Olivier Sandre

Odile Stéphan

Sofia Kantorovich

Rafal Dunin-Borkowski

Franck Vidal

pour leur présence lors de ma soutenance de thèse. Les échanges et les commentaires constructifs qui ont suivi ont grandement enrichi ma réflexion.

Un chaleureux merci à mes directrices, Amélie Juhin et Claire Carvallo. Leur encadrement durant mon stage et tout au long de ma thèse a été précieux tant sur le plan scientifique qu'humain. Leur méthode de travail, leur qualité relationnelle et leur expertise scientifique ont contribué à rendre ces années de recherche non seulement enrichissantes, mais ont également suscité chez moi une pleine appréciation pour la profession de chercheur. Je mesure ma chance d'avoir bénéficié de l'implication soutenue de telles directrices dans mon projet de recherche.

Un profond remerciement à ma famille pour son soutien et son amour. En particulier, mes parents, sans lesquels je n'aurais pas atteint le niveau d'études requis pour entreprendre une thèse. Ma grand-mère a également été un exemple inspirant de femme engagée dans la recherche scientifique française, et ma soeur constitue un modèle à part entière. Je remercie également Quentin pour sa présence et son aide quotidienne précieuse, ainsi que Basile et Courgette, dans une moindre mesure.

Un sincère merci à mes amis et collègues de bureau (ou couloir), dont la compagnie et les moments de détente ont joué un rôle essentiel dans le maintien de mon équilibre mental pendant cette période de thèse. Ces connaissances de géographie me seront peut-être utiles un jour... Enfin, je tiens à exprimer ma profonde gratitude envers toutes les personnes qui ont collaboré et évolué à mes côtés au cours de cette aventure intellectuelle.

Abstract

The main objective of this thesis is to explore the effects of the assembly caused by dipolar magnetic interactions between magnetic nanoparticles suspended in a liquid (socalled ferrofluid) on the magnetic properties of this ferrofluid. It is based on the in-depth characterization of ferrofluids made up of flower-shaped nanoparticles composed of hard magnetic materials such as cobalt ferrite (CoFe 2 O 4 ), or soft magnetic materials such as manganese ferrite (MnFe 2 O 4 ) and maghemite (γ-Fe 2 O 3 ). The magnetic properties of these ferrofluids were measured using standard magnetometry methods, highlighting the significant influence of the chemical composition of the nanoparticles on the macroscopic characteristics of the ferrofluid. In addition, this research focused on the structuring of nanoparticles in liquid ferrofluids, by observing isolated particles, as well as the formation of assemblies and aggregates, using a cryogenic Transmission Electron Microscopy method, with a protocol developed specifically during the thesis. The impact of nanoparticle morphology on their magnetic properties was explored using tomography, (i.e. threedimensional imaging of nanoparticles), in collaboration with the IPCMS laboratory in Strasbourg. At the nanoscale, the magnetic properties of the assemblies were measured using electron holography, in collaboration with the CEMES laboratory in Toulouse. The study of binary ferrofluids, defined as ferrofluid physical mixtures composed of nanoparticles of hard and soft magnetic materials, has enabled new dipolar magnetic interactions to be explored. These new materials allow creating ferrofluids with novel properties that may be of interest for applications. These binary ferrofluids have revealed original bulk magnetic properties that differ from the simple addition of the individual properties of the original ferrofluids. In addition, the organization of nanoparticles in the binary ferrofluid has been meticulously studied using chemically selective and spatially resolved transmission X-ray microscopy on the HERMES beamline at the SOLEIL synchrotron, yielding chemical mappings of CoFe 2 O 4 and MnFe 2 O 4 nanoparticle assemblies. The separation of the magnetic contributions of both types of nanoparticles composing the binary ferrofluid was achieved using a magnetometry technique known as the FORC (First Order Reversal Curve) diagram, in collaboration with the IPGP laboratory. FORC diagrams were used to assess the influence of CoFe 2 O 4 nanoparticles on the magnetic behavior of MnFe 2 O 4 nanoparticles in the binary ferrofluid. In addition, spectroscopic measurements of chemically selective magnetization curves were carried out using a liquid cell for in-situ measurements, with experiments carried out on the GALAXIES beamline at the SOLEIL synchrotron. Finally, a comparison of the magnetic properties of different binary ferrofluids was undertaken, by varying the ratio between hard and soft magnetic components, the composition of the soft material as well as the size of the nanoparticles, thus providing a comprehensive perspective on the design and optimization possibilities of these advanced magnetic materials. This thesis establishes a significant relationship between the structuring of nanoparticles in ferrofluid and their magnetic properties.

General introduction

Ferrofluids are colloidal suspensions of magnetic nanoparticles dispersed in a solvent. Particles are composed of a ferro/ferrimagnetic material with a typical diameter in the 5-25 nm range, each of them being regarded as a single magnetic dipole, i.e. nano-magnet. The surface of nanoparticles is functionalized by surfactants to stabilize particles in solution, preventing aggregation due to attraction between nano-magnets or sedimentation by gravity. Nano-magnets can be oriented by an external magnetic field, which modifies the macroscopic properties of the ferrofluid. Being liquids controllable by a magnetic field, ferrofluids have found since 50 years numerous applications in engineering fields [START_REF] Torres-Díaz | Recent Progress in Ferrofluids Research: Novel Applications of Magnetically Controllable and Tunable Fluids[END_REF], biomedical fields [2], environmental fields [START_REF] Jiang | Advances of Magnetic Nanoparticles in Environmental Application: Environmental Remediation and (Bio)Sensors as Case Studies[END_REF] and fine arts [4]. One of the main medical applications is the possibility to destroy cancerous tumors without damaging the surrounding healthy tissue [START_REF] Dutz | Magnetic Particle Hyperthermia-a Promising Tumour Therapy?[END_REF] through magnetic hyperthermia, i.e. the ability to generate heat when magnetic nanoparticles are subjected to an alternating magnetic field. Moreover, magnetic nanoparticles can be used in drug delivery with stimuli-sensitive nanoparticles where therapeutic molecules grafted on the surface can be released by an alternating magnetic field [START_REF] Chen | Spatial, Temporal, and Dose Control of Drug Delivery Using Noninvasive Magnetic Stimulation[END_REF]. Finally, magnetic nanoparticles could be used as information storage devices for hard disks [START_REF] Terris | Patterned Media for Future Magnetic Data Storage[END_REF], or as treatments for water pollution [START_REF] Vallinayagam | Recent Developments in Magnetic Nanoparticles and Nano-Composites for Wastewater Treatment[END_REF].

Structuration within the liquid, also known as self-assembly, occurs when the magnetic dipole moment of the particles reaches a large enough value, enabling the formation of chains, rings and networks thanks to the magnetic interactions occuring between nanomagnets [START_REF] Gennes | Pair Correlations in a Ferromagnetic Colloid[END_REF]. When an external magnetic field is applied to the ferrofluid, the magnetic dipoles of the nanoparticles align with the field, leading to the formation of long chains aligned parallel to the direction of the magnetic field [START_REF] Mendelev | Ferrofluid Aggregation in Chains under the Influence of a Magnetic Field[END_REF]. This organization has a significant impact on the macroscopic magnetic properties of the ferrofluid like viscosity or optical properties, generating considerable variations depending on the presence or absence of chains [START_REF] Mendelev | Magnetic Properties of Ferrofluids: An Influence of Chain Aggregates[END_REF].

The study of magnetic nanoparticles that are dispersed in a liquid has proved challenging, and theoretical models [START_REF] Chuev | Generalized Stoner-Wohlfarth Model and the Non-Langevin Magnetism of Single-Domain Particles[END_REF] [START_REF] Solovyova | Modified Mean-Field Theory of the Magnetic Properties of Concentrated, High-Susceptibility, Polydisperse Ferrofluids[END_REF] and simulations play a crucial role in understanding their behavior. Theoretical models have been found to be effective in describing the behavior of nanoparticles in the presence of minimal or moderate interparticle interactions. They offer accurate predictions of the magnetic properties of nanoparticles, and enable to understand how they react to external magnetic fields. However, when the interactions between nanoparticles become significant, particularly in the case of intense dipolar coupling or high nanoparticle concentration, theoretical models show their limitations. They are not always able to match experimental results, which highlights the complexity of collective nanoparticle dynamics [START_REF] Hergt | Validity Limits of the Néel Relaxation Model of Magnetic Nanoparticles for Hyperthermia[END_REF]. Numerical simulations have also been of great benefit in exploring the possible assemblies created by nanoparticles in the presence of interactions. They have demonstrated that these interactions can lead to the formation of chains and other complex magnetic structures, providing valuable insight into nanoparticle structuration. Some experimental studies have evidenced the presence of chains or aggregates or other types of structuration, but there are only a few because of the technical challenges of working on a liquid sample with nanoscale resolution. The connection between nanoscale structuration and magnetic properties is not straightforward to establish, because magnetic properties are usually measured at the macroscopic scale.

Nanoparticle morphology, size and composition play an essential role in determining the macroscopic properties of the ferrofluid. To fully understand these properties in the context of ferrofluids, it is critical to first investigate the characteristics of the individual particle. For instance, the increasingly studied flower-shaped particles exhibit particularly appealing properties, especially with regard to their application in hyperthermia. The particles used for magnetic hyperthermia are generally composed of magnetite, a soft magnetic material. Their morphology, characterized by a porous structure, makes them easier to stabilize in water than dense spheres of comparable diameter. This feature offers the advantage of a size large enough to allow self-assembly to occur, while ensuring a stable colloidal suspension at the same time.

The most commonly studied magnetic nanoparticles in ferrofluids are made of magnetite. This iron oxide is a naturally occurring mineral on Earth and is a permanent magnet. Historically, the first synthesis of magnetic nanoparticles produced magnetite nanospheres 12 nm in diameter. Some organisms are able to biomineralize magnetite and use it to orient themselves to the Earth's magnetic field. This is the case with magnetotactic bacteria, which have a membrane containing magnetite crystals 40-50 nm in diameter called magnetosomes. Magnetosomes have properties that distinguish them from chemically produced nanoparticles. They have a narrow size distribution, uniform morphology, and a high degree of crystallinity. They are typically single magnetic domain nanoparticles with high magnetization, meaning that their magnetic moment is thermally stable at room temperature and easily manipulated by an external magnetic field. They exhibit high biocompatibility and low toxicity to living organisms, necessary requirements for biomedical applications.

Magnetic nanoparticles composed of other ferrites have then become available by chemical synthesis. Cobalt ferrite nanoparticles, as a hard magnetic material, exhibit a rigid, thermally stable magnetic moment and behave like theoretical magnetic dipoles. The comparison of their magnetic properties with simulations represents a promising area of research aimed at better understanding the complex interactions between nanoscale structuration and macroscopic magnetic properties of ferrofluids. In short, the study of these materials promises significant advances in our understanding of the relationship between structuring and magnetic properties, with potentially major implications in various fields of application.

Another way to vary magnetic interactions and their connection to structuration is to investigate binary (or "magnetic bidisperse") ferrofluids, i.e. ferrofluids composed of nanoparticles of two different chemical composition. When these two ferrofluids are mixed, emergent new magnetic properties emerge that are not simply the sum of the properties of the original ferrofluids. However, the study of these complex systems requires the development of novel experimental methods to quantify the structuration and magnetic properties of nanoparticles in an element-selective way.

My thesis was carried out at the Institute of Mineralogy, Physics of Materials, and Cosmochemistry (IMPMC) and Physicochemistry of Electrolytes and Interfacial Nanosystems (PHENIX) laboratories. It is funded by the Physics and Chemistry of Materials doctoral school (ED397). Three experimental collaborations were funded by the French electron microscopy network METSA. Several beamtimes on synchrotron source (ESRF, SOLEIL, ALS) were also granted.

Chapter 1 provides a general overview of the theory of magnetism and the relevant quantities associated with magnetic materials. Some of the properties of ferrite nanoparticles are also presented. The Langevin and Stoner Wohlfarth models are described, along with dynamic relaxation mechanisms in a ferrofluid. A review of the literature on magnetic nanoparticles and ferrofluids is also presented.

In Chapter 2, the experimental methods that were used during the thesis work are presented. Ferrofluid synthesis is briefly discussed, followed by a brief description of conventional laboratory techniques. Then, more advanced experimental techniques that are less commonly used in the field of ferrofluids are presented. These are divided into three categories: transmission electron microscopy (TEM), magnetometry, and X-ray based techniques.

The principle of TEM is outlined and the various applications of this versatile instrument are described. Cryogenic TEM has been used to observe the structural properties of ferrofluids. In collaboration with the IPCMS laboratory, a tomography experiment was performed to access the three-dimensional morphology of nanoflowers. Electron holography experiments were performed in collaboration with the Centre d'Elaboration de Matériaux et d'Etudes Structurales (CEMES) laboratory. This experiment was used to observe the orientation of magnetic moments in nanoparticles at the nanoscale. Regarding magnetometry, two techniques providing different types of information are presented: bulk magnetization curves, and First Order Reversal Curve (FORC) diagrams which give access to coercive and interaction field distributions. Finally, X-ray based measurements are described. Small-angle X-ray scattering was performed in the PHENIX laboratory to measure ferrofluid structuration under different parameters (concentration and external field). Element-selective spectroscopy techniques have also been in use. X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD) are synchrotron-based techniques which are unique tools for investigating magnetic systems. These techniques combine the advantages of elemental selectivity, valence state and site symmetry sensitivity. Using a liquid cell previously designed by the team, we were able to perform chemically selective magnetometry measurements on binary ferrofluids in the frozen liquid phase. Finally, using transmission X-ray microscopy, chemical mappings were also measured on assemblies of cobalt ferrite and manganese ferrite nanoparticles to explore the structuring properties of binary ferrofluids.

Chapter 3 and 4 are dedicated to the results obtained during my thesis. Chapter 3 focuses on single-phase ferrofluids, i.e. those composed of a single type of magnetic nanoparticle. The objectives are to (i) understand how the magnetic properties of the nanoparticles are modified by composition, size and shape and (ii) link self-assembly to macroscopic magnetic properties of the ferrofluid.

Eight ferrofluids have been synthesized at the PHENIX laboratory. Their magnetic and structuring properties were characterized. Magnetometry data were analyzed to extract information about the individual particles. The presence of assemblies or clusters was ob-served by cryo-TEM. A ferrofluid of CoFe 2 O 4 nanoflowers presenting self-assembly and with interesting properties was then selected for further study using more advanced experimental techniques. Electron tomography provided information about the morphology of the nanoflowers. Cryo-TEM images were analyzed to quantify self-assembly by separating the assemblies into categories sorted by shape and number of nanoparticles per shape. Electron holography studied the nanoscale magnetic coupling between the nanoparticles inside a given assembly. FORC diagrams measured distributions of magnetic properties (coercive and interaction field) into three different configurations of nanoparticles: selfassembly, chains parallel to the magnetic field and chains perpendicular to the magnetic field. Moreover, FORC diagrams were simulated to help understanding the magnetic behaviour at play in each configuration, and the impact of inherent magnetic properties of the individual nanoparticle on the collective magnetic response. Finally, based on these results, a comparison between ferrofluids with different composition and sizes was discussed to understand the relationship between structuration and magnetic properties.

Once the properties of single phase ferrofluids are well understood, it is possible to combine two ferrofluids with different chemical compositions to give rise to new magnetic properties. Chapter 4 introduces the concept of binary ferrofluid by briefly summarizing precedent work done in our team [START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF], which was the starting point of my work regarding binary ferrofluids. The binary ferrofluids investigated are composed of cobalt ferrite and manganese ferrite or maghemite. The nanoparticles are flower-shaped and combined together with different ratios to understand the trend in modification of magnetic properties in the binary ferrofluid.

First, I studied a binary ferrofluid composed of nanoflowers of CoFe 2 O 4 and MnFe 2 O 4 , both presenting magnetic interactions between the nanoparticles strong enough to create self-assembly or clustering but with very different magnetic anisotropy. The magnetic properties of the single phase ferrofluids and the binary ferrofluids were measured by bulk magnetometry and compared to theoretical averaged magnetization curves. The experimental and theoretical comparison shows interesting new magnetic properties, which were probed by FORC diagrams and element-selective X-ray magnetic spectroscopy, that allowed a separation of the hard from the soft magnetic material in the binary ferrofluid. To understand the modification of magnetic properties in the binary ferrofluid, chemical mapping was performed on assemblies composed of both components by X-ray microscopy. Studying of the structuration of binary ferrofluids allows to understand how and why magnetic properties are modified.

Second, a binary ferrofluid composed of nanoflowers of CoFe 2 O 4 and γ-Fe 2 O 3 is presented. In this ferrofluid, the nanoparticles of CoFe 2 O 4 and γ-Fe 2 O 3 have a different magnetic anisotropy as well as different magnetic moments. FORC diagrams and bulk magnetometry were measured on the binary ferrofluid with varying ratios of single phase ferrofluids. The modification of magnetic properties are discussed and compared to the previous binary ferrofluid studied. Finally, a third binary ferrofluid consisting of large CoFe 2 O 4 nanoflowers mixed with MnFe 2 O 4 nanoflowers is shown.

In the last section, a general conclusion recalls the main results of this thesis and the remaining open questions. To answer these questions, ideas of new experiments and simulations are proposed. Prospects for future samples and research topics are also discussed.

Chapter 1

Concepts and studies relevant to magnetic nanoparticles and ferrofluids

Introduction

My thesis work deals with the study of the magnetic anisotropies of ferrite nanoparticles dispersed in water and magnetic interactions between those nanoparticles. The magnetic anisotropies of these materials govern some of their magnetic response under an external magnetic field, which is of great interest for applications ranging from biomedical treatments to high-density data storage devices. This is mainly due to the reduced size of nanoparticles, their tunable magnetic properties depending on the synthesis and their ability to be used in ferrofluids.

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

First, I describe magnetism in bulk materials and the crystallographic and magnetic structure of cubic spinel ferrites. In a second section, I review the magnetic properties that arise from the nanoscale size of the nanoparticles and that are not present in the bulk. In particular, the various effects that can modify the magnetic anisotropies of nanoparticles are recalled. Quasi-static models used to describe the magnetic behavior of non-interacting magnetic dipoles are also described. Ferrofluids are then introduced, as well as their various applications.

In Section 1.5, a brief review of the literature is presented: a first section is devoted to the synthesis of magnetic nanoparticles and flower-shaped nanoparticles are presented. Then, the different investigations performed on ferrofluids are reported, from models, simulations to experimental techniques. Finally, the definition of binary ferrofluids is given with its original motivation, as well as the few studies that deal with this topic.

Magnetism in bulk magnetic materials 1.2.1 Historical origin of studies on magnetism

The historical origin of magnetism can be traced back to ancient civilizations through the discovery of the specific properties of lodestones, naturally occurring forms of the magnetic mineral magnetite (Fe 3 O 4 ). Early observers noticed that magnetite could attract iron objects, sparking curiosity and practical applications. Notably, the Chinese developed the first compass around the 4 th century CE, utilizing lodestones to create the "south-pointing spoon, " a pioneering navigational tool. The concept of magnetism continued to evolve through the centuries, with contributions from figures like William Gilbert during the Renaissance. In the 19 th century, Maxwell's equations provided a unified understanding of electricity and magnetism, paving the way for modern electromagnetism and technologies like radio and wireless communication.

Definitions

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

B = µ 0 (H + M ) (1.1)
The unit of B in SI units is in Tesla and H in A/m, with µ 0 the magnetic permeability of free space and M the magnetization of the material (in A/m). Magnetization is defined as the net magnetic moment µ (in Am 2 ) per unit volume V :

M = µ V (1.2)
The magnetization, and in particular the variation of this quantity, is dependent on the behavior of the individual magnetic moments of the elementary components of the material.

