thus no orbital moment is expected. On the opposite, when the Co 2+ ion is in a 𝑂 ℎ site, its configuration is 𝑡 5 2𝑔 𝑒 2 𝑔 in the ground state where the 𝑡 2𝑔 orbitals are at lower energy than the 𝑒 𝑔 ones. The corresponding spectroscopic term is 4 𝑇 1 which is split by first-order spin-orbit coupling and a large magnetic moment is found in the ground state. 210 Moreover, 𝑂 ℎ Co 2+ undergoes a strong Jahn-Teller distortion. In the spinel structure, the exact symmetry for the 6-fold site is not O ℎ but D 3𝑑 so that Jahn-teller distortion is fully compatible with the crystal structure and the interplay between spin-orbit coupling and crystallographic distortion is then at the origin a large orbital magnetic moment and magnetocrystalline anisotropy for Co ions in distorted O ℎ symmetry. 211 Many studies have reported discrepancies of the magnetocrystalline anisotropy observed between the bulk and the nanoparticles in terms of spin-canting. [212][213][214] . Spincanting arises from the subtle interplay between the chemical disorder, that modifies the superexchange interactions, and the formation of an external layer of non-collinear spin arrangement at the surface of the nanoparticles where the ion coordination symmetry is broken. 182,183,215 . In the present case, we have measured magnetization curves by setting the monochromator at energies specific for Fe ions on O ℎ and T 𝑑 sites and for Co ions on O ℎ and T 𝑑 sites. The magnetization curves for one specific sample clearly show the expected antiferromagnetic coupling between O ℎ and T 𝑑 sub-lattices (See Supplementary Informations Figure 4.3.4. However, the shape of the curves are exactly the same, so that is no indication for any specific magnetic disorder originating from surface defects. On the other hand, there is a clear indication that the synthesis route that imposes the particle From the isotropic and XMCD spectra, we know that when the particle size increases, The smaller CoFe25_7 particles present a slightly larger coercive field and a much smaller remanent magnetization accompanied by a slanted shape for high fields.

the
The Co L 2,3 edges spectra of the CoFe25_7 and CoFe25_9 samples are presented in Influence of the cationic molar ratio X M . From the two previous series X M =33 % and X M =25 %, it is clear that the knowledge of the size of the nanoparticles does not give non ambiguous clues concerning the expected magnetic anisotropy or the coercive field.

One important physical parameter that scales with the magnetic anisotropy is the content of Co ions in the O ℎ sites. It then appears interesting to compare the magnetic properties of the two samples with the same size (9 nm) but belonging to the two different series X M =33 % and X M =25 %. Sample CoFe25_9 is obtained from the same synthesis batch as CoFe33_9 except that an excess of Fe 3+ nitrate has been added in the case of CoFe25_9 while Co 2+ nitrate were used in the synthesis of CoFe33_9 (see Supplementary information or oxy-hydroxydes in the core of CoFe 2 O 4 that would contribute to lower the X M value. 204 The stoichiometry of the core would be then X M =33% with a distribution of the Co ions in O ℎ sites that is similar to the one observed for CoFe33_9. Another evidence of a core/shell structure for CoFe25_9 nanospinels is brought by calculated sites occupancy performed in the LFM theory (See Table 4 is similar to CoFe33_9 with a surrounding 𝛾-Fe 2 O 3 shell, one would indeed expect that both samples have very similar magnetic properties despite different apparent stoichiom-etry. On the contrary CoFe25_7 is obtained by blocking the growth of the nanoparticles by adjunction of complexing species agent (tartrate ions). For these very small particles, one would observe a partial, non-congruent dissolution of Co and Fe so that the initial X M =33% stoichiometry is reduced to X M =25%. The complexation for this very small particles coupled to a preferential dissolution T 𝑑 Co ions would then lead to a larger concentration of Co ions in O ℎ sites. From a simple geometric estimation, one determines that a surrounding 𝛾-Fe 2 O 3 shell of ≈ 0.5 nm accounts for the change of stoichiometry.

Conclusion

Magnetic sol of CoFe 2 O 4 nanoparticles with different sizes are obtained from the versatile coprecipitation process. Playing with the temperature treatments or with the adjunction of tartrate ions, Fe nitrates or Co nitrates, it has been possible to modulate the size of nanoparticles between 7 nm and 21 nm. For most synthesis the expected stoichiometry of 1 Co ion for 2 Fe ions has been obtained, and in two cases the stoichiometry was partially lowered to 1 Co ion for 3 Fe ions. The main outcome of the present study is that neither the size, nor the stoichiometry can determine the magnetic properties such as the coercive field nor the remanent magnetization. XMCD allowed the determination of the proportion of Co ions in O ℎ sites and it is found that this is the parameter governing magnetic coercivity.

In addition, the comparison of the data for both Fe and Co L 2,3 edges showed that some of the particles were very likely built from a core with high Co concentration surrounded by an iron rich shell (probably 𝛾-Fe 2 O 3 ). Such study could be extend to investigate the intimate relations existing between the magnetic properties and crystallographic structures of magnetic nanoparticles obtain with others synthesis processes. Inferences to be drawn would helped chemists for the development of rationalized synthesis.

Supplementary Information of Paper I

Introduction

Nanoparticles composed of ferrite nanospinels are used in various applications ranging from medicine to optical devices. 45,216 Among these nanospinels, cobalt ferrite (CoFe 2 O 4 ) is a promising material because in the nanosize range it presents a high magneto-crystalline anisotropy energy and a high magnetization saturation. These appealing properties are particularly necessary for hard record devices. 173 For such applications, overcoming the so-called superparamagnetic limit 50 is one of the current biggest challenges. In this direction, various strategies have been developed such as multi-shell structuration 217,218 , particle doping 219 , or coordination of molecules to nanoparticles surfaces 167,220 . However, it is well-known that the preparation route of magnetic nanoparticles can influence in many ways the morphology, their chemical composition or the crystallographic structure which in turn strongly impact the magnetic properties. Among all possible synthesis routes, soft chemical synthesis has become a very convenient way to obtain magnetic ferrite nanospinels. Various synthesis processes have been developed to obtain ferrofluids with long-term stable nanoparticles. In this study we choose three different synthesis that are very common in the preparation of ferrofluids : (i) the coprecipitation process is a cost-effective and versatile synthesis that allows to obtain a large amount of nanomaterial 140 , (ii) the polyol process allows original structures of flower-shaped nanoparticles with enhanced magnetic properties but allows less control on the crystallographic structure 221 and (iii) the thermal decomposition route is found to be a very effective method to prepare monodisperse nanoparticles with controlled morphology, although involving higher temperature and more expensive reactants 166 . In the present paper, we investigate the magnetic properties of CoFe 2 O 4 nanoparticles with diameter ranging between 6 and 7 nm and that have been synthesized by the three different pathways. Correlations between the original effects of a synthesis process on the magnetic properties of CoFe 2 O 4 nanoparticles obtained has been established by several groups. [222][223][224][225] In particular, small spherical CoFe 2 O 4 nanoparticles synthesized in polyol medium were found to have a saturation magnetization comparable to that of the bulk structure. a unique tool to probe the 3d magnetic orbitals of the transition elements. 13 The method provides a chemical selectivity used to disentangle the magnetic signatures of the cobalt and iron ions. In addition, XMCD is also sensitive to the site symmetry of the absorbing element. The cationic distribution of cobalt and iron between octahedral (O ℎ ) symmetry sites and tetrahedral (T 𝑑 ) symmetry sites in the nanospinels structures is determined with the investigation of the 6 nm CoFe 2 O 4 nanoparticles with XMCD. The influence of the synthesis on the crystallographic structure and the magnetic properties of the nanoparticles is thus revealed.

Experimental

Synthesis Co-coprec sample. The iron-cobalt nanospinels Co-coprec were obtained by using a modified Massart process. 203 It consists in precipitating Co 2+ and Fe 3+ hydroxydes followed by a heating at boiling temperature to obtain nanoparticles with mean size of 11 nm. In order to obtain smaller nanoparticles, the Massart process was slightly modified by adding complexing species (tartrate ions) in the mixture of cobalt and ferric nitrates before the addition of sodium hydroxide. The different steps of the synthesis are reported elsewhere. 149

Co-acac sample. Following the route of thermal decomposition of metal precursors developed by Sun et al. 166 , we have synthesized a second set of small nanoparticles of CoFe 2 O 4 named Co-acac. The different steps of the so-called acac synthesis are reported elsewhere 228 .

Co-polyol sample. The third set of small particles of iron-cobalt nanospinels is obtained by using the polyol processwhich consist in a forced hydrolysis of Fe 3+ and Co 2+ mixture in a polyol solution. 176 Depending on the polyol used for the synthesis, the morphology of the nanoparticles obtained differs. When the reaction is realized in diethylene glycol (DEG) small spherical nanoparticles are obtained. 165 Methods Chemical composition of cobalt and iron of the nanoparticles was measured by Atomic Absorption Spectrometry using Perkin Elmer Analyst 100 with an air-acetylene flame at a mean temperature of 2300°C. Table 4.4.1 presents the ratio of the cationic concentrations of each sample calculated using the molar ratio X M as detailed in equation 4.4.1 : The size of crystallites domains were calculated on the mean peak (311) using the Scherrer equation. 205 The XRD patterns are presented in where 𝜎 𝐿 (respectively 𝜎 𝑅 ) is the absorption cross section measured with left (respectively right) helicity. The measurements were performed on magnetic nanoparticles powders, therefore the XAS spectra were obtained by taking the isotropic absorption cross-section as:

𝑋 𝑀 = [𝐶𝑜] [𝐶𝑜] + [𝐹 𝑒]
𝜎 𝑋𝐴𝑆 = (𝜎 -+ 𝜎 + )/2 (4.4.5)
To extract quantitative determinations of the cationic distributions of the iron-cobalt nano-spinels, simulations of the XAS and XMCD signals were performed using the Ligand Field Multiplet theory developed by Theo Thole. 15 The parameters used for the calculations were reported in Hochepied et al. 14 for the Co 2+ ions in CoFe 2 O 4 and in Carvallo et al. 208 for the Fe 2+ and Fe 3+ ions in magnetite. The weighted sums of the calculated spectra were fitted to the experimental ones in order to obtain quantitative sites distributions of the Co 2+ and Fe 3+ ions among O ℎ and T 𝑑 sites.

Results and discussion

Size, morphology and chemical composition Iron-cobalt nanospinels from the different synthesis routes present similar mean sizes: 6.8 nm for the Co-coprec nanoparticles,

Conclusion

Small magnetic nanoparticles of iron-cobalt nanospinels were obtained through three different synthesis processes. The nanospinels obtained were found to have different chemical compositions, stoichiometries, and shapes. The coercivity measured in the three samples

Introduction

In single-domain superparamagnetic nanoparticles, magnetic anisotropy has a direct impact on the magnetization, its remanence, reversal and relaxation. Magnetic anisotropy is therefore a key parameter in the preparation of magnetic nanocrystals designed for highdensity data storage applications or for medical applications 173,[229][230][231][232][233][234] . For such applications, achieving a controlled modulation of the magnetic anisotropy for a given size of crystals represents thus one of the most efficient ways to improve and tune their magnetic properties. For example, the optimization of the specific loss power of nanocrystals for magnetic hyperthermia and the comprehension of the interplay between magnetic anisotropy and magnetization is of crucial importance for applications in nano-medicine. 217,235 On the other hand, the fabrication of small magnetic nanocrystals displaying high blocking temperature while maintaining magnetic bistability-that is, large coercive fields-remains a considerable challenge aimed at overtaking the so-called superparamagnetic limit and increasing data storage densities. [START_REF] Skumryev | [END_REF] Different chemical approaches have been used so far to alter the magnetic anisotropy of single-domain magnetic nanoparticles: particle doping or formation of alloys 219,[236][237][238] , coordination of solvent or organic molecules to the nanoparticles surface 220,239,240 , preparation of core-shell systems incorporating highly anisotropic components 217,218,235,237,[241][242][243][244][245] and insertion of the nanoparticles into magnetic host matrices [START_REF] Skumryev | [END_REF]246 . Herein, we report a strategy for the preparation of anisotropically enhanced magnetic nanoparticles. Our synthetic strategy is based on the direct coordination of magnetic molecular complexes to the surface of the nanoparticles. Using molecular complexes as the enhancing unit is a straightforward approach to improve the nanoparticles properties and it also represents a very advantageous functionalization tool. Indeed, coordination chemistry with its great versatility allows the design and the use of specific complexes where both the local ion anisotropy and the nature of the coordination sphere are controlled. The use of coordination complexes to achieve surface functionalization will also prevent diffusion of the ions into the particles. Decorating magnetic nanoparticles with molecular complexes is thus equivalent to building a new surface with ions whose environment and hence local anisotropy is predetermined. This represents an efficient way to not only modify but also tune the nanoparticles surface anisotropy, which is known to contribute greatly to the whole magnetic anisotropy and actually be one of its most influential components in small systems. 247,[START_REF] Fiorani | Surface Effects in Magnetic Nanoparticles; Nanostructure Science and Technology[END_REF] Furthermore, investigations motivated by the study of the possible interactions between two magnetic components in hybrid materials made from inorganic nanomaterials and coordination compounds remain scarce. [START_REF] Zoppellaro | [END_REF] In another type of multi-scale hybrid system, it has been shown that the magnetization relaxation of deposited mononuclear complexes can be influenced by a magnetic substrate. 250 Our work, however, is motivated by the opposite phenomena, that is the influence of the complexes on the magnetic behaviour of the nanoparticles. We demonstrate here that the grafting of an adequate magnetic complex-even for a low quantity-on a superparamagnetic nanoparticle leads to a massive improvement of the magnetic properties.

Methods

Preparation of 0a. The solution was prepared according to literature procedures31,32

(5.1 nm, 𝜎 = 0.12, [Fe] = 0.87 M, %m = 6.96%, %v = 1.39%, pH = 1.8).

Preparation of 0b.

A measure of 250 ml of 0a were diluted 10 times with a The solution is placed in a 0.2 ml eppendorf and inserted in the cryostat of the SQUID magnetometer and frozen directly from room temperature to 100K in zero magnetic induction (lowering the rod takes a few seconds) before any measurement. The temperature sweeping rate for ZFC/FC measurements was 2K.min -1 .

Anisotropy constants calculations Anisotropy constants calculations. Following

Tamion et al 251 we have used their semi-analytical model to describe the temperature dependence of the ZFC magnetization and extract an estimate of the magnetic anisotropy energy density K eff .

Having defined a switching-field frequency:

𝜈(𝑇 ) = 𝜈 0 exp[ -𝐾 𝑒𝑓 𝑓 𝑉 𝑚𝑎𝑔 𝑘 𝐵 𝑇 ] (4.5.1)
with 𝜈10 9 Hz the attempt frequency and a characteristic time 𝛿 𝑡 (T), which depends on the temperature sweeping rate (here 2 K.min -1 ), the magnetic moment measured during a ZFC protocol is given by 3) is the initial ZFC susceptibility in the frozen low temperature state and P(D 𝑚𝑎𝑔 ) is the size distribution function taken here as a lognormal with characteristic parameter taken from the TEM characterization of the particles. In the equations above, 𝜇 0 and k 𝐵 denote the magnetic permeability of vacuum and the Boltzmann constant, H is the magnetic field strength, M S is the saturation magnetization of the maghemite and N 𝑇 is the number of magnetically active clusters.

𝑚 𝑍𝐹 𝐶 (𝑇 ) = 𝑁 𝑇 ∫ ∞ 0 𝑀 0 𝑉 𝑚𝑎𝑔 [𝑒 𝜈(𝑇 )𝛿𝑡(𝑇 ) ]𝑃 (𝐷 𝑚𝑎𝑔 )𝑑𝐷 𝑚𝑎𝑔 (4.5.2) where M 0 V 𝑚𝑎𝑔 =𝜇 0 m 2 𝑆 H/(3K eff V 𝑚𝑎𝑔 ) (equation
Using this equation, it is quite straightforward to obtain a calculated ZFC curve and optimize the value of K eff in order that make it best match the experimental data.

57 Fe Mössbauer spectroscopy 57 Fe Mössbauer spectra were performed at 77 K using a conventional constant acceleration transmission spectrometer with a 57 Co source (Rh matrix) and a bath cryostat and at 12 K in a 8 T external field applied parallel to the 𝛾-beam in a cryomagnetic device. The spectra were fitted by means of the MOSFIT program and an 𝛼-Fe foil was used as the calibration sample.

X-ray photoemission spectroscopy analyses (XPS)

At various times of adsorption, t = 30 s, 1 min, 3 min and 30 min, the chamber was evacuated to some 10 -10

Torr, and the sample was analysed by X-ray photoemission spectroscopy using an Omicron NanoTechnology GmbH (Taunusstein, Germany) Argus hemispherical analyser and a monochromatised AlK𝛼 X-ray source (1486.6 eV). After recording a broad range spectrum (pass energy 100 eV), high-resolution spectra were recorded for the N 1s, C 1s, O 1s and Fe 2p core levels (pass energy 20 eV). High-resolution XPS conditions have been fixed: "sweep" analysis mode and an electron beam power of 280 W (14 kV and 20 mA).

The spectra were fitted using Casa XPS v.2.3.16 Software [Casa Software Ltd., UK] and applying a Gaussian/Lorentzian ratio G/L equal to 70/30.

XAS and XMCD measurements XAS and XMCD spectra at Fe and Co L 2,3 edges were recorded on the soft X-ray beamline DEIMOS 85 at synchrotron SOLEIL (France).

Circularly polarised photons delivered by an Apple II undulator are monochromatised by a VGD grating monochromator working in the inverse Petersen geometry. All reported spectra were measured using total electron yield (TEY) detection under a 10 -10 mbar ultra-high vacuum (UHV). The XMCD signals were recorded by both flipping the circular polarisation (either left or right helicity) and the applied magnetic induction (either +6 T or -6 T). The XMCD signal is obtained as the difference

𝜎 𝑋 𝑀 𝐶𝐷 = 𝜎 --𝜎 + where 𝜎 - = [𝜎 𝐿 (B -) + 𝜎 𝑅 (B + )]/2, 𝜎 + = [𝜎 𝐿 (B + ) + 𝜎 𝑅 (B -)]/2, 𝜎 𝐿 (𝜎 𝑅 )
is the cross-section with left (right) polarised X-rays, and B + (B -) the magnetic induction parallel (antiparallel)

to the X-ray propagation vector. This procedure ensured a high signal-to-noise ratio and allowed us to discard any spurious systematic signals. XAS and XMCD spectra were measured for samples cooled to 5 K and in a 6 T applied magnetic induction. The XMCD detected magnetisation curves are the field dependence of the dichroic signal. The XMCD amplitude is recorded at the energy of its maximum amplitude (716.39 eV for Td Fe, 717.02 eV for Oh Fe and 786.96 eV for Co) by quickly switching the circular polarisation thank to the EMPHU undulator available on DEIMOS beamline. Due to the presence of TMA + cations, drop-casts of the nanoparticles solution on gold-coated silicon plate yielded highly hydroscopic deposits. The solid samples were thus prepared by precipitation in acetone.

The solid was suspended in ethanol, drop-casted on a slide, dried on a hot plate and fixed on carbon conductive tape to the copper sample holder. Traces of Fe(II) have been detected on the XAS spectrum of 1 and estimated at 2% of the iron signal. This cannot be the result of an electron transfer from the Co 2+ to the Fe 3+ (Supplementary methods).

Results

Strategy. In combining small superparamagnetic nanoparticles and magnetic molecular complexes we wished to efficiently transmit the anisotropy of the complex to the particles and thus achieve the modulation of the particles magnetic anisotropy. As the magnetic moment originating from mononuclear complexes (few Bohr magnetons) is weak compared to that of a particle (thousands of Bohr magnetons), weak interactions or electrostatic interactions between the complexes and the particles were not suitable for the occurrence of a significant magnetic effect. Therefore, we have targeted the formation of a chemical bond between the complexes and the particles as the best way to promote a strong exchange pathway, namely, a coordination bridge between the metal ions of the complexes and the ones located at the surface of the particles. To successfully coordinate complexes at the surface of nanoparticles and yield an anisotropically enhanced system, we have followed three prerequisites. First, we have selected a magnetic complex made with a polydentate ligand and bearing labile groups. Such a ligand should warrant the stability and the geometry of the complex while the labile groups will promote the coordination of the complex to the particle surface. In this work, we have chosen the complex [Co(TPMA)Cl 2 ] (ref.