When a magnetic field is applied, the magnetic moment of each of the constituents, i.e. ions, atoms, particles, etc., orients itself in the direction of the field like a small magnetic dipole. The way magnetic moments react and interact with each other to the applied magnetic field is characterized by the magnetic susceptibility χ (dimensionless):

χ = ∂M ∂H H=0 (1.3)
Depending on the sign of the susceptibility, samples with no net magnetization can be classified as diamagnetic (χ < 0) or paramagnetic (χ > 0) systems:

• Diamagnetism: in diamagnetic materials, atoms possess no net magnetic moments (no unpaired electrons). They only acquire a weak induced moment when exposed to a magnetic field. The induced magnetization is oriented opposite to the applied field, resulting in a negative susceptibility χ (typically around 10 -5 ) that remains temperature-independent. The magnetization is also reversible with respect to the magnetic field;

• Paramagnetism: atoms have a non-zero permanent magnetic moment and tend to align parallel to an applied magnetic field. Susceptibility χ is inversely proportional to temperature T (Curie's law) and of the order of 10 -4 -10 -5 , and magnetization is reversible.

In some materials, one may observe the appearance of a cooperative magnetic order: ferromagnetism, antiferromagnetism or ferrimagnetism (Fig. 1.1). The orientation of magnetic moments within the material depends on its specific magnetic properties:

• Ferromagnetism: in ferromagnetic materials, exchange interactions J ⃗ S A • ⃗ S B between neighboring spins ⃗ S A,B encourage the parallel alignment of their magnetic moments and the exchange coupling constant J is positive. Below a critical temperature called Curie temperature (T C ), these interactions dominate over thermal agitation, leading to the spontaneous appearance of magnetization and a long range order even in the absence of an external field; • Antiferromagnetism: below a critical temperature called Néel temperature (T N ), antiferromagnetic materials exhibit an ordered state of magnetic moments. These moments align themselves antiparallel into sub-lattices with equal and opposite magnetizations, resulting in a zero net magnetization;

• Ferrimagnetism: ferrimagnetic materials are a variation of antiferromagnetism, but in this case, the moment carriers are not equivalent. Consequently, there is no complete cancellation of magnetization between the two sub-lattices. Below the critical temperature T C , spontaneous magnetization emerges.

It is important to note that for bulk materials above the critical temperatures T C or T N , thermal agitation disrupts the ordered magnetic states in ferro-, antiferro-, or ferrimagnetic materials, leading to susceptibilities similar to that of paramagnetic materials.

Magnetic domains and magnetization curve

Ferromagnetic or ferrimagnetic materials, despite the presence of spontaneous magnetization in the absence of an external magnetic field, they lack a permanent macroscopic magnetic moment. Instead, these materials are divided into distinct magnetic domains (Fig. 1.2) known as Weiss domains, each possessing its own inherent magnetization direction. These domains exhibit varying moment orientations, resulting in a net macroscopic magnetic moment of the sample equal to zero.

When subjected to an external magnetic field, the domain walls begin to shift, causing domains with matching orientations to expand while gradually diminishing the others. At high magnetic fields (typically when µ 0 H > 2 T), magnetization tends to saturate, reach- ing its maximum value denoted as M s , commonly referred to as saturation magnetization. Upon removal of the external field, the domains partially revert to their random orientations. Depending on the mobility of these domain walls, the moments within each domain remain partially aligned with the initial field. This leads to the persistence of remanent magnetization (M r ) and the characteristic hysteresis cycle (as illustrated in Fig. 1.3). The remanent magnetization, however, diminishes if temperature increases or if an opposing magnetic field is applied. The coercive field (H c ) corresponds to the magnitude of the applied field required to reduce the magnetization to zero. In materials with fewer defects, the Bloch walls (domain walls) exhibit easy mobility, resulting in rapid saturation Chapter 1 and demagnetization. These materials are often referred to as "soft. " Conversely, in samples containing numerous defects, these defects act as hindrances to domain wall movement, causing magnetization to increase more slowly with the applied field. Such materials are termed "hard" due to their wider hysteresis cycles. Magnetic material can also be hard due to a large magnetocrystalline anisotropy.

Magnetocrystalline anisotropy

In a ferromagnetic material, the magnetic order originates from the exchange energy favouring the alignment of spins in the same direction. However, due to spin-orbit coupling [START_REF] Yosida | Magnetic Properties of Cu-Mn Alloys[END_REF], there is another energy at play, that of magnetocrystalline anisotropy, which tends to orientate the direction of the spins along a preferred crystalline direction, called the axis of easy magnetization. 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 (Fig. 1.4). If we consider a crystal with cubic symmetry, the magnetocrystalline anisotropy energy E c (in Joule) is given by:

E c = K 1 (α 2 1 α 2 2 + α 2 2 α 2 3 + α 2 1 α 2 3 ) + K 2 α 2 1 α 2 2 α 2 3 + ... (1.4)
where K i is the crystalline anisotropy constant, which depends on the type of material and on temperature, and α i the cosines of the angles between the magnetization and the three axes of the cube. If K 1 > 0, E c is minimum for α 1 = α 2 = α 3 = 0 which is along a <100> axis (easy axis) and E c is maximum along a <111> hard axis. If K 1 < 0, the easy axis are along <111> axis and hard axis along <100> axis. The values of K 1 for ferrites studied in this thesis are reported in Table 1.1. Most ferrites have their easy axis oriented along the <111> diagonals of the cubic cell (K 1 < 0), except for cobalt ferrite where the magnetic moments align along the <100> axis (K 1 > 0).

Figure 1.4:

Various possible axes of magnetization in a cubic fcc crystal. In this example <111> is the easy axis while <100> is the hard axis. From [START_REF] Fernando | Chapter 4 -Magnetic Anisotropy in Transition Metal Systems[END_REF].

Spinel ferrites

The term "ferrites" pertains to transition metal oxides bearing iron. Magnetic ferrites are broadly categorized into two groups based on their crystal structures:

• Cubic ferrites: these ferrites follow the general formula MFe 2 O 4 , with M representing divalent metal ions like Mn 2+ , Ni 2+ , Fe 2+ , Co 2+ , or Mg 2+ . Among these, cobalt ferrite exhibits magnetic hardness (high magnetocrystalline anisotropy), while other mentionned ferrites display magnetic softness (low magnetocrystalline anisotropy). Magnetite, often referred to as iron ferrite, is one of the oldest known magnetic materials and falls within this group;

• Hexagonal ferrites: this group includes for example barium ferrite (Ba 0.6 Fe 2 O 3 ) and strontium ferrite (Sr 0.6 Fe 2 O 3 ), both characterized by magnetic hardness.

This thesis primarily investigates cubic ferrites crystallizing in the spinel structure, named after the mineral spinel MgAl 2 O 4 . This structure, conveniently described by a cubic cell containing 8 formula units and 56 ions, is a face-centered cubic arrangement structure (Fig. 1.5). The structure features tetrahedrally coordinated A-sites (T d ) and octahedrally coordinated B-sites (O h ) among the oxygen ions, occupied by cations. However, only a fraction of A and B sites are filled, with the distribution varying based on the type of ferrite. In the normal spinel structure, divalent ions occupy A-sites exclusively, while all Fe 3+ ions are in B-sites. In contrast, the inverse spinel structure positions M 2+ ions in B-sites, with Fe 3+ ions equally distributed between A and B sites. Ferrites like cobalt ferrite (CoFe 2 O 4 ), nickel ferrite (NiFe 2 O 4 ), and magnetite (Fe 3 O 4 ) adopt the inverse structure. Additionally, partially inverse ferrites also exist, with both divalent and trivalent cations occupying A and B sites in varying proportions, as exemplified by MnFe 2 O 4 being partially inverse spinel structure, where 80% of Mn 2+ resides in A-sites and 20% in B-sites.

Chapter 1

In the case of a spinel structure, all the exchange integrals between neighbouring cations are negative (antiferromagnetic coupling) but the interactions between T d -O h cations are stronger than O h -O h interactions. If the moment carriers are not equivalent, the material is ferrimagnetic.

The net magnetization of the structure results from the sum of the contributions of magnetic interactions between cations.

CoFe 2 O 4 CoFe 2 O 4 has an inverse spinel structure. Co 2+ are in B-sites and Fe 3+ are evenly distributed between and A-and B-sites. The magnetic moments carried by Fe 3+ in A-sites are aligned parallel to each other, but are antiparallel to the magnetic moments carried by Fe 3+ in B-sites. Thus, the magnetic moment of Fe 3+ cations cancels out due to the antiferromagnetic coupling between A-and B-sites. This means that the net magnetization in CoFe 2 O 4 is equal to the magnetic moment of the Co 2+ ions. This is calculated to be 3 µ B , but the magnetic moment of the Co 2+ ions has been measured to 3.7 µ B [START_REF] Cullity | Introduction to Magnetic Materials[END_REF]. The discrepancy is due to the orbital moment not being fully quenched and contributing to the total moment. γ-Fe 2 O 3 γ-Fe 2 O 3 has an inverse spinel structure with Fe vacancies in octahedral positions. All magnetic ions in γ-Fe 2 O 3 are identical, namely Fe 3+ , and the ferrimagnetism results from an unequal distribution of these ions in the A and B sites. Each ion has a moment of 5 µ B . Therefore, the net moment is 2.50 µ B per molecule of Fe 2 O 3 . This is in good agreement with the experimental M s value of 2.39 µ B /molecule = 83.5 Am 2 /kg. At 20°C M s is 76.0 Am 2 /kg [START_REF] Cullity | Introduction to Magnetic Materials[END_REF].

MnFe 2 O 4 MnFe 2 O 4
is a special case of partially inverse spinel in which Mn 2+ and Fe 3+ have the same magnetic moment (5 µ B ). This means that the net magnetization of MnFe 2 O 4 is ≃ 5 µ B /f.u. regardless of the cation distribution between A-and B-sites.

Magnetic properties of nanoparticles 1.3.1 Critical diameter

The Bloch wall thickness depends on the competition between the exchange energy and the magnetocrystalline anisotropy energy and is given by the ratio J/K. When the particle size is smaller than or equal to this thickness, a magnetic single domain arrangement of spins is energetically more favourable. Thus below a critical diameter D c , nanoparticles become single domain and according to Ref. [START_REF] Torres | Validity of the Néel-Arrhenius Model for Highly Anisotropic Co x Fe 3-x O 4 Nanoparticles[END_REF]:

D c = 36 √ AK eff µ 0 M 2 s (1.5)
with A the exchange stiffness constant, estimated to 15.10 -12 J/m for cobalt ferrite, yielding a critical diameter of 37 nm at 0 K.

The critical diameter as well as important magnetic constants for the materials relevant Concepts and studies relevant to magnetic nanoparticles and ferrofluids for this thesis are summarized in Table 1 ) bulk materials. D c is the critical diameter for magnetic single domain nanoparticle, a is the lattice parameter of the cubic cell of the spinel structure, ρ is the density, M 0 is the magnetization at 0 K, M s the magnetization at 300 K and K 1 is the second order magnetocrystalline anisotropy constant [START_REF] Cullity | Introduction to Magnetic Materials[END_REF].

.1. Ferrite D c (nm) a (Å) ρ (kg/m 3 ) M 0 (kA/m) M s (kA/m) K 1 (kJ/m

Magnetic anisotropy

Shape anisotropy

In addition to magnetocrystalline anisotropy, shape anisotropy can be induced in the case of non-spherical monodomain particles due the demagnetizating field [START_REF] Joseph | Demagnetizing Field in Nonellipsoidal Bodies[END_REF]. The discontinuity in magnetization at the particle surface leads to the creation of a demagnetizing field. In the case of an ellipsoidal particle, the shape anisotropy energy E s is:

E s = 1 2 µ 0 V (N x M 2 x + N y M 2 y + N z M 2 z ) (1.6)
with N x,y,z the demagnetization factors (verifying N x + N y + N z = 1) and M x,y,z the components of the magnetization along the x, y, z axis of the ellipsoidal particle. For a spherical nanoparticles, the shape anisotropy is zero.

Surface anisotropy

Finally, for a single-domain particle, the anisotropy energy also depends on surface interactions. When the size of the particles decreases, the magnetic contributions from the surface can become more important than those of the particles themselves. The surface anisotropy energy will then dominate over the magnetocrystalline and shape anisotropy energies.

For a spherical particle of diameter d, the effective anisotropy constant K eff follows the following empirical law: Chapter 1

K eff = K v + S V K s (1.7)
with K v the volume anisotropy constant, K s the surface anisotropy constant, S the surface and V the volume of the particle. Then, the anisotropy energy is expressed as:

E a = K eff V (1.8)
For uniaxial anisotropy, the remanent magnetization M r /M s = 0.5, while for cubic anisotropy M r /M s = 0.831 if K 1 > 0 and 0.866 for K 1 < 0 [START_REF] Usov | Theoretical Hysteresis Loops for Single-Domain Particles with Cubic Anisotropy[END_REF]. For nanoparticles, coexistence of both uniaxial and cubic anisotropy is possible, with pure uniaxial anisotropy for ultra small nanoparticles [START_REF] Trohidou | Magnetic Nanoparticle Assemblies[END_REF].

As nanoparticles are rarely independent, other factors contribute to the effective anisotropy, such as dipolar interactions between nanoparticles. In the following sections, the anisotropy constant will be written as an effective anisotropy constant K eff . For two interacting magnetic dipoles ⃗ µ 1 and ⃗ µ 2 , the magnetic dipole-dipole interaction E dip is:

Magnetic dipolar interactions

E dip = - µ 0 4π 3( ⃗ µ 1 • û)( ⃗ µ 1 • û) -⃗ µ 1 • ⃗ µ 2 r 3
(1.9) with û the unit vector parallel to the line joining the centers of two dipoles and r the distance between the centers. When the dipoles are aligned head-to-tail, the energy is minimized Concepts and studies relevant to magnetic nanoparticles and ferrofluids (see Figure 1.6). Another stable configuration occurs when the dipoles are antiferromagnetically coupled.

For magnetic nanoparticles, each nanoparticle can be associated to a single magnetic dipole moment when the diameter is below the critical diameter (single domain regime). The dipolar coupling λ parameter is defined as the ratio between E dip and thermal energy k B T :

λ = µ 0 µ 2 4πd 3 k B T (1.10)
with k B the Boltzmann constant, T the temperature, µ and d the magnetic moment and mean diameter of the nanoparticle respectively. When λ > 2, interactions overcome thermal energy enough to induce assembly between nanoparticles. The nanoparticles are then able to assemble into chains and rings, which creates local anisotropy.

Quasi-static models

The magnetic behaviour of non-interacting magnetic nanoparticles depends on the temperature and their anisotropy energy:

• if k B T » E a , the particles exhibit superparamagnetic behaviour ;

• if k B T « E a , the particles are in a blocked regime and follow the Stoner-Wohlfarth model.

Langevin model

For superparamagnetic nanoparticles, the magnetization curve follows the Langevin model:

M L (H) = µϕ V L(x) (1.11)
with L(x) = cothan(x)-1/x the Langevin function, x = µ 0 µH k B T , µ the magnetic moment, ϕ the volume fraction, V the volume, H the external magnetic field, µ 0 the permeability of empty states, k B the Boltzmann constant and T the temperature.

The Langevin model assumes monodisperse sizes as well as the absence of magnetic dipolar interactions between the nanoparticles. The Langevin function describes the orientation of the magnetic moments, and x is the ratio between the magnetic energy µ 0 µH and the thermal agitation energy k B T . When the value of the magnetic field increases, the magnetization increases until it reaches a maximum, which corresponds to M s and is known as the saturation magnetization. The magnetization curve as a function of the magnetic field applied is reversible.

Chapter 1

Stoner-Wohlfarth model

If the thermal energy is not sufficient to overcome the anisotropy energy (k B T « E a ), the nanoparticles are in the blocked regime. The magnetization then depends on the history of the hysteresis cycle as a function of the field. The system is then characterised by M r ̸ = 0 and H c ̸ = 0, the magnetization curve presents a hysteresis.

In isolated nanoparticles (no magnetic dipolar interactions) and at T = 0 K, thermal agitation does no longer exist and the energy is the sum of two competing terms, with θ the angle between the magnetization and the easy axis and ϕ the angle between the applied field and the easy axis (Fig. 1.7):

• the anisotropy energy written as E a = K a V sin 2 θ, which tends to ensure that the moment is aligned along the axis of easy magnetization;

• the field coupling energy or Zeeman energy written as E z = µ 0 M s Hcos(ϕ -θ), which tends to align the moment along the applied magnetic field. The competition between the two energies E a and E z is at the origin of the hysteresis cycle. The shape of the cycle depends on the angle between the axis of easy magnetization and the applied magnetic field. For an individual particle, when the magnetic field is in the same direction as the easy axis (ϕ = 0 or 180°, Fig. 1.7), the hysteresis cycle is rectangular. For a large, macroscopic amount of particles, since the axes of anisotropy are randomly Concepts and studies relevant to magnetic nanoparticles and ferrofluids oriented with respect to the magnetic field H, we need to average the magnetization curves of each particle. The coercivity is obtained as a function of anisotropy constant [START_REF] Stoner | A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys[END_REF]:

H c = 0.96 K a µ 0 M s (1.12)
This equation allows the determination of an anisotropy constant by measuring the coercivity at very low temperature in a diluted system with no magnetic dipolar interactions.

Dynamical magnetic properties

Relaxation times and blocking temperature

In the case of quasi-static magnetic properties of nanoparticles, the response time τ of the nanoparticles was not taken into account. At T = 300 K, particles follow the Langevin model and τ « τ exp , where τ exp is the experimental measurement time (10-100 s). At T = 0 K, particles follow the Stoner-Wohlfarth model and τ » τ exp . In reality, τ exp governs the magnetic properties of particles when we are interested in the dynamics for τ ∼ τ exp .

The medium in which the particles are dispersed has an influence on their magnetic properties. Particles synthesized in the laboratory are colloidally stabilized in a carrier liquid (ferrofluid). The carrier liquid may be aqueous or organic, depending on the nature of the molecules present on the surface of the nanoparticles. The magnetic moment of nanoparticles dispersed in a solvent has two modes of rotation: an internal rotation (Néel Chapter 1 relaxation, Fig. 1.8a) and an external rotation (Brownian relaxation, Fig. 1.8b). The predominant mode is the one with the shortest mean time between two reversals of the magnetic moment along the axis of easy magnetization axis.

The response time τ is defined as [START_REF] Rosensweig | Ferrohydrodynamic Fluids for Direct Conversion of Heat Energy[END_REF]:

1 τ = 1 τ N + 1 τ B (1.13)
with τ B = 3ηV H /k B T , η the carrier liquid viscosity and V H the hydrodynamic volume; and τ N = τ 0 exp(E a /k B T ), τ 0 = 10 -9 -10 -10 s a characteristic time and E a the anisotropy energy.

On Figure 1.9a, each relaxation times τ B , τ N and τ is plotted as a function of particle diameter. One can note that for nanoparticles with a diameter larger than 8 nm, the Néel relaxation greatly exceeds Brownian relaxation and the total response time of the nanoparticles is thus dictated by Brownian relaxation time, which is of the order of 1 µs in water. As a typical magnetometry measurement time τ m ∼ 20 s, the ferrofluid at room temperature is in a superparamagnetic state (Fig. 1.9b) and the magnetization is reversible. When the ferrofluid is subjected to low temperatures, viscosity → ∞ as the water is frozen, there is no longer any Brownian relaxation. The only possible rotation of the magnetic moment is Néel relaxation. If τ m > τ N , the nanoparticles are at equilibrium and exhibit superparamagnetic behaviour, M (H) is reversible (Fig. 1.9b). If τ m < τ N , the nanoparticles are in a blocked state and the magnetization curve shows a hysteresis (Fig. 1.3).