TPMA, tris(2-pyridylmethyl) amine, Figure 4.5.2(a)). Because its intrinsic magnetocrystalline anisotropy, cobalt(II) was an obvious choice of metal ion. [252][253][254] The tetradentate TPMA ligand occupies four positions in the cobalt(II) coordination sphere leaving two cis-coordinated chloride groups that are easily substitutable. As the geometry of the mononuclear cobalt(II) complex allows no more than one layer of complex at the surface of the particles, this approach guarantees a low increase of the nanoparticle size. Second, we have chosen magnetic nanoparticles possessing coordinating atoms at their surface that could be synthesized without any stabilizing organic species. The use of bare nanoparticles is indeed necessary to promote the approach of the complexes to the particles surface and then the coordination reaction. The well-known Massart procedure along with a thorough size sorting procedure allows the synthesis of maghemite nanoparticles 𝛾-Fe 2 O 3 with a relatively low polydispersity and a small size. 175,255 The colloidal solutions of the particles are stabilized by the pH-dependent surface charge (positive or negative under acidic or basic conditions, respectively) that prevents the use of any stabilizing organic species.

Finally, it was crucial to maintain colloidal stability during and after the coordination reaction of the complexes at the nanoparticles surface. We took special care to ensure that no aggregation of the particles was occurring in the solution, since it would have led to undesirable magnetic dipolar interactions. Indeed, such inter-particle interactions would have masked the actual impact of the complexes on the nanoparticles magnetic behaviour. and Supplementary Table 1). Sample 1, which corresponds to the nanoparticles functionalized by the addition of ca. 60 complexes per particle in the first synthesis step, shows a similar increase. This can be ascribed to the coordination of the complexes and to the presence around the particles of TMA + counterions, which accompany the modification of the nature of the surface charge (from positively to negatively charged). Indeed, for bare nanoparticles, DLS shows a similar increase of the hydrodynamic diameter (from 7.3 to 9.5 nm) when performing the brutal pH change in the absence of complexes: passing from 0a (pH 2.4) to the basified colloidal solution (sample 0b, pH 11) with the addition of TMAOH. For the functionalized nanoparticles, the absence of any additional peaks in DLS indicates that there are neither aggregation of particles nor side nucleation of cobalt oxide that could have occurred were the complexes unstable. No evolution of the single peak has been observed over weeks. The addition of 485 complexes per particle induces a dramatic increase of the hydrodynamic diameter, followed by the flocculation of the particles. The latter is probably caused by the loss of the electrostatic repulsion-induced stabilization that should accompany the increase of the grafting rate. In the following we will focus on 0b and 1. Transmission electron microscopy (TEM) indicates that very similar sizes and distributions are observed for 0b and 1 (5.1 nm, 𝜎=0.12 and 5.0 nm, 𝜎=0.09, respectively; The spectra of the bare nanoparticles 0b and of the complex display only one peak at 403 and 398 eV, respectively. As the presence of nitrogen atoms can originate from the TMA + counterions in 0b and in 1, and from the TPMA ligand in 1 and in [Co(TPMA)Cl 2 ] the low energy contribution at 399 eV can be assigned to the nitrogen atoms from the TPMA ligand and the high energy peak at 404 eV to the contribution from the TMA + counterion.

The experimental Fe/N 𝑙𝑖𝑔 atomic ratio of the peaks has been found equal to 1.00 for sample 1, which differs from the calculated one (10 accounting for the TPMA ligands only).

Nevertheless, the experimental Fe/N 𝑙𝑖𝑔 ratio agrees well with the calculated one if only surface iron ions ( 10%) are taken into account. Atomic absorption spectroscopy (AAS) measurements made on a precipitated sample of 1 confirm the presence of cobalt(II) ions.

The found 46±4 Fe/Co ratio corresponds to 52 complexes per particle (considering 2418

Fe 3+ ions for a spherical 5 nm 𝛾-Fe 2 O 3 nanoparticle). This would indicate an 86% grafting rate corresponding to a surface density of 0.66 complex per nm 2 . The presence of complexes coordinated to the nanoparticles surface has been further evidenced by X-ray AS (XAS) measurements at the L 2,3 edges of the iron and cobalt ions for sample 1 and at the cobalt L 2,3 edges for the [Co(TPMA)Cl 2 ] complex. For 1, the spectra at the cobalt edges confirm the presence of octahedral Co 2+ and the absence of Co(III) (Supplemen- The presence of the complexes impressively increases the coercive field of the particles, multiplying the value by 13 (from 62 Oe for 0b to 839 Oe for 1). In an attempt to differentiate the effect of a surface modification due to the coordination of the complexes from that of a magnetic coupling between the Co 2+ complexes and the particle, a Zn(II)

analogue of 1 has been prepared and measured (2). The same quantity of the diamagnetic ZnII(TPMA)2 + fragment grafted on the particle surface does not induce a comparable effect on the temperature of the maximum in the zero-field-cooled magnetization curve (from 11 to 14 K; Supplementary Figure 4.6.9). In the magnetization vs field curve, the presence of the ZnII(TPMA)2 + complex has a slight effect on the remnant magnetization but an almost negligible one on the coercive field (from 62 to 73 Oe; Supplementary Figure 4.6.10). These results indicate that the effect of the CoII(TPMA)2 + units on the magnetic properties does not originate from a simple modification of the environment of the iron ions located at the nanoparticles surface. Moreover, since no aggregation of the nano-objects is observed after the condensation of the complexes the observed effect is necessarily owing to the magnetic interaction of the complexes with the particles, leading to an increase of the magnetic anisotropy. The transmission of the anisotropy from the complexes to the particles is possible only if there is an exchange interaction between the Co 2+ and the Fe 3+ ions. As the observed enhancement of the magnetic properties is important and effective at relatively high temperature, electrostatic interactions must be ruled out. Only the occurrence of a chemical bond such as an oxo-bridge between the Co 2+ and the Fe 3+ ions can support the effective anisotropy enhancement, source of the improved properties. 57 Fe Mössbauer spectrometry has been performed at 77 K on frozen solutions of 0b and 1 ( the hyperfine interactions. [START_REF] Yoshida | Mössbauer Spectroscopy[END_REF] Indeed, this local probe technique remains a powerful tool for investigating Fe-containing nanoparticles and the influence of the functionalization, thanks to its high sensitivity to electron transfer. [START_REF] Fouineau | [END_REF] The 77 K spectra result from a minor central quadrupolar doublet and a prevailing broadened lines magnetic sextet: they have exactly the same isomer shift and their proportions are rather independent of the samples.

These two contributions are unambiguously assigned to Fe species with fast and weak superparamagnetic relaxation phenomena, due to size distributions in the samples.

The lack of resolution does not allow the proportions of iron in tetrahedral and octahedral sites to be estimated but they were accurately estimated from in -8 T field Mössbauer plexes. The mean hyperfine field distribution profiles, which correspond to the shape of the magnetic lines, indicate clearly that the grafting of the complexes gives rise to both a shrinkage of the distribution and a shift towards larger hyperfine fields, that is a significant increase of the mean hyperfine field (28.4(5) and 35.1(5) T, respectively). These features distinctly attest a slowdown of the relaxation phenomena of the magnetization in 1 because the attached Co 2+ complexes increase the magnetic anisotropy of the Fe 3+ moments, strengthening thus the magnetization of each nanoparticle, in agreement with the ZFC measurements. The shape and intensity of the XMCD signals at the Fe L 2,3 edges for 1 are similar to those observed for previously reported maghemite nanoparticles. 207 It bears the signature of antiferromagnetic coupling between Fe 3+ ions in tetrahedral sites and Fe 3+ ions in octahedral sites (Figure 4.5.7). The magnetic moment for Fe 3+ ions in the sub-network of the octahedral Fe 3+ is parallel to the external magnetic induction. The ratio between the occupation of the tetrahedral and octahedral sites can be determined from the ligand field multiplet analysis of the XMCD shape and a Fe 𝑂 ℎ (III)/Fe 𝑇 𝑑 (III) ratio close to 5/3 is found, as expected for maghemite. Traces of Fe(II) have also been detected.

The latter are due to sample preparation (see methods). The XMCD at Co L 2,3 edges in 1 is mainly negative at the L 3 edge indicating that the Co 2+ magnetic moment is, at 6 T, parallel to the octahedral Fe 3+ ions and antiparallel to the tetrahedral Fe 3+ ions. ion. For 1, the magnetization increases abruptly and saturates above 2 T. This behaviour evidences and confirms that the Co 2+ ions within the grafted complexes are magnetically coupled to the iron(III) ions at the nanoparticles surface.

Discussion

We have presented in this work a new synthetic strategy, which, in combining molecular and nano chemistry, offers a way towards control and modulation of the magnetic anisotropy in nanoparticles. Magnetic measurements, Mössbauer spectrometry and XMCD measurements show that CoII(TPMA) 2+ complexes grafted on the surface of maghemite nanoparticles massively enhance the magnetic properties of the nano-objects. Our results also indicate that the strong influence of the molecular component on the nanoparticle comes from the covalent linking of the two species through oxo-bridges and the resulting magnetic interaction. This work opens tremendous prospects in the design of nanomagnets and of multifunctional nano-platforms. Provided that the choice of nanoparticle to functionalize allows the formation of a coordination bridge able to promote magnetic exchange,

Supplementary Information of Paper III

X-ray Powder Diffraction

The XRD powder patterns of 0b and 1 display a cubic structure (Fd-3m). XRD patterns were fitted using Maud program (http://maud.radiographema.com/), which is based on the Rietveld method combined with Fourier analysis to describe the broadening of Bragg peaks. 260 This analysis allows the mean lattice parameters, the mean crystalline grain sizes to be estimated. The lack of agreement between experimental and theoretical curves may originate from the very small contribution of the absorption due to the sample compared to that of the substrate.

Cell parameter a (Å) Crystallite Size (nm) R.m.s microstrain (hkl) (420) (430) (620) (800) (753) Presence of Fe 2+ : Traces of Fe 2+ have been detected on the XAS spectrum of 1 and estimated at 2 % of the iron signal. This cannot be the result of an electron transfer from the Co 2+ ) to the Fe 3+ . Indeed, the quantity of grafted cobalt complexes amounts for 2.2 % of the total iron ions. A reduction of the iron ions coordinated to the cobalt complexes at the nanoparticle surface would result in no Co 2+ being observed. This is clearly not the case, and furthermore the XAS spectrum at the Co L 2,3 edge shows no evidence of Co 3+ . We also believe that the traces of Fe 2+ cannot result from a chemical reduction occurring during the synthesis of the nanoparticles. Indeed the functionalisation reaction takes place at pH 12 where the reduction reaction is unlikely.

0b

Transmission Electronic Microscopy

d(Å -1 ) d(Å -1 ) d(Å -1 ) d(Å -1 ) d(Å -
Besides Mössbauer spectrometry on the nanoparticles solution shows no Fe 2+ . This could leave the precipitation of the nanoparticles and the preparation of solid samples as a potential source of undesired reduction recations. However, XPS shows pure maghemite.

We think then that the particular solid sample preparation we have used for our XAS measurements, which differs from XPS (see methods), may have cause the occurrence of Fe 2+ . Finally, pollution from the substrate can unfortunately not be discarded.

Magnetic Measurements

Anisotropy constants calculations: Following Tamion et al., 251 we use their semianalytical model to describe the temperature dependence of the ZFC magnetisation and extract an estimate of the magnetic anisotropy energy density K eff . Having defined a switching field frequency:

𝜈(𝑇 ) = 𝜈 0 exp[ -𝐾 𝑒𝑓 𝑓 𝑉 𝑚𝑎𝑔 𝑘 𝐵 𝑇 ] (4.6.1)
with 𝜈10 9 Hz the attempt frequency and a characteristic time 𝛿 𝑡 (T), which depends on the temperature sweeping rate (here 2 K.min -1 ), the magnetic moment measured during a ZFC protocol is given by

𝑚 𝑍𝐹 𝐶 (𝑇 ) = 𝑁 𝑇 ∫ ∞ 0 M 0 𝑉 𝑚𝑎𝑔 [𝑒 𝜈(𝑇 )𝛿𝑡(𝑇 ) ]𝑃 (𝐷 𝑚𝑎𝑔 )𝑑𝐷 𝑚𝑎𝑔 (4.6.2)
where M 0 V 𝑚𝑎𝑔 =𝜇 0 m 2 𝑆 H/(3K eff V 𝑚𝑎𝑔 ) (equation 3) is the initial ZFC susceptibility in the frozen low temperature state and P(D mag ) is the size distribution function taken here as a lognormal with characteristic parameter taken from the TEM characterization of the particles. In the equations above, 𝜇 0 and k B denote the magnetic permeability of vacuum and the Boltzmann constant, B is the magnetic induction strength, m 𝑆 is the saturation magnetisation of maghemite and N T is the number of magnetically active clusters. Using this equation, it is quite straightforward to obtain a calculated ZFC curve and optimize the value of K eff in order that make it best match the experimental data.

Mössbauer spectroscopy measurements

Summary and Conclusion

Synthesis routes

In sections 4.2 to 4.4, I have presented two papers reporting the influence of the synthesis process on the crystallographic order of iron-cobalt nanospinels prepared in ferrofluids.

The coprecipitation process was used to obtain particles with different sizes. XMCD investigations of the cations distributions among the spinels crystallographic structure combined with magnetometry measurements revealed that the coercive field of CoFe 2 O 4 nanospinels is governed by the concentration of Co 2+ ions sitting in octahedral sites. The temperature of the synthesis process is found to have a significant effect on the magnetic order. The higher the temperature during the synthesis, the larger is the concentration of Co 2+ ions on the octahedral sites. The relatively low temperature needed for the formation of cobalt ferrites in the coprecipitation route makes it an easy process but does not favor the thermodynamic equilibrium and hence the Co 2+ occupation of O ℎ sites. When the temperature of the synthesis steps is increased to yield larger particles (hydrothermal treatment at 200 °C for 13 or 21 nm particles), the O ℎ site occupation by Co 2+ ions increases and larger coercive fields are measured. These general results are believed to be valid for any type of CoFe 2 O 4 nanospinels and the methodology that we have developed can be extended to similar systems.

The volume of the nanoparticles is well known to affect the coercive field. 157,[START_REF] Pianciola | [END_REF] To this contribution, we add the effect of the Co 2+ occupation that also directly contributes to the magnetic anisotropies as can be seen from the comparison of the CoFe 2 O 4 nanoparticles with a diameter of 9 nm, 11 nm and 13 nm (samples CoFe33_11, CoFe33_9 and CoFe33_13 of section 4.2). The coercive field of the 11 nm nanoparticles is very similar to the one of the 9 nm nanoparticles, while the coercive field of the 13 nm nanoparticles is 33 % larger. These differences cannot be attributed only to the volume of the particles and I show how the enhanced coercive field of the 13 nm nanoparticles can be related to the crystallographic structure that benefited from a hydrothermal treatment (1 hour at 200 °C) at the difference of the 9 nm and 11 nm nanoparticles.

CoFe 2 O 4 nanoparticles obtained via polyol or acac syntheses that are high-temperature synthesis compared to coprecipitation exhibit a better crystallographic order with a distribution of the Co 2+ and Fe 3+ ions among octahedral and tetrahedral sites closer to that of the bulk. In line with this result, CoFe 2 O 4 nanoparticles with 7 nm size and obtained by polyol and acac syntheses show a coercive field almost twice larger than the ones obtained with the coprecipitation route. It is worth noticing that polyol and acac syntheses yielded iron-cobalt nanospinels with slightly different chemical compositions. Hence, it is found that the first approach to modulate magnetic anisotropies and more generally the magnetic properties resides in the choice of the synthesis that conditions the size and the chemical composition (i.e. the X M =[Co]/([Co]+[Fe]) values) of the nanoparticles.

The element selectivity of the X-ray magnetic spectroscopies was essential to get better insights on the origin of the variations of the magnetic properties. New modified processes arising from the coprecipitation synthesis have been implemented during the recent past years, such as electrochemical, 263 microfluidics 177 or reverse micelle processes 172 . A deeper knowledge on the impact of parameters playing a significant role on the magnetic properties in existing syntheses would help the development of rationalized syntheses which in turn would help the scientists in the creation of new materials with enhanced magnetic properties.

We have reported that synthesis effectively controls the magnetic anisotropies where cobalt(II) ions are incorporated within the spinel structure with compositions close to the

Introduction

This chapter is dedicated to the investigation of the magnetic anisotropies using RIXS and RIXS-MCD spectroscopies with hard X-rays. RIXS-MCD is a recent method that has been developed less than 10 years ago on ID26 beamline at ESRF. During my RIXS experiments, I had the chance to benefit from the great expertise of Marcin Sikora and Amélie Juhin who first got involved in the development of the method. We wanted to perform magnetic spectroscopies in the hard X-ray range for the following reasons:

(i) we wanted to work with "real" ferrofluids where the carrier liquid was preserved and this was possible thanks to liquid cells compatible with hard X-rays, (ii) for liquid cells the preferred detection mode is the fluorescence mode that allows to probe the whole nanoparticles with a depth penetration of several microns, (iii) in liquid cells, the liquid sample can be solidified by cooling it below the solidification temperature of the solvent. The solid sample thus obtained is expected to present structures similar to the one existing in the liquid phase.

By means of a liquid cell that I have developed on purpose during a short stay at ESRF (see section 3.3) we have been able to investigate the ferrofluids directly in their liquid phases or in the low temperature solidified phase.

In addition, RIXS-MCD gives mainly information on the pre-edge region in the case of K -edges for 3𝑑 transition ions. From the magneto-optical sum rules for the electric dipole and electric quadrupole transitions, the XMCD signal from this region is known to carry information on the 3𝑑 orbital magnetic moment of the absorbing atom. Then the variations of the intensity of the RIXS-MCD signal in the pre-edge region yield directly magnetization curves for the 3𝑑 orbitals of the absorbing ion. Beyond recording magnetization curves, RIXS-MCD is a photon-in / photon-out spectroscopy where 2D maps can be collected with abscissae corresponding to the incoming photon energy and the ordinates corresponding to the energy transfer (i.e. the difference between the energy of the incoming photon and the energy of the outgoing photon). The 2D maps for RIXS and RIXS-MCD are full of spectroscopic information that would require LFM calculations for a complete analysis. I have had no time to perform this deep analysis and I mainly proceeded by a finger print approach. More experimental and theoretical details on RIXS and RIXS-MCD can be found in Chapter 2.

In this chapter, I have been playing with two different magnetic spinels that I associate In section 5.2, we study a core@shell system where a core made of MnFe 2 O 4 is surrounded by a uniform shell of CoFe 2 O 4 . Our target is to determine, the possible coupling that exist between the shell and the core and to see if the magnetic properties of the core@shell particles are the simple sum of the contributions from the core and the shell or whether some emerging physical properties stem from the core@shell structure. In section 5.4, we are interested in a mixture with equal volumes of CoFe 2 O 4 ferrofluid and MnFe 2 O 4 ferrofluid. We call this mixture a "binary" ferrofluid and our target is to determine how the two ferrofluids interact and if we can put in evidence an eventual structuration of the liquid phase or the solidified phase.

Abstract

Magnetic anisotropies in a ferrofluid of core@shell MnFe 2 O 4 @CoFe 2 O 4 nanoparticles are studied in the liquid and frozen states using a unique sample cell developed for element specific hard X-ray magnetic spectroscopies. The MnFe 2 O 4 @CoFe 2 O 4 6.7 nm particles reveal original magnetic properties, with a gradient in coercive field inside a nanospinel.

The very thin (0.35 nm) CoFe 2 O 4 shell is found to impose a strong magnetic anisotropy to the otherwise very soft MnFe 2 O 4 core, so that the inner core presents a large coercive field (0.56 T) and an unexpectedly high remanent magnetization (95% of the saturation magnetization) for such a non-oriented system. The possibility to investigate ferrofluid samples where interparticle interactions have been preserved opens new perspectives in the domain of magnetic liquids.

Introduction

Ferrite nanoparticles with a spinel structure (𝛾-Fe 2 O 3 , Fe 3 O 4 , MnFe 2 O 4 , CoFe 2 O 4 ) have become very popular for their original magnetic properties that are not shown in bulk materials. The reduced size combined to enhanced magnetic properties has led to numerous applications from biomedicine to highly density storage devices, 173,264,265 although further development and miniaturization of magnetic storage devices based on nanoferrites are now limited by the "superparamagnetic limit". [START_REF] Skumryev | [END_REF] To overcome this, chemists have imagined new synthesis pathways to tune further the magnetic properties of nanospinels by playing on their structuration, leading to the emergence of core@shell nanostructures which rapidly focused interest. 266 Since they allow the possibility to combine a core and a shell from two different magnetic species (such as for example a ferro/ferrimagnetic phase with an antiferromagnetic one, [267][268][269] or a soft magnetic with a hard magnetic one 218,270,271 ), bimagnetic core@shell nanospinels offer a fertile ground to overtake the limits of conventional magne-tization parameters (anisotropy constant K, blocking temperature T B , saturation magnetization M 𝑆 and coercive field H 𝑐 ) 94,272,273 or to observe strong exchange coupling between both magnetic phases, such as exchange bias or exchange-spring coupling effects. [274][275][276][277] In parallel, magnetic nanoparticles have found a rich field of application where they are usually dispersed in liquids and form stable magnetic colloids. 168 Such systems are also called ferrofluids when magnetic particles are single domain and have a typical diameter in the 5 nm-30 nm range. In biomedicine, one application of ferrofluids is based on magnetophoresis (magnetic separation), such as for example, for protein and cell manipulation, or drug delivery. [278][279][280][281][282] More advanced applications, either as contrast agent in Magnetic Resonance Imaging or as nanoheaters in cancer therapy (magnetic hyperthermia), make use of radiofrequency fields. 43,45,169,283,284 They rely on the magnetic anisotropy of the ferrofluid, which appears at high frequency because fluctuations of the particle magnetic moment are produced. In addition to biomedical applications, stable ferrofluids have been produced for 50 years for applications in technology (microfluidic devices, loudspeakers, seals, dampers, purification devices) or art (where their spectacular surface instabilities are highlighted). 5,[285][286][287] In this work, we study the magnetic anisotropies in a ferrofluid of well-crystallized, mono-dispersed core@shell nanoparticles dispersed in heptane, which combine a soft core of MnFe 2 O 4 with a hard shell of CoFe 2 O 4 . Using an original experimental approach, we are able to investigate separately the cationic distribution and magnetic anisotropies in the core and those in the shell, as well as their mutual influence. Among the techniques dedicated to study magnetic nanoparticles, X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD) have now become standard techniques and are mainly performed using soft X-ray photons (∼600 eV for Mn L 2,3 absorption edges) delivered by synchrotron radiation facilities. Thanks to its element specificity, XMCD allows disentangling the magnetic signature of the core by measuring at the Mn absorption edge, from that of the shell by measuring at the Co absorption edge.

Possible magnetic coupling between both components can be therefore determined. 245,288 Additionally, the cationic distribution can be solved thanks to the sensitivity of the spectral shape to the site symmetry of the absorbing atom and to its valence, which is crucial to rationalize the magnetic properties of these materials. However, XMCD experiments have been largely limited so far to the dried, solid phase of the samples, because investigating liquid phases such as ferrofluids remains an experimental challenge when using soft X-ray photons. Nevertheless, both the surface of nanoparticles and interparticle interactions are likely to be highly modified in the dried powder as compared to those in the liquid phase, as underlined in several papers which have reported the important role played by interparticle interactions in the magnetic anisotropy energy of nanoparticles. 289,290 In order to circumvent this issue, we have investigated the MnFe 2 O 4 @CoFe 2 O 4 ferrofluid using the RIXS-MCD technique, which consists in coupling hard X-ray MCD and Resonant Inelastic X-ray Scattering (RIXS) spectroscopy at the K -edge of 3d ions. 77,78 RIXS-MCD was recently used to investigate the buried interface in bi-magnetic core@shell 𝛾-Fe 2 O 3 @Mn 3 O 4 nanoparticles. 79 Since then, the experimental setup has been further developed with the aim of measuring a ferrofluid sample in which interparticle interactions have been pre-served, which is a crucial prerequisite to rationalize the magnetic properties of such an interacting system. To that goal, we have developed a liquid cell dedicated to RIXS-MCD experiments at room and low temperatures, which allows selectively measuring magnetic properties of nanoparticles dispersed in a liquid both in the liquid and in the frozen phase. 1 This is, to our knowledge, the first investigation of its kind. This could be achieved using a dedicated liquid cell that was developed on purpose (see below). The incident energy was selected using a pair of Si(311) crystals. The intensity of Mn and Co K𝛼 emission lines (of the inelastically scattered beam) was analyzed using a set of four spherically bent Ge (111) and Si (531) crystals, respectively, arranged with an Avalanche Photo Diode in the Rowland Geometry with a scattering angle of 90°. The overall resolution was measured at 0.7 eV and 0.8 eV for Mn and Co respectively. For both Co and Mn edges, 1s2p RIXS planes were recorded as a set of Constant Energy Transfer scans over the energy of the K𝛼1 line and of the K pre-edge. Additionally, absorption spectra were measured using High Energy Resolution Fluorescence Detection (HERFD) by setting the emission energy to the maximum of the K𝛼 line (6.9313 keV for Co, 5.8998 keV for Mn), namely HERFD-XAS. HERFD-MCD and RIXS-MCD experiments were carried out with the same setup as for HERFD-XAS and RIXS measurements, the differences being that (i) the incident beam is circularly polarized (instead of linearly polarized in the case of HERFD/RIXS), (ii) samples are kept in magnetic saturation using an electromagnet allowing to reach a magnetic field of 1.5 T, for which a detailed calibration curve was measured. The circular polarization was obtained using a 500 𝜇m thick diamond (111) quarter wave plate set downstream the Si(311) monochromator, with a circular polarization degree estimated to be 75 %. RIXS-MCD planes were recorded by reversing the photon helicity at each incident energy. RIXS-MCD and HERFD-MCD spectra were recorded in the region of the Co and Mn K pre-edge. Spectra were normalized such that the maximum of the polarization-averaged absorption spectrum is equal to 1 in the pre-edge region. Since (i) self-absorption corrections were found to be weak in the pre-edge range, (ii) all samples were measured in the same conditions and (iii) all MCD spectra are normalized to the pre-edge maximum, we assume that self-absorption effects do not impact our analysis.

Experimental

Synthesis

Development of a liquid cell dedicated to RIXS-MCD measurements in liquid and frozen ferrofluids. The cryo-liquid cell setup was designed in collaboration with the Sample Environment group of the ESRF. The setup is custom made and optimized to be compatible with the experimental chamber volume, high magnetic field, and ferrofluid materials. The sample holder is made of copper. A square cavity machined to suit the 90°scattering geometry used in the experiment is surrounded by a 50 𝜇m thick Kapton layer. The sample holder square cavity is filled by injecting ferrofluids with a syringe through a side hole, which is later closed by a Viton O-ring and a non-magnetic screw. The sample holder is screwed to a cold plate cooled with a mini-cryostat using the principle of continuous flow helium circuit. The mini-cryostat consists of two heat exchangers. The main exchanger (the cold plate) cools the sample holder and the secondary heat exchanger recovers the remaining enthalpy of the helium gas for cooling the heat shield. A thermal screen protects the main exchanger and the sample itself from thermal radiation from the surrounding.

The beam goes through the thermal screen to the sample holder by a first Kapton layer.

The setup allows a good vacuum with a pressure of 10 -7 mbar and the temperature is set by limiting the helium flow rate of the mini-cryostat and/or by the pumping speed of the vacuum pump connected to the thermal screen. The control of temperature is made by two thermometers, one located in the main exchanger and the other near the sample. Temperature can be regulated from 4 K to 300 K. However, in order to ensure the setting temperature as the effective temperature of the sample, one has to work above a temperature of 25 K. A 3D model of the setup is provided in Supplementary Information (Figure 5.3.10, Supplementary Information).

Results and discussion

Three different types of nanoparticles were synthesized: MnFe 2 O 4 , CoFe 2 O 4 , and MnFe 2 O 4 @CoFe 2 O 4 core@shell (also labeled Mn@Co hereafter). The latter were synthesized using the seeded-growth approach, i.e., Mn@Co particles are built up from the pre-made nanoparticle core of MnFe 2 O 4 sample on which a shell of CoFe 2 O 4 is grown.

Atomic Absorption Spectrometry measurements provide an estimate of the metallic molar concentration in each sample (Table 5. The temperature dependence of magnetization was measured using a Vibrating Sample In a second step, ferrofluid samples were prepared by dispersing each type of nanoparticles in heptane with the same volume concentration of 0.2%. Their structural and magnetic properties were then characterized in the liquid and frozen states using Resonant Inelastic X-ray Scattering. RIXS is a photon-in, photon-out element selective X-ray spectroscopy that provides for the absorbing atom a unique bi-dimensional mapping of its spectral signature. [START_REF] Glatzel | [END_REF] The latter is intimately related to its electronic structure, i.e., mainly its valence (number of 3d electrons) and site symmetry (tetrahedral or octahedral). When RIXS is further combined with XMCD, which is the difference in the absorption of circularly polarized X-rays for opposite sample magnetization direction, one retrieves additional information on the magnetic properties. The use of hard X-rays at the metal K -edges allows bulk sensitivity and compatibility with a sample holder suitable for liquids, which we have designed on purpose to achieve temperature dependent RIXS-MCD measurements of ferrofluid samples.

In Figure 5.2.4 are shown the RIXS and RIXS-MCD planes measured on the Mn@Co ferrofluid in its frozen phase and below the blocking temperature, at the Mn edge (panels (a) and (b)) and at the Co edge (panels (c) and (d)). This allows probing selectively the speciation of Mn ions (that are located in the MnFe 2 O 4 core) and that of Co (that are expected in the CoFe 2 O 4 shell). At the Mn edge, the large intensity of the RIXS-MCD signal (∼20% peak-to-peak) and its characteristic shape (one positive peak at lower incident energy and lower energy transfer, accompanied by one negative peak) reveal the and Co inside a Mn@Co particle, despite significant differences between both techniques (i) in the sample investigated (a frozen ferrofluid at ambient pressure versus a dropcast of Mn@Co particles in High Vacuum conditions), and (ii) in the probing depth (a few 𝜇m vs a few nm of one particle). Indeed, the XMCD spectra measured at the different metal L 2,3 edges (Figure 5 MCD spectra that are identical within noise level (note that the signal from the 0.3-0.4 nm thin shell is very weak). This indicates that in Mn@Co particles interdiffusion between the core and the shell is very limited. In addition, since the magnetic moments of tetrahedral Mn 2+ ions are opposite to the magnetic field direction and those of octahedral Co 2+ ions are along the field direction, we can conclude that the coupling between the core and the shell is ferromagnetic. In other words, magnetic moments in the tetrahedral sites of the core and the shell are all antiparallel to the external magnetic field, while those in the octahedral sites of the core and the shell are all parallel to the field. the Mn@Co ferrofluid, doing such a measurement successively at the Mn and Co edges is particularly relevant because it allows disentangling the magnetic anisotropy of the core and that of the shell, respectively. At 300 K, no opening of the magnetization curve is observed for any of the samples (Figure 5.2.6), as expected from superparamagnetic ferrite nanoparticles in a liquid phase. For the curves measured at the Mn edge, the derivative at zero field is ∼1.45 times higher for the Mn@Co ferrofluid than for the MnFe 2 O 4 ferrofluid, which implies that the magnetic susceptibility 𝜒 of the former is ∼1.45 times higher. This is mainly due to the increase in particle size with respect to the MnFe 2 O 4 particles. Indeed, influence of particle chaining is very unlikely at such low particle volume fraction (0.2 %). When ferrofluids are frozen down to T = 39 K (below the solidification temperature of heptane), the coercivity measured at the Co edge in the Mn@Co ferrofluid is 0.18 Tesla, which is significantly lower than the coercivity measured in the CoFe 2 O 4 frozen ferrofluid (0.32 Tesla). Although both values are consistent with a hard magnet behavior, the difference is due to the fact that a CoFe 2 O 4 particle with 5.9 nm diameter has a very different magnetic anisotropy from that of a CoFe 2 O 4 shell with 0.3-0.4 nm thickness, hence the necessity of measuring the specific magnetic properties of the shell in the Mn@Co ferrofluid rather than using those of reference samples. The normalized remanent magnetization (remanent magnetization divided by magnetization at saturation) is only ∼50%, which is the result of strong magnetic spin canting for the Co ions in the Mn@Co nanoparticles. The canting is expected to be rather large because of the high proportion of Co ions situated at the particle surface that have less magnetic neighboring atoms than inside the bulk. 291 For such Co ions, the antiferromagnetic coupling between octahedral sites competes efficiently with the antiferromagnetic coupling of Co ions to the tetrahedral Mn ions, which results in the breaking of the collinear spin configuration. 207,[START_REF] Krupička | In Chapter 4 Oxide spinels[END_REF] When ferrofluids are frozen down to 26 K (i.e., below the blocking temperature of dried Mn@Co particles but above that of MnFe 2 O 4 ), one finds that the coercivity measured at the Mn edge in the Mn@Co ferrofluid is 0. [START_REF] Wohlfarth | [END_REF] Such a high value reveals the lack of magnetic spin canting for the Mn ions. This is consistent with most of the Mn ions being in the "bulk" on the particle rather than at the interface. In addition, since Mn ions are on the Td sites they tend to be much less sensitive to spin canting that is preferentially affecting the Oh sites. 207,215 Nevertheless, the coercivity induced in the core by the shell (H c (core = 0.54 Tesla at T = 26 K) is much larger than the coercivity of the shell itself (H c (shell) = 0.18 Tesla at T = 39 K, a value that would be only slightly higher at T = 26 K, as can be guessed from the VSM magnetization vs field measurement shown in Figure 5.3.7, Supplementary Information). This seems at first surprising, because one would expect the coercive field in the shell to induce a coercivity of the same magnitude in the single domain core. Instead, when the magnetic field is set to the value of H c (shell), leading In summary, we have developed a completely original sample cell that is well suited to study liquid systems by RIXS and RIXS-MCD spectroscopies. The cell is mounted inside a He cryostat, so that the temperature of the sample can be varied between 300 K and 25 K. The whole set-up is then well adapted to studying liquid phases and phase transitions between liquid and solid. When the sample is a dilute ferrofluid, it is possible to study highly homogeneous samples obtained from the frozen phase where highly isolated nanomagnets are randomly distributed. From RIXS-MCD measurements at K -edges and XMCD at L 2,3 edges on such samples, we found that core@shell MnFe 2 O 4 @CoFe 2 O 4 6.7

nm particles present unexpected emergent magnetic properties. The coercive field is not constant on the whole nanospinel. The very thin (0.35 nm) CoFe 2 O 4 shell imposes a strong magnetic anisotropy to the otherwise very soft MnFe 2 O 4 core, so that the core presents a rather large coercive field (0.56 T) and a very high remanent magnetization (95% of the magnetization at saturation) although it is a non-oriented system. Such original findings stem from the chemical selectivity of XMCD and RIXS-MCD. In a near future and thanks to our liquid cell, we plan to study the interaction of the magnetic nanospinels with the carrier fluid when the temperature is lowered and the viscosity of the liquid phase increases.

By varying the nanoparticle concentration and playing with field-frozen versus zero-fieldfrozen ferrofluids, one expects to determine at the atomic scale the existence of possible chaining between nanospinels.

Supplementary Information of paper IV

Binary ferrofluids

Introduction

Nanoparticles dispersed in ferrofluid are so small, so that they can be regarded as magnetic dipoles with single moment. This results in possible particle-particle interactions that are enhanced if an external magnetic field is applied. 294 Interparticles interactions can be characterized by two parameters, the dipole coupling parameter 𝜆, and the volume fraction of the particles 𝜑. The dipole coupling parameter is proportional to the magnetic moment carried by the particles and inversely proportional to their size, so that 𝜆 mainly depends on the intrinsic nature of the particles. 295,296 It is usually considered that for 𝜑 < 1%, particles interactions are negligible, although this volume fraction is typically a few percent in ferrofluids. 297 Particles interactions induce the formation of microstructures in the fluid that are governed by 𝜆 and 𝜑. Simulations attempting to describe the effect of particles interactions have been reported in litterature. 298,299 The models failed to reproduce experimental data and the failure was attributed to the fact that the models were only considering exactly monodispersed systems, while particles of ferrofluids always present a finite size distribution. A first approximation of polydispersed systems was made with theoritical models of bidisperse ferrofluids containing "large" and "small" particles. 101,300 The models revealed microstructures that are mainly formed by large nanoparticles, organized in chain-like and ring-like formations in a "gas", i.e. nonaggregated state, of small particles. Depending on their relative content, small particles supress or enhance magnetic-induced structures of large particles. Still, such bidisperse systems of small and large particles are difficult to implement experimentally because ferrofluids are polydispersed by nature. 175 As already mentionned, interactions occuring between particles not only depend on the diameter of the particles, but also on the magnetic moments. Binary ferrofluids consist of mixture of two materials with different magnetization. Most of the studies on binary ferrofluids published so far concern strong magnetic particles (e.g., ferromagnetic and ferrimagnetic) mixed with weak magnetic particles (e.g., antiferromagnetic and paramagnetic). Another type of binary ferrofluids consist in bi-dispersed particles with identical formulae since bidisperse systems made of large and small particles can be regarded as a mixture of strong and weak magnetic particles. From the literature, we learn that binary ferrofluids made of strong and weak magnetic particles have an apparent magnetization that results mainly from the strong system. Nevertheless, binary mixtures exhibit novel magnetic behavior, different from that of single particle ferrofluids. They established that the magnetic properties of the binary ferrofluid contrast with that of similar nanoparticles in thin films.

In this chapter, we present the study of the magnetic properties of a binary ferrofluid

Experimental details

Results and discussion

Size and morphology of pure phases. TEM micrographs presented in Figure 5. (ii) From the analysis of the magnetization curve of the binary ferrofluid, two reversals of the magnetization can be extracted, one at low field ≈0.17 T and another one at higher fields ≈1.4 T. A similar behavior has already been reported in literature for thin films. 171,[START_REF] Rigato | [END_REF] . The two magnetization reversals can be explained by the contributions from have changed but we guess that the magnetic coupling induces some mesoscopic organization of the nanoparticles that is responsible for the observed changes in the magnetic anisotropy. experimentally. Chain-like and ring-like structures of magnetite have been observed in situ by A. P. Philipse and co-workers using Cryogenic Transmission Electron Microscopy (Cryo-TEM). 98,305 We have tried to implement the same experiments for our ferrofluids with the help of the Cryo-TEM team from IMPMC that is specialized in Cryo-TEM applied to biological samples. Unfortunately we faced many experimental difficulties because of the nature of our solvent that is not water but the highly volatile heptane and the experiments were not successful.

Conclusion

We have investigated the magnetic properties of binary ferrofluid consisting in a 1: nanoparticles. We believe that such a behavior is the consequence of some microstructures where magnetic clusters or chains consisting of few magnetic nanoparticles are formed, resulting in magnetic interactions between the CoFe 2 O 4 and MnFe 2 O 4 nanoparticles. In order to confirm that experimentally, we plan to investigate the microstructure in the binary ferrofluid with First Order Reversal Curve (FORC) measurements in collaboration with Claire Carvallo (IMPMC). These measurements should provide information about the coercivity distribution and interaction field distribution. 79,306 Cryo-TEM would be also needed and to cope with the heptane solvent, we plan to build a collaboration with microscopists from the Debye Institute for Nanophysics in Utrecht who possess the knowhow to perform Cryo-TEM with highly volatile solvents. I hope to have time to participate to these two campaigns of measurements before the end of my Ph.D. thesis.

Summary, conclusion and outline

In nanoparticles exhibit a gradient of coercive field. These findings have been obtained by a combined set of X-ray magnetic spectroscopy : XMCD at the Mn, Fe and Co L 2,3 edges and RIXS-MCD at the Mn and Co K -edges.