The temperature at which the system changes from blocked to superparamagnetism is called the blocking temperature:

T B = KV k B ln τm τ 0 (1.14)
with τ m the "time of measurement". T B depends on τ m since the magnetic probe will "see" the magnetic moment as motionless if τ m is slower than its frequency of oscillation.

Magnetic hyperthermia

Hyperthermia measurements are used to gain information about the heating power of a sample, i.e. the ability of the sample to release heat when submitted to an alternating magnetic field (AMF). It is an important measurement to evaluate the efficiency of a sample in potential cancer treatment. Temperature is acquired as a function of time, during the application of an AMF, until an equilibrium temperature is reached (about 15 min). The SAR is then calculated using the slope of the curve T (t) at the origin, as:

SAR = c water χ Fe × ∆T δt (1.15)
the χ Fe iron concentration of the sample and c water the heat capacity of water in J.L -1 .K -1 and SAR expressed in W/g.

Applications of MNPs

Magnetic nanoparticles (MNPs) can be used as the recording media in various magnetic data storage devices, such as hard disk drives and magnetic tape storage [START_REF] Terris | Patterned Media for Future Magnetic Data Storage[END_REF] [START_REF] Terris | Nanofabricated and Self-Assembled Magnetic Structures as Data Storage Media[END_REF]. They store binary data as magnetic domains with different orientations, representing ones and zeros.

The key properties of MNPs exploited for these applications include superparamagnetism, high coercivity, and a well-defined switching field distribution. Superparamagnetism allows for stable storage of data bits at nanoscale sizes, while high coercivity ensures the stability of stored data. The primary objective is achieving high data storage density, allowing for the storage of extensive data volumes in a compact format by increasing the areal density of data bits on a storage medium. Challenges include magnetic interactions between neighboring bits and the precise fabrication and positioning of MNPs on recording media [START_REF] Albrecht | Bit-Patterned Magnetic Recording: Theory, Media Fabrication, and Recording Performance[END_REF]. Ongoing efforts in this field are dedicated to overcoming these challenges to attain higher data storage capacities, faster access times, and enhanced reliability in magnetic data storage technologies. Innovations in materials science, nanotechnology, and data storage technology continue to propel progress in this domain.

Additionally, magnetic nanoparticles play a crucial role in wastewater treatment processes, removing contaminants like heavy metals and organic pollutants and facilitating pollutant monitoring in the environment (Fig. 1.10). They are essential for tracking contaminant dispersion in aquatic ecosystems and evaluating soil and air quality [START_REF] Mohamadiun | Removal of Cadmium from Contaminated Soil Using Iron (III) Oxide Nanoparticles Stabilized with Polyacrylic Acid[END_REF] [START_REF] Abdel Maksoud | Insight on Water Remediation Application Using Magnetic Nanomaterials and Biosorbents[END_REF]. Their magnetic properties enable efficient separation and concentration of targeted chemical product from complex environments [START_REF] Dave | Application of Iron Oxide Nanomaterials for the Removal of Heavy Metals[END_REF]. Their high surface area and functionalization capabilities enhance the sensitivity and selectivity of environmental monitoring techniques.

Chapter 1 [START_REF] Jiang | Advances of Magnetic Nanoparticles in Environmental Application: Environmental Remediation and (Bio)Sensors as Case Studies[END_REF] MNPs find diverse applications, and their properties can be tailored depending on the synthesis method employed.

Ferrofluids

Definition

Ferrofluids are stable colloidal suspensions of nano-sized ferro/ferrimagnetic particles (typically < 100 nm) in small concentration (below 10% in volume). Coined by Neuringer and Rosensweig, the term "ferrofluid" captures the idea of the magnetic response of these nanoparticles in a liquid state. Although ferrofluids do not exhibit ferromagnetic properties due to the Brownian motion of the particles in the fluid, they are superparamagnetic when in their liquid state. When frozen, these motions are blocked, allowing ferrofluids to display ferro/ferrimagnetic behavior as long as the temperature is below the blocking temperature of the nanoparticles. In addition to "ferrofluids, " these materials are also known as "magnetic fluids" or "magnetic liquids. " The first stable ferrofluid was synthesized by S.S. Papell at NASA in the early 1960s, initially developed for use in rocket engines. Over the years, ferrofluids have found applications in diverse fields, from energy conversion devices to medical applications like immune magnetic separation techniques and contrast agents for Magnetic Resonance Imaging (MRI).

Synthesis and colloidal stability

The synthesis of ferrofluids involves careful consideration of the nature of the colloids, the choice of carrier liquid, and the stabilizers utilized. Iron oxide nanoparticles can be synthesized through chemical, physical, or biological methods. The carrier liquid serves as the dispersing medium for these particles and can be either polar or non-polar, selected based on specific application requirements and properties such as boiling point, vapor pressure, freezing point, viscosity, and toxicity. A wide range of carrier liquids, including water, alcohols, glycols, esters, organic solvents like benzene, toluene, heptane, ethers, silicone oils, mineral oils, vegetable oils, and even ionic liquids, have been employed. In this thesis, water is exclusively used as the solvent.

Concepts and studies relevant to magnetic nanoparticles and ferrofluids

To maintain the stability of the ferrofluid, stabilizers are crucial. These substances introduce repulsive interactions that counteract the attractive forces between magnetic nanoparticles, which tend to aggregate due to magnetic dipolar and van der Waals-London forces, even at low concentrations. Repulsive interactions can take the form of steric or electrostatic repulsions. Ionic ferrofluids are primarily stabilized by electrostatic repulsions, achieved by creating mutually repelling charged double layers on the colloid surfaces. In organic-based ferrofluids, steric repulsions play a key role in stability. Stabilizers, which can be surfactants or polymers, are physically or chemically adsorbed onto the colloid surfaces. In addition to stability, these stabilizers can also prevent surface oxidation and enhance compatibility with the carrier fluid. Examples of stabilizers include oleic acid for dispersing nanoparticles in hydrocarbons, nitrate ions for dispersion in acidic water-based mediums, and citric acid for water-based ferrofluids, a choice applied to all ferrofluids in this thesis.

Applications of ferrofluids

Ferrofluids have several potential applications in the biomedical field due to their unique properties. They can be used as carriers for targeted drug delivery [START_REF] Israel | Magnetic Iron Oxide Nanoparticles for Imaging, Targeting and Treatment of Primary and Metastatic Tumors of the Brain[END_REF] [START_REF] Ikoba | Nanocarriers in Therapy of Infectious and Inflammatory Diseases[END_REF]. By functionalizing the nanoparticles in the ferrofluid with ligands or antibodies, they can be directed to chosen cells or tissues. When exposed to an external magnetic field, the ferrofluid can then be guided to the target location, allowing for controlled drug release. This enhances the therapeutic effect while minimizing side effects. Moreover, they can generate heat when exposed to an alternating magnetic field. This property is exploited in magnetic hyperthermia for cancer treatment [START_REF] Polla | Nanomaterials for Magnetic Hyperthermia[END_REF]. Ferrofluids are injected into tumors, and when subjected to an alternating magnetic field, they heat up, selectively killing cancer cells while sparing healthy tissue.

Ferrofluids can serve as contrast agents in MRI scans [START_REF] Reddy | Magnetic Nanoparticles: Design and Characterization, Toxicity and Biocompatibility, Pharmaceutical and Biomedical Applications[END_REF] [START_REF] Pourtau | Antibody-Functionalized Magnetic Polymersomes: In Vivo Targeting and Imaging of Bone Metastases Using High Resolution MRI[END_REF]. When introduced into the body, they can enhance the visibility of specific tissues or structures, aiding in the diagnosis of diseases or injuries. In cell biology and diagnostics, ferrofluids can be used to separate and manipulate cells [START_REF] Zhang | Multifunctional Superparamagnetic Iron Oxide Nanoparticles: Design, Synthesis and Biomedical Photonic Applications[END_REF] [START_REF] Kim | Multiplexed Detection of Pathogens Using Magnetic Microparticles Encoded by Magnetic Axes[END_REF]. By labeling target cells with ferrofluids and using magnetic fields, specific cells can be isolated from complex mixtures. This is valuable in research and clinical applications. Ferrofluids can be employed in the development of sensitive magnetic biosensors. By functionalizing the nanoparticles with biomolecules that bind to proteins or DNA, changes in the magnetic properties of the ferrofluid can be used to detect the presence of these biomolecules.

Synthesis methods

Two synthesis methods to produce magnetic nanoparticles relevant to this work are Massart synthesis and polyol synthesis.

Massart synthesis [START_REF] Massart | Preparation of Aqueous Magnetic Liquids in Alkaline and Acidic Media[END_REF], also referred to as co-precipitation, represents a widely used technique for synthesizing magnetic nanoparticles, particularly iron oxide nanoparticles, valued for its cost-effectiveness and versatility while allowing to obtain a large amount of nanomaterial. The resulting MNPs have possible applications in diverse fields, including magnetic data storage, biomedical imaging, and environmental remediation.

Polyol synthesis [START_REF] Caruntu | Synthesis of Variable-Sized Nanocrystals of Fe3O4 with High Surface Reactivity[END_REF], another method for generating magnetic nanoparticles, particularly iron oxide ones, offers less control on the crystallographic structure [START_REF] Hugounenq | Iron Oxide Monocrystalline Nanoflowers for Highly Efficient Magnetic Hyperthermia[END_REF] but allows to obtain different morphology of MNPs (nanocubes [START_REF] Wiley | Polyol Synthesis of Silver Nanoparticles: Use of Chloride and Oxygen to Promote the Formation of Single-Crystal, Truncated Cubes and Tetrahedrons[END_REF], nanowires [START_REF] Cha | Ferromagnetic Cobalt Nanodots, Nanorices, Nanowires and Nanoflowers by Polyol Process[END_REF], nanoflowers [START_REF] Cheng | Facile Synthesis and Morphology Evolution of Magnetic Iron Oxide Nanoparticles in Different Polyol Processes[END_REF]).

It is essential to note that polyol synthesis typically requires elevated temperatures and strict control over reaction conditions, which may necessitate specialized equipment. Additionally, achieving precise control over particle size and shape, especially for intricate or non-spherical forms, can be challenging due to potential variations in reaction conditions leading to different particle morphologies and size distributions.

Following synthesis, magnetic nanoparticles are often coated or functionalized with stabilizing agents such as citrate molecules or surfactants [START_REF] Lefebure | Monodisperse Magnetic Nanoparticles: Preparation and Dispersion in Water and Oils[END_REF]. This surface modification plays a critical role in preventing nanoparticle aggregation when dispersed in a liquid medium and ensuring their colloidal stability in various solvents.

Nanoflowers

Flower-shaped magnetic nanoparticles are nanomaterials with a distinctive three-dimensional morphology resembling the petals of a flower (Fig. 1.11a) [START_REF] Bender | Influence of Clustering on the Magnetic Properties and Hyperthermia Performance of Iron Oxide Nanoparticles[END_REF]. These nanoparticles offer high surface areas and complex structures, and the possibility to control their size and morphology [START_REF] Bertuit | High Temperature Continuous Flow Syntheses of Iron Oxide Nanoflowers Using the Polyol Route in a Multi-Parametric Millifluidic Device[END_REF] [START_REF] Gavilán | Formation Mechanism of Maghemite Nanoflowers Synthesized by a Polyol-Mediated Process[END_REF]. Flower-shaped magnetic nanoparticles find utility in biomedicine, particularly for targeted drug delivery, hyperthermia therapy, and MRI contrast agents [START_REF] Hugounenq | Iron Oxide Monocrystalline Nanoflowers for Highly Efficient Magnetic Hyperthermia[END_REF] [52] [START_REF] Curcio | Iron Oxide Nanoflowers @ CuS Hybrids for Cancer Tri-Therapy: Interplay of Photothermal Therapy, Magnetic Hyperthermia and Photodynamic Therapy[END_REF], as well as in materials science and environmental applications. They can be surface-modified for improved stability and biocompatibility and hold promise for advanced biomedical uses, where their unique shape and multifunctionality play crucial roles in cancer therapy and diagnostics [START_REF] Bertuit | Angular Orientation between the Cores of Iron Oxide Nanoclusters Controls Their Magneto-Optical Properties and Magnetic Heating Functions[END_REF].

The polyol synthesis was introduced by Caruntu et al. [START_REF] Caruntu | Synthesis of Variable-Sized Nanocrystals of Fe3O4 with High Surface Reactivity[END_REF] using a mixture of DEG and NMDEA. Further characterizations showed these nanoparticles have a remarkable ef-Figure 1.11: (a) Flower-shaped nanoparticles obtained from a polyol synthesis with a mixture of DEG and NMDEA from [START_REF] Caruntu | Synthesis of Variable-Sized Nanocrystals of Fe3O4 with High Surface Reactivity[END_REF], (b) SAR performance for disk-, splindes-and flowershaped nanoparticles of different diameters from [START_REF] Gavilán | How Size, Shape and Assembly of Magnetic Nanoparticles Give Rise to Different Hyperthermia Scenarios[END_REF]. ficiency for magnetic hyperthermia. Indeed, in Ref [START_REF] Gavilán | How Size, Shape and Assembly of Magnetic Nanoparticles Give Rise to Different Hyperthermia Scenarios[END_REF], particles with different shapes are compared in relation to their specific absorption rate (SAR) and nanoflowers of 27 nm in diameter present a SAR of 2400 W/g F e (Fig. 1.11b) compared to 1500 W/g F e for 47 nm cubes. The high hyperthermia performance of nanoflowers is reported in several studies [START_REF] Bertuit | Structure-Property-Function Relationships of Iron Oxide Multicore Nanoflowers in Magnetic Hyperthermia and Photothermia[END_REF] [56] [START_REF] Hemery | Monocore vs. Multicore Magnetic Iron Oxide Nanoparticles: Uptake by Glioblastoma Cells and Efficiency for Magnetic Hyperthermia[END_REF]. Moreover, recent preliminary work shows that for different sizes magnetite nanoflowers, the maximum of SAR is reached for diameter d = 22 nm [START_REF] Bejko | Optimal Sizes of Iron Oxide Nanoflowers for Magnetic Hyperthermia Depend on the Alternating Magnetic Field Conditions[END_REF].

Nanoflowers are regurarly investigated in numerous studies [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] [59] [START_REF] Bender | Supraferromagnetic Correlations in Clusters of Magnetic Nanoflowers[END_REF] and their hyperthermia performance is now related to the magnetic ordering at the grain interface causing exchange coupling between the cores. This induces a remanent magnetization for the individual nanoflower as well as superparamagnetic behavior, which prevents thermal losses. However, it is worth noting that magnetic hyperthermia measurements did not follow the Linear Response Theory (widespread framework for analyzing magnetic hyperthermia [START_REF] Torres | The Relevance of Brownian Relaxation as Power Absorption Mechanism in Magnetic Hyperthermia[END_REF]) or Stoner Wohlfarth model in [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF]. More advanced characterizations are still necessary to fully understand the complex magnetic configuration of a nanoflower at the nanoscale.

Experimental measurements on MNPs

In advanced characterizations, magnetic measurements at the nanoscale are also sometimes used but are possible on non liquid, dried samples. Electron holography allows observations of the magnetic induction lines produced by the MNPs. From first measurements on single domain Co nanoparticles rings [START_REF] Dunin-Borkowski | Off-Axis Electron Holography of Magnetic Nanowires and Chains, Rings, and Planar Arrays of Magnetic Nanoparticles: Electron Holography of Magnetic Nanostructures[END_REF] illustrating magnetostatic interactions to magnetic vortex in Fe cubes [START_REF] Gatel | Size-Specific Spin Configurations in Single Iron Nanomagnet: From Flower to Exotic Vortices[END_REF], electron holography has proven to be a powerful and precise technique for magnetic measurements at the nanoscale. Recent progress in elec-Chapter 1 tron microscopy now allows 3D observations of magnetic induction lines with electron holographic tomography. Co nanowires [START_REF] Wolf | 3D Magnetic Induction Maps of Nanoscale Materials Revealed by Electron Holographic Tomography[END_REF] and Co-Ni nanowires [START_REF] Andersen | Field Tunable Three-Dimensional Magnetic Nanotextures in Cobalt-Nickel Nanowires[END_REF] were successfully magnetically resolved in three dimensions, unveiling field tunable magnetic structures with potential significance for future spintronic applications.

First-Order Reversal Curve (FORC) diagrams, as introduced by Roberts et al. [START_REF] Roberts | First-Order Reversal Curve Diagrams: A New Tool for Characterizing the Magnetic Properties of Natural Samples[END_REF] and stemming from Preisach diagrams [START_REF] Mayergoyz | Mathematical models of hysteresis[END_REF], represent a magnetometry technique that offers a more precise and comprehensive understanding of magnetic properties compared to traditional magnetization measurements. Notably, this method can be implemented using standard measuring instruments such as the Vibrating Sample Magnetometer (VSM).

Popular within the field of paleomagnetism [START_REF] Roberts | First-Order Reversal Curve Diagrams: A New Tool for Characterizing the Magnetic Properties of Natural Samples[END_REF], FORC diagrams are now also used in other field. While they were primarily employed for the analysis of mineralogical samples, this approach is now finding applications in various magnetism-related domains. These extensions include the exploration of magnetic nanostructures and ferrofluids, exemplified by recent research employing FORC diagrams to quantify magnetostatic interactions among nanowires arranged in arrays [START_REF] Zamani Kouhpanji | Exploring Effects of Magnetic Nanowire Arrangements and Imperfections on First-Order Reversal Curve Diagrams[END_REF]. Such valuable insights are often challenging to obtain at the nanoscale without the aid of spatial resolution and modeling, highlighting the robustness and potential of FORC diagrams. Furthermore, there is an emerging trend of incorporating FORC diagrams into simulations. Notably, dedicated software has been developed for simulating FORC diagrams on nanoparticles structured in chains or clusters [START_REF] Harrison | FORCulator: A Micromagnetic Tool for Simulating First-Order Reversal Curve Diagrams[END_REF]. Additionally, Molecular Dynamics simulations have been applied to magnetic elastomers using FORC diagrams [START_REF] Dobroserdova | Measuring FORCs Diagrams in Computer Simulations as a Mean to Gain Microscopic Insight[END_REF]. These advancements underscore the versatility and growing significance of FORC diagrams in various scientific investigations.

Previous studies on ferrofluids

Self-assembly and chain formation Historically, the first syntheses of magnetic nanoparticles using the Massart process produced nanoparticles with a diameter of 5-15 nm and composed of magnetite, with a magnetic dipole moment of ∼ 10 -19 Am 2 . The dipolar coupling constant is small, λ < 2, and the Langevin model is highly successful in describing the magnetic behavior of ferrofluids. When syntheses began to produce nanoparticles of size d > 20 nm or composed of materials with large saturation magnetization (Fe, Co...), magnetic dipolar interactions became nonnegligible and the Langevin model no longer adequately described the magnetic properties of the macroscopic fluid. Studies began to take these interactions into account. Chain formation due to magnetic interactions between particles was theorized as early as the 1970s by De Gennes and Pincus [START_REF] Gennes | Pair Correlations in a Ferromagnetic Colloid[END_REF]. Monte Carlo and molecular dynamics simulations have been used to demonstrate the self-assembly process of magnetic nanoparticles [START_REF] Yener | Self-Assembly of Three-Dimensional Ensembles of Magnetic Particles with Laterally Shifted Dipoles[END_REF] [72] [START_REF] Kostopoulou | Assembly-Mediated Interplay of Dipolar Interactions and Surface Spin Disorder in Colloidal Maghemite Nanoclusters[END_REF]. The diversity of shapes of these assemblies was explored and phase diagrams according to temperature, concentration and dipolar coupling constant were established [START_REF] Kantorovich | Temperature-Induced Structural Transitions in Self-Assembling Magnetic Nanocolloids[END_REF] [START_REF] Rovigatti | Structural Properties of the Dipolar Hard-Sphere Fluid at Low Temperatures and Densities[END_REF].