In the binary ferrofluid we have observed a magnetic coupling between MnFe For such applications, the superparamagnetic properties can be designed and controlled with a fine adjustment of the magnetic anisotropies. Spinel ferrites offer a fertile playground for materials with magnetic properties that can be tuned through crystal structure, composition or synthesis. In this thesis, we used XAS and XMCD spectroscopies to obtain information on the local electronic and magnetic structures of spinel ferrites. Alternatively, we also used RIXS and the newly developed 1s-2p RIXS-MCD technique in the hard Xray range where a liquid sample environment and bulk sensitivity were required. The topic addressed here concerns various systems where cobalt is used as a true maker of the magnetic anisotropies. In this conclusion, I will first discuss the original points of my thesis. Secondly, the main conclusions of the studies carried will be summarize. Finally, this conclusion closes on an outlook of ongoing works with consideration for larger prospects.

Overview

In this thesis, the magnetic anisotropies of ferrites nanospinels in ferrofluids were investigated with the chemical selectivity and site symmetry sensitivity of XMCD spectroscopy with special attention to the magnetic coupling between the cations present in the nanospinels. The aim was threefold: (i) to achieve better insights on the features that are driving the magnetic properties of the ferrofluids, (ii) to connect the magnetic properties of the ferrofluids with the synthesis mode of the nanospinels they contain, (iii)

to extend the XMCD technique to the in situ study of the local structure of magnetic nanoparticles in the ferrofluid in its liquid or frozen phase.

The first goal of the present thesis was to gather a research consortium between different teams to solve puzzling questions dealing with ferrofluids. This has been achieved through the building of a thoughtful project between IMPMC, PHENIX and SOLEIL, which was granted financial support by the LabEx MATISSE. The expertise brought by the protagonists who supervised this thesis are various and therefore, allowed me to approach the subject at all levels, from the synthesis of the systems, to their characterization and to the computational simulations. The expert view of Sophie Neveu and Vincent

Dupuis on ferrofluids allowed me to select suitable systems that are of main interests today.

With their close collaboration, I took part in the synthesis, the structural and chemical characterizations, and the investigations with SQUID and VSM magnetometry. The XAS and XMCD experiments were successfully implemented on these systems with the wise experience of the IMPMC research team (Philippe Sainctavit, Marie-Anne Arrio, Amélie Juhin) and DEIMOS staff (Fadi Choueikani, Philippe Ohresser). In total 165 shifts (1320 hours) of beamtime were employed during this thesis to solve the different questions we addressed. Moreover, I also benefited from the expertise of Marie-Anne Arrio at IMPMC for the LFM calculations. The extremely broad skills of the protagonists gave an original aspect to my thesis that is particularly adapted to the research in ferrofluids, where multidisciplinary fields and knowledge are required to solve the puzzling questions emerging from the ferrofluid community. Concerning the simulations (LFM, DFT or micromagnetic calculations), I am aware that this aspect has not been fully exploited in this thesis and that there is still much place for a more profound theoretical interpretation of the magnetic signatures that we have recorded. Most of the time, the main conclusions could be drawn from a qualitative analysis of the data with comparison with well chosen standards, so that simulations were not always needed for the scientific statements we made.

The second aim of this thesis was more technological and was focussed on the development of experiment devices compatible with the measurement of XMCD signals for samples in the liquid phase such as ferrofluids. On the DEIMOS beamline at SOLEIL, we wanted to develop a flow-through liquid cell compatible with soft X-ray MCD environment, i.e. UHV conditions and limited soft X-rays penetration depth. We achieved to develop a first design, but it proved to be quite difficult to handle so that the first experimental

Summary

In chapter 3, I present two types of liquid cells that I have developed during my Ph.D.

thesis in order to answer the questions that I wanted to solve. The first one is a flowthrough liquid cell developed for the DEIMOS beamline at SOLEIL, the second one is a static liquid cell developed for ID26 beamline at ESRF. Developing a cell for liquids that would allow the measurement of XMCD on a soft X-ray beamline is challenging since the environment of soft X-ray beamlines requires UHV conditions and the X-ray penetration depth of soft X-rays is quite small (less than 200 nm for magnetite). The liquid flowthrough cell, was designed to detect the transmitted X-rays and the Total Fluorescence

Yield for experiments at 300 K. The thickness of the liquid sample was limited to 500 nm and the liquid could be circulated in the measuring position allowing possible in situ changes. The charging of the liquid cell and the XMCD measurements in the transmission mode were successfully validated. However we were not able to preserve the liquid phase in the sample cell due to leaks of the membrane seal. An upgraded version is presently under construction. On the ID26 beamline at ESRF, I developed a static liquid cell in collaboration with Mauro Rovezzi. The liquid cell was implemented to be compatible with RIXS-MCD measurements in the fluorescence mode and adapted to the specific geometry of the beamline. In addition, the liquid cell could be mounted on a cold finger developed by the Sample Environment group from ESRF so that RIXS-MCD experiments between 25 K and 300 K could be recorded. We have used this liquid cell for three different campaigns of beamtime and we recorded successful measurements on ferrofluids containing either core@shell ferrofluids or a mixture of hard and soft nanospinels. To our knowledge, this is the first time that such a device was indeed implemented for XMCD measurements.

In chapter 4, three papers are presented showing that magnetic anisotropies can be modulated by a rationalized approach of the synthesis routes by playing with the morphology, the cationic distributions, the composition and the functionalization of the nanospinels. A combination of XAS and XMCD at the L 2,3 edges was used to determine the site occupancy and local magnetic order of iron or cobalt ions.

The first paper presents a study on chemical coprecipitation which is the easiest and the most widely employed method for ferrofluids synthesis. Contrary to bulk CoFe 2 O 4 spinel, the nanospinels obtained with the coprecipitation process are only partially inversed, with an inverse degree between 0.5 and 0.8. This means that a non negligible part of the tetrahedral sites are occupied by Co ions. The results show strong arguments relating the proportion of Co 2+ ions in octahedral sites with the magnetic coercivity. In addition, the distribution of Co 2+ ions among the crytallographic sites of the structure is directly linked to the temperature process: the higher the temperature, the larger the inversion degree. Moreover, the study showed that the nanoparticles stabilized with nitrate ions are very likely built from a core of CoFe 2 O 4 surrounded by an iron rich shell. This core@shell structure explains why an averaged Fe/Co stoichiometry cannot explain the magnetic properties. The main outcome of the paper is that only the knowledge of nanoparticles sizes as well as their stoichiometry is not enough to predict the expected magnetic properties that are very dependent on the repartition of the Co ions between the tetrahedral and octahedral sites.

In the second paper, we have compared the coprecipitation synthesis with two others synthesis routes: the polyol method and the thermal decomposition of metal acetylacetonates precursors (acac process). The analysis shows that the crystallographic order of the particles obtained with polyol and acac process are quite similar to that of the bulk. The large amount of Co ions on the octahedral sites implies higher coercivity for the nanospinels obtained with polyol and acac that are two times larger than the one obtained for nanospinels prepared by coprecipitation.

The third paper presents another strategy to modulate the magnetic anisotropies of nanoparticles. Co complexes are grafted at the surface of maghemite nanoparticles 𝛾- The very thin (0.35 nm) CoFe 2 O 4 shell is found to impose a strong magnetic anisotropy to the otherwise very soft MnFe 2 O 4 core, so that the inner core presents a large coercive field (0.56 T) and an unexpectedly high remnent magnetization (95% of the saturation magnetization). The combination of large coercive field and large remanent magnetization is an emerging property directly connected to the core@shell structure.

Secondly, we focussed on the formation of dipolar chains and self-assembly of magnetic nanoparticles within ferrofluids that have been said to exist. We have investigated a binary ferrofluid that was a mixture of MnFe

Prospects

Core@shell and core@shell@shell nanoparticles I have been investigating several other core@shell systems that are not presented in this manuscript. The surface sensitivity of TEY detection at L 2,3 edges was used to probe the interface of MnFe 2 O 4 @CoFe 2 O 4 core@shell nanoparticles. At the difference of a similar MnFe 2 O 4 @CoFe 2 O 4 core@shell system, in the one under study the Mn ions at the core@shell interface present an unexpected paramagnetic behavior. XMCD spectra measured at the L 2,3 edges of Mn in MnFe 2 O 4 @CoFe 2 O 4 show an "extra" negative peak that is not showed by the MnFe 2 O 4 single phase reference. Hysteresis detected in XMCD revealed that the magnetic moments of Mn 2+ ions in this environment do not tend to align along the magnetic induction applied, even at 6.8 T (see Figure 5.5.1). Comparisons of the XMCD spectra to atomic multiplet calculations are in progress in order to gain insights on the structural environment of Mn 2+ ions at the interface as well to determine the magnetic coupling with the core and the shell.

XAS and XMCD measurements were also carried on the inverse core@shell system, where the core is a hard magnet of CoFe NiFe 2 O 4 @CoFe 2 O 4 @MnFe 2 O 4 ). The exploration of these various phase combinations is not yet completed since it requires an heavy application of the LFM approach in order to yield a solid, quantitative analysis.

Binary ferrofluids

As the RIXS-MCD experiments were successfully applied on binary ferrofluids of MnFe

Instrumentation

The liquid cell setup for RIXS-MCD measurements is currently available on ID26 beamline and open to other users. Concerning the flow-through liquid cell developed for the DEIMOS beamline, a second prototype that will include new improvements is currently under construction under the supervision of DEIMOS staff.

Outlook

The XMCD technique is a unique tool to determine the relative sites occupations in spinels and others ternary oxides. In that extent, the experimental methods used to investigate synthesized nanospinels with soft chemical process can be applied to natural spinel ferrites that are the main contributors to rock magnetism, 307,308 or to biogenic magnetosomes which can be seen as promising, environmentally friendly good candidates for many biological applications such as malignant glioma destruction by hyperthermia treatment 193,198,208,309 .

The possibility to extend XMCD to the investigation liquid ferrofluids where interparticle interactions have been preserved opens new perspectives in the domain of magnetic liquids. For instance, the influence of the viscosity of the carrier liquid in the magnetic dynamics of these systems could be explored. Better insights could be gained in ring-like and chain-like microstructures predicted by computational modeling, notably in binary systems where the chemical selectivity of XMCD is crucial.

Introduction 1 Materials 1 . 1 2 Methods 2 . 1

 111221 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Spinel ferrites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Magnetic properties of nanoparticles . . . . . . . . . . . . . . . . . . . . . . 1.4 Ferrofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental methods using Synchrotron radiation . . . . . . . . . . . . . . 2.2 Experimental aspects of Synchrotron experiments . . . . . . . . . . . . . . . 2.3 Magnetometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Instrumentation 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Liquid Cell for soft X-ray MCD environment . . . . . . . . . . . . . . . . . 3.3 Liquid Cell for hard X-ray MCD environment . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Synthesis routes 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Paper I : Magnetic Anisotropies and Cationic Distribution in CoFe 2 O 4 nanoparticles prepared by Coprecipitation Route : Influence of Particles Size and Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Supplementary Information of Paper I . . . . . . . . . . . . . . . . . . . . . 4.4 Paper II: Small CoFe 2 O 4 magnetic nanoparticles in ferrofluids, influence of the synthesis on the magnetic properties . . . . . . . . . . . . . . . . . . . . 4.5 Paper III: Enhancing the magnetic anisotropy of maghemite nanoparticles via the surface coordination of molecular complexes . . . . . . . . . . . . . 4.6 Supplementary Information of Paper III . . . . . . . . . . . . . . . . . . . . 4.7 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  spectroscopies. My thesis was supported by the LabEx MATISSE through a consortium involving the Institute of Mineralogy, Physics of Materials, and Cosmochemistry (IMPMC), the laboratory of Physicochemistry of Electrolytes and Interfacial Nanosystems (PHENIX) and the French synchrotron facility (SOLEIL).

2 O 4

 24 and CoFe 2 O 4 nanoparticles in ferrofluids. In the MnFe 2 O 4 -CoFe 2 O 4 mixture we show that the coercive field of CoFe 2 O 4 nanospinels is modified by the presence of the MnFe 2 O 4 nanospinels and vice versa for the MnFe 2 O 4 nanospinels. This might be an indication that a clustering coupling the two different types of nanospinels is likely to be present.

4 and

 4 MgAl 2 O 4 belongs to the space group Fd 3m (n o 227). The structure of spinel is complex. It contains eight formula units which corresponds to 56 ions per cubic cell. Therefore, the cubic cell is likely not the best approach for a convenient description. Instead, the cubic close-packed (i.e. face centered cubic) arrangement of the structure has to be considered for which the rhombohedral unit cell contains two formula units. The interstices between O 2-ions form tetrahedrally coordinated A-sites called tetrahedral sites (T 𝑑 ) and octahedrally coordinated B-sites called octahedral (O ℎ ) sites (see Figure 1.2.1). These sites are occupied by the cations, however only 1/2 (respectively 1/8) of the A-sites and 1/2 of the B-sites of the spinel structure are occupied in the rhombohedral unit cell (respectively in the cubic cell). In the mineral spinel reference MgAl 2 O 4 , the Mg 2+ ions are in A-sites and the Al 3+ ions are in the B-sites. Other ferrite spinels are thus named according to the cations distribution between the A and B-sites. If the divalent ions are located on the A-sites, the spinel is called a normal spinel structure of general formula (M 2+ ) 𝐴 [2Fe 3+ ] 𝐵 O 4 . In the normal spinel structure, M 2+ ions only occupy A-sites and all Fe 3+ cations are in B-sites. ZnFe 2 O CdFe 2 O 4 both crystallize in the normal spinel structure. However, many other ferrites are inverse spinel structure, which means that the M 2+ ions are located in the B-sites. Then the Fe 3+ ions are equally distributed between A and B-sites. Examples of such ferrites include CoFe 2 O 4 , NiFe 2 O 4 and Fe 3 O 4 . Finally, there is also the intermediate case of partially inverse ferrites, where the divalent and trivalent cations both occupy A and B-sites. MnFe 2 O 4 spinel crystallizes in a partially inverse (or partially normal) spinel structure, with 80% of Mn 2+ (20% Fe 3+ ) in A-sites and 20% (80% of Fe 3+ ) in B-sites.

NiFe 2 O 4 .MnFe 2 O 4

 2424 As NiFe 2 O 4 has an inverse spinel structure with a magnetic structure similar to the one of CoFe 2 O 4 . The magnetic moments of Fe 3+ cancel out and the divalent Nickel ions only are responsible for the net magnetization in NiFe 2 O 4 , equal to ≈ 2𝜇 𝐵 /f.u.. MnFe 2 O 4 is a particular case of partially inverse spinels for which Mn 2+ and

Figure 1 . 2 . 2 :

 122 Figure 1.2.2: Magnetization curve for Fe 3 O 4 along easy ⟨111⟩ and hard ⟨100⟩ directions.The area between the two curves equals the magnetocrystalline anisotropy energy. Inset: easy, medium and hard directions of magnetization in a unit cell of Fe 3 O 4 .[START_REF] Dunlop | Rock Magnetism: Fundamentals and Frontiers[END_REF]

Figure 1 . 3 . 1 :

 131 Figure 1.3.1: Schematic of a spheroid single domain nanoparticle with uniaxial magnetic anisotropy in the presence of an external magnetic induction B. The magnetic induction (respectively the magnetic moment)is related to the easy axis by the angle 𝜑 (respectively 𝜃).

Figure 1 . 3 . 2 :

 132 Figure 1.3.2: (a) Reversible magnetic curve (b) Hysteresis and virgin magnetic curve: the features characterizing the hysteresis is the remnant magnetization M r (residual magnetism), the coercive field H c (field necessary to demagnetize the material) and the magnetization at saturation M s .

4 Figure 1 . 3 . 3 :

 4133 Figure 1.3.3: Hysteresis measurements at 20 K of soft magnetic MnFe 2 O 4 nanoparticles (black square) and hard magnetic CoFe 2 O 4 nanoparticles (red square).

Figure 1 . 3 . 4 :

 134 Figure 1.3.4: Schematic of the magnetic moment relaxations for a single domain particle: (A) Brownian relaxation (rotation of the particle), (B) Néel relaxation (rotation of the moment within the particle).

  der Walls-London attractive forces between the particles. Even at low concentrations at which the particles are statistically well separated in the ferrofluid, they are submitted to Brownian motions which can lead to particles collisions. The stability of the colloids is then obtained by introducing repulsive interactions balancing the attractive ones. The repulsive interactions can be steric or electrostatic repulsions (Figure1.4.1). Electrostatic repulsions are the dominant mechanism stabilizing ionic ferrofluids. The electrostatic repulsions are provided by mutually repelling charged double layers introduced at the surface of the colloids. Steric repulsions are used to support the stability in organic based ferrofluids. The stabilizers are surfactants or polymers, adsorbed physically or chemically at the surface of the colloids. Besides their function of stabilization, stabilizers can also prevent from surface oxidation and provide compatibility with fluid. Examples of stabilizers are oleic acid, used to disperse nanoparticles into hydrocarbons, nitrate ions, used to dispersed the colloids in water based acidic medium and citric acid for water based ferrofluids.

Figure 1 . 4 . 1 :

 141 Figure 1.4.1: Repulsive interactions in stable colloidal suspensions of ferrofluids. (a) Electrostatic repulsions (b) Steric repulsions.

Figure 2 . 1 .Figure 2 . 1 . 1 :

 21211 Figure 2.1.1: Model of a synchrotron ring. (1) The Linac, (2) The booster, (3) The storage ring, (4) Wigglers, (5) Radiofrequency sockets, (6) Undulator, (7) Beamline.1

Figure 2 . 1 . 2 :

 212 Figure 2.1.2: Comparisons of the Radiation form provided by a bending magnet, a wiggler and an undulator.52

Figure 2 . 1 . 3 :

 213 Figure 2.1.3: Model of the principle of XAS on synchrotron. The synchrotron source provides a polychromatic beam. Energy range is selected with a monochromator. Specialised mirrors and crystal optics focus the beam and select the wavelength (or energy) desired. X-rays pass through the sample and the transmitted beam is recorded by a detector.

Figure 2 . 1 . 4 :

 214 Figure 2.1.4: Principle of X-ray Magnetic Circular Dichroism (XMCD)

Figure 2 . 1 . 5 :

 215 Figure 2.1.5: Scheme of the Inelastic X-ray Scattering process. The incident and scattered photons are characterized by their energy ( 𝜔), polarization (𝜖), and wavevector (𝑘 .

Figure 2 . 1 . 6 :

 216 Figure 2.1.6: Schematics of the RIXS process. Left panel: general process, Right panel: 1s2p RIXS process at the K pre-edge applied to 3d elements.

Figure 2 . 1 . 7 :

 217 Figure 2.1.7: Left panel: RIXS contour intensity map measured at the Mn K pre-edge of MnFe 2 O 4 nanoparticles plotted as a function of the incident energy and the energy transfer: lines are cut at Constant Tranfer Energy (CTE); Constant Emission Energy (CEE), and Constant Incident Energy (CIE). Intermediate (Γ 𝑛 ) and Final(Γ 𝑓 ) state lifetime broadening the spectra are indicated. Top Right panel: line scan obtained from the RIXS plane at Constant Emission Energy, Bottom Right panel: line scan obtained from the RIXS plane at Constant Incident Energy also known as High Energy Resolution Fluorescence Detection (HERFD-XAS).

Figure 2 . 2 . 1 :

 221 Figure 2.2.1: Left panel: Geometry environment of the spectrometer on ID26 beamline.The spectrometer is composed of analyzer crystals and is surrounded by a helium bag. Right panel: X-ray emission spectrometer with vertical scattering geometry employing five analyzer crystals.84

Figure 2 . 2 . 2 :

 222 Figure 2.2.2: Samples preparation for XAS and XMCD experiments. Drop-casting of ferrofluid in Si wafer are dried at room conditions (left panel). Si wafers with nanopowders are mounted on the copper sample holder (right panel).

Figure 2 .

 2 3.1 was implemented as follow. The ferrofluid sample is introduced in the chamber and cooled in zero-field down to ∼20 K. At this point both nanoparticles and magnetic moments are blocked. A Magnetic induction of 5 mT is applied. The magnetization is then measured while the temperature of the sample is progressively increased in a constant applied field.The magnetization increases first with temperature and reaches a maximum. This maxi-mum corresponds to the blocking temperature. As the temperature continues to increase, the magnetization decreases : the thermal energy overcome the anisotropy energy. The system reaches the equilibrium state. When the temperature reaches 300 K, magnetic induction of 5 mT is applied, and the sample is field-cooled. The FC and ZFC curves intercepts at the equilibrium, when the temperature reaches T B . Experimentally, an average value of T B is measured at the maximum of the ZFC curve due to the polydispersity of the sample. The determination of T B is discussed in literature. Alternatively, some authors propose to determine T B at the inflection point of the ZFC.90

Figure 2 . 3 . 1 :

 231 Figure 2.3.1: Left panel: Protocol of Zero Field Cooled and Field Cooled measurements. Right panel: Temperature dependent ZFC-FC magnetic curve measured for CoFe 2 O 4 ferrofluids.