Several models were built, such as the modified Weiss model [START_REF] Ivanov | Theory of the Dynamic Magnetic Susceptibility of Ferrofluids[END_REF], Modified Mean Field [START_REF] Ivanov | Revealing the Signature of Dipolar Interactions in Dynamic Spectra of Polydisperse Magnetic Nanoparticles[END_REF] and second order Modified Mean Field [START_REF] Ivanov | Interparticle Correlations and Magnetic Properties of Concentrated Ferrocolloids[END_REF] [79] to describe ferrofluids with lambda ≥ 2, Concepts and studies relevant to magnetic nanoparticles and ferrofluids and showed good agreement with experimental data [START_REF] Ivanov | Magnetic Properties of Polydisperse Ferrofluids: A Critical Comparison between Experiment, Theory, and Computer Simulation[END_REF]. However, the presence of chain within the fluid was only experimentally demonstrated directly in 2004 by Klokkenburg [START_REF] Klokkenburg | Direct Imaging of Zero-Field Dipolar Structures in Colloidal Dispersions of Synthetic Magnetite[END_REF] through cryo-TEM measurements. These observations validated years of theoretical modelling.

Experimental measurements

MNPs and ferrofluids can be characterized using a variety of experimental techniques that probe their magnetic, optical or rheological properties at the macroscopic scale.

DC-magnetometry techniques are commonly used in laboratories studying magnetic nanoparticles and ferrofluids. They provide information about magnetization as a function of temperature or magnetic field for macroscopic samples. They are therefore averaged measurements over a large number of nanoparticles. AC-magnetometry is also widespread, in which an alternative magnetic field is applied on the sample. This allows susceptibility measurements [START_REF] Ludwig | Analysis of AC Susceptibility Spectra for the Characterization of Magnetic Nanoparticles[END_REF] and magnetic losses measurements for magnetic hyperthermia [START_REF] Mille | Probing Dynamics of Nanoparticle Chains Formation during Magnetic Hyperthermia Using Time-Dependent High-Frequency Hysteresis Loops[END_REF].

Moreover, Small Angle X-ray Scattering (SAXS) is frequently used to characterize the morphology of the nanoparticles, as well as distinguish between isolated or aggregated nanoparticles. Different models can be applied to the SAXS data sets and help resolve the shape of the individual nanoparticles [START_REF] Li | Small Angle X-ray Scattering for Nanoparticle Research[END_REF] or the structuration of nanoparticles in the samples, for example with magnetosomes [START_REF] Rosenfeldt | Probing the Nanostructure and Arrangement of Bacterial Magnetosomes by Small-Angle X-Ray Scattering[END_REF] where the chain like arrangement and the average distance between individual magnetosomes were succesfully determined.

To study the structuration Small Angle X-Ray Scattering (SAXS) is often used as it provides an averaged view of the dispersion in the liquid while also giving insight on the individual particle morphology and size. Moreover, cryogenic Transmission Electron Microscopy (cryo-TEM) has been employed in several studies from Klokkenburg [START_REF] Klokkenburg | Direct Imaging of Zero-Field Dipolar Structures in Colloidal Dispersions of Synthetic Magnetite[END_REF] and Butter [START_REF] Butter | Direct Observation of Dipolar Chains in Iron Ferrofluids by Cryogenic Electron Microscopy[END_REF]. This technique allows a snapshot view of the positions of the nanoparticles in the ferrofluid. It enabled the first direct observation of self-assembly in a ferrofluid composed of magnetite nanospheres.

Binary ferrofluids

A binary ferrofluid is a ferrofluid composed of two different types of nanoparticles NP a and NP b with magnetic moment µ a and µ b respectively. If their magnetic moment differ, it results in three different magnetic dipolar interactions:

E total = E dip (µ a , µ a ) + E dip (µ b , µ b ) + E dip (µ a , µ b ) (1.16)
These interactions give rise to new magnetic properties that are different from the properties of both single phase ferrofluids containing only NP a and NP b . Initial studies on binary ferrofluids started as a way to introduce polydispersity in theoretical calculations on ferrofluids. Indeed, molecular dynamics or Monte-Carlo simulations first used perfectly mono dispersed spheres for the nanoparticles [START_REF] Weis | Chain Formation in Low Density Dipolar Hard Spheres: A Monte Carlo Study[END_REF]. However, synthesis always yields some polydispersity, and some experimental results were not similar to theoretical results due to the difference in magnetic dipole interactions between a monodisperse and a polydisperse system. Thus, bidiperse systems were studied, where two different diameters are introduced which leads to two different magnetic moment in interaction. Within the context of bidisperse ferrofluids, ϕ S denotes the volume fraction attributed to small magnetic nanoparticles, while ϕ L represents the volume fraction attributed to large MNPs. For example, Ivanov et al. [START_REF] Ivanov | Phase Separation in Bidisperse Ferrocolloids[END_REF] approximated an experimental log normal size distribution by a bidisperse size distribution (Fig. 1.12a). The fraction of large particles is much lower (ϕ L = 0.06%) than the smaller ones (ϕ S = 99.4%).

Wang et al. [START_REF] Wang | Structure and Magnetic Properties of Polydisperse Ferrofluids: A Molecular Dynamics Study[END_REF] unveiled a compelling relationship between these fractions by employing molecular dynamics. It revealed that as ϕ S increases, the average size of aggregates formed by large MNPs decreases significantly (Fig. 1.12b), showing the notable influence of small MNPs on the system structural properties. This influence becomes particularly evident when ϕ S becomes comparable to or surpasses ϕ L , leading to alterations in the aggregation behavior of large MNPs. Kantorovich et al. [START_REF] Kantorovich | Chain Aggregate Structure in Polydisperse Ferrofluids: Different Applications[END_REF] introduced the concept of "poisoning effect", linking the growth of the volume fraction of small MNPs to chain-shortening phenomena (Fig. 1.13a-b). This microscopic behavior was associated with the macroscopic magnetoviscous effect in bidisperse ferrofluids. The theory predicted that as the volume concentration of small MNPs exceeds a specific threshold, while the volume concentration of large MNPs remains constant, the magnetoviscous effect is reduced.

In a contrasting experimental investigation conducted by Sierbert et al. [START_REF] Siebert | Rheological Investigations on the Theoretical Predicted "Poisoning" Effect in Bidisperse Ferrofluids[END_REF], bidisperse ferrofluids were measured through magnetometry and rheological experiments, yielding unexpeted results that deviated from previous observations. The study involved the synthesis of two single-phase ferrofluids, each composed of magnetite MNPs with diameters of 5 nm and 20 nm, along with varying dipolar coupling parameters λ of 0.34 for small MNPs and 9.41 for large MNPs. By mixing different volume fractions (ϕ L and ϕ S ) of these MNPs The change of the magneto-viscous effect forced by the presence of small particles -expressed using the small particle influence parameter SPIP -plotted against shear rate in the presence of an external magnetic field . Data points of A, B, and C denote respectively bidisperse ferrofluids with ϕ L = 25, 5 and 3%. The dotted lines represent a linear fit for the sample set A and an exponential fit for sample sets B and C. From [START_REF] Siebert | Rheological Investigations on the Theoretical Predicted "Poisoning" Effect in Bidisperse Ferrofluids[END_REF]. together, different bidisperse ferrofluids were produced and their magnetization measured by VSM. Notably, the magnetization curves at 300 K demonstrated an increase in saturation magnetization with increasing amount of large MNPs in the bidisperse ferrofluids. Magnetorheological measurements in shear flow and external magnetic field of 44 mT were conducted on three distinct bidisperse ferrofluids, featuring varying proportions of large and small MNPs (ranging from 3% to 25% for large MNPs). These measurements yielded a magneto-viscous effect R i from which a Small Particle Influence Parameter: SPIP = (R i -R i=0 ) / R i=0 was calculated, with R i=0 in the single-phase ferrofluid containing only large nanoparticles. Thus, the SPIP encapsulates the variation of magneto-viscous effect for each bidisperse ferrofluid for each shear flow measured (Fig. 1.13c).

Interestingly, the results were not consistent with the poisoning effect, as an augmented magnetoviscous effect was observed with an increased quantity of small particles. This phenomenon suggested that the presence of small MNPs exerts a pronounced impact on the chaining behavior of large MNPs, promoting the formation of chain-like agglomerates and favouring the spread of particles involved in chain formation. Hence, the coexistence of small and large MNPs appeared to create energetically advantageous conditions for the aggregation of large MNPs into microstructures, contrary to the anticipated poisoning effect.

While mixing nanoparticles with two different sizes creates a bidisperse ferrofluid with novel magnetic properties, one can also vary the shape and/or composition of the nanoparticles. This will result in MNPs with two different magnetic anisotropy and/or magnetic moment. Ovejero et al. [START_REF] Ovejero | Mixing Iron Oxide Nanoparticles with Different Shape and Size for Tunable Magneto-Heating Performance[END_REF] investigated a unique magnetic system created by mixing iron oxide nanoparticles with different shapes: elongated and spherical. Elongated MNPs have Chapter 1 an aspect ratio of approximately 5.2, while spherical MNPs are one order of magnitude larger in volume. Spherical MNPs remain stable against thermal effects at room temperature, while elongated MNPs exhibit superparamagnetic behavior. Mixing these MNPs in various proportions allow modulation of the macroscopic magnetic properties, affecting the magnetic hyperthermia performance. The SAR shows large modifications, with the mixed samples demonstrating higher heating efficiency than expected from a simple sum of the SAR values measured on the original single-phase MNPs. The authors explained this phenomenon by a mean-field mechanism, where spherical NPs stabilized the thermally fluctuating moments of elongated NPs, enhancing heat production. This approach offers a promising strategy for achieving tunable magneto-heating performance.

In the study by Vamvakidis et al. [START_REF] Vamvakidis | Magnetic Hyperthermia Efficiency and MRI Contrast Sensitivity of Colloidal Soft/Hard Ferrite Nanoclusters[END_REF], magnetic nanoparticles were synthesized using a microemulsion-based method. This approach allowed for the incorporation of both soft (MnFe 2 O 4 ) and hard (CoFe 2 O 4 ) MNPs at the same weight concentration, resulting in spherical and compact nanoaggregates covered by a biocompatible polymer. The original MNPs have a mean size of approximately 9 nm, while the final structures reached a size of about 81 nm. Under an applied magnetic field of up to 1 T at room temperature, CoFe 2 O 4 MNPs exhibited higher magnetization (85 Am/kg 2 ) and coercivity (25 mT) compared to MnFe 2 O 4 MNPs (66 Am/kg 2 , 15 mT). The magnetic properties of the binary aggregates are a superposition of the properties of each phase, with the soft phase contributing to moderate coercivity and the hard phase contributing to high magnetization. The binary aggregates also display remarkable heating properties in an alternating magnetic field, with a specific loss power as high as 525 W/g attributed to the synergy between the two magnetic phases.

Very few binary ferrofluids with two different magnetic materials have been investigated. A mix of paramagnetic (p-NiFe 2 O 4 ) and ferrimagnetic (CoFe 2 O 4 ) nanospheres in liquid phase shows that saturation magnetization depends non-monotonically on the volume fraction of the paramagnetic nanoparticles [START_REF] Han | The Modification Effect in Magnetization Behaviors for CoFe2O4-p-NiFe2O4 Binary Ferrofluids[END_REF]. Another binary ferrofluid where paramagnetic (ZnFe 2 O 4 ) and ferrimagnetic (CoFe 2 O 4 ) nanospheres are mixed and a decrease in coercivity is observed for increasing fraction of CoFe 2 O 4 nanoparticles. The authors conclude that CoFe 2 O 4 chains formed under magnetic field are shortening due to the poisoning effect from ZnFe 2 O 4 nanoparticles [START_REF] Li | Study of Coercive Force for y ZnFe 2 O 4 -(1-y) CoFe 2 O 4 Magnetic Nanoparticles System[END_REF]. However, this conclusion is entirely based on models, no experimental observations of chains are presented.

In a more recent study from our team, a binary ferrofluid composed of MnFe 2 O 4 and CoFe 2 O 4 nanospheres was investigated by cryo-TEM and element-selective magnetometry. Changes in the magnetic properties of the two components of the binary ferrofluid show that the hard magnetic component becomes soft in the presence of the soft magnetic component, and the soft phase becomes harder. A fuller description of these results is given in Chapter 4.

Motivations

In this thesis I will discuss ferrofluids composed of CoFe 2 O 4 , MnFe 2 O 4 and γ-Fe 2 O 3 nanoflowers. The previous studies on these systems are mostly average experimental measurements Concepts and studies relevant to magnetic nanoparticles and ferrofluids without access to the magnetic or structural properties of individual nanoparticles, or numerical simulations that explore their properties but are rarely validated by direct observations at the nanoscale. Moreover, interactions between nanoparticles are still difficult to model and strongly modify the magnetic properties of ferrofluids.

Therefore, the first goal of my work is to set up experiments that are rarely used in the field of ferrofluids. These experiments will provide information at the scale of single nanoparticles as well as assemblies formed by interacting particles. Experimental data can then be used to feed the models and better constrain their output. Simulations aid in comprehending the behavior of ferrofluids and clarifying complex experimental results. Secondly, binary ferrofluids are a new class of controllable magnetic materials that are currently under investigation and poorly understood. The goal is to understand their novel properties through original experiments, and to explore variations between different binary ferrofluids.

Introduction

The ferrofluids studied in this thesis are composed of interacting magnetic nanoparticles. This creates microstructures in the fluid and affects the magnetic properties of the ferrofluid. The goal of this work is to provide an overview of both the structuration and the magnetic properties from the nanoscale to the macroscopic scale.

For the magnetic properties, I used conventional magnetometry, which provides information on bulk magnetic parameters, as well as more advanced magnetometry techniques. These experimental methods allow magnetic measurements combined with spatial resolution at the nanoscale (electron holography), element selectivity (X-ray magnetic circular dichroism) or distribution of magnetic properties and separation of hard from soft magnetic contributions (First Order Reversal Curve diagrams).

The structuration was studied by Small Angle X-ray Scattering (SAXS) at the macroscopic scale. In addition, I quantitatively analyzed the self-assembly process at the nanoscale using cryogenic transmission electron microscopy (cryo-TEM).

In binary ferrofluids, the nanoparticles have the same shape, I used chemical sensitivity microscopy with Scanning Transmission X-rays Microscopy (STXM) to image the structuration, allowing the discrimination of the chemical composition of each material at the nanoscale.

In this chapter, I first present the synthesis that produce the ferrofluids studied in this thesis. Then, the principle of TEM and several TEM-based techniques are described. Next, the two magnetometry methods are presented. Finally, X-ray based techniques are described.

Synthesis and conventional laboratory characterization

Each synthesized sample was characterized to determine the quality of the nanoparticles produced. First, the presence of a spinel phase was validated using X-ray diffraction. The stoichiometry of the ferrites and the volume concentration of particles in the solvent were determined by Atomic Absorption Spectroscopy.

Synthesis

The synthesis were done by Sophie Neveu and Enzo Bertuit at PHENIX laboratory. Two different synthesis methods were used:

• Co-precipitation: precipitation of Co 2+ or Mn 2+ and Fe 3+ hydroxydes;

• Polyol process: forced hydrolysis of Co 2+ or Mn 2+ and Fe 3+ in a polyol solution.

Experimental methods

Co-precipitation is a Massart process [START_REF] Massart | Preparation of Aqueous Magnetic Liquids in Alkaline and Acidic Media[END_REF] that begins by preparing a precursor solution containing metal cations in the form of soluble salts, such as iron chloride. This solution is then mixed with an alkaline solution, typically sodium hydroxide (NaOH) or ammonium hydroxide (NH 4 OH). The introduction of the base initiates a precipitation reaction, leading to the formation of metal hydroxide nanoparticles. These resultant metal hydroxide nanoparticles are generally amorphous and unstable. To convert them into magnetic nanoparticles exhibiting the desired crystalline structure and magnetic properties, a heating step is employed. During heating, the metal hydroxides undergo a transformation into the corresponding metal oxides. The size of these magnetic nanoparticles can be controlled by adjusting various parameters, including the concentration of metal precursors, the choice of base, reaction temperature and reaction time, which collectively influence the rate of nucleation and growth, ultimately defining the particle size. It is worth noting that Massart synthesis predominantly yields spherical nanoparticles with diameter ranging from 8 to 11 nm [START_REF] Massart | Preparation of Aqueous Magnetic Liquids in Alkaline and Acidic Media[END_REF], which does not cover all specific shapes or morphologies are required for particular applications.

The polyol process [96] [42] involves preparing a precursor solution comprising metal cations in the form of soluble salt, with a selected polyol serving as the solvent. The polyol provides a controlled reaction environment and serves as a reducing agent for the metal cations. The precursor solution is then heated to a specific temperature, typically ranging from 150°C to 300°C. Under these controlled conditions, the polyol reduces the metal cations, leading to the formation of metal nuclei. These nuclei subsequently grow into magnetic nanoparticles through the reduction of additional metal ions in the precursor solution. The size and shape of the resulting nanoparticles can be finely tuned by adjusting various reaction parameters, including temperature, reaction time, and metal precursor concentration. A distinctive feature of polyol synthesis is its ability to produce nanoparticles with specific shapes, such as nanowires, nanocubes, or nanoflowers, through variations in reaction conditions like polyol selection and the inclusion of capping agents. When the polyol is diethylene glycol (DEG) and N-methyl diethylamine (NMDEA) mixed in a 50:50 volume ratio, the synthesis yields flower-shaped nanoparticles. The diameter of the nanoflowers are controlled by the heating time and heating ramp and can range from 15 to 70 nm [50] [57].

In both cases, the ferrofluids are transferred into an aqueous solvent with pH 7 and the surface of the nanoparticles is functionalized by citrates molecules for colloidal stability.

X-Ray diffraction

Once the nanoparticles are synthesized, the crystalline structure can be determined using X-Ray diffraction (XRD). XRD is a technique based on the diffraction of X-rays by crystalline matter. The method involves illuminating the sample with X-rays, and recording the intensity of the scattered beam according to its orientation in space. The scattered X-rays interfere with each other, so that the intensity is maximum in certain directions determined by the wavelength λ of the X-rays and the lattice parameters and the symmetries of the crystal structure (Bragg's law). The intensity detected is recorded as a function of the beam angle of deflection 2θ. In a powder, all crystallographic orientations are present Here, XRD was measured using a diffractometer ANALYTICAL X'pert Pro MPD with a Co anode. The nanoparticles are first dried and grinded into a fine powder to eliminate clusters and preferential orientations. The powder is then deposited on a silicium substrate and flattened to obtain a smooth even surface. The diffractogram allows to confirm if the synthesis yielded a spinel phase, and one obtains the mean size d XRD of the crystallites from Scherrer equation:

d XRD = Kλ βcosθ (2.1)
with K a shape factor with a value close to 1 for spherical crystallites, λ the wavelength of the incident beam (λ Kα1 = 1.789 Åand λ Kα2 = 1.793 Åfor a Co anode), β the full width at half maximum and θ the Bragg angle of the peak.

Atomic absorption spectroscopy

Atomic absorption spectroscopy (AAS) is an atomic spectroscopy technique used to determine the concentration of metallic elements in a sample. These are atomized using a gasfed flame or an electromagnetic furnace. The technique makes use of the atomic absorption spectrum of a sample in order to assess the concentration of specific metals within it. It re-Experimental methods quires standards with known metal content to establish the relation between the measured absorbance and the metal concentration and relies therefore on the Beer-Lambert law.

The stoichiometry of the nanoferrites is determined by AAS using a PinAAcle 500, Perkin Elmer. The nanoparticles, in liquid phase, are degraded in HCl and diluted in HNO 3 . The concentration of iron and other transition metals M are measured 3 times to obtain the stoichiometry ratio x in M x Fe 2-x O 4 and a volume fraction ϕ in % from:

ϕ = 1.57 [F e] M F e + [M ] M M (2.2)
with [F e] or [M ] the respective concentration of iron and transition metal M in g/L and M F e and M M the molar mass of iron and transition metal M , respectively.

Transmission Electron Microscopy

One objective in this thesis is to investigate individual nanoparticles and establish a correlation between their unique nanoscale properties and the magnetic characteristics displayed by the nanoparticles as a whole. Electron microscopy techniques, specifically focused on examining the crystalline structure and morphology of the nanoflowers, were employed for this purpose.

Conventional Transmission Electron Microscopy

Principle of TEM Electron microscopy (EM) was first developed in the 1930s to surpass the limitations of visible-light microscopes in terms of spatial resolution. The wavelength of accelerated electrons (λ) is related to the acceleration voltage (V ):

λ = h 2m 0 eV + (1 + eV 2m 0 c 2 ) 1/2 (2.3)
where c is the speed of light in vacuum, h is the Planck constant, m 0 and e the electron mass and charge respectively. As V increases, the wavelength decreases. For a typical voltage of 200kV, λ ≈ 2pm.

Transmission EM (TEM) is a versatile observation method that encompasses multiple techniques in a single instrument, including high-resolution imaging, diffraction, spectroscopy, and magnetic imaging. A TEM is composed of several parts (see Fig. At the top of the TEM column, the electron gun produces and accelerates electrons. Electron emission can be achieved through thermoionic emission (using tungsten or LaB 6 filaments) or by utilizing a Field Emission Gun (FEG), where a sharp tungsten needle acts as a cathode. Two anodes extract and accelerate the electrons within an ultrahigh vacuum, preventing scattering from air particles.

The electron beam is then shaped and focused using electromagnetic lenses. These lenses consist of coils through which a current passes, determining the intensity and direction of the induced electromagnetic field, which deflects the electron beam. The condenser lens focuses the beam onto the specimen, and the objective lens magnifies the transmitted beam after the specimen. The transmitted beam comprises various scattered electrons, each carrying distinct information about the specimen. In this thesis, multiple techniques based on TEM where used to extract different information about the nanoparticles.

Experimental methods

When the TEM is set in the imaging mode (Fig. 2.2 left), a parallel beam illuminates the specimen. Transmitted electrons are focused by the objective lens, magnified by intermediate lens and projected on a detector. In this case, the intermediate lens is positioned in the image plane of the objective lens.

When using the diffraction mode (Fig. 2.2 right), or selected area electron diffraction (SAED), the intermediate lens is in the back focal plane of the objective lens. This selects only electrons diffracted by the specimen and a diffraction pattern on the detector is obtained. The area of interest is selected by a diaphragm called selected area aperture. When the incident beam is parallel to the zone axis, or direction common to all the planes of the zone, the diffraction pattern can be labeled by Miller index and the crystalline orientation of the zone is known.

In assemblies of nanoparticles, it may be useful to know the crystallographic orientation of each particle in relation to the others [START_REF] Alphandéry | Assemblies of Aligned Magnetotactic Bacteria and Extracted Magnetosomes: What Is the Main Factor Responsible for the Magnetic Anisotropy?[END_REF]. This gives information on the magnetic dipolar interactions between the nanoparticles, knowing the easy axis of the material. However the crystalline orientation of each particles is difficult to establish. Indeed, as SAED uses a diaphragm with a diameter often larger than the nanoparticle diameter (in our case, the diaphragm is 50 nm wide while one nanoparticle is around 25 nm wide), the technique cannot resolve the orientation of a given unique particle when it is in close proximity to another like in an assembly. Thus, it is possible to use nano beam diffraction (NBD) where the electron beam is converged to a nanometric size, which allows measuring the orientation of one particle at a time inside an assembly.

Determination of nanoparticle size

The size distribution of the nanoparticles is determined via TEM using a JEOL 2100 LaB 6 . A 5µL drop of the diluted solution (ϕ ≈ 10 -3 %) was deposited on a carbon-coated grid and left to dry for several hours. The diameters of the nanoparticles were manually measured using the ImageJ software, examining at least 350 different particles to ensure statistical significance. The diameter distribution was then fitted with a lognormal or Gaussian function to obtain the mean diameter d T EM and the polydispersity or standard deviation σ T EM .

High resolution TEM

Nanoparticles exhibit various intriguing properties attributed to their size, including the high surface-to-volume ratio that induces internal spin canting [START_REF] Morales | Surface and Internal Spin Canting in γ-Fe 2 O 3 Nanoparticles[END_REF] and crystalline defects leading to anti-phase boundary distortions [START_REF] Köhler | Mechanism of Magnetization Reduction in Iron Oxide Nanoparticles[END_REF]. In nanoflowers, the crystalline structure has an influence on the magnetic properties (saturation magnetization and coercivity) [START_REF] Bertuit | Angular Orientation between the Cores of Iron Oxide Nanoclusters Controls Their Magneto-Optical Properties and Magnetic Heating Functions[END_REF]. Comparatively, a nanoflower and a spherical nanoparticle with similar diameters exhibit different magnetic properties. To investigate the crystalline structural properties of the nanoflowers, high-resolution transmission electron microscopy (HRTEM) was employed.

HRTEM requires a fine tuning of the alignment of the microscope. The parallel beam interacts with the specimen, and transmitted electrons interfere with diffracted electrons, creating a phase contrast representing the atomic columns of the crystal (see example on Chapter 2 Fig. 2.3). We can then gather information on the crystalline organization and defects (grain boundaries, dislocations...) of the nanoparticles.

Specimen preparation

In HRTEM, carbon contamination can be a significant difficulty. In this thesis in particular, the surfactants stabilizing the nanoparticles in solution contain carbon chains and interact with the electron beam. After a few minutes, amorphous carbon spreads on the nanoparticle, blurs the signal and degrades spatial resolution. To decrease this effect, the nanoparticles need to be free of surfactants. Thus, the ferrofluid is first diluted in ethanol, which leads to the precipitation of nanoparticles. The supernatant is removed and the pellet dispersed in water. This process is repeated 3-4 times to obtain a pellet of nanoparticles that are "free" of surfactants. This pellet is then dispersed in distilled water. Then, a 20 µL drop of the solution is deposited onto a lacey or holey carbon-coated membrane grid.

Cryogenic TEM Principle of cryo-TEM

Cryogenic Transmission Electron Microscopy, or Cryo-TEM, is a powerful imaging technique originally used to study the detailed structure and morphology of biological macromolecules, cells, and materials at the nanoscale. It is particularly valuable for visualizing delicate and sensitive samples, such as proteins, viruses, and biomolecular complexes, without causing significant damage or distortion. Cryo-TEM finds many applications in biology and biomedical fields for studies on proteins and biomolecules [START_REF] Murata | Cryo-Electron Microscopy for Structural Analysis of Dynamic Biological Macromolecules[END_REF].

In 2017, the Nobel Prize was awarded to Dubrochet, Frank and Henderson for "high res- olution structure determination of biomolecules in solution by cryo electron microscopy". In addition, the development of a direct electron detector permitted low dose observation of vitrified specimen without damaging the biomolecules or melting the frozen ice matrix. In 2003, Butter et al. [START_REF] Butter | Direct Observation of Dipolar Chains in Iron Ferrofluids by Cryogenic Electron Microscopy[END_REF] as well as, in 2004, Klokkenburg et al. [START_REF] Klokkenburg | Direct Imaging of Zero-Field Dipolar Structures in Colloidal Dispersions of Synthetic Magnetite[END_REF] applied cryo-TEM to ferrofluids. This was the first experimental observations of self-assembly between magnetic nanoparticles in the absence of a magnetic field, predicted by theoretical simulations. Apart from two other studies [START_REF] Klokkenburg | Comparison of Reversible and Irreversible Dipolar Assemblies in a Ferrofluid[END_REF] [103], the technique was not exploited further, due to the difficulty of the experiment. Indeed, a large number of image must be produced to ensure that they are representative of the whole specimen, and the reproducibility is difficult to achieve. Manual preparation of cryo-TEM grids requires a lot of experience and mastery, which is why our team invested in a automatic, commercial cryo-plunger.

Protocol for specimen preparation

Cryo-TEM samples are prepared in a Vitrobot model cryo-plunger (see steps on Fig. 2.4). A 2.5 µL drop of the initial sample solution is deposited on "quantifoil" (Quantifoil Micro Tools GmbH, Germany) carbon membrane grids previously plasma cleaned for 30s on the membrane side. The excess of liquid on the grid is absorbed for 3s by blotting with a filter paper, and the grid is quench-frozen quickly in liquid ethane to form a thin vitreous ice film (> 100 nm). Once placed in a Gatan 626 cryo-holder cooled with liquid nitrogen, the sample is transferred to the microscope and observed at low temperature (-180 °C). Cryo-TEM images were recorded on ultrascan 1000, 2k x 2k pixels CCD camera (Gatan, USA), using a LaB 6 JEOL JEM2100 cryo microscope operating at 200kV. Chapter 2

Electron tomography

Electron tomography allows a three-dimensional observation of nanomaterials by acquiring a series of two-dimensional images of the sample at different viewing angles. To perform electron tomography, a specimen is tilted incrementally inside the transmission electron microscope while collecting images at each tilt angle. These tilt series of images are then computationally reconstructed to generate a three-dimensional representation of the nanoflower structure. The reconstruction process involves aligning the images, correcting for distortions, and applying algorithms to reconstruct the three-dimensional morphology of the nanoflower with a spatial resolution of ≈ 2-3 nm. Electron tomography provides valuable insights into the internal arrangement and shape of nanoparticles, allowing for a comprehensive understanding of their three-dimensional structure and which could be connected to their magnetic properties.

Specimen preparation and 3D reconstruction.

Electron tomography experiments were realized at IPCMS (Strasbourg, France) by O. Ersen and W. Baaziz thanks to the French microscopy network METSA. They used a JEOL 2100 FEG S/TEM microscope operated at 200 kV equipped with a spherical aberration corrector on the probe-forming lens. Samples were dispersed by ultrasonication in ethanol and deposited on a holey carbon coated TEM grid. The acquisition of tilt series was acquired in TEM mode using the tomography plug-in of the Digital Micrograph software by tilting the specimen in the angular range from -70.5°to 67.5°using an increment of 1.5°in the equal mode, giving thus a total number of images of 93 images.

The recorded images of the tilt series were spatially aligned by cross correlating consecutive images using IMOD software. For the volume calculation, algebraic reconstruction technique (ART) implemented in the TomoJ plugin working in the ImageJ software were then used to compute the reconstructed volumes. Finally, the visualization and the analysis of the final volumes were carried out using the displaying capabilities and the isosurface rendering method in the Slicer software.

Electron holography

From the Greek 'holos' meaning 'whole', holography refers to a technique allowing the recovery of both amplitude and phase information from a medium where only intensity data has been recorded. Since a first paper by Gabor in 1949 [START_REF] Gabor | Microscopy by reconstructed wave-fronts[END_REF], several methods have been implemented in electron microscopy to retrieve phase information from holograms. One of these methods called off-axis electron holography allows a measurement of electric fields and magnetic induction lines at the nanoscale, which could not be detected easily by conventional electron microscopy.

Electron holography is carried out in a TEM. The same elements are used, from the electron beam to the electromagnetic lenses. However, instead of just observing the intensity transmitted through the sample, one produces a hologram which contains information about the phase of the transmitted beam. To achieve this, a reference wave passing through

ψ t ∝ exp i( ⃗ k. ⃗ R+ϕ( ⃗ R)) (2.5)
with ⃗ k the wave vector and ⃗ R the position. The nanoparticles in the sample deflect the electron beam by the Lorentz and Coulomb forces and induce a phase shift ϕ( ⃗ R) in the transmitted wave. This phase shift is both due to the magnetic moment creating a magnetic induction B and the electrostatic mean internal potential (MIP) V (x, z) of the nanoparticles. The total phase is therefore the sum of both contributions (in one dimension for simplicity):

ϕ(x) = 2π λ E + E 0 E(E + 2E 0 ) V (x, z)dz - e ℏ B ⊥ (x, z)dxdz (2.6)
where E and E 0 are the kinetic and rest mass energies of the electrons, respectively and B ⊥ is the component of the magnetic induction perpendicular to both x and z. A biprism causes the rays to converge and interfere on the detector to create the hologram (Fig. 2.5a).

One then obtains the intensity of the hologram as:

I = |ψ r + ψ t | 2 ∝ cos ϕ(x) (2.7)
It is directly proportional to the cosine of the phase shift induced by both magnetic induction and the MIP. The electron source must be sufficiently coherent so that the phase of the Chapter 2 incident beam does not change and the interference fringes contain only the information about the phase induced by the sample. The objective lens before the specimen needs to be switched off to avoid its magnetic field drowning the magnetic signal of the specimen, and can be replaced by a Lorentz lens.

A conventional image of the sample is obtained (Fig. 2.5b) but additionally, the interference fringes in the hologram contain information about the phase (Fig. 2.5c). To obtain only the contribution of the magnetic phase, the contribution of the MIP must be subtracted from the intensity. This is done by turning the sample upside down and measuring a new hologram. Subtraction of the two intensities then cancels out ϕ M IP . This is because under the effect of a change in coordinates z → -z the electrostatic potential remains the same while the magnetization becomes negative. Thus, the intensity obtained by subtracting holograms contains only the magnetic contribution (Fig. 2.5d), while their sum gives both the mean internal potential (Fig. 2.5e). The magnetic isophase lines are then plotted on the image which allows retrieving the local orientation of the magnetic moment of each nanoparticle.

Specimen preparation

Electron holography experiments were carried out at Centre d'Elaboration de Matériaux et d'Etudes Structurales (Toulouse, France) by C. Gatel, E. Snoeck and M. Andersen via the METSA network. A lacey, carbon coated TEM grid was plasma cleaned for 20s and a 5µL drop of the ferrofluid was deposited on the grid. The measurements were carried out at room temperature. First, we located particle assemblies resembling the ones observed by Cryo-TEM (e.g. rings, chains...). We then measured the hologram of the assembly by making the transmitted electron beam interfere with a reference beam going through a hole in the grid. The same hologram was measured again after turning the grid by 180°in order to remove the phase shift contribution from the electric potential of the nanoparticles. The resulting image after treatment shows the magnetic induction lines of the nanoparticles projected in the plane of the grid.

Magnetometry

Magnetometry measures the magnetic response of a magnetic sample to an applied magnetic field. In the following, two techniques are described, "classical" magnetometry where hysteresis loops M (H) are measured, and First Order Reversal Curve diagrams, where a distribution of partial M (H) are measured to obtain a 2D diagram of the coercive and interaction fields in the sample.

SQUID magnetometry

A magnetization curve M (H) (magnetization as a function of applied magnetic field) of the nanoparticles in powder and in colloidal suspensions were measured with a Superconducting Quantum Interference Design (SQUID) magnetometer.

A SQUID magnetometer uses two Josephson junctions in a superconductor loop whose critical current i c is sensitive of the magnetic flux through the loop. This allows a very sensitive measurement (<10 -8 Am2) of the magnetic moment under high magnetic fields. The temperature can be decreased to 2 K by injecting liquid He in the chamber. The SQUID magnetometer I used during my PhD is a Quantum Design MPMS3 at the Low Temperature Physical Measurement Platform.

The room temperature saturation magnetization, denoted as M s , is determined by measuring the magnetic moment with a magnetic field ranging from 0 to 3 T. This measurement is carried out on a powdered sample, grounded to avoid aggregates. The mass of the sample is adjusted by accounting for the loss of organic material originating from surfactants and ligands, which is quantified using thermogravimetric analysis. The resulting value of M s is expressed in units of Am/kg2 when normalized by the mass of material or A/m when normalized by the volume.

The blocking temperature T B is determined from a M (T ) curve, where the sample is cooled without external field and the magnetization measured as a function of increasing temperature. The temperature at which the magnetization is maximum can be approximately associated to T B . To accurately determine the blocking temperature, it is essential to measure it on stationary and isolated nanoparticles, in order to avoid Brownian relaxation and magnetostatic interactions. Therefore, measurements are carried out on diluted liquid phase samples (not powders), preventing interactions, and between 2 and 250 K so that the solvent (water) is frozen, preventing Brownian motion. I also measured magnetic hysteresis at various low temperature (2 to 250 K) on liquid phase samples in magnetic fields ranging from -3 to 3 T. Before inserting the sample into the magnetometer, a decreasing oscillating magnetic field is employed within the SQUID magnetometer until the magnetic field reaches a zero value. This step serves to eliminate any eddy currents that may generate residual fields of approximately 3 mT in a MPMS3 (Fig. 2.6). By doing so, the sample is effectively prepared in a Zero Field Cooled state.

Field Cooled experiments can also be done. In this case, a magnetic field is applied while the sample is still in its liquid state for a duration of 5 minutes. The sample is then cooled to the desired temperature. An additional waiting time of 5 minutes is observed to allow the liquid to freeze completely before starting the actual measurements.

Sample preparation

For liquid samples, a 20µL droplet is deposited into an Eppendorf tube to obtain an approximate spherical shape. This is important because the model used in SQUID magnetometry converts the measured magnetic flux into a magnetic moment, assuming that the magnetic signal originates from a single point. Prior to sealing the Eppendorf tube, it is purged with gaseous helium to eliminate most of the air. This step aims to minimize the paramagnetic contribution arising from oxygen at low temperatures. [START_REF] Roberts | First-Order Reversal Curve Diagrams: A New Tool for Characterizing the Magnetic Properties of Natural Samples[END_REF] have become a standard tool to determine the magnetic mineralogy and domain state of natural samples used for environmental magnetism and paleomagnetism. They contain useful information about magnetic mineral assemblages and mixture of magnetic components within a natural sample. They are also used in material science and solid state physics, to understand the physics of magnetization process within such materials.

Unlike conventional magnetometry, a FORC diagram measurement browses the interior of a magnetization curve. A saturation field is first applied on the sample, then the field is lowered to a value H a and the magnetization is measured until saturation as a function of fields H b (Fig. 2.7a). This defines a FORC [START_REF] Mayergoyz | Mathematical models of hysteresis[END_REF]. A set of FORCs (100-300) are measured to create a FORC diagram (Fig. 2.7b). It is formed by the FORC distribution ρ(H a , H b ) which is defined as:

ρ(H a , H b ) = - 1 2 ∂ 2 M ∂H a ∂H b (2.8)
With a change of coordinates such that H u = (H a + H b )/2 and H c = (H a -H b )/2, one obtains a 2D diagram where in first approximation the horizontal axis is related to the coercive field distribution H c and the spread along the vertical axis is caused by magnetic interactions and is related to the interaction field distribution H u . The marginal distribution (i.e. the FORC horizontal distribution integrated on H u ) is often used as an estimate of the switching field distribution.