Contents 3 . 1 3 . 2 3 . 3

 313233 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Cell for soft X-ray MCD environment . . . . . . . . . . 3.2.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Specification and needs . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Results and errors analysis . . . . . . . . . . . . . . . . . . . . . Liquid Cell for hard X-ray MCD environment . . . . . . . . . . 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Forsberg et al. developed a former static liquid cell that can be implemented with features that allow in situ sample change to study corrosion phenomena.115 They added two tubes, one for ingoing flow and one for outgoing flow, that connect the probing internal part of the cell to outside the chamber. Such design allowed to mimic the actual environment in which corrosion happens controlling conditions such as humidity or presence of salts by bringing water or NaCl via the tubing. This kind of advanced liquid cells are referred to as "flow-through liquid cells" in literature. As illustrated by the design of Forsberg et al., the important difference with a static liquid cell is that the probing volume is connected to inlet and outlet tubes via which the liquid can be pumped through the cell during the measurements. This allows to perform realtime measurements of chemical processes that are almost impossible with static liquid cells considering the most time constants for chemical reactions. Another advantage of liquid flow-through cells against the static ones, is that potential local heating by the synchrotron beam can be minimized as highlighted by Fuchs et al.116 High X-rays intensity are needed for XES measurements which leads to local temperature rising close to the membrane.

Figure 3 . 2 . 1 :

 321 Figure 3.2.1: Photons transmission in the range of 0-1000 eV through Si 3 N 4 membrane of 50 nm (green line), 100 nm (blue line), 200 nm (orange line) and 300 nm (pink line).

Figure 3 . 2 . 2 :

 322 Photon energy (eV)

Figure 3 . 2 . 3 :

 323 Figure 3.2.3: MK2T endstation on the DEIMOS beamline as seen with the beam pointing toward us

Figure 3 . 2 . 4 :

 324 Figure 3.2.4: Sample cell chip, Si 3 N 4 membranes chip sandwiched in two Si wafers with the inlet and outlet liquid ports. Left panel: cut-view model, right panel: photograph

Figure 3 . 2 . 5 :

 325 Figure 3.2.5: Sample Holder, front plate and lower part assembled with bolts. Top panel: 3D model assembly (left panel) and 3D model cut view (right panel). Bottom panel : photograph top view (left panel) and photograph side view (right panel). and picture, right panel: assembly 3D cut view model and picture

Figure 3 .

 3 Figure 3.2.6: Sample Holder. Left panel: lower part with the VITON O-rings, Middle panel: lower part with the sample cell, Right panel: assembly of the lowert part and the front plate holding the sample cell

Figure 3 . 2 . 8 :

 328 Figure 3.2.8: Sample holder connected to the horizontal insert. Left panel: 3D model of the sample holder connected to the horizontal insert, Right panel: photograph of the sample holder head connecting the horizontal insert with the copper O-ring.

  photodiode present in the MK2T endstation. Both diodes work in integration mode.

Figure 3 . 2 . 9 :

 329 Figure 3.2.9: Photograph of the photodiode detector for Transmission mode. Left panel: photodiode positionned in the flange, Middle panel: backside view pf the flange, Right panel: photodiode and flange mounted with the sample holder (backside view of the sample holder).

  First the liquid is injected to the sample cell through TEFLON tubes with 1/16 inch (≈1.6 mm) internal diameter (ID). A connector is used to couple the 1/16 inch ID tubes with 200 𝜇m ID PEEK. The microtubes are connected to the sample holder head and fit to the internal micro-channels of the sample holder (Figure 3.2.10).

Figure 3 . 2 . 10 :

 3210 Figure 3.2.10: Liquid flow circuit for sample filling. The liquid is injected with a syringe pump (A) connected to the 1/16 inch ID tubing (B). The liquid goes through the opened valves (C) and the 200 𝜇m ID tubing and reach the sample holder where the sample cell is filled (D). The liquid goes out the 200𝜇m ID outlet tubing connected to the 1/16 inch ID tubing (E).

  photon flux upstream the sample, 𝐼( 𝜔) is the photon flux downstream the sample. The sample profile along the 𝑥 axis and the 𝑦 axis shows some sample thickness inhomogeneities.For the measurements we positioned the sample in a flat portion of the profile where the

Figure 3 . 2 .

 32 Figure 3.2.11: XAS (black lines) and XMCD (red lines) spectra recorded at the Fe and Co L 2,3 edges with the liquid flow-through cell

Figure 3

 3 Figure 3.2.12: XMCD detected magnetic curves recorded at the Fe (left panel-green square) and Co (right panel-orange square) L 2,3 edges.

Figure 3 . 2 . 13 :

 3213 Figure 3.2.13: Model of the sample cell for the new prototype. setup

  3.1). When the liquid cell is full and no air bubbles can be seen inside the cavity, the injecting hole is closed by inserting a molybdenum screw pressing a Viton O-ring (see left panel of Figure3.3.2).The concept of the liquid cell is extremely simple at the expense of a great deal of experimental work that requires skill and several hours of preparation. Indeed, every time a new sample has to be prepared, one needs to remove all the glued Kapton, remove all the remaining glue from the copper sample holder in order to clean the whole parallelepiped cavity with hydrochloric acid. Then a new Kapton foil is glued on top of the parallelepiped cavity and dried into an oven. The ferrofluid is introduced with the syringe and the operation is repeated as much times as needed until the filling is made with no visible bubbles within the cavity. The cavity is then sealed by the O-ring and the Mo screw and one checks that there is no non-detected leak after 12 hours.

Figure 3 . 3 . 1 :

 331 Figure 3.3.1: Static liquid cell with the side hole for liquid injection. Top panel: 3D model, Bottom panel: photograph

Figure 3 . 3 . 2 :

 332 Figure 3.3.2: Static liquid cell. Left panel: liquid cell and the home-made non-magnetic screw, Right panel: Liquid Cell filled with ferrofluid

  I have tested the regulation of the temperature from 300 K down to 70 K as a function of time on the two thermometers and the results are presented in Figure3.3.4. A good accordance between the two thermometers is observed. T A can be regulated from 2 K to 300 K but T B does not cool much below 25 K since the whole copper sample holder receives the 300 K infra-red heating from the cryostat hood. To reduce helium consumption, T A and T B are usually set between 25 and 30 K.During the photon in -photon out process of the RIXS-MCD experiment, the incoming X-rays go through the 50 𝜇m Kapton foil of the hood and the 50 𝜇m Kapton foil of liquid cavity. The outgoing X-rays go through the same Kapton foils so that a total 200 𝜇m Kapton attenuation is observed.

Figure 3 . 3 . 3 :

 333 Figure 3.3.3: Model of the liquid cell setup. The sample holder is screwed to the cold finger of ab cryostat and protected by a hood.

Figure 3 . 3 . 4 :

 334 Figure 3.3.4: Tests of temperature regulation of the cold finger. T A is the temperature of the main exchanger, T B is the temperature near the sample. The temperature is regulated with the helium flow rate.

Figure 3 . 3 . 5 :

 335 Figure 3.3.5: Cold-Finger insert.

Figure 3 . 3 . 6 :Figure 3 Figure 3 . 3 . 8 :

 3363338 Figure 3.3.6: Liquid Cell setup adapted to the ID26 endstation geometry. Left Panel: model, Right Panel: photograph

Contents 4 . 1 4 . 2 4 . 3 4 . 4

 41424344 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Coprecipitation synthesis . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Influence of the synthesis process . . . . . . . . . . . . . . . . . . 4.1.3 Nanoparticles functionnalization . . . . . . . . . . . . . . . . . . Paper I : Magnetic Anisotropies and Cationic Distribution in CoFe 2 O 4 nanoparticles prepared by Coprecipitation Route : Influence of Particles Size and Stoichiometry . . . . . . . . . . . 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supplementary Information of Paper I . . . . . . . . . . . . . . Paper II: Small CoFe 2 O 4 magnetic nanoparticles in ferrofluids, influence of the synthesis on the magnetic properties . . . 4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Paper III: Enhancing the magnetic anisotropy of maghemite nanoparticles via the surface coordination of molecular complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Step 4 is modified by adding citrate trisodium salt (3 mmol) to the sol. During citratation the hydroxyl groups at the surface of the particles are replaced by citrate anions. The particles obtained by Step 4 ′′ were dispersed in distilled water in Step 5. Step 4 ′′ is used instead of Step 4 to obtain CoFe25_7, CoFe33_11, CoFe33_13 and CoFe33_21. Characterizations Transmission Electron Microscopy. The morphology of the nanospinels for the six samples has been measured on a JEOL 100 CX2 Transmission Electron Microscope (TEM) (Electronic microscopy platform of the Fédération des Matériaux -UPMC).

  Figure 4.2.1 shows TEM micrographs and size histograms. The TEM images reveal irregular spheroidal shape nanoparticles for the six samples. The analysis of the diameter of more than 2000 particles for each sample leads to size histograms fitted with a log-normal distribution. Results are reported in Table 4.2.1. X-Ray Diffraction. The coherent domain size of the nanoparticles were determined with a PANALYTICAL X'pert Pro MPD diffractometer with the CoK𝛼 radiation (K𝛼= 1.79 Å) (See Supplementary Information Figure 4.3.2). All diffraction peaks can be indexed with the CoFe 2 O 4 spinel structure (reference code pattern 96-5941-0064). From the XRD profile of the (311) peak, one can compute the nanospinel size (d 𝑋𝑅𝐷 ) with the Debye-Sherrer expression 205,206 . The mean d 𝑋𝑅𝐷 sizes are repported in Table 4.2.1. Atomic Absorption Spectrometry. The cationic concentrations of cobalt and iron are determined by Atomic Absorption Spectrometry after degradation of the nanoparticles in concentrated hydrochloric acid. We used a Perkin Elmer Analyst 100 spectrometer with an air-acetylene flame at a mean temperature of 2300˚C. Experiments were repeated at least three times on each sample. The molar ratio X M is determined from the Fe and Co concentrations (Table 4.2.1). SQUID Magnetometry. Magnetometry measurements were recorded using either a Superconducting QUantum Interference Device (SQUID) Magnetometer (Quantum Design MPMS-XL7) or a Vibrating Sample Magnetometer (QuantumDesign PPMS) (Plateforme de mesures physiques à basse température -UPMC). Measurements are performed on dried powders of nanoparticles at 300 K and 4 K, and on liquid ferrofluids frozen at 4 K. The 4 K magnetization curves for frozen ferrofluids and for dried nanoparticles almost superimpose. The small discrepancies observed between the dried nanoparticles and the ferrofluids measurements show that inter-particles interactions can be neglected in nanoparticles solid phase compare to ferrofluids where colloids are far from each others. Table 4.2.1 reports the values of the magnetization at saturation (M S ) for powders nanoparticles at 300 K. Magnetization curves for frozen ferrofluids are plotted in Figure 4.2.4.

Figure 4 . 2 . 1 :

 421 Figure 4.2.1: TEM images and size distribution histograms : (A) 7 nm non-stoichiometric nanoparticles CoFe25_7, (B) 9 nm non-stoichiometric nanoparticles CoFe25_9, (C) 9 nm stoichiometric nanoparticles CoFe33_9, (D) 11 nm stoichiometric nanoparticles CoFe33_11, (E) 13 nm stoichiometric nanoparticles CoFe33_13, (F) 20 nm stoichiometric nanoparticles CoFe33_21

  XAS and XMCD signals for both Fe and Co L 2,3 edges were recorded on the DEIMOS beamline at the French synchrotron, SOLEIL.85 All spectra were measured in Total Electron Yield (TEY) at 4.2 K and in UHV conditions (10 -10 mbar). In the presence of an external magnetic induction B + (respectively B -) parallel (respectively antiparallel) to the X-ray propagation vector, XMCD signals are obtained by taking the difference 𝜎 𝑋𝑀 𝐶𝐷 = 𝜎 --𝜎 + where 𝜎 + =[𝜎 𝐿 (B + ) + 𝜎 𝑅 (B -)]/2 and 𝜎 -=[𝜎 𝐿 (B -) + 𝜎 𝑅 (B + )]/2, and 𝜎 𝐿 (respectively 𝜎 𝑅 ) is the absorption cross-section measured with left (respectively right) circularly polarized X-rays. The XMCD signals were recorded by flipping both the circular polarization (either left or right helicity) and the external magnetic induction (either +6.6 Tesla or -6.6 Tesla). The circularly polarized X-rays are provided by an Apple-II HU-52 helical undulator for both XAS and XMCD measurements. Ferrofluids are dropcasted on silicon plates and dried at room temperature. The silicon plates are screwed on a non-magnetic sample holder which is entered into the air-lock chamber and transfered into

Figure 4 . 2 . 2 :

 422 Figure 4.2.2: XAS and XMCD spectra at the Fe (left side) and Co (right side)L 2,3 edges for the CoFe33_9 sample measured at 4 K with an applied field of +/-6.6 Tesla. The different peaks relevant for the discussion have labels beginning with 'I ' for the features of the isotropic spectrum edges and with 'X ' for the features of the XMCD signal.

  .8 and 4.3.9). Samples are grouped into three sets for the presentation and the discussion of the results. The four samples of the first set (CoFe33_9, CoFe33_11, CoFe33_13 and CoFe33_21) present a stoichiometric composition with a molar ratio X M =33 %. The second set (CoFe25_7, and CoFe25_9) groups samples with X M =25 % where vacancies are present on the O ℎ sublattice. For the two first sets of samples, the cationic distribution is discussed as a function of size and synthesis route. The third set (CoFe33_9, CoFe25_9) groups the two samples with 9 nm size nanospinels and for which the cationic distribution is examined as a function of two different X M and two different amounts of vacancies in the O ℎ sub-lattice.

Figure 4 . 2 . 3 :

 423 Figure 4.2.3: Isotropic XAS and XMCD spectra at the Fe L 2,3 edges ((A) and (B)) and Co L 2,3 edges ((C) and (D)) for CoFe33_9, CoFe33_11, CoFe33_13, CoFe33_21 samples at 4 K. XMCD spectra are plotted in percent of the maximum of the XAS spectra. Inset : zoom in the 𝐿 3 edges of the XMCD spectra.

Figure 4 . 2 . 4 :

 424 Figure 4.2.4: Magnetization curve versus field measurement of ferrofluids measured at 4 K of : CoFe33_9, CoFe33_11, CoFe33_13 and CoFe33_21 (A), CoFe25_9 and CoFe25_7 (B), CoFe25_9 and CoFe33_9 (C)

Figure 4 . 2 . 5 :

 425 Figure 4.2.5: Isotropic XAS and XMCD spectra at the Fe L 2,3 edges ((A) and (B)) and Co L 2,3 edges ((C) and (D)) for CoFe25_7 and CoFe25_9 samples at 4 K

Figure 4 . 2 .

 42 Figure 4.2.5 panels (C) and (D). At the difference of what has been observed at the Fe L 2,3 edges, the two spectra present a series of differences that can be readily analyzed as it has been done for the X M =33% series. A sharper I3 peak, a larger ratio of I4/I5 and the shape of the L 2 edge (see Figure4.3.8 in Supplementary Informations) indicate that the CoFe25_7 sample contains a larger amount of Co ions in the O ℎ sites than the CoFe25_9 sample. This trend is fully supported by the XMCD signals at the Co L 2,3 edges which present a smaller X3/X4 ratio for CoFe25_7 sample compare to CoFe25_9 sample (see Figure 4.2.5). Contrary to what has been observed for the X M =33% series, one obtains that the larger the particles the smaller the proportion of Co ions on the O ℎ sites. On the other hand, one sees that the larger the proportion of Co ions in O ℎ sites, the larger the coercive field and this conclusion is fully satisfied for both X M =33% and X M =25% series (Figure 4.2.4).

Figure 4 . 3 . 1 )

 431 Figure 4.3.1). Following the analysis developed for the X M =33 % series, one notices from the Fe XAS and XMCD signals that the CoFe33_9 sample has a slightly larger proportion of Fe ions in O ℎ sites (Figure 4.2.3). Similarly, the Co XAS and XMCD signals indicate that the sample with X M =33 % has a slightly larger proportion of Co ions in T 𝑑 sites (Figure 4.2.6). Interestingly the increase of Co ions in O ℎ sites does not induce a much larger coercive field for CoFe25_9 compared to CoFe33_9. The shape observed for the Fe and Co isotropic and XMCD signals can be further understood by assuming a core/shell structure for sample CoFe25_9 . Iron nitrates would induce the growth of a small shell of 𝛾-Fe 2 O 3

Figure 4 . 2 . 6 :

 426 Figure 4.2.6: Isotropic XAS and XMCD spectra at the Fe L 2,3 edges ((A) and (B)) and Co L 2,3 edges ((C) and (D)) for CoFe33_9 and CoFe25_9 samples at 4 K

Figure 4 . 3 . 1 :

 431 Figure 4.3.1: Scheme of the different synthesis steps used to obtain samples of iron-cobalt nanospinels

Figure 4 . 3 . 2 :

 432 Figure 4.3.2: X-Ray Diffractograms recorded for CoFe25_7, CoFe25_9, CoFe33_9, CoFe33_11, CoFe33_13, CoFe33_21 samples.

Figure 4 . 3 . 3 :

 433 Figure 4.3.3: Magnetization vs. field measurements on the dried powder nanoparticles recorded at 300K.

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

 434435 Figure 4.3.4: XMCD detected magnetic curves measured at the Fe L 3 edge in CoFe25_9 sample at T 𝑑 sites energy (E=776.56 eV, X1 peak) and O ℎ sites energy (E=777.54 eV, X2 peak)

Figure 4 . 3 . 6 :Figure 4 . 3 . 7 :

 436437 Figure 4.3.6: Fe and Co selective magnetic curves measured for the CoFe25_7 and CoFe25_9 samples at E=777.54 eV. The magnetic curves are measured at O ℎ sites energy and multiplied by (-1) for the standard of reading.

4. 4

 4 Paper II: Small CoFe 2 O 4 magnetic nanoparticles in ferrofluids, influence of the synthesis on the magnetic properties STATUS : Submitted to The Journal of Magnetism and Magnetic Materials on May 20 th , 2016.

( 4 . 4 . 1 )

 441 Nanospinels morphologies and sizes were determined by Transmission Electron Microscopy (TEM) using a JEOL-100 CX2 microscope (UPMC). The analysis of the micrographs of more than 2000 particles leads to size histograms fitted with a log-normal distribution presented in Figure4.4.1.X-ray Diffraction (XRD) patterns were recorded on the nanoparticles powders using a PANALYTICAL X'Pert Pro MPD diffractometer with the Co K𝛼 radiation (𝜆 = 1.79 Å).

Figure 4 . 4 . 2 .

 442 Magnetizations vs. magnetic induction at 4 K and 300 K have been recorded with a Vibrating Sample Magnetometer (VSM) using a Quantum Design PPMS. Magnetization vs. magnetic induction measurements at 4 K were performed on frozen diluted ferrofluid dispersions (Figure4.4.3) while magnetization curves at 300 K were measured on the nanoparticles powders. The magnetization at saturation (M S ) at 300 K was determined and normalized by the mass of the sample corrected after ThermoGravimetric Analysis.Mass losses of organic species of about 10% were determined for the Co-acac and Copolyol samples, and 20% for the Co-coprec sample. The magnetization at saturation of the nanoparticles at 300 K and the coercive field of the nanoparticles measured at 4 K are presented in Table4.4.1.X-ray Absorption Spectroscopy (XAS) and XMCD measurements were recorded on the DEIMOS beamline at the French synchrotron facility SOLEIL.85 XAS and XMCD signals were recorded at the Co and Fe L2,3 edges at 4 K under ultra-high vacuum (10 -10 mbar) in the presence of a 6.4 Tesla magnetic induction. The circularly polarized x-rays are provided by an Apple-II HU52 undulator. The XMCD signals were recorded by flipping both the circular polarization (left and right helicity) and the external magnetic induction (either B + = + 6.4 T or B -= -6.4 T). Each XMCD spectra was thereby acquired by taking the difference: 𝜎 𝑋𝑀 𝐶𝐷 = 𝜎 --𝜎 + (4.4.2) where 𝜎 -= [𝜎 𝑅 (𝐻 + ) + 𝜎 𝐿 (𝐻 -)] (4.4.3) and 𝜎 + = [𝜎 𝑅 (𝐻 -) + 𝜎 𝐿 (𝐻 + )] (4.4.4)

6. 7

 7 nm for the Co-acac nanoparticles and 5.6 nm for the Co-polyol nanoparticles and. TEM micrographs show the dependence of the nanoparticles morphology with the synthesis process (Figure4.4.1). The coprecipitation synthesis leads to non-spherical nanoparticles with a high polydispersity (𝜎 = 0.43). Nanospinels obtained with the polyol process are spherical but the nanoparticles are highly polydisperse (𝜎 = 0.55). iron-cobalt nanospinels synthesized with the acac process are also spherical but the process allows to obtain monodisperse nanoparticles with narrower size distribution (𝜎 = 0.28). Nanoparticles sizes were also determined by XRD measurements (Figure 4.4.2). The samples present between 30˚and 80˚(2𝛾) five peaks that correspond to a spinel structure indexed for CoFe 2 O 4 (reference code pattern 96-5941-0064) with mean size for coherent domain of 5.4 nm for the Co-coprec nanoparticles, 6.5 nm for the Co-acac nanoparticles and 5.5 nm for the Co-polyol nanoparticles.

Figure 4 . 4 . 1 :

 441 Figure 4.4.1: TEM micrographs and size distributions histograms of A) Co-coprec (6.8 nm), B) Co-acac (6.7 nm), C) Co-polyol (5.6 nm) nanoparticles

Figure 4 . 4 . 2 :

 442 Figure 4.4.2: XRD patterns of the Co-acac (blue line), Co-polyol (dark yellow line) and Co-Coprec (dark cyan line) samples

Figure 4 . 4 . 3 :

 443 Figure 4.4.3: Magnetization curves measured on ferrofluids samples of Co-acac (blue line), Co-polyol (dark-yellow square) and Co-Coprec (Dark cyan triangle) at 4 K.

Figure 4 . 4 . 4 :

 444 Figure 4.4.4: XAS and XMCD spectra measured at 4 K on the dried nanoparticles of Co-coprec (dark cyan triangle), Co-polyol (dark yellow square) and Co-acac (blue circle) samples at the (a) Fe L 2,3 edges ((a) and (c)) panels) and Co L 2,3 edges ((b) and (d) panels)

Figure 4 . 4 . 5 :

 445 Figure 4.4.5: Evolution of the octahedral symmetry sites occupation of Co 2+ (red square) and Fe 3+ (black square) with the coercivity. The occupancy of the O ℎ sites by the metal M, where M is either Co 2+ or Fe 3+ is calculated with M(O ℎ )/M(total)

4. 5 Figure 4 . 5 . 1 :

 5451 Figure 4.5.1: Figure of theTable of Content

H 2 OPreparation of 2 .

 22 :MeOH 50% v/v mixture. Then, 500 ml of an aqueous TMAOH solution(2.8 M) were brutally added to the solution under strong stirring leading to the sample 0b. Preparation of 1. A measure of 250 ml of 0a were diluted 10 times with a H 2 O:MeOH 50% v/v mixture. A volume of 0.550 ml of a [Co(TPMA)Cl 2 ] solution (10 mM, H 2 O:MeOH 50% v/v) were added dropwise under stirring, followed by the rapid addition of 500 ml of an aqueous TMAOH solution (2.8 M) under strong stirring. Then, the solution was stirred for 4 h at 60 ˚C and for 24 h at room temperature leading to sample 1. The sample was prepared following the procedure described for 1using [Zn(TPMA)Cl 2 ] instead of [Co(TPMA)Cl 2 ].Precipitation of the particles. The addition of three volumes of acetone into the solutions led to the precipitation of the particles. The suspension was placed on a NdFeB magnet to settle the particles and the supernatant was removed. The obtained paste-like solid was washed with an aliquot of ethanol and dried in an oven at 40 ˚C for 48 h.Atomic absorption spectroscopy (AAS).The total iron, cobalt and Zinc concentration (mol.l -1 ) was determined by AAS with a Perkin-Elmer Analyst 100 apparatus after degrading the precipitated particles in HCl (37%).Transmission electron microscopy (TEM). Images have beenperformed on a JEOL 100CX2 microscope with 65 keV incident electrons focused on the specimen. Highresolution TEM has been achieved on a JEOL JEM 2011 microscope with an acceleration voltage of 200 kV and a resolution of 0.18 nm. Dynamic light scattering. The DLS measurements have been performed on a Malvern Zetasizer nanoZS model equipped with a backscattering mode on the solutions containing the particles using the intensity profile. The sizes given in the article correspond to the Z average measurements. X-ray powder diffraction. Patterns were collected on a Philips X'pert Pro diffractometer using Co-K𝛼1 monochromatic radiation (𝜆=1.78901 Å) and equipped with a X'celerator linear detector. Magnetic measurements. Magnetic measurements were carried out with Quantum Design MPMS-XL and MPMS-5S magnetometers working in d.c. mode on frozen solutions of the samples. The solution was diluted in a H 2 O:MeOH 50% v/v mixture before measurements. The solution volume was 150 𝜇l and the weight concentration 0.4%.

Figure 4 . 5 . 2 :

 452 Figure 4.5.2: Enhancing molecular complex and functionalized maghemite nanoparticles. (a) Representation of the [Co(TPMA)Cl 2 ] complex used to enhance the magnetic anisotropy of the 𝛾-Fe 2 O 3 nanoparticles. (b) TEM image of the 𝛾-Fe 2 O 3 nanoparticles functionalized with the cobalt(II) complex: 1(5.0 nm, 𝜎=0.09) and (c) schematic view of the coordination of the complex with the iron ions. (d) Synthesis scheme with measured pH values, hydrodynamic diameters (Zav), sizes (D) and distributions (s).

Figure 4 .

 4 5.2(b) and Supplementary Figure 4.6.3). Along with the DLS experiments, this supports the absence of aggregation or of higher size particles. It also indicates that the functionalization has a negligible effect on the size of the objects. X-ray powder pattern analysis shows that 0b and 1 both display the cubic structure of the maghemite (Fd-3m) while the estimated crystallite sizes are in agreement with TEM imaging (Supplementary Figure 4.6.4 and Supplementary Table 4.6.3). High-resolution TEM also confirms the cubic structure for the particles and indicates that no structural evolution has occurred during the functionalization reaction (Supplementary Figure 4.6.2 and Supplementary Table4.6.2). In addition, X-ray photoelectron spectroscopy (XPS) measurement at the Fe 2p edges shows an energy gap between 2p 1/2 and 2p 3/2 (13.7 eV) that is, in agreement with the 𝛾-Fe 2 O 3 structure 256 (Supplementary Figure 4.6.5). XPS measurements at the N 1s edge show two peaks at 404 and 399 eV for 1 (Figure 4.5.3).

Figure 4 . 6 . 6 )Figure 4 . 6 . 7 and

 466467 Figure 4.6.7 and Supplementary Methods). In summary, the combination of XPS, AAS and XAS measurements clearly confirms the presence of the CoII(TPMA)2 + complex at the surface of the nanoparticles and the formation of an oxo-bridge between Co 2+ and Fe 3+ ions.

Figure 4 . 5 . 3 :

 453 Figure 4.5.3: Presence of the enhancing unit in the functionalized maghemite nanoparticles. XPS spectra at the N1s edge of samples 0b (a), 1 (b) and of the [Co(TPMA)Cl 2 ] complex (c).

Figure 4 .

 4 5.5 and SupplementaryFigure4.6.11) to discriminate the chemical environment and magnetic properties of the different Fe species, through the analysis of

Figure 4 . 5 . 4 :

 454 Figure 4.5.4: Enhanced anisotropy and improved magnetic properties.(a) Fieldcooled and zero-field-cooled (FC/ZFC) magnetization curves measured in the 5-80 K temperature range under an applied field of 50 Oe and (b) magnetization vs field curves measured at 5 K for 0b and 1 in diluted solutions (%v<0.15). Lines in the ZFC plots represent the best fit (see Methods for calculation details).

spectra at 12 K

 12 (Fe 𝑂 ℎ (III)/Fe 𝑇 𝑑 (III)=1.70 close to 5/3 as expected for maghemite; SupplementaryFigure 4.6.11). The mean values of isomer shift (at 77 K 0.41(2) mms -1 ), which probes the electronic density at the57 Fe nuclei, that is the valence state, are consistent with the presence of pure ferric species for both 0b and 1. This excludes the presence of a ferric impurity and the occurrence of Fe 2+ species or intermediate valence state. It further evidences that no electron transfer is induced by the presence of the Co 2+ com-

Figure 4 . 5 . 5 :

 455 Figure 4.5.5: Slowdown of the relaxation of the magnetization. Zero field 57 Fe Mössbauer spectra (circles: experimental; lines: calculated) measured at 77 K for 0b (a) and 1 (b) and corresponding hyperfine field distributions (P(B ℎ𝑓 )) vs hyperfine field (B ℎ𝑓 ) plot (c).

Figure 4 . 5 . 6 :Figure 4 . 6 .

 45646 Figure 4.5.6: Fe-specific and Co-specific XMCD-detected magnetization curves at 5 K. The XMCD curves for octahedral Fe 3+ and for Co 2+ were multiplied by -1 before normalization. All the curves were normalized to one at the highest field value, error bars are s.d.

Figure 4 . 5 . 7 :

 457 Figure 4.5.7: Element-specific characterization of the functionalized nanoparticles. XAS and XMCD signals measured on sample 1 at the Fe (a,c) and Co (b,d) L 2,3 edges at 5 K and 6 T.

Figure 4 . 6 . 1 : 2 Table 4 . 6 . 1 :

 4612461 Figure 4.6.1: Hydrodynamic size distribution in a H 𝑂 : MeOH 50% v/v mixture at 25°C for the bare nanoparticles (0a and 0b) and the nanoparticles functionalised with the complex {CoII(TPMA)} 2+ in basic pH from Neq = 3 to Neq = 210.

Figure 4 .

 4 Figure 4.6.2: X-ray powder diffraction patterns of 0b and 1, and calculated diagram for 𝛾-Fe 2 O 3 in Fd-3m.

Figure 4 . 6 . 3 :

 463 Figure 4.6.3: TEM images of the bare nanoparticles 0b (top) and of 1 (bottom) (insert: distribution made on approx. 200 nanoparticles and log normal fit).

Figure 4 . 6 . 4 :

 464 Figure 4.6.4: TEM, HR-TEM and SAED images of the bare nanoparticles 0a (top), 0b (middle) and of 1 (bottom).

Figure 4 . 6 . 7 :

 467 Figure 4.6.7: Influence of the ligand field strength on the XAS spectra at Co L 2,3 edges calculated in the Ligand Field Multiplet model.

Figure 4 . 6 .

 46 6 presents the XAS spectra calculated with 𝜅=0.7, 𝜅=0.1eV, 𝜅=0.2eV (=0.4eV) at L 3 edge (L 2 edge) and 10Dq varying from 0.6 eV to 1.2 eV. The experimental XAS of the complex [Co(TPMA)Cl 2 ] corresponds to the calculation with a small ligand field strength, 10Dq = 0.6eV, and the experimental XAS of 1 corresponds to the calculation with stronger ligand field, 10Dq = 1eV.

Figure 4 . 6 . 8 :

 468 Figure 4.6.8: Field-dependence of the XMCD signals at 5 K measured at 711.39 eV for tetrahedral Fe 3+ , 712.02 eV for octahedral Fe 3+ , 777.96 eV for Co 2+ in 1 and 777.85 eV for Co 2+ in [Co(TPMA)Cl 2 ]

Figure 4 . 6 . 9 :

 469 Figure 4.6.9: Magnetisation vs. field curves for frozen solutions of 0b and 1 at 5 K.

Figure 4 .

 4 Figure 4.6.10: ZFC/FC curves for a frozen solution of 2 under an applied field of 50 Oe compared to 0b.

Figure 4 . 6 . 11 :

 4611 Figure 4.6.11: Magnetisation vs. field curves for a frozen solution of 2 at 5 K compared to 0b.

Figure 4 . 6 . 12 :

 4612 Figure 4.6.12: 57 Fe Mössbauer spectra (circles: experimental; lines: calculated) measured at 12 K for 0b (top) and 1 (bottom) in a 8 T external field. One can distinguish two different sextets: the external and internal ones are attributed to the tetrahedral and octahedral Fe sites, respectively.

CoFe 2 O

 2 4 bulk structure. A second synthesis strategy to control magnetic anisotropies of ferrite nanospinels consists in grafting cobalt(II) complexes at the surface of a soft nanospinel such a nanomaghemite. In the case of 𝛾-Fe 2 O 3 nanoparticles functionnalized with [Co(TPMA)Cl 2 ] complexes, the magnetic anisotropy of the Co ions is transferred to the 𝛾-Fe 2 O 3 nanoparticles via oxo bridges linking the complex to the nanospinel. The distinct magnetic contributions of Co and Fe ions were measured by XMCD thus showing the existing magnetic coupling between the Co complex and the 𝛾-Fe 2 O 3 nanoparticles. Such a phenomenon is somewhat similar to the Co-Fe exchange interaction in CoFe 2 O 4 nanospinels. As mentioned in section 4.1, the study of nanoparticles functionnalized with cobalt molecular complexes was initiated by scientists from the Institut Parisien de Chimie Moléculaire and the PHENIX laboratory. I have been associated to this work in order to bring my expertise of the XAS and XMCD measurements applied to nanospinels. It gave me the opportunity to enter the field of the coordination chemistry where achieving larger magnetic anisotropy in nanoparticles is also a "hot topic".

  following two very much different methods. The two spinel phases are MnFe 2 O 4 and CoFe 2 O 4 that present different superparamagnetic behaviors. MnFe 2 O 4 is a soft magnetic material with a small anisotropy constant, whereas CoFe 2 O 4 is a hard magnetic material. The chemical selectivity of the RIXS-MCD spectroscopy is paramount since it allows to probe either the magnetic behavior of MnFe 2 O 4 by recording the Mn K -edge or the magnetic behavior of CoFe 2 O 4 by recording the Co K -edge. I have investigated two different types of samples where the two spinel phases are coupled in a very different way.

5. 2

 2 Paper IV: Nanoscale distribution of Magnetic Anisotropies within Bimagnetic Core@Shell Nanoparticles Dispersed in Ferrofluid STATUS : Not yet submitted. Will be submitted to Nanoscale in September 2016.

Figure 5 . 2 . 1 :

 521 Figure 5.2.1: Figure of theTable of Content

  Nanoparticles are prepared following the thermal decomposition process of metallic acetylacetonates precursors in the presence of oleic acid, 1,2-hexadecanediol, oleylamine and benzyl ether. Monodispersed nanoparticles with controlled morphology and excellent crystallinity are obtained following the process of Sun et al.. 166 The synthesis of MnFe 2 O 4 , CoFe 2 O 4 and MnFe 2 O 4 @CoFe 2 O 4 nanoparticles has been described elsewhere. 228 Transmission Electron Microscopy. TEM micrographs were obtained using a JEOL 100 CX2. Size histograms were obtained from the analysis of the TEM micrographs over more than 10,000 nanoparticles. These histograms were fitted by a lognormal law with a least-square refinement that provides particles mean diameter d 0 and their respective polydispersity 𝜎.X-Ray Diffraction. XRD 𝜃/2𝜃 patterns were recorded with a PANALYT-ICAL X'Pert Pro MPD diffractometer using Fe filtered the Co K𝛼1 (𝜆 = 1.79Å) radiation from a mobile anode at 40 kV, 40 mA. The measurements were carried out in a range of 30-80°2𝜃 in steps of 0.02°and collection time of 7200s. Coherent domain sizes are calculated from the Scherrer equation. 205 Atomic Absorption Spectrometry. Measurements were performed using a Perkin Elmer Analyst 100 with an air-acetylene flame at a mean temperature of 2300°C. Experiments were repeated at least three times on each sample. Molar concentrations of cobalt, manganese and iron are determined after degradation of the nanoparticles in concentrated hydrochloric acid. From the metallic concentrations species, the volume fraction of the nanoparticles was calculated and molar ratios X M are determined for each sample (Table 5.2.1): X M = [M]/([M]+[Fe]) where [M] is [Mn] for MnFe 2 O 4 , [Co] for CoFe 2 O 4 and [Mn]+[Co] for Mn@Co. Bulk magnetic measurements. They were performed using a Vibrating Sample Magnetomer Quantum Design PPMS. Blocking Temperatures were determined from the Zero-Field Cooled and Field Cooled (ZFC/FC) temperature dependence of magnetization measured under a 70 Oe field on the particles dispersed in paraffin. Paraffin is used here to avoid the critical fusion point of heptane. Magnetization at saturation of the MnFe 2 O 4 , CoFe 2 O 4 and Mn@Co nanoparticles are determined from room temperature magnetization vs. Field measurements performed on the powder samples and corrected with thermogravimetric analysis determining proportions of organic ligands (Figure 5.3.9, Supplementary Information). Magnetization curve vs. Field measurements were performed at 26 K and 39 K on the ferrofluids of the MnFe 2 O 4 , CoFe 2 O 4 and MnFe 2 O 4 @CoFe 2 O 4 particles (Figure 5.3.7, Supplementary Information) Soft XAS and XMCD measurements. XAS and XMCD signals were recorded at the Mn and Co L 2,3 edges on the DEIMOS beamline at the French synchrotron, SOLEIL. Spectra were measured in Total Electron Yield at 50 K and in HV conditions (10 -8 mbar) on a dropcast of Mn@Co particles. XMCD signals were recorded by flipping both the circular polarization (either left or right helicity) and the external magnetic field (either +1.5 Tesla or -1.5 Tesla). Circularly polarized X-rays are provided by an Apple-II HU52 helical undulator for both XAS and XMCD measurements. Element-specific magnetization curves were measured using the EMPHU-65 undulator which allows the fast switching (1 Hz) of the X-ray helicity. 85 RIXS and RIXS-MCD spectroscopies. Experiments were carried out at ID26 beamline of the European Synchrotron Radiation Facility (Grenoble, France). Measurements were performed at the Co and Mn K -edges (i) at room temperature on the liquid phase of the different ferrofluids, (ii) at low temperature on the frozen phase of the same samples.

  2.1), showing that the obtained stoichiometry is close to the expected one for a spinel, i.e. 1 divalent ion for 2 trivalent ions. The TEM micrographs illustrated in Figure 5.2.2 show that all particles are spherical. The respective particle size histograms are well-fitted using log normal distributions, leading to a mean diameter of 6.0 nm (𝜆 = 0.22) for MnFe 2 O 4 , 5.8 nm (𝜆 = 0.25) for CoFe 2 O 4 and 6.7 nm (𝜆 = 0.34) for MnFe 2 O 4 @CoFe 2 O 4 , respectively (Table 5.2.1). These values are consistent with the size of coherent domains obtained from the XRD pattern (Figure 5.3.1, Supplementary Information). From the difference in particle size, the thickness of the outer cobalt ferrite layer in the MnFe 2 O 4 @CoFe 2 O 4 particles can be estimated to be ∼0.3-0.4 nm.

Figure 5 . 2 . 2 :CoFe 2 O 4

 52224 Figure 5.2.2: TEM images and distribution in particle size for the CoFe 2 O 4 (top), MnFe 2 O 4 (middle), and Mn@Co dried powder samples (bottom). Size distributions are determined using a Gaussian fit of histograms (red line).

  Magnetometer (VSM) magnetometer for particles dispersed in paraffin. The value of the superparamagnetic blocking temperature (T B ) is determined from the maximum of the Zero Field Cooled curve plotted in Figure 5.2.3 together with the Field Cooled temperature dependence of magnetization. The Mn@Co nanoparticles in the frozen liquid show a higher blocking temperature (T B = 150K) than the MnFe 2 O 4 nanoparticles (T B = 20K), while CoFe 2 O 4 nanoparticles show the highest value of T B (200K), which is typical for such particle size and composition. Since T B = KV 25k B , (where K is the magnetic anisotropy, V the volume and k 𝐵 the Boltzmann constant), the increase of T B for the Mn@Co nanoparticles with respect to the MnFe 2 O 4 seeds can be attributed to the slight volume increase due to the growth of the shell and to the increase in magnetic anisotropy due to the formation of the harder CoFe 2 O 4 outer layer.