For a ferrofluid of non-interacting nanoparticles with uniaxial anisotropy, H c is directly tied to magnetic anisotropy and size distribution. Indeed, a FORC diagram of a single parti- cle yields a point-like pattern, while a experimental FORC diagram always has some dispersion along the horizontal axis, since particles with different sizes have different magnetic switching fields, and thus a distribution of coercive fields (Fig. 2.8d). When a mean field B int is felt by the particles, H u is not centered on zero (Fig. 2.8b). Interactions between particles result in a broad dispersion in H u (Fig. 2.8c). In general, a mix of both situations is observed like on Fig. 2.8e, where arrays of nickel nanopillar with various sizes are interacting (simulations from [START_REF] Roberts | Understanding Fine Magnetic Particle Systems through Use of First-Order Reversal Curve Diagrams: FORC Diagrams[END_REF]).

In [START_REF] Vargas | Magnetization Analysis of Oriented Chains of Hexagonal Cobalt Nanoplates[END_REF] [START_REF] Vargas | Magnetization Analysis of Oriented Chains of Hexagonal Cobalt Nanoplates[END_REF], magnetic properties of Co hexagonal nanoplatelets were investigated by FORC diagrams in three configurations: no magnetic field applied before cooling (ZFC), a magnetic field applied before cooling parallel to the field during the measurements (FC) and a magnetic field applied perpendicular to the measuring field (FC90). These configurations allowed a better understanding of the complex magnetic interactions between the nanoplatelets. In chapter 3, similar measurements have been applied to CoFe 2 O 4 nanoflowers.

Sample preparation

FORC diagrams were measured with a magnetometer (µ-VSM) equipped with a cryostat from Princeton Measurements Corporation at the IPGP-IMPMC Mineral Magnetism Analytical Facility. The ferrofluid is deposited in a pharmaceutical gel cap closed with kapton scotch tape and placed at the end of a sample holder attached to the vibrating head of the VSM, between the poles of an electromagnet. The sample holder is also surrounded by the a Helium flow from the cryostat. Small heaters and a temperature probe are placed around the sample to accurately control the temperature at which the measurements are carried out, with available temperatures ranging from 5 K to 300 K.

Experimental parameters

A measurement in ZFC configuration starts with no external magnetic field so the electromagnet is off when cooling the sample. In FC configuration, the electromagnet is turned on and 1.8 T are applied on the sample during the cooling step. The head of the sample holder can be turned around the z direction, allowing FC90 measurements: a magnetic field H x is applied in x direction on the sample during freezing step. When the ferrofluid is frozen, the sample holder is turned 90°and the magnetic field during measurements is applied along the x direction, which is perpendicular to the direction of H x (Fig. 2.9).

The parameters used for measurements are the number of FORCs N FORC , the field step H step and the averaging time t avg . Moreover, the range of magnetic fields H c and H u can vary according to the magnetic material being measured, as well as H sat the saturation field applied at each FORC.

The measurement time for a FORC diagram is about one hour. The FORC diagrams are analyzed with the FORCinel software [START_REF] Harrison | FORCinel: An Improved Algorithm for Calculating First-Order Reversal Curve Distributions Using Locally Weighted Regression Smoothing: FORCINEL ALGORITHM[END_REF], with a variable smoothing factor [START_REF] Egli | VARIFORC: An Optimized Protocol for Calculating Non-Regular First-Order Reversal Curve (FORC) Diagrams[END_REF]. The variable smoothing considerably reduces the noise levels by applying larger smoothing factors to the background, while preserving the areas along the axes with relatively small smoothing factors. The parameters for variable smoothing are: • λ: values between 0 and 1 to implement progressive smoothing factor between S c0 and S c1 .

FORC simulations

In order to improve the qualitative analysis of FORC diagrams, which is usually done in a "fingerprinting" approach with a comparison to known reference samples, I used the FORCulator software [START_REF] Harrison | FORCulator: A Micromagnetic Tool for Simulating First-Order Reversal Curve Diagrams[END_REF] to simulate FORC diagrams. FORCulator considers the switching field B SW of each particle, as well as an interaction field B int from magnetostatic interactions between particles. An external field B app can also be applied on the system, with varying amplitude and direction. The algorithm is based on the Landau-Lifshitz-Gilbert equation:

d ⃗ m dt = - γ 1 + α 2 ⃗ m × ⃗ B eff - γα (1 + α 2 )M s ⃗ m × ( ⃗ m × ⃗ B eff ) (2.9)
with ⃗ m and M s the magnetic moment and saturation magnetization respectively, the effective magnetic field B eff = B app + B int + B SW , γ the gyromagnetic frequency and α the damping parameter. Instead of solving the equation for each particles (which would be slow), the software uses an approximate method where the total magnetic configuration converges by placing each magnetization vector close to the effective field vector in iterations. • number of chains (N chain );

• number of particles per chain (N N P );

• distance between particles in the chains e;

• rigidity of the chain or collapse factor (c, 0 ≤ c ≤ 1 with c = 0 for a perfectly straight chain);

• general orientation of the chains along the axis x, y, z

Polydispersity is taken into account in the software by considering a lognormal distribution of switching fields with mean β and standard deviation σ. The anisotropy easy axis can be randomly distributed in space or aligned with the axis of the chains.

The software was originally built to simulate FORC diagrams of magnetite at room temperature. Therefore the saturation magnetization is set to that of magnetite, M s = 480 kA/m. However, it is possible to fix the value of individual moments µ = V M s by artificially modifying the diameter, and thus the volume V , of individual particles. Small Angle X-ray Scattering (SAXS) gives information on the structural properties of the ferrofluid, both on the individual nanoparticle (shape, surface, size) and the collective behavior. A liquid sample is illuminated with X-rays at wavelength λ and the scattering pattern is collected on a 2D detector (see example on Fig. 2.11a). The photons interact elastically with the electronic structure of the sample and are scattered at different angles θ, with scattering vector of magnitude q = 4π sin θ/λ. The intensity I(q) is the product of the form factor P (q) and the structure factor S(q). The form factor provides information about the size, shape, and composition of the scattering object, while the structure factor characterizes the arrangement and interactions between nanoparticles in the sample. SAXS experiments are very useful to determine the sizes as well as the shape of nanoparticles [START_REF] Honecker | Using Small-Angle Scattering to Guide Functional Magnetic Nanoparticle Design[END_REF] or their spatial configurations [START_REF] Rosenfeldt | Probing the Nanostructure and Arrangement of Bacterial Magnetosomes by Small-Angle X-Ray Scattering[END_REF] (see example of form factor for monodisperse spherical nanoparticles in Figure 2.11c). SAXS experiments were carried out at PHENIX laboratory (Paris, France) on a Xeuss 2.0 equipment equipped with a GeniX source operating at λ = 1.54 Å -1 and a Pilatus detector.

Experimental methods

X-Ray based techniques 2.5.1 Small Angle X-ray Scattering

Sample preparation

Samples were conditioned in glass capillaries with a diameter of 1 mm, and two sampleto-detector distances, 0.3 m and 2.5 m. In such conditions, the investigated q-range goes Chapter 2 from ≈ 4.10 -3 to 1.2 Å -1 . For experiments involving a magnetic field, a magnet was placed near the sample with the magnetic field (≈ 300 mT) oriented parallel to the capillary (Fig. 2.11b), and the SAXS pattern was then recorded.

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. One of the major characteristics of synchrotron radiation resides in its high brilliance, defined as radiated number of photons per time unit s, per source unit area ∆A, per unit solid angle ∆Ω and per 0.1% bandwidth:

Brilliance = Number of photons s∆A∆Ω0.1% (2.10)
Synchrotron radiation is characterized by a very high brilliance, exceeding X-ray sources found in laboratory by a factor of 10 12 . At the European Synchrotron Radiation Facility (ESRF), brilliance levels can reach 8.10 20 photons.s -1 .mm -2 .mrad -2 .0.1%. Meanwhile, at SOLEIL, the brilliance is still substantial, measuring at 10 16 photons.s -1 .mm -2 .mrad -2 .0.1%. The photons are emitted towards experimental stations called beamlines 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 a broad range of energies:

• hard X-rays: 4 keV < E < 100 keV;

• tender X-rays: 1 keV < E < 4 keV (not used in this thesis);

• soft X-rays: 100 eV < E < 1.5 keV;

The limits of each spectral range have no physical meanings, are somewhat arbitrary and mainly established by instrumental considerations. 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: X-ray Absorption Spectroscopy (XAS), X-ray Magnetic Circular Dichroism (XMCD) at DEIMOS beamline (SOLEIL) in the soft X-rays range, and GALAX-IES beamline (SOLEIL), ID26 beamline (ESRF) in the hard X-rays range;

Experimental methods -emission: X-rays Emission Spectroscopy (XES), High Energy Resolution Fluorescence Detection (HERFD) at GALAXIES beamline (SOLEIL) and ID26 beamline (ESRF);

-inelastic scattering: Resonant Inelastic X-rays Scattering (RIXS) at GALAXIES beamline (SOLEIL) and ID26 beamline (ESRF).

• X-ray microscopy combined with XAS and XMCD at HERMES beamline (SOLEIL) and COSMIC beamline (ALS)

-Scanning Transmission X-rays Microscopy (STXM);

-ptychography with coherent X-rays.

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 synchrotron. I have also performed Resonant Inelastic X-ray Spectroscopy combined with XMCD (RIXS-MCD) using hard X-rays on the ID26 beamline at the ESRF European Synchrotron and the GALAXIES beamline at the SOLEIL 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 spinel 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 signature. In RIXS-MCD, we used the high sensitivity of RIXS coupled with XMCD to disentangle hard from soft magnetic contribution in binary ferrofluids. Scanning Transmission X-ray Microscopy (STXM) is a microscopy technique where the specimen is illuminated in a scanning motion by the incident beam and the transmitted beam is recorded by a detector. The incident wavelength can vary which allows spatially resolved elementselective spectroscopy. XAS, XMCD, RIXS-MCD and STXM 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.

X-ray absorption spectroscopy

X-ray absorption spectroscopy (XAS) is based on the absorption of a photon by a material which promotes a core electron into an empty state. The Beer-Lambert law states that the intensity of an illuminated sample at energy E = ℏω is:

I(ω) = I 0 exp(-µ(ω)d) (2.11)
with d the thickness of the specimen, I 0 the intensity of the incident beam and µ the photoabsorption coefficient, which depends on the incident wavelength ω. The transmitted Chapter 2 intensity I depends on the cross section σ abs = Γ if I 0 which is proportional to the probability Γ if of an electron being excited from an initial state |i⟩ to a final state |f ⟩. The Fermi Golden rule describes this probability as:

Γ if = 2π ℏ | ⟨f | H int |i⟩ | 2 δ(E f -E i -ℏω) (2.12)
with ℏω the energy of the incident photon, δ the Dirac distribution for conservation of energy, E i,f the energies of the initial and final states |i⟩ and |f ⟩ respectively and H int the light-matter interaction Hamiltonian. The Fermi Golden rule expresses chemical and orbital selectivity. A photon is absorbed by the material when its energy ℏω ≥ ∆E = E f -E i , the binding energy of the electron. A jump in intensity is observed, the absorption edge, and the structure and position of this edge is unique to the energy states of the material.

There are two possible electronic transitions described by H int , electric dipole transitions and electric quadrupole transitions (magnetic dipole transitions being negligible in the X-ray range).

L 2,3 edge
At the L 2,3 -edges, a 2p electron is excited. The electric dipole selection rules only permit transitions where ∆l = ± 1 and ∆s = 0, corresponding to a transition from 2p to 3d states for 3d transition elements, while electric quadrupole transitions (2p to 4s) are negligible. These transitions are in the soft X-ray energy range. Measurements must therefore be set up in ultra-high vacuum. There are different methods of detection. Most experiments are performed using the Total Electron Yield (TEY) detection mode (i.e. detection of all electrons that emerge from the sample surface). When the TEY is measured, only 60% of electrons are detected, i.e. only 2-5 nm of penetration into the material, it is surface sensitive. Another method of detection, Total Fluorescence Yield (TFY), is bulk sensitive. When the core-hole created after the excitation of an electron is filled by the transition of another electron from a higher energy level, it results in the emission of a photon (X-ray fluorescence) or an Auger electron. The mean free path of this photon is in the same order of magnitude as the incident X-rays. However, self-absorption effects induce distortion in the spectra that are difficult straight forwardly to correct. In practice, most measurements are done in TEY. This method is not compatible with a liquid sample in standard liquid cells, however a prototype is being developed at DEIMOS beamline.

K edge

At the K-edge, a 1s electron is excited to an empty p level (electric dipole transition) or empty 3d levels (electric quadrupole transition) with selection rule ∆l = ± 2. The latter transitions correspond to the pre-edge, much weaker than the edge in intensity, however the 3d levels are often hybridized with p levels. The energy range for such transitions are in the hard X-rays which provides high penetration in the material, thus bulk sensitivity. This is compatible with demanding sample environments such as liquid cells.

X-ray Magnetic Circular Dichroism

X-ray magnetic circular dichroism (XMCD) is a specialized form of XAS that takes advantage of the occupancy levels of electrons with regards to their spins within the 3d shell of magnetic transition metals like Fe, Co or Mn. Under an external magnetic field B, when the net magnetic moment of the material is not zero, a right circular polarized photon (µ+) will not yield the same cross-section as a left polarized photon (µ-) (Fig. 2.12a). This magnetic circular dichroism signal was first observed experimentally in 1987 on a Fe foil [START_REF] Schütz | Absorption of Circularly Polarized x Rays in Iron[END_REF]. The XMCD signal ∆σ XM CD = σ µ+ -σ µ-is negative at L 3 edge when the magnetic moment is parallel to the field B. By measuring the absorption at an incident energy maximizing ∆σ XM CD under a varying magnetic field, one can measure element specific magnetization curves since the XMCD signal is proportional to the magnetization of the probed absorbing atom.

To extract quantitative determinations of the cationic distributions of the cobalt-iron nanospinels, simulations of the XAS and XMCD signals can be performed using the Ligand Field Multiplet theory for the Fe 2+ and Fe 3+ ions in magnetite (Fig. 2.13a) for the Co 2+ ions in CoFe 2 O 4 (Fig. 2.13b). The parameters used for the calculations are reported in Ref. [START_REF] Daffé | Small CoFe2O4 Magnetic Nanoparticles in Ferrofluids, Influence of the Synthesis on the Magnetic Anisotropies[END_REF]. The weighted sums of the calculated spectra can be fitted to the experimental ones in order to obtain quantitative distributions of the Co 2+ and Fe 3+ ions among O h and T d sites.

At the L 2,3 edges, magneto-optical sum rules have been developed [START_REF] Thole | X-Ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF] to determine the magnetic spin S z and orbital moment L z of the absorbing atom, directly from the experimental data. To access element-selective and orbital-selective values of the magnetic moment, appropriate linear combination of left and right spectra are used. This information is not available by magnetometry. In short, at the L 2,3 edges, one has the advantage of being able to use sum rules to determine the magnetic moment of the absorbing atom, but it is the nanoparticle surface that is measured mainly. Conversely, at the K pre-edge, sum rules are much more complicated, one does not have access to m s and m orb and the XMCD signal is small. However, hard X-rays enable measurement on liquid samples because they can penetrate in such samples. To combine advantages from both edges, one can use RIXS-MCD, a two photon resonant process where the final state is the same as in L 2,3 spectroscopy but using hard X-rays. Moreover, comparing RIXS-MCD with XMCD at the K pre-edge, the intensity increases by a factor 10 [115].

Resonant Inelastic X-ray Scattering Principle of RIXS-MCD

Resonant Inelastic X-Ray Scattering (RIXS) is a photon-in photon-out X-ray spectroscopy. The principle of 1s2p RIXS is the following. An incident photon of energy ω excites an electron from 1s to 3d orbital, resulting in a hole in the core orbital, which is filled by the decay of a 2p electron, emitting a photon of energy Ω (Fig. 2.14a). The emission energy Ω is detected by a spectrometer composed of analyzer crystals and a photon counter in a Rowland geometry. Both incident and emitted energies are simultaneously scanned. A RIXS map (see example on 2.14b,c) is a 2D graph showing the incident energy on the x-axis and the energy transfer defined as ω -Ω on y-axis. When the circular polarization of the incident beam is changed from left to right, one can obtain a RIXS-MCD map. By choosing an incident energy and transfer energy that maximize the RIXS-MCD (for example red cross on Fig. 2.14), we can measure element-selective magnetization curves.

Element-selective magnetometry using RIXS-MCD

With hard X-rays, a liquid cell was developped in a previous PhD thesis [START_REF] Daffe | Anisotropies and Magnetic Couplings of Texturable Ferrofluids[END_REF] allowing a measurement of frozen binary ferrofluids at the Fe, Co and Mn edges. The liquid cell (Fig.

Experimental methods

Magnetic imaging in X-ray microscopy

By combining XMCD with STXM, one can image a magnetic contrast with chemical sensitivity. Indeed, by imaging the sample with a left and a right circular polarized incident beam and doing the substraction of both images, one obtains the magnetic contrast for the element probed.

We attempted to image the magnetic signal at room temperature using STXM at the HERMES beamline (SOLEIL) and at low temperature using ptychography at the COSMIC beamline (ALS). Unfortunately, the remanence of the sample was too weak to be measured in both cases.

Chapter 3

Single phase ferrofluids Once a synthesis successfully produced satisfactory nanoparticles, initial characterizations have been performed on the ferrofluids. We then delved into a more comprehensive analysis of a specific ferrofluid and its magnetic response under different conditions, including variations in concentration and applied external magnetic field. This study takes a multiscale approach, examining both the nanoscale properties of individual particles and their macroscopic behavior.

The primary objective of this research is to access novel information and insight into the relationship between collective magnetic properties and self-assembly or structuration. In this optic, experimental techniques that are not commonly used for magnetic nanoparticles were implemented, from electron microscopy to synchrotron based experiments. Additionally, we compare our experimental findings with theoretical models and numerical simulations.