Figure 5 . 2 . 3 :

 523 Figure 5.2.3: Field Cooled and Zero Field Cooled curves measured on ferrofluids of MnFe 2 O 4 (blue dots), CoFe 2 O 4 (green triangles), Mn@Co nanoparticles (red squares).

Figure 5 . 2 . 4 :

 524 Figure 5.2.4: Low temperature RIXS and RIXS-MCD planes measured on the frozen ferrofluid of MnFe 2 O 4 @CoFe 2 O 4 particles at the Mn edge (panels (a) and (b)) and at the Co edge (panels (c) and (d)). For both edges only the part of the planes corresponding to the K𝛼1 emission region is shown.

Figure 5 . 2 . 5 :

 525 Figure 5.2.5: Low Temperature absorption and XMCD spectra measured at Constant Emission Energy at the Co edge (panels (a) and (b), T = 39 K, CEE =6.9313 keV) and at the Mn edge (panels (c) and (d), T = 26 K, CEE=5.8998 keV).

Figure 5 . 2 . 6 :

 526 Figure 5.2.6: Element selective magnetization curves measured by RIXS-MCD at ambient and low temperatures, at the Co edge (top panels) and at the Mn edge (bottom panels)

Figure 5 . 3 . 1 :Figure 5 . 3 . 2 :Figure 5 . 3 . 4 :Figure 5 . 3 . 5 :

 531532534535 Figure 5.3.1: XRD pattern of the CoFe 2 O 4 (green line), MnFe 2 O 4 (blue line) and Mn@Co (red line) samples.

Figure 5 . 3 . 7 :

 537 Figure 5.3.7: Hysteresis loops measured by VSM on Mn@Co samples at 26 K and 39 K.

Figure 5 . 3 . 8 :

 538 Figure 5.3.8: Element specific magnetization curves measured on a dropcast of Mn@Co sample using surface sensitive XMCD at the Mn and Co L 2,3 edges (T=50K).

Figure 5 . 3 . 9 :

 539 Figure 5.3.9: VSM magnetometry measurements at 300 K of MnFe 2 O 4 , CoFe 2 O 4 and Mn@Co powder nanoparticles and saturation magnetization values.

Figure 5 . 3 . 10 :

 5310 Figure 5.3.10: Experimental setup implemented for the RIXS-MCD measurements, i.e., a cryo-liquid cell inserted in the electromagnet and adapted to the scattering geometry: model (a), real assembly (b), model of the liquid cell, and its photography (d).

  consisting of two ferrimagnetic nanoparticles : CoFe 2 O 4 nanoparticles that are hard magnetic particles and MnFe 2 O 4 that are soft magnetic ones. The magnetic barrier energies of the two types of nanoparticles are very different and we have studied the effect of their mutual interactions upon their magnetic anisotropies. In the frozen phase, the magnetization curve exhibits a wasp-waist shape with a zero coercive field. But the magnetization curve of the 1:1 CoFe 2 O 4 -MnFe 2 O 4 binary ferrofluid does not superimpose with the linear combination of the magnetization curves measured for the single phase ferrofluid of CoFe 2 O 4 and MnFe 2 O 4 (Figure 5.4.3-b). In order to disentangle the magnetic signatures of individual magnetic particles we have performed RIXS-MCD experiments at the Co and Mn K -edge of the CoFe 2 O 4 single phase reference, the MnFe 2 O 4 single phase reference and the binary ferrofluid of CoFe 2 O 4 -MnFe 2 O 4 . In a first section, I describe the experimental details of the various characterization methods. Then the results are presented in a following section and a conclusion is drawn in the last section.

4 . 1 -

 41 (a) indicate that the morphology of the particles are spherical with similar sizes close to 6.0 nm and narrow size distributions (𝜎 = 0.25 for CoFe 2 O 4 and 𝜎 = 0.22 for MnFe 2 O 4 ). The results of the XRD measurements are shown in Figure 5.4.1 (b). X-Ray diffraction patterns of both CoFe 2 O 4 and MnFe 2 O 4 correspond to the cubic spinel structure Fd 3m. The diffraction peaks are broad as expected for small particles. Magnetometry measurements. The magnetization at 300 K has been measured for the binary ferrofluid and the two single phase ferrofluids. All magnetization curves are closed as can be expected for magnetic nanoparticles in a liquid phase (Figure 5.4.2). The susceptibility of the binary ferrofluid is very similar to the one of the pure CoFe 2 O 4 ferrofluid. The magnetization curves measured in the frozen phase (26 K) of the binary ferrofluid and the two pure phases are reported in Figure 5.4.3-(a). The MnFe 2 O 4 ferrofluid has zero coercivity with no opening on the whole range of induction variation while CoFe 2 O 4 ferrofluid presents a magnetic hysteresis with a coercive field H c = 1.6 T. The comparison of the magnetization curve of the binary ferrofluids with those of the pure single phase ferrofluids provide two types of information:

Figure 5 . 4 . 1 : 4 Figure 5 . 4 . 2 :

 5414542 Figure 5.4.1: Structural characterization of the pure CoFe 2 O 4 and MnFe 2 O 4 nanoparticles: (a)TEM micrographs and associated histograms, (b) XRD patterns of the CoFe 2 O 4 (green triangle) and MnFe 2 O 4 (blue square) nanoparticles.

either the CoFe 2 O 4

 24 nanoparticles or from the MnFe 2 O 4 ones. However, the magnetization curve of the binary ferrofluid do not superimpose perfectly with the linear combination of the magnetization curves from the single phase ferrofluids as can be observed in Figure 5.4.3 (b).

Figure 5 . 4 . 3 : 4 Figure 5 . 4 . 4 :Figure 5 . 4 . 5 :Figure 5 . 4 . 6 :

 5434544545546 Figure 5.4.3: Magnetization curves measured with VSM at 26 K (a) on the pure CoFe 2 O 4 (green), pure MnFe 2 O 4 (blue) and binary ferrofluids (red). Binary ferrofluid magnetic curve (red) and linear combination of the pure phases (black) at 26 K (b).

Figure 5 . 4 . 7 :

 547 Figure 5.4.7: Low Temperature absorption and XMCD spectra measured at Constant Emission Energy at the Co edge (panels (a) and (b), T = 39 K, CEE =6.9313 keV) and at the Mn edge (panels (c) and (d), T = 26 K, CEE=5.8998 keV) of the binary ferrofluid (red square), pure reference CoFe 2 O 4 (green triangle) and pure reference MnFe 2 O 4 (blue circle).

Figure 5 . 4 . 8 :

 548 Figure 5.4.8: Element selective magnetization curves measured by RIXS-MCD at ambient temperatures at the Co edge (a) and Mn edge (b).

Figure 5 . 4 . 9 :

 549 Figure 5.4.9: Element selective magnetization curves measured by RIXS-MCD at low temperatures at the Co edge (a) and Mn edge (b).

  1 mixture of 6 nm CoFe 2 O 4 and MnFe 2 O 4 nanoparticles. From VSM magnetic measurements, we find that the magnetization curve of the binary ferrofluid displays a curious but expected, wasp-waist shape which does not superimpose to the linear combination of its pure components. To gain insight on the magnetic properties of the individual components of the binary ferrofluid, we have performed RIXS and RIXS-MCD measurements at Mn and Co K -edges. The RIXS-MCD magnetization curves measured at Co or Mn K -edges have revealed that CoFe 2 O 4 and MnFe 2 O 4 nanoparticles are magnetically coupled in the binary ferrofluid. The magnetic coupling is suggested by the coercive fields of the individual components of the binary ferrofluid that are much different from those of their associated single phase ferrofluids. The presence of CoFe 2 O 4 nanoparticles induces an increase by 100 % of the measured coercive field of the MnFe 2 O 4 nanoparticles. Similarly the presence of the MnFe 2 O 4 nanoparticles reduces by 25 % the observed coercive field of the CoFe 2 O 4

2 O 4

 24 and CoFe 2 O 4 nanoparticles and we presume that this coupling is due to the formation of clusters or chains by the nanoparticles in the fluid. The atomic selectivity of RIXS-MCD at Mn and Co K -edges was essential to reach this conclusion. Although the formation of microscopic structures has long been predicted in several theoretical papers, we have not yet been able to image them directly. The team I have been working in is pursuing this goal by FORC and Cryo-TEM and results are expected likely after the end of my Ph.D.Both core@shell ferrofluids and binary ferrofluids represent a new class of magnetic materials in the domain of ferrofluids with emerging properties. Both systems allow a fine control of their magnetic properties by tuning the size of the core, the size of the shell for core@shell ferrofluids or the nature and the concentration of the respective components of binary ferrofluids.Thanks to the liquid cell that I have developed for RIXS-MCD spectroscopy, we were able to probe ferrofluids with X-Ray magnetic spectroscopy for the first time. Such experiments were very adequate for the study of superparamagnetic binary ferrofluids where the liquid structure must be preserved in its liquid form or in its frozen phase. In addition to what I have been presenting in the present chapter, we have also investigated another binary ferrofluid consisting of large CoFe 2 O 4 and MnFe 2 O 4 nanoparticles (∅ ≈ 20 nm) obtained with polyol synthesis process (see paper II in section 4.4). Additional experimental measurements are still needed and the analysis is not yet completed. Comparison between the binary ferrofluid obtained by acac and the one obtained by polyol is likely to yield valuable insight on the microstructures since the nanoparticles obtained by acac process have completely different magnetic properties compared to the ones obtained by polyol route. Ferrofluids are unique materials because they are highly homogeneous fluids exhibiting magnetic properties with no equivalent occuring in nature. Their unique features have created a wide interest among several different research fields. Their remarkable ability to exhibit dual features such as the property of a normal liquid flow coupled to a magnetic controllability are advantageous to fulfill diverse requirements in many fields. Ferrite spinels are among the most important ferrimagnetic materials for industrial applications.

  outcomes were lower than expected. The conception of the UHV compatible liquid cell for DEIMOS is still a subject of instrumental development and a new up-graded version is expected to be tested in 2017. I have been much more successful with the conception and development of a liquid cell for RIXS-MCD measurements in the hard X-ray range at ESRF. This new instrumental achievement has been used several times by our consortium with a high level of satisfaction. The expertise of IMPMC was crucial to implement the RIXS-MCD experiments. The use of the liquid cell is presently open to the whole community of RIXS users working at ESRF. Again, this thesis benefited greatly from its multidisciplinary aspect.

Fe 2 O 3 .

 23 Magnetic measurements indicate the significant enhancement of the anisotropy of the functionalized nanoparticles : the blocking temperature is three times larger and the coercive field is one order of magnitude larger. The XMCD detected magnetization curves of Co and Fe ions show the existence of magnetic coupling via oxo-bridges between the Co complex and the 𝛾-Fe 2 O 3 nanoparticles.In chapter 5, we gather the results on two different ferrofluids studied by 1s2p RIXS-MCD spectroscopy. The ferrofluids were either in their liquid phase or in a frozen phase obtained from the liquid phase.Firstly, a combination of XMCD spectroscopies with surface sensitive L 2,3 edges and bulk sensitivity of K -edges was used to investigate core@shell nanostructures where the core is a soft magnet of MnFe 2 O 4 and the shell is a hard magnet of CoFe 2 O 4 . The element specific magnetization curves recorded by XMCD allowed to explore the gradient of coercive field from the center to the surface of MnFe 2 O 4 @CoFe 2 O 4 6.7 nm nanoparticles.

2 O 4

 24 and CoFe 2 O 4 nanospinels. Using the liquid cell developed for RIXS-MCD experiments, we have measured the Co and Mn magnetization curves detected at 40 K. We observed a small magnetic coupling between MnFe 2 O 4 and CoFe 2 O 4 nanospinels and we presume that this coupling is due to the self-formation of clusters that might be magnetic chains of nanoparticles.

2 O 4 Figure 5 . 5 . 1 :

 24551 Figure 5.5.1: XMCD measurements of MnFe 2 O 4 @CoFe 2 O 4 core@shell system at the Mn L 2,3 edges (4 K): (a) XMCD spectrum measured at 6.4 T showing an extra negative peak at E=639.72 eV not showed by single phase MnFe 2 O 4 , (b)XMCD detected hysteresis curves measured at E=639.72 eV (orange plot) and E=640.65 eV (green plot).

2 O 4 and

 24 CoFe 2 O 4 , we extended these experiments to binary ferrofluids of big flower-like shape nanoparticles prepared by the polyol process. By TEM, we observed that the CoFe 2 O 4 nanospinels form self-assembly of nanoparticles chains in zero field and the chains orientate along the field direction when an external field is applied. In the presence of MnFe 2 O 4 flower-like shape nanoparticles, magnetization curves detected by RIXS-MCD were measured for field-cooled and zero field-cooled binary ferrofluids and a clustering of the nanospinels was observed. In the near future, Cryo-TEM experiments will be carried in order to correlate the local magnetic structure detected in RIXS-MCD to the microstructure of the nanoparticles in the ferrofluid.

  • Metallic (Fe, Co, Ni, Gd) or intermetallic (Ni-Fe, Fe-Pt, Fe-Co, Sm-Co ...) particles,• Nitrides M 𝑥 N where M is a metal such as Fe, Co, Ni, Gd,• Metal oxides, and in particular spinel ferrites (Fe3 O 4 , 𝛾-Fe 2 O 3 , MnFe 2 O 4 , CoFe 2 O 4 , NiFe 2 O 4 , ZnFe 2 O 4 ),• Iron garnets (Fe 5 Y 3 O 12 )

  example, the irreducible representations for 𝑇 𝑑 point group show that a p orbital component and d orbital component belong to the same irreducible representation 𝑇 2 .

	Thus a p-d hybridized orbital can be formed and dipole transitions accompany quadrupole
	transitions. In O ℎ point group, there are no irreducible representation grouping p and d
	orbital components. thus, for metal ions in O ℎ , only quadrupole transitions occur in the
	pre-edge region and the pre-edge peak intensity is much more smaller than for metal ions
	in T 𝑑 symmetry. As a consequence, it can be seen that the experimental results presented
	Chapter 5 show a much weaker signal at the Co edge (essentially in O ℎ symmetry) than
	at the Mn edge (essentially in T 𝑑 symmetry).

  61,62 However, due to cation intermixing between T 𝑑 and O ℎ sites in the nanospinels studied, the validity of the orbit and spin sum rules is ruined. Alternatively, calculations in the Ligand Field Multiplet theory can be performed.

	Principle
	Simulations of XAS and XMCD spectra can be calculated in the Ligand Field Multiplet
	(LFM) theory. The semi-empirical parameters used in the model (such as crystal field pa-
	rameters) are fitted by comparison to the XAS and XMCD spectra recorded experimentally
	at the L 2,3 edges. When the LFM calculations are in agreement with the experimental
	data, this yield to a quantitative determination of the cationic distribution among the
	crystallographic structure of the systems, and spin and orbit 3𝑑 magnetic moments of the
	absorbing atom in the ground state can be extracted from the program. For in-depth
	understanding of the theoretical concepts of multiplet calculations, readers can consult
	The hitchhiker's guide to multiplet calculations by Gerrit Van der Laan 63 and the book
	by Kotani and de Groot. 64 The principles of these simulations and their implementation
	are indepted to the seminal work of Theo Thole. 15 LFM caculations use a multi-electronic
	description of the atomic ground-state and the final state carrying a core-hole. For 3𝑑
	ions, XAS at the L 2,3 edges corresponds to electric dipole of 2𝑝 -→ 4𝑠 and 2𝑝 -→ 3𝑑
	transitions. Transitions from 2𝑝 to empty 4𝑠 levels being negligible in this approximation,
	only 2𝑝 -→ 3𝑑 contributions to the cross-section are considered.
	The exact diagonalization of the atomic Hamiltonian yields to the multielectronic
	wavefunctions and energies associated to the ground and the excited state. Electrostatic
	potential due to neighbors creates what is commonly named the crystal field. In the case
	of 3𝑑 orbitals of transition metal ion, the crystal field potential has the same symmetry
	as the absorbing ion site (i.e, 𝑂 ℎ or 𝑇 𝑑 symmetry for instance). The atomic Hamiltonian
	can be written as follows :

  The LFM theory is also based on the group subduction theory of Butler 66 . To the spherical Hamiltonian ℋ 0 one adds a crystal field contribution and a Zeeman term. Crystal field is expressed by making an extensive use of the subduction theory of Butler 66 so that only non-zero matrix elements are computed. For spinels, the site symmetries for cations are O ℎ or T 𝑑 and then the crystal field can be best described

	5 3𝑑 6 . The program computes the direct Slater integrals 𝐹 2 (3𝑑, 3𝑑) and 𝐹 4 (3𝑑, 3𝑑) must be calculated as well as the direct 𝐹 2 (3𝑑, 3𝑑), 𝐹 4 (3𝑑, 3𝑑), 𝐹 2 (2𝑝, 3𝑑) and the exchange 𝐺 1 (2𝑝, 3𝑑) and 𝐺 3 (2𝑝, 3𝑑) Slater integrals, the others integrals radials with angular parts being nul. The spin-orbit coupling constants on the open-shells (i.e. the 3d shell for the initial configuration on the 2p and 3d shells for the final state configuration) are also computed. The Slaters integrals are reduced using the 𝜅 factor (smaller than 1) which takes into account the delocalization orbitals. In order to obtain a LFM cross-section, one first solves the Schrödinger equation for the initial state configuration. Then one solves the Schrödinger equation for the final state configuration where a core-hole has been created. When the multielectronic wave-functions for the initial and the final states are known, one computes the cross-section following Equation 2.1.7 to yield a discrete set of transitions. For comparison with XMCD experimental results, the transitions are convoluted by a Lorentzian broadening function to take into account the core-hole lifetime and by a Gaussion function to account for the due to the chemical bound. by the single parameter 10Dq which describes the splitting between the 3d monoelectronic instrumental resolution.

  1.13) where |𝑖⟩, |𝑛⟩, |𝑓 ⟩ are the ground, intermediate and final states with 𝐸 𝑖 , 𝐸 𝑛 and 𝐸 𝑓 energies. Γ 𝑛 represents the energy broadening of the intermediate state, Γ 𝑓 of the final state due to the core-hole lifetime. 𝑇 1 and 𝑇 2 are the operators of optical transitions.

	Equation 2.1.13 shows also that interference may occurs between intermediate states that
	would decay to the same final state.

  1 3𝑑 6 intermediate state is reached. The intermediate state is split by 3d spin-orbit

	coupling and exchange field. Different intermediate states are reached selectively by left
	and right circular polarized X-rays and decay into final states with different orbital and
	spin momenta. The final state are finally split by 2p-3d Coulomb repulsions combined

Table 3 .

 3

	Mn	649.9	638.7
	Fe	719.9	706.8
	Co	793.2	778.1
	Ni	870.0	852.7

3

N 4 membranes which are transparent to the whole energy range of the 3d elements I am interested in for ferrofluids measurements. The energies of the L 2,3 edges of Mn, Fe, Co and Ni ions are reported in Table

3

.2.1.

Element L 2 2p 1/2 (eV) L 3 2p 3/2 (eV) 2.1: Electron binding energies for the elements of spinels ferrites studied in this thesis. The energy are reported in their natural form and reproduced from the Center for X-ray Optics and Advanced Light Sources data booklet.

1

  2 . The results are presented in Fig-ure 3.2.1. The transmission by a 100 nm thick Si 3 N 4 membrane in the photon energy range of the 3d transition metals (∼600 eV to 900 eV) is between 74% and 90%. As two Si 3 N 4 membranes would be used, this leads to a transmission between 54% and 81%.

		1.0
		0.8
	Transmission	0.4 0.6
						Si 3 N	4 50 nm
		0.2				Si 3 N	4 100 nm
						Si 3 N	4 200 nm
						Si 3 N	4 300 nm
		0.0
		0	200	400	600	800	1000
				Photon energy (eV)

  .2.2.

		Sample holder empty (no cell) Empty Cell Filled Cell
	Current (Amp)	1.48.10 -11	1.8.10 -10	1.10 -10

Table 3 .

 3

2.2: Current of the transmitted signal on the photodiode of the sample holder without sample cell, of the sample cell and of the sample cell with ferrofluid.

  𝑑 A sites are occupied by divalent ions whereas O ℎ B sites are occupied by trivalent ions. In inverse spinels, A sites are occupied exclusively by trivalent ions and B sites are occupied by both trivalent and divalent ions. Intermediate situations between direct and inverse spinels are characterized by a degree of inversion 𝛾 which is the fraction of divalent cations in octahedral sites. Hence, the cationic order of iron-cobalt spinels is described by equation (4.2.2) as : [𝐶𝑜 1-𝛾 𝐹 𝑒 𝛾 ] 𝑇 𝑑 [𝐶𝑜 𝛾 𝐹 𝑒 2-𝛾 ] 𝑂 ℎ 𝑂 4 (4.2.2)

.2.1) Co 𝑥 Fe 𝑦 O 4 crystallizes in the AB 2 O 4 spinel structure that belongs to the F𝑑 3𝑚 space group. 17

It is a face centered cubic (fcc) structure in which the oxygen anions O 2-are ordered in a cubic close-packed lattice. The rhombohedral unit cell contains two AB 2 O 4 formula units, where A are tetrahedral sites (T 𝑑 ) and B are octahedral ones (O ℎ ). In direct spinels, T

  The precipitation of Co 2+ and Fe 3+ hydroxides is carried out at room temperature. Sodium hydroxide (400 mmol) solution is added to a mixture of Co(NO 3 ) 2 .6H 2 O (25 mmol) and Fe(NO 3 ) 3 .6H 2 O (33 mmol) dissolved in distilled water (80 mL) under stirring. The mixture was kept under vigorous stirring for 30 min and results in nonmagnetic amorphous suspension of hydroxides species.

	Step 2-Ferrite formation. The reaction medium is stirred and heated at 100˚C
	for 2 hours. During this step hydroxides transform into cobalt ferrites with sizes ranging
	between 8 nm and 13 nm. 142

1-Hydroxides precipitation.

Table 4 .

 4 2.1: Physicochemical characteristics of the magnetic iron-cobalt nanospinels. d 𝑇 𝐸𝑀 and 𝜎 𝑇 𝐸𝑀 are the mean diameter and the polydispersity deduced from TEM micrographs,d 𝐷𝑅𝑋 the particle diameter measured from patterns, X M the molar ratio and M S the saturation magnetization measured at 300K.

	Sample	d 𝑇 𝐸𝑀 (nm) 𝜎 𝑇 𝐸𝑀 d 𝑋𝑅𝐷 (nm) X M (%) M S (A.m 2 .kg -1 )
	CoFe25_7	6.8	0.4	5.4	26.9	65.8
	CoFe25_9	8.9	0.5	10.6	26.4	72.8
	CoFe33_9	8.6	0.5	10.5	32.7	67.8
	CoFe33_11	10.7	0.4	12.8	35.3	72.5
	CoFe33_13	13.3	0.4	13.0	35.5	76.2
	CoFe33_21	20.9	0.5	18.0	34.2	76.1

  eV for Fe ions in T 𝑑 sites, 708.72 eV for Fe ions in O ℎ sites, 776.56 eV for Co ions in T 𝑑 sites and 777.55 eV for Co ions in O

ℎ sites. Magnetization curves are measured by using the EMPHU-65 undulator which allows fast switching (5 Hz) of the X-ray circular helicity.

  𝑑 and the O ℎ sites. It is well known from literature that the X1 peak at 707.98 eV is the signature of Fe 3+ in T 𝑑 sites whereas the X2 peak at 708.72 eV is the signature of Fe 3+ in O ℎ sites.208 The corresponding signals have opposite signs which reveal the antiferromagnetic coupling between the T 𝑑 sub-lattice and the O ℎ one. The Co L 2,3 edges spectra are typical for an iron-cobalt spinel containing Co 2+ ions in both T 𝑑 and O ℎ sites 193 . In the Co 2+ XMCD spectrum the X3 peak at 776.56 eV corresponds mainly to the T 𝑑 sites (where a small fraction of this positive contribution arises from the signal of the O ℎ sites -See figure 4.3.8 in Supplementary Informations) while the X4 peak at 777.54 eV corresponds to the contribution of Co 2+

.2.2 we present the XAS and XMCD spectra of Fe and Co L 2,3 edges for sample CoFe33_9. The different features of the spectra are labelled to simplify the discussion and the labels are reported in Figure

4

.2.2. As expected from the stoichiometry, we notice the absence of Fe 2+ ions.

207

Iron ions thus exist only as fully oxidized Fe 3+ ions distributed between T

Table 4 .

 4 amount of Co ions in O ℎ sites and the amount of Fe ions in T 𝑑 sites both increase.Thus in the case of the present series of samples with X M =33%, one can conclude that the increase in magnetic anisotropy is governed by larger concentration of Co ions in O ℎ sites which can be illustrated by a larger inversion parameter 𝛾. Numerical values of 𝛾 were calculated from the determination of the cations occupancy in LFM calculations fitted with XMCD experimental data(See the variation of 𝛾 in Supplementary Informations 3.2). From the coprecipitation synthesis, the variation of 𝛾 with the size can be directly related to heat treatments. Heat treatments have already been reported as being at the origin of the cations distribution in CoFe 2 O 4 .20,184,185 Kim et al. have also reported that temperature can increase the coercivity. CoFe25_7 and CoFe25_9 have been obtained from two rather different synthesis routes leading both to a partial loss of stoichiometry from pure CoFe 2 O 4 nanospinels. For the two samples CoFe25_9 and CoFe25_7 X M = 25% one has [Fe]=3x[Co]. From the XAS spectra at the Fe L 2,3 edges one notices that the decrease of divalent cobalt ions is not accompanied by the appearence of divalent iron ions so that one expects the presence of vacancies on the O ℎ sites as it is commonly observed in maghemitizated iron bearing spinels. If the nanospinels are homogeneous with a constant X M for the whole particle, then the actual chemical formula is Fe 3+ 24/11 Co 2+ 8/11 O 4 which correspond to a small fraction (1/11) of O ℎ vacancies per formula unit. In order to account for the degree of inversion, the formula for a sample with X M =25% can be written [Co 2+ 1-𝛾 Fe 3+ 𝛾 ] 𝑇 𝑑 [Co 2+ 𝛾-3/11 Fe 3+ 24/11-𝛾 ] 𝑂 ℎ O 4 . It is to be stressed that if Fe 2+ ions had been present to compensate the small amount of cobalt ions, then the stoichiometry formula would have been much different. But in the absence of Fe 2 +, the chemical composition of iron-cobalt nanospinels with X M =25% differs from only 1/11 of vacancies to the ones showing X M =33%.

142

Here the largest 𝛾 is found for the CoFe33_21 which underwent heat treatment at higher temperature of 200˚C for several hours. The hydrothermal treatment was already known to increase the size and the crystallinity of the grains. This step also improves the preferential distribution of Co 2+ ions in O ℎ sites.

Second set-Influence of particle size for X M =25 %.

  account the formula [Co 2+ 1-𝛾 Fe 3+ 𝛾 ] 𝑇 𝑑 [Co 2+ 𝛾-3/11 Fe 3+ 24/11-𝛾 ] 𝑂 ℎ O 4 for CoFe25 samples while cationic distributions in CoFe33 samples are obtained using the formula [Co 1-𝛾 Fe 𝛾 ] 𝑇 𝑑 [Co 𝛾 Fe 2-𝛾 ] 𝑂 ℎ O 4 . Cationic distributions calculated are consistent with coercive fields measured in XMCD detected magnetic curves (see Supplementary Informations Table 4.3.1) for all samples except for the CoFe25_9 sample. For the CoFe25_9 nanospinels one obtains a smaller amount of Co 2+ in O ℎ sites than for the CoFe33_9 while they show identical coercive fields. One can explain these discrepancies assuming a inho-

	mogeneous chemical composition inside CoFe25_9 nanospinels. In that case, the formula
	[Co 2+	1-𝛾 Fe 3+	𝛾 ] 𝑇 𝑑 [Co 2+	𝛾-3/11 Fe 3+	24/11-𝛾 ] 𝑂 ℎ O 4 cannot be applied in CoFe25_9 as in
	CoFe25_7 nanospinels which exhibit a steady chemical composition X M =25% in a whole
	nanospinel.

.3.2 in Supplementary Informations). Calculations were per-formed taking into

Table 4 .

 4 Calculated isotropic XAS (top panel) and XMCD (bottom panel) L 2,3 edges spectra for Fe 3+ ion for 100% occupation of T 𝑑 sites and O ℎ sites. 3.2: Occupancy of O ℎ and T 𝑑 sites in the iron-cobalt spinel samples calculated with the Ligand Field Multipley model. Fit of the experimental spectra were performed from the weighted sums of O ℎ and T 𝑑 sites occupancies of the calculated spectra.

		0.06				Isotropic spectra
		0.04
	Absorption (arb. units)	0.04 0.06 0.08 0.10 0.12 0.00 0.02				XMCD spectra
		0.02
		0.00
		-0.02
		-0.04				Co 2+	O
		-0.06				h
		-0.08				Co 2+	T
		-0.10				d
		775	780	785	790	795
				Energy (eV)

Figure 4.3.8: Calculated isotropic XAS (top panel) and XMCD (bottom panel) L 2,3 edges spectra for a Co 2+ ions for 100% occupation T 𝑑 sites and O ℎ sites.

  156,165 Large coercive field were measured at 5 K on small CoFe 2 O 4 nanoparticles prepared through high temperature decomposition route: Song and Zhang measured coercive field of 1.1 T on 6 nm CoFe 2 O 4 nanoparticles 94 and Torres and co-workers measured a coercive field of 1.4 T on 5.7 nm large CoFe 2 O 4 nanoparticles 226 . In this study, we want to emphasize the fact that magnetic anisotropies of CoFe 2 O 4 nanoparticles with similar sizes are strongly modulated by the synthesis process. We propose hereby to relate the synthesis routes (coprecipitation, polyol, thermal decomposition) route with the cationic reorganization of the nanoparticles and yielding the observed magnetic properties. Bulk CoFe 2 O 4 crystallizes in an inverse spinel structure that belongs to the Fd3 m space group. All Co 2+ ions occupy octahedral

symmetry sites while Fe 3+ ions are equally distributed between octahedral and tetrahedral symmetry sites. 227 X-ray Magnetic Circular Dichroism (XMCD) at the L 2,3 edges is

Table 4 .

 4 4.1: Physico-chemicals characteristics of Co-coprec, Co-polyol and Co-acac nanoparticles. d 𝑋𝑅𝐷 is the particles diameter determined in XRD, d 𝑇 𝐸𝑀 the mean diameter of the nanoparticles measured from TEM micrographs, 𝜎 𝑇 𝐸𝑀 the size distribution, X

	Sample	d 𝑋𝑅𝐷 (nm)	d 𝑇 𝐸𝑀 (nm)	𝜎 𝑇 𝐸𝑀	X M (%)	M S (Am 2 .kg -1 ) H 𝑐 (T)	M 𝑟 /M S
	Co-coprec	5.4		6.7	0.43	26.9	66	0.99	0.54
	Co-polyol	5.5		5.6	0.55	8.2	51	1.8	0.91
	Co-acac	6.5		6.9	0.27	27	59	1.77	0.75
		Sample	Co 2+ T 𝑑	Co 2+ O ℎ	Fe 3+ T 𝑑	Fe 3+ O ℎ	Fe 2+ O ℎ
		Co-coprec		0.10	0.69	0.86	1.28	-
		Co-polyol		0.00	0.22	1.00	1.52	-
		Co-acac 0.02	0.79	0.98	1.03	0.18

M the cationic molar ratio, M S the saturation magnetization measured at 300 K on the powders nanoparticles, H 𝑐 the coercive field measured at 4K on the frozen phase of ferrofluids, M 𝑟 /M S the normalized remanent magnetization, and Co 2+ T 𝑑 , Co 2+ O ℎ , Fe 3+ T 𝑑 , Fe 3+ O ℎ and Fe 2+ O ℎ the occupation of T 𝑑 and O ℎ sites by the different cations.

Table 4 .

 4

		8.349	5.6 (0.5)	0.003
	1	8.346	5.6 (0.5)	0.004

6.2: Refinement results and crystallite size evaluation.

Table 4 .

 4

	1 )

6.3

: Calculated d values for 0a, 0b and 1 (on 100 particles each) and theoretical values for maghemite.

[START_REF] Cornell | The iron oxides : structure, properties, reactions, occurrences and uses[END_REF]

Table of Content

 of

Table 5 .

 5 2.1: Structural and magnetic properties of the CoFe 2 O 4 , MnFe 2 O 4 and Mn@Co nanoparticles. For = 0.33 the spinel is stoichiometric while for X M = 0.25, if no divalent iron ions are present, the fraction of cationic vacancies is 1/11 per formula unit (i.e., for four oxygen ions).

  .3.2, Supplementary Information) show that almost 100% of Mn ions are divalent and in tetrahedral sites, while Co ions are found mainly divalent in octahedral extracted from the 2D planes, either as Constant Emission Energy (CEE) scans (as a diagonal cut in the plane, Figure 5.2.5) or as Constant Incident Energy (CIE) scans (a vertical cut in the plane, Figure 5.3.5 and 5.3.6, Supplementary Information). The spectral signature of Mn ions in the Mn@Co ferrofluid, which arises from the MnFe 2 O 4 core, is very similar to that of the Mn ions in the MnFe 2 O 4 ferrofluid. Likewise, Co ions in the CoFe 2 O 4 ferrofluid and those of the CoFe 2 O 4 shell in the Mn@Co ferrofluid show

sites. The RIXS and RIXS-MCD signatures measured in the Mn@Co ferrofluid are then compared with those measured in reference ferrofluid samples, i.e., a ferrofluid of the parent MnFe 2 O 4 particles at the Mn edge and a ferrofluid of CoFe 2 O 4 particles at the Co edge. This comparison can be made on the 2D planes (Figure 5.2.4, Figure 5.3.3 and 5.3.4, Supplementary Information) which contain the full information, or more conveniently, on 1D spectra

  54 Tesla, while it is almost zero (0.013 Tesla) in the MnFe 2 O 4 ferrofluid. This evidences that the CoFe 2 O 4 shell and the MnFe 2 O 4 core are magnetically coupled: (i) core@shell particles in the Mn@Co ferrofluid have a higher blocking temperature than bare MnFe 2 O 4 particles, which confirms the results obtained from ZFC on the dried particles (Table5.2.1), (ii) the large coercivity induced in the soft MnFe 2 O 4 core is due to the presence of the hard CoFe 2 O 4 shell. The normalized remanent magnetization is ∼95%, which is higher than the expected value of 83-87% for randomly spherical ferrite nanoparticles.

  Han et al. studied CoFe 2 O 4 -NiFe 2 O 4 ferrofluid and found that for low concentration of NiFe 2 O 4 the values of magnetization at saturation of the binary ferrofluid are larger than that of the CoFe 2 O 4 Moreover, these studies have been interpreted as an experimental validation of the theoretical models that predicted microstructures formed by the strong particles, the shape of which is determined by the weak magnetic particles. Except this indirect confirmation, such microstructures have never been directly observed in binary ferrofluids. Besides binary ferrofluids of strong and weak magnetic nanoparticles, Trudel et al. have reported the magnetic properties of a mixture of CoFe 2 O 4 and 𝛾-Fe 2 O 3 . 302

ferrofluid, while for high concentration of NiFe 2 O 4 they obtained smaller magnetization values for the binary than for single CoFe 2 O 4 ferrofluid.

102

One striking feature is that the magnetization at saturation is not a monotonous function of the NiFe 2 O 4 concentration. Similar results were observed in 𝛾-Fe 2 O 3 -ZnFe 2 O 4 binary ferrofluid.

301

Hence, the magnetic properties of binary ferrofluids can be modulated by the concentration of their magnetic components.

  O 4 -MnFe 2 O 4 binary ferrofluid is obtained by mixing equal volumes of pure CoFe 2 O 4 and MnFe 2 O 4 ferrofluids in which 𝜑 Co =0.2% and 𝜑 Mn =0.2% where by definition 𝜑 MnFe 2 O 4 = Vol MnFe 2 O 4 /(Vol Solvent + Vol MnFe 2 O 4 ) and 𝜑 CoFe 2 O 4 = Vol CoFe 2 O 4 /(Vol Solvent + Vol CoFe 2 O 4 ).Thus, the binary ferrofluid obtained has a total volume fraction of CoFe 2 O 4 and MnFe 2 O 4 nanoparticles equal to 0.2%. The volume fractions of the pure CoFe 2 O 4 and MnFe 2 O 4 XRD and TEM measurements were performed on the dry powder phases of pure CoFe 2 O 4 and pure MnFe 2 O 4 nanoparticles. XRD and TEM measurements do not allow to preserve the liquid phase of ferrofluids, so that these characterization techniques could not be performed on the binary ferrofluid. However, we assume that the structural properties of CoFe 2 O 4 and MnFe 2 O 4 nanoparticles in the binary mixture remain the same as in the pure phases. Magnetometry measurements. VSM was used to measure the magnetization curves of the pure CoFe 2 O 4 and MnFe 2 O 4 ferrofluid, and of the binary ferrofluid at 26 K and 300 K. The magnetizations at saturation (M S ) of the pure CoFe 2 O 4 and MnFe 2 O 4 nanoparticles were determined on dried nanoparticles. The blocking temperatures of the pure CoFe 2 O 4 and MnFe 2 O 4 ferrofluids, and the binary ferrofluid are compared from ZFC-FC curves.

	(ii) low polydispersity,
	(iii) particles with a crystallographic structure close to that of the bulk (see paper II,
	section 4.4).
	The CoFe 2

Synthesis. Pure CoFe 2 O 4 (d TEM = 5.8 nm) and MnFe 2 O 4 (d TEM = 6.0 nm) particles are prepared by high temperature decomposition (acac) synthesis following the process developed by Sun et al..

166

The acac process was chosen because it provides:

(i) small and spherical particles, ferrofluids that have been measured in the experiments were also fixed to 0.2%. Since the volume fraction for the three ferrofluids is much less than 1%, the static magnetic interactions are negligible.

297,[START_REF] Dubois | Stabilite des solutions colloidales magnetiques (ferrofluides)[END_REF]

Structural Characterizations.

RIXS-MCD measurements. RIXS-MCD spectroscopy was performed at room temperature (300 K) and at 26 K at the Co K -edge in pure CoFe 2 O 4 and binary ferrofluid, and at the Mn 𝐾-edge in pure MnFe 2 O 4 and binary ferrofluid. The ferrofluid samples were measured in a liquid cell developed for that purpose (see section 3.3). The experimental setup is also detailed in section 5.3.

  this chapter we have studied two different types of systems where MnFe 2 O 4 and CoFe 2 O 4 nanoparticles are present but engaged in a very different relationship. The first system is a ferrofluid with core@shell nanoparticles that are MnFe 2 O 4 @CoFe 2 O 4 and the second system is a binary ferrofluid where MnFe 2 O 4 and CoFe 2 O 4 nanoparticles are in interaction. For the MnFe 2 O 4 @CoFe 2 O 4 ferrofluid, we have observed a strong ferromagnetic coupling between the core and the shell. The CoFe 2 O 4 thin shell imposes a strong magnetic anisotropy to the soft MnFe 2 O 4 core. Interestingly we found that the coercive field is not constant within individual nanoparticles so that MnFe 2 O 4 @CoFe 2 O 4

:http://www.cxro.lbl.gov/

We mean by "frozen phase" the solodified state after cooling down below the solidification point of the solvent (∼ 182 K for heptane)

Abstract

The magnetic properties of cobalt ferrites nanoparticles prepared using three different processes (thermal decomposition, polyol and coprecipitation synthesis routes) are investigated by X-ray Absorption Spectroscopy and X-ray Magnetic Circular Dichroism.

The repartition of cobalt and iron ions amongst the interstitial sites of the spinel structure is determined and correlated with their magnetic properties. The study reports on the influence of the synthesis method on the crystallographic order within a nanoparticle, and hence, on the magnetic anisotropy. Magnetic measurements indicate the significant enhancement of the anisotropy in the final objects. Indeed, the functionalised nanoparticles show a three-fold increase of the blocking temperature and a coercive field increased by one order of magnitude.

Abstract

X-Ray Photoelectron Spectroscopy

XAS and XMCD measurements and Ligand Field Multiplet calculations