Introduction

Ferrofluids are defined as colloidal suspensions of magnetic nanoparticles (MNPs) in a liquid. Nanoparticles have a typical diameter in the 5-25 nm range and are composed of a ferri/ferromagnetic material. Each MNP can be considered as a single magnetic domain, with a magnetic dipole moment on the order of 10 4 µ B , where µ B is the Bohr magneton (9.24 10 -24 Am 2 ). Ferrofluids are considered as model systems for dipolar fluids. They find numerous current and potential applications in biomedicine (e.g., magnetic hyperthermia [START_REF] Dutz | Magnetic Particle Hyperthermia-a Promising Tumour Therapy?[END_REF] [34], contrast agents for magnetic resonance imaging [2]), in technology (magnetic recording materials, sensor components [START_REF] Torres-Díaz | Recent Progress in Ferrofluids Research: Novel Applications of Magnetically Controllable and Tunable Fluids[END_REF]) and art [4]. These applications take advantage of their low cost and high chemical stability [118]. The modification of macroscopic properties by an applied magnetic field finds its origin in the ferrofluid nanoscale structuration, where nanoparticles aggregate to form linear chain-like structures resulting from strong dipole-dipole interactions. Previous investigations have underlined the relevance of studying field-induced structures in ferrofluids, in order to optimize the efficiency of biomedical applications [START_REF] Martinez-Boubeta | Learning from Nature to Improve the Heat Generation of Iron-Oxide Nanoparticles for Magnetic Hyperthermia Applications[END_REF], develop new magneto-optical applications [START_REF] Di | Magnetic-Field-Induced Birefringence and Particle Agglomeration in Magnetic Fluids[END_REF] or understand original phase transitions occurring with temperature [START_REF] Kantorovich | Nonmonotonic Magnetic Susceptibility of Dipolar Hard-Spheres at Low Temperature and Density[END_REF]. At zero applied magnetic field, as initially predicted by De Gennes and Pincus [START_REF] Gennes | Pair Correlations in a Ferromagnetic Colloid[END_REF], MNPs can self-assemble spontaneously when dipolar interactions in ferrofluids are large enough, i.e. the dipole-dipole energy exceeds thermal fluctuations, which is quantified by the ratio λ between the magnetostatic energy and the thermal energy. Theoretical simulations, such as Monte Carlo-based ones [START_REF] Kantorovich | Temperature-Induced Structural Transitions in Self-Assembling Magnetic Nanocolloids[END_REF] [START_REF] Elfimova | Static Magnetization of Immobilized, Weakly Interacting, Superparamagnetic Nanoparticles[END_REF], have been used to calculate the structural assembly of particles as a function of λ, concentration, and temperature, and they have predicted the existence of nanoparticles self-assembled in chains, rings, or a combination of both. These assemblies significantly change the ferrofluid macroscopic properties [START_REF] Usov | Magnetic Nanoparticles with Combined Anisotropy[END_REF] [124] [START_REF] Ivanov | Temperature-Dependent Dynamic Correlations in Suspensions of Magnetic Nanoparticles in a Broad Range of Concentrations: A Combined Experimental and Theoretical Study[END_REF] [START_REF] Holm | Equilibrium Properties of a Bidisperse Ferrofluid with Chain Aggregates: Theory and Computer Simulations[END_REF].

The Stoner-Wohlfarth model [START_REF] Stoner | A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys[END_REF], commonly used to describe magnetic colloids with non-interacting, single domain MNPs with uniaxial anisotropy, does not account for dipoledipole interactions. New models [START_REF] Weis | Chain Formation in Low Density Dipolar Hard Spheres: A Monte Carlo Study[END_REF] [START_REF] Camp | Modified Mean-Field Theory of One-Dimensional Spin Models with Anisotropy and Long-Range Dipolar Interactions[END_REF] have been developed to include the influence of dipolar interactions on ferrofluids, allowing better refinement of magnetic properties, but these models have been so far mostly applied to spherical nanoparticles in a small size range (5-10 nm).

On the experimental side, chain-like assemblies have rarely been imaged directly, and only by cryo-transmission electron microscopy (TEM) in zero-field [START_REF] Klokkenburg | Direct Imaging of Zero-Field Dipolar Structures in Colloidal Dispersions of Synthetic Magnetite[END_REF] and field-cooled [START_REF] Klokkenburg | In Situ Imaging of Field-Induced Hexagonal Columns in Magnetite Ferrofluids[END_REF] experiments. Since these pioneering studies, information on clustering or aggregation of particles has been obtained experimentally by small-angle scattering measurements (with both X-rays and neutrons) [START_REF] Rosenfeldt | Probing the Nanostructure and Arrangement of Bacterial Magnetosomes by Small-Angle X-Ray Scattering[END_REF] [60], but they remain indirect probes and are not able to distinguish between the different shapes of assemblies predicted by simulations [START_REF] Kantorovich | Temperature-Induced Structural Transitions in Self-Assembling Magnetic Nanocolloids[END_REF]. Other imaging techniques, such as electron holography [START_REF] Dunin-Borkowski | Off-Axis Electron Holography of Magnetic Nanowires and Chains, Rings, and Planar Arrays of Magnetic Nanoparticles: Electron Holography of Magnetic Nanostructures[END_REF] or magnetic force microscopy [START_REF] Rastei | Defect-Driven Magnetization Configuration of Isolated Linear Assemblies of Iron Oxide Nanoparticles[END_REF], allow to make the connection between nanoscale organization and local magnetic properties in assembled nanoparticles on dried samples, but few of these studies exist. In general, apart from bulk magnetometry experiments, experimental studies of ferrofluid remain scarce and there is especially a lack of quantitative investigation of particle assembly and its relationship with collective magnetic properties. A deeper understanding of the latter would open new perspectives to design novel or more efficient magnetic responsive ferrofluids, by tuning magnetic dipolar interactions with magnetic anisotropy, size or shape of MNPs.

Most studies have so far focused on the influence of the particle size, concentration and particle saturation magnetization on the formation of self-assembled structures at zero field. They have largely focused on magnetite Fe 2 O 3 [START_REF] Klokkenburg | Dipolar Structures in Magnetite Ferrofluids Studied with Small-Angle Neutron Scattering with and without Applied Magnetic Field[END_REF], maghemite γ-Fe 2 O 3 [START_REF] Salazar-Alvarez | Cubic versus Spherical Magnetic Nanoparticles: The Role of Surface Anisotropy[END_REF], iron [START_REF] Butter | Direct Observation of Dipolar Chains in Iron Ferrofluids by Cryogenic Electron Microscopy[END_REF], and more recently (but much less extensively) cobalt ferrite CoFe 2 O 4 [START_REF] Peddis | Beyond the Effect of Particle Size: Influence of CoFe2O4 Nanoparticle Arrangements on Magnetic Properties[END_REF] or manganese ferrite MnFe 2 O 4 [133] [134]. The effect of particle shape (cube, sphere, rod, flower. . . ) has been little studied so far [START_REF] Gavilán | How Size, Shape and Assembly of Magnetic Nanoparticles Give Rise to Different Hyperthermia Scenarios[END_REF], although it seems of strong interest. For example, it was shown that cubic particles in ferrofluids are more prone to form chains in zero magnetic field than spheres [START_REF] Martinez-Boubeta | Learning from Nature to Improve the Heat Generation of Iron-Oxide Nanoparticles for Magnetic Hyperthermia Applications[END_REF]. Furthermore, flower-shaped nanoparticles (or nanoflowers) of magnetite have been shown to exhibit better hyperthermia performance than dense spherical nanoparticles with similar size [START_REF] Bender | Dipolar-Coupled Moment Correlations in Clusters of Magnetic Nanoparticles[END_REF], but this was attributed to the multicore structure of nanoflowers rather than to particle assembly. Since the magnetic configuration of a nanoflower is difficult to reproduce with micromagnetic simulations, being a disordered spin system with exchange interactions between the different cores, it is still presently unclear whether a nanoflower behaves like a single magnetic domain.

A necessity arises to employ a blend of methodologies to comprehensively investigate both the intricate nanoscale attributes of flower-shaped nanoparticles and their collective magnetic behaviors within a liquid medium. This chapter presents the outcomes of a series of experiments, conceived to elucidate the relationships between size, morphology, composition, assembly properties and macroscopic magnetic properties exhibited by these nanoparticles.

Firstly, I will present the basic characterizations required to select a ferrofluid with interesting properties. Next, I will show how to measure the structuring properties of the Chapter 3 particles as well as their magnetic properties and the information we can derive from them about the single particle will be shown. Finally, a complete study of a selected sample is presented. Additional results on other single phase ferrofluids allowing various comparisons and a discussion will conclude the chapter.

Sample description and basic characterization

The samples are labeled according to the following nomenclature M_d_S or M_d_F: the cation is M in the ferrite formula MFe 2 O 4 , the mean diameter d, and the particle shape is indicated by S for a sphere or F for a flower. For instance, a sample labeled Co_13_S refers to cobalt ferrite nanospheres with a diameter of [START_REF] Chuev | Generalized Stoner-Wohlfarth Model and the Non-Langevin Magnetism of Single-Domain Particles[END_REF] 3.2.1 Synthesis, size distribution and molar ratio.

Synthesis

All the synthesis were produced by S. Neveu and E. Bertuit (PHENIX laboratory). The volume fraction of a ferrofluid is typically around ϕ ≈ 0.1%, but the ferrofluid can be concentrated by dialysis to obtain the desired volume fraction.

Two ferrofluids, Co_13_S (Fig. 3.1a) and Co_17_S (Fig. 3.1e), were synthesized using the coprecipitation synthesis method [START_REF] Massart | Preparation of Aqueous Magnetic Liquids in Alkaline and Acidic Media[END_REF]. These samples were heated in an autoclave for 24 hours at 200°C. Additionally, six ferrofluids were synthesized using the polyol process [START_REF] Ammar | Magnetic Properties of Ultrafine Cobalt Ferrite Particles Synthesized by Hydrolysis in a Polyol Medium[END_REF], employing DEG and NMDEA solvents. The heating step for samples Mn_13_S (Fig. 3.1c), Co_16_F (Fig. 3.1i), Mn_21_F (Fig. 3.1k), and Co_53_F (Fig. 3.1o) was carried out using a microwave oven. For samples Co_24_F (Fig. 3.1g) and Fe_27_F (Fig. 3.1m), the heating was conducted in a round-bottom flask. The heating time was 1 hour for Co_16_F (T=257°C), Co_21_F (T = 260°C), and Mn_13_S (T = 200°C). On the other hand, samples Fe_27_F and Co_53_F were heated for 2 hours at 300°C. Finally, sample Co_24_F was heated for 4 hours at 200°C. It is worth noting that sample Fe_27_F was initially composed of magnetite. However, during the final step, when citrate molecules were added to the surface of the nanoparticles in an aqueous solvent, magnetite was oxidized to maghemite.

Size distribution

The morphology of the particles and the diameter distribution were determined from TEM images. The histograms are reported on Figure 3.1 from TEM images. Samples Co_13_S (Fig. 3.1b), Mn_13_S (Fig. 3.1d) and Co_17_S (Fig. 3.1f) are composed of spherical nanoparticles. The diameter distributions were fitted with a lognormal distribution with mean diameter d 0 and dispersion σ such that d 0 = 14.0 nm, σ = 0.38, d 0 = 14.0 nm, σ = 0.42 and d 0 = 17.0 nm, σ = 0.25 respectively. Samples Co_24_F (Fig. 3.1h), Co_16_F (Fig. 3.1j), Mn_21_F (Fig. 3.1l) and Fe_27_F (Fig. 3.1n) are composed of flower-shaped nanoparticles. The diameter distributions were fitted using a Gaussian distribution with mean diameters d 0 and standard deviation and σ such that d 0 = 23.7 nm, σ = 6.4 nm, d 0 = 15.8 nm, σ =3.8 nm, d 0 = 21.3 nm, σ =7.4 nm and d 0 = 26.3 nm, σ =4.1 nm respectively. All these nanoparticles have a rather narrow size distribution as expected from a polyol synthesis.

However, sample Co_53_F (Fig. 3.1p) is composed of nanoparticles with a mean diameter d 0 = 52.8 nm, σ = 26.4 nm. The initial aim of the synthesis was to obtain larger (d > 40 nm) nanoflowers to compare their magnetic properties to more "standard" samples like Co_24_F. The ferrofluid obtained comprises spherical crystallites with a diameter of ∼ 8 nm as well as flower-shaped nanoparticles with diameters ranging from 40 to 100 nm. The presence of such a wide range of sizes in the sample prompted the need for size sorting methods to improve the sample's quality. These methods will be discussed in Section 3.2.4. In the polyol synthesis, during the heating step in the synthesis, small (i.e. 8-10 nm) crystallites begin to form, which later aggregate into multicore flower-shaped particles. In this particular batch, some of the crystallites did not aggregate into nanoflowers, resulting in the coexistence of nanoflowers with different sizes, leading to a very large distribution with small sizes and larger ones.

Stoichiometry

The molar ratio X m is measured by AAS and defined as:

X m = [M ] [M ] + [F e] (3.1)
with [M] the molar concentration of the transition metal M. In a stoichiometric crystal of cobalt or manganese ferrite, X m = 33%. The molar ratio measured for each sample is reported in 111), ( 220), (311), (400), ( 422) and (333).

X-ray diffraction

All the samples studied exhibit a coherent domain size much smaller than the mean diameter of the nanoparticles, estimated by TEM. This phenomenon is commonly observed in spherical nanoparticles and is typically attributed to a layer of disordered spins on the surface of the particles. However, for the nanoflower samples, the reduction in size is much larger than what could be explained by surface disorder alone.

A similar effect was observed by Lartigue et al. [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] in flower-shaped nanoparticles with diameters ranging from 20 to 30 nm and coherent domain sizes from 11 to 16 nm. They proposed that this discrepancy could be due to misalignments between the cores within the nanoflowers, as observed in high-resolution TEM. This hypothesis will be tested with HRTEM observations that will be presented further (Section 3.6).

Saturation magnetization

In order to measure saturation magnetization with the SQUID magnetometer, a volume (≈ 1mL) of ferrofluid was left to dry at room temperature and then ground to a fine powder. An accurately weighted mass (≈ 10 mg) of the powder was placed in a pharmaceutical gelcap and inside a straw. The magnetic moment µ max at 5 T was normalized to the mass of the powder m powder , corrected for the loss of organic mass from TGA %m organic , to give the value of saturation magnetization M s :

M s = µ max m powder (1 -%m organic ) (3.3)
The saturation magnetization values for each sample are summarized in

Single phase ferrofluids

In all cases, the measured saturation magnetization is reduced compare to the bulk value. This reduction in M s may be attributed to different chemical or physical effects. One possibility is the low-stoichiometric composition of each sample (except Co_17_S) in Co or Mn, which can modify the magnetic properties of the nanoparticles. A deficiency of Co or Mn atoms may be replaced by Fe 2+ atoms or leave vacancies in the unit cell, resulting in a lower overall occupancy in the crystal structure. These modifications of the atomic composition can influence the magnetic behavior of the nanoparticles, leading to a decrease in their saturation magnetization [START_REF] Brice-Profeta | Magnetic Order in γ-Fe2O3 Nanoparticles: A XMCD Study[END_REF]. Another possibility is the presence of disordered spins at the surface of the nanoparticle which do not contribute to the magnetic moment [START_REF] Morales | Surface and Internal Spin Canting in γ-Fe 2 O 3 Nanoparticles[END_REF]. Finally, defects such as antiphase boundaries have been proven to cause a reduced M s in iron oxide nanospheres [START_REF] Köhler | Signature of Antiphase Boundaries in Iron Oxide Nanoparticles[END_REF]

Size sorting of sample Co_53_F

The size distribution of sample Co_53_F is fitted by a lognormal (Eq. 3.4) or a Gaussian (Eq. 3.5) law depending on the best fit. It is generally assumed that the size distribution follows a lognormal law due to the linear dependence between volume growth and time [START_REF] Kiss | New Approach to the Origin of Lognormal Size Distributions of Nanoparticles[END_REF]. However, the synthesis of nanoflowers has a different chemical process than a coprecitation synthesis. For nanoflowers, the Gaussian law provides a better fit (Fig. 3.3). When the particles have a spherical shape, a lognormal law was used.

P (d, d 0 , σ) = 1 √ 2πdσ exp -ln (d/d 0 ) 2 2σ 2 (3.4) P (d, d 0 , σ) = 1 √ 2πσ exp (d -d 0 ) 2 2σ 2 (3.5)
The synthesis of cobalt ferrite nanoflowers is very dependent on heating parameters. Two batches can yield different diameter distributions, such as samples Co_16_F and Co_24_F. Increasing the heating time extends the growth step of the nanoflowers, and yields bigger particles, like in sample Co_53_F. However the resulting nanoparticles are very polydisperse (with an average diameter d 0 = 53 ± 26nm according to the gaussian fit). In addition, the solution is not a colloidal suspension because it is unstable over time, as a fraction of particles are > 100 nm (Fig. 3.3). The sample also shows the presence of "petals", i.e. crystallites that did not aggregate into flowers during the synthesis (small size below 10 nm). Size sorting was experimented in order to reduce polydispersity and obtain a ferrofluid with nanoflowers of smaller diameter (around 50 nm), by removing both the petals and the larger particles preventing colloidal stability. Several techniques were applied: • Decantation: the sample is left for several minutes to decant under gravity and the supernatant is separated from the pellet;

• Magnetic decantation: the sample is left on a magnet for 10 minutes, supernatant and pellet are separated;

• Centrifugation: the sample is centrifuged at 4000 rpm for 6 minutes, supernatant and pellet separated.

Decantation did not decrease polydispersity and was difficult to control. However, centrifugating the sample allowed a significant modification of the size distribution. The supernatant was composed of petals (≈ 13 nm) and flowers of smaller diameters (d 0 = 34 nm) than the original sample (Fig. 3.4). The pellet yielded mostly full formed flowers with diameters closer to the original sample and with smaller polydispersity (σ original = 26 nm and σ pellet = 22 nm, see Fig. 3.5). Similarly, magnetic decantation reduced the polydispersity and removed a fraction of the petals (Fig. 3.6), with more efficiency than the centrifugation method. Finally, a combination of both centrifugation and magnetic decantation methods worked best. The sample was first decanted on a magnet and the resulting pellet was centrifuged. The final pellet contained flowers of average diameter d 0 = 54 ± 14 nm (Fig. 3.7), and most of the petals and larger flowers were removed. However, the sample was not fully stable and had a tendancy to decante after a few hours or even a few minutes under magnetic field. The concentration and volume after size sorting were also too low for the planned experiments on binary ferrofluids. The original sample Co_53_F was then used for following studies.

Structuration properties

Cryo-TEM offers a powerful means to explore and analyze the structuration properties of the ferrofluids, enabling the examination of the nanoparticle arrangement, as preserved in a frozen solution. The experimental process involves depositing a drop of the ferrofluid Chapter 3 at room temperature onto a grid, which is then rapidly plunged into liquid ethane at a temperature of 90 K. Since the solvent of the ferrofluid is water, it quickly solidifies upon entering the liquid ethane due to vitrification.

The vitrification process is exceedingly fast, taking just a few microseconds, resulting in the formation of amorphous ice. This amorphous ice forms a transparent and solid matrix, enabling the visualization of the magnetic nanoparticles by TEM, as long as the layer of vitrified water remains under approximately 100 nm. Crucially, the rapid vitrification process immobilizes the magnetic nanoparticles, preventing them from moving and allowing the specimen to capture a static snapshot of the structural organization of the particles in the ferrofluid.

To ensure robust reproductibility, each specimen is prepared at least twice using the same procedure. Because mapping the entire grid would be impractical and time-consuming, I observed and imaged a representative sample of a dozen squares from each specimen, ensuring an homogeneous behavior across the sample.

The ferrofluids observed in Cryo-TEM are the following:

• Co_24_F (ϕ = 0.14%, ϕ = 0.1%, ϕ = 0.07% and ϕ = 0.014%)

• Co_16_F (ϕ = 1%, ϕ = 0.1% and ϕ = 0.04%)

• Mn_21_F (ϕ = 1.4% and ϕ = 0.1%) • Fe_27_F (ϕ = 0.1% and ϕ = 0.01%)

• Co_53_F (ϕ = 0.2%, ϕ = 0.06% and ϕ = 0.02%) Figure 3.8 displays representative cryo-TEM images of sample Co_24_F imaged at four different volume fractions. At ϕ = 0.14% (Fig. 3.8a-i), self-assembly of nanoparticles is observed, forming various structures such as chains, rings, and networks. A detailed statistical analysis of these shapes is described in Section 3.6. As the volume fraction decreases, the distance between nanoparticles reduces until self-assembly is no longer observed at ϕ = 0.014% (Fig. 3.8a-iv), leaving only isolated nanoparticles. At intermediate volume fractions, ϕ = 0.1% (Fig. 3.8a-ii) and ϕ = 0.07% (Fig. 3.8a-iii), the nanoparticles still form chains, but the inter-particle distance is larger, with no formation of rings or networks.

It is important to note that since sample Co_16_F and Co_24_F have different mean diameters, at an equal volume fraction, the number of particles per volume ϕ N differs. For sample Co_24_F , the volume of one nanoparticle is approximately V 1 NP ≈ 7240 nm 3 , while for sample Co_16_F, V 1 NP ≈ 2150 nm 3 . For instance, when ϕ = 0.14%, an estimation of ϕ N for sample Co_24_F gives ϕ N = ϕ/V 1 NP = 2 × 10 -5 %. To achieve a similar ϕ N for sample Co_16_F, the volume fraction needs to be ϕ = ϕ N V 1 NP = 0.04%. This adjustment ensures a comparable number of nanoparticles per unit volume for both samples, allowing for more meaningful comparisons between their self-assembly behavior at equivalent concentrations. So ϕ = 0.04% for Co_16_F and ϕ=0.14% for Co_24_F correspond to similar ϕ N .

Chapter 3

In Figure 3.8b, images of sample Co_16_F reveal self-assembly at two different volume fractions: ϕ = 0.1% (Fig. 3.8b-i, ii) and ϕ = 0.04% (Fig. 3.8b-iii, iv). At a volume fraction of ϕ = 0.1%, cryo-TEM images show the presence of both chains and clusters of nanoparticles in close proximity to each other (Fig. 3.8b-i, ii). When the volume fraction is reduced to ϕ = 0.04%, the self-assemblies are still present, but they are now more sparsely distributed on the grid (Fig. 3.8b-iii, iv).

Concerning soft magnetic materials, nanoparticles in samples Mn_21_F and Fe_27_F (Fig. 3.8c) do not presente self-assembly but are agglomerated into large clusters of hundreds of particles. At ϕ = 0.1%, both ferrofluids are stable for ∼ 1 hour but the aggregation due to magnetic dipolar interaction between the nanoparticles induces sedimentation. We attempted to correct the stability by adjusting the amount of surfactants but it was unsuccessful. For static magnetic measurements, the ferrofluids are studied in their frozen state and one must keep in mind that the clusters might not be evenly distributed in the fluid. Moreover, some chaining is present as seen on Figure 3.8c. At ϕ = 0.01%, cryo-TEM images of Fe_27_F show only isolated nanoparticles (no cryo-TEM images at that volume fraction are shown here because they only consist of one nanoparticle per image). Finally, sample Co_53_F was observed at different volume fraction: ϕ = 0.2% (Fig. 3.8di,ii) and ϕ = 0.06% (Fig. 3.8d-iii, iv). The first sample with ϕ = 0.2% was observed only once, a short amount of time after the synthesis was realised, and shows networks of chains composed by large (d > 70 nm) nanoflowers, as well as clusters. At ϕ = 0.02%, only a few isolated nanoparticles were observed. However when the same sample was observed again at ϕ = 0.06%, some months later, only clusters were observed and the networks were not present anymore. The dilution was done in a water with the same concentration of citrate molecules than the original ferrofluid, but due to either aging or dilution, the nanoparticles aggregated and the ferrofluid was not stable for more than 15 minutes.

Field induced structuration

By placing a permanent magnet on the tip of non-magnetic tweezers holding the TEM grid, it is possible to submit the ferrofluid to an external magnetic field before plungefreezing with the cryo-plunger. The magnetic field applied on the nanoparticles is a field gradient of magnitude ∼ 20 mT (measured at the grid position with a Hall probe). Micrometric parallel chains are observed, as presented in Figure 3.9a. This technique is delicate and hard to reproduce as the magnet needs to be close to the grid to have an effect on the ferrofluid, but the tweezers are not designed for this purpose. In many attempts, the magnet moves during the rapid plunge step and no chains were observed in the resulting specimen. Moreover, if the ferrofluid is too concentrated, the drop placed on the grid is attracted to the magnet and leaves the grid. An improved design using an electro-magnet is currently being developed but is not yet operational.

Dry method of specimen preparation

In this thesis, the primary focus is to study the self-assembly of magnetic nanoparticles. Several techniques presented in the following sections (electron holography, electron tomography or STXM) do not allow for a cryogenic environment (lack of cryostat in the setup). I needed a way to prepare specimens with similar assemblies as observed in cryo-TEM but on a dry substrate at room temperature, without freezing the ferrofluid. To observe these assemblies at room temperature on dried TEM grids, a specific specimen preparation method was developed to preserve the spatial organization of the nanoparticles without inducing aggregation between them.

Depositing a drop of solution on TEM grid often leads to nanoparticle aggregation, which prevents the observation of the desired assemblies. To address this issue, a modified procedure was implemented. The carbon membrane of the TEM grid is subjected to a plasma cleaner and ionized in an argon atmosphere for 30 seconds. This ionization process transforms the hydrophobic amorphous carbon surface into a hydrophilic one by introducing hydroxyl (OH), carboxyl (COOH), and carbonyl (CO) groups. Additionally, surface contaminants are removed. Importantly, argon, as a noble gas, does not chemically react with the surface, ensuring the preservation of the original properties of carbon membrane and the nanoparticles once deposited.

Chapter 3 Subsequently, a 5 µL drop of a diluted ferrofluid (ϕ ≤ 10 -3 %) is deposited on the ionized grid hold by reverse tweezers. The sample is then left to dry in air for 12 hours. Remarkably, with this method, the nanoparticles tend to form fewer clusters, and the same assemblies than those observed in cryo-TEM are present. Figure 3.9 shows an example of each observations. This approach allows to observe the desired self-assemblies on dried TEM grids at room temperature without the presence of artificial aggregation. Additionally, the dry method allows for the convenient addition of an external magnetic field to the system. By placing the TEM grid between two permanent magnets before deposition, a controlled magnetic field can be applied to the ferrofluid during the evaporation process. The field lines are aligned parallel to the plane of the grid, and the strength of the magnetic field is calibrated using a Hall probe. The field magnitude can be adjusted by varying the distance between the magnets. Figure 3.9b shows the results of such a setup, where a magnetic field of 50 mT was applied to the ferrofluid during evaporation. Interestingly, the observations reveal the formation of similar chains of nanoparticles as those obtained by the cryo-TEM field cooling method.

It is essential to acknowledge that with this preparation method, the observed assemblies or clusters are "artificially" produced in the sense that they are not observed in their natural state in the ferrofluid. However, it is hypothesized that these artificially induced structures resemble the natural organization of the magnetic nanoparticles in the ferrofluid as they present similar arrangements as the ones observed in cryo-TEM. This approach enables the investigation of the self-assembly behavior of the nanoparticles under room temperature conditions and using microscopy techniques that are not equiped with cryostat, like electron holography or X-ray microscopy. The results obtained with this method will be presented in Section 3.6.

Magnetic properties

Magnetic anisotropy

Temperature dependence of magnetization

By measuring the magnetization as a function of temperature M(T), we can access the blocking temperature T B , which is related to the magnetic anisotropy of the nanoparticles. The cobalt ferrite ferrofluids all have a blocking temperature T B > 270 K and so above the fusion point of water. When the solvent of the ferrofluid is liquid, Brownian relaxation prevents the determination of the blocking temperature as the nanoparticles are superparamgnetic due to Brownian motion. Other methods will be used to determine the magnetic anisotropy of CoFe 2 O 4 samples.

The ferrofluids were cooled to 5 K with no external magnetic field in the SQUID at ϕ = 0.1%. Then the field was turned on to 5 mT and the magnetization measured with increasing temperature to 250 K. The M(T) curves for samples Mn_13_S and Mn_21_F are presented in Figure 3.10. The blocking temperature T B can be estimated to the temperature at which magnetization is maximum. In our case, we have T B = 185 and 147 K for samples Mn_13_S and Mn_21_F respectively. From T B = KV /k B ln(τ m /τ 0 ), with τ m = an approximative value for magnetic anisotropy is deduced, K = 57 and 15 kJ/m 3 for samples Mn_13_S and Mn_21_F respectively.

Temperature dependence of coercivity

The magnetization curves (M vs H) were measured by SQUID magnetometry between 10 and 240 K (Fig. 3.11) These measurements were performed when the solvent was frozen, allowing only Néel relaxation to occur. From these magnetization curves, the remanence M r and coercivity H c were extracted and H c extrapolated linearly to T = 0 K (Fig. 3.12a). Using the Stoner-Wohlfarth model [START_REF] Stoner | A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys[END_REF], the effective anisotropy constant value (K eff ) can be extracted as follows:

K eff = M s µ 0 H c (T → 0) 0.96 (3.6)
It is important to note that the Stoner-Wohlfarth model does not consider magnetic dipolar interactions. Therefore, the magnetization curves need to be measured at a diluted concentration, preferably with ϕ ≤ 0.1%, to minimize these interactions and ensure the reliability of the extracted effective anisotropy constant values. For all samples, both the coercivity (Fig. 3.12a) and remanence (Fig. 3.12b) increase as the temperature decreases. For the cobalt ferrite samples, the flower-shaped nanoparticles consistently exhibit a remanence ratio M r /M s of 90% at low temperatures, whereas the spherical nanoparticles have lower remanence ratios, ranging between 70% and 80%. Comparing these findings with the theoretical work of Usov et al. [START_REF] Usov | Theoretical Hysteresis Loops for Single-Domain Particles with Cubic Anisotropy[END_REF], particles with cubic magneto-crystalline anisotropy are expected to have a 85% remanence, while those with uniaxial anisotropy would have 50%. The LAS method can be used to determine the magnetic anisotropy of both uniaxial and cubic materials from magnetic characterization methods like SQUID magnetometry. Akulov's pioneering work [START_REF] Akulov | Über den Verlauf der Magnetisierungskurve in starken Feldern[END_REF] introduced the LAS concept for polycrystalline ferromagnets. It involved fitting magnetization curve M (H) to a 1/H 2 dependency in high field regions. This model attributes magnetization behavior to magnetocrystalline anisotropydriven magnetization vector rotation near saturation. An added interaction term linked to the internal magnetic field accommodates nonmagnetic inclusions beyond saturation field. Moreover, researchers extended LAS to explore the dependency of magnetization processes on applied magnetic fields, especially within the high field region characterized by reversible magnetization rotations. The form of LAS appears adaptable to specific materials and their compositions, yielding diverse mathematical expressions. New additional terms beyond 1/H 2 , reflecting structural defects (a/H) and paramagnetism-like influences (kH) were added [START_REF] Sivaranjani | Comprehensive Law-of-Approachto-Saturation for the Determination of Magnetic Anisotropy in Soft Magnetic Materials[END_REF], to finally obtain the following expression:

M = M s 1 - a H - b H 2 + kH (3.7)
The constant b can then be related to K 1 the cubic magnetocrystalline anisotropy constant, such that b = 8K 2 1 /105M 2 s . In the literature, the LAS method applied on cobalt ferrite nanoparticles yielded K 1 = 357 kJ/m 3 [START_REF] Anantharamaiah | Enhancing the Strain Sensitivity of CoFe 2 O 4 at Low Magnetic Fields without Affecting the Magnetostriction Coefficient by Substitution of Small Amounts of Mg for Fe[END_REF]. In Sivaranjani et al. [START_REF] Sivaranjani | Comprehensive Law-of-Approachto-Saturation for the Determination of Magnetic Anisotropy in Soft Magnetic Materials[END_REF], another form of LAS was used, including a 1/ √ H term corresponding to a ferromagnetic ordering at zero field.

Single phase ferrofluids

However in our case, we find that this term does not modify the performance of the fit, and we restrict ourselves to Equation 3.7.

Figure 3.13 a-b presents an example of a magnetization curve for samples Co_24_F (ϕ = 0.014%) and Co_16_F (ϕ = 0.005%) at T = 100 K. The red curve corresponds to the LAS fit in the high-field region (µ 0 H > 500 mT). This method was applied across temperatures ranging from 5 to 250 K. In Figure 3.13c-d, the value of K 1 deduced from parameter b in the LAS fit is plotted as a function of temperature. By considering an empirical equation for K 1 :

K 1 ∝ exp -BT 2 (3.8)
as established by Shenker [START_REF] Shenker | Magnetic Anisotropy of Cobalt Ferrite (Co 1.01 Fe 2.00 O 3.62 ) and Nickel Cobalt Ferrite (Ni 0.72 Fe 0.20 Co 0.08 Fe 2 O 4 )*[END_REF], the K 1 values at room temperature are found to be K 1 (300) = 41 kJ/m 3 for the Co_24_F sample and 34 kJ/m 3 for the Co_16_F sample. Moreover, we can compare K 1 (0) to K eff found by extrapolating the coercivity at low temperature from previous section. Using LAS method, K 1 (0) = 278 and 466 kJ/m 3 for samples Co_24_F and Co_16_F respectively (against 244 and 445 kJ/m 3 previously). We find a good agreement between the LAS method and the determination of K eff from coercivity at low temperature. The Langevin model is a theoretical model that describes the response of non-interacting point-like magnetic dipoles to a continuous magnetic field H. In this model, the magnetization curve M (H) is reversible and can be described using the Langevin function L(x) = coth(x) -1/x such that:

Magnetic moment distribution

M (H) = µ s ϕL µ 0 µH k b T (3.9)
where µ is the magnetic moment, µ s the specific magnetization of the material, ϕ the volume fraction, k b the Boltzman constant and T the temperature. By fitting the experimental magnetization curves using the Langevin function, it is possible to estimate the mean magnetic moment <µ> of the nanoparticles. However, in real ferrofluids, magnetic nanoparticles are not monodispersed in size, and polydispersity needs to be considered. The model for magnetization in the presence of polydispersity is given by [START_REF] El-Hilo | Nano-Particle Magnetism with a Dispersion of Particle Sizes[END_REF]:

M (H) = µ s ϕ ∞ 0 L(µ, H)P (µ)dµ (3.10)
with the magnetic moment distribution P (µ) that can be a lognormal or gaussian distribution. A numerical inversion method was developed by Bender et al. [START_REF] Bender | Distribution Functions of Magnetic Nanoparticles Determined by a Numerical Inversion Method[END_REF] to extract the magnetic moment distribution P (µ) without making any assumption about its nature. To determine P (µ), magnetization curves M (H) were obtained using SQUID magnetometry on diluted ferrofluids (ϕ ≤ 0.1% to minimize magnetic dipolar interactions). The measurements were performed at 300 K, and a fine magnetic field step was used to achieve optimal fitting (Fig. 3.14). distribution P (µ), the mean magnetic moment µ 0 , the dispersion σ, and the standard deviation error for each parameter.

If the distribution is Gaussian, σ represents the standard deviation with the same units as <µ>. On the other hand, if the distribution is lognormal, σ is the dimensionless dispersion. Most samples were fitted with a lognormal and a Gaussian distribution successively to compare the performance of each law. I found that the validity of the fit was better for the Gaussian distribution, and these are the values I will use in the following sections. This is also adequate as the diameter distribution was also fitted by a Gaussian distribution for nanoflowers.

Sample Co_24_F shows the largest mean magnetic moment (Fig. 3.14) of the samples measured, with <µ> = 21.5 10 -19 Am 2 . It is worth noting that samples Co_16_F and Mn_21_F have almost the same magnetic moment distribution (Fig. 3.15), which will be important in the next chapter.

Remanence ratio

According to the Stoner-Wohlfarth model, randomly oriented magnetic moments with uniaxial anisotropy have a magnetization curve with remanence M r /M s of 50%. In Usov et al. [START_REF] Usov | Theoretical Hysteresis Loops for Single-Domain Particles with Cubic Anisotropy[END_REF], particles with cubic magnetocrystalline anisotropy have a remanence of 83.1% for K 1 > 0 and 86.6% for K 1 < 0.

For the cobalt ferrite samples studied in this thesis, remanence ratios varied between 75% and 91%. A decrease in M r can be justified by the presence of both uniaxial and cubic anisotropy in the nanoparticles, due to different contribution to the total effective anisotropy (such as surface anisotropy or magnetocrystalline anisotropy). Samples Mn_21_F and Fe_27_F present a remanence of 15% and 18% respectively (Fig. 3.16). As this value is much lower than the theoretical values of 50% and 80%, we cannot explain it by a presence of uniaxial and cubic anisotropy. However, Dutz et al. [START_REF] Dutz | The Role of Interactions in Systems of Single Domain Ferrimagnetic Iron Oxide Nanoparticles[END_REF], observed similar remanent magnetization in powders of iron oxide nanoparticles (with a mean diameter of 21 nm). In this study, the powder is diluted in a nonmagnetic matrix with different volume fraction or packing density, from 0.24% to 68%. When the packing density increases, the remanence decreases, with M r /M s = 18% for the highest packing density.

By using the FORCulator software, I simulated 5 clusters of 20 nanoparticles in a 500 3 nm 3 box, with for each cluster an intra-particle packing density ranging from 10% to 70%. For comparison, randomly distributed nanoparticles were also simulated, with volume fraction 0.01%, so that all nanoparticles were isolated. The anisotropy was set to uniaxial, with a switching field distribution parameters α = 0.5 and β = 20 (corresponding to the switching field of magnetite). The simulation solves the LLG equations with damping factor of 0.9. For each configuration, 150 individual FORCs were calculated with a field step of 2 mT and H b = 12 mT and H u = ± 5 mT. In order to increase the quality of the data, 50 configurations were averaged together to obtain the final magnetization curve and FORC diagram. The total number of particles simulated is always equal to 5000 to ensure good statistics.

The dependence of coercivity and remanence with packing density is presented in Figure 3.17. Both remanence and coercivity decrease with increasing packing density. Coercivity takes values between 14 and 9 mT, as expected for magnetite. At 0.01% (non-interacting nanoparticles), the remanence is 50%, as per the Stoner-Wohlfarth model. Moreover, as observed in Dutz et al. [START_REF] Dutz | The Role of Interactions in Systems of Single Domain Ferrimagnetic Iron Oxide Nanoparticles[END_REF], remanence decreases with increasing packing density as more nanoparticles start to interact and it reaches 16% at high density. Samples Mn_21_F and Fe_27_F observed in cryo-TEM present densely packed clusters of hundreds of nanoparticles. The low remanence measured is thus probably due to the magnetic interactions inside the clusters as particles come into closer contact with each other, leading to the appearance of exchange interactions and more complex magnetic structures. Chapter 3

Cobalt ferrite nanoflowers

In this section, we focus our attention on sample Co_24_F by doing an experimental multi-scale analysis of its properties. Our goals were to : (i) finely characterize the morphology and magnetic properties of these nanoflowers, (ii) elucidate the nature of the magnetic domain (multidomain, monodomain...), (iii) study in a quantitative way the assembling and magnetic properties under different interaction regimes and the absence or presence of external magnetic field. Chaining properties and colloidal stability were key factors in the choice of sample. Since cobalt ferrite is a hard magnetic material with an exceptionally high anisotropy constant, the nanoparticles can be considered as stable magnetic dipoles that do not exhibit time-dependent fluctuations about the easy axis of magnetization. In addition to conventional techniques (XRD, bulk magnetometry, standard TEM), advanced experimental approaches were combined to access (i) the single particle morphology and crystal structure (high resolution TEM, electron tomography), (ii) the quantitative nanoscale characterization of particles assemblies (cryo-TEM, preserving the native organization in the ferrofluid, (iii) the collective macroscopic assembling properties (SAXS), (iv) the distribution of magnetic coercivity and interaction fields (measurement and simulation of First Order Reversal Curve FORC diagrams), (v) the local orientation of magnetic moments within particle assemblies (electron holography). Using this methodology, we were able to to build a comprehensive multi-scale picture of this ferrofluid, from the collective behavior down to the particle level, and we provide a set of original quantitative findings on its structuration and magnetic properties.

Results

Characterization of a single nanoflower

From TEM images (Fig. 3.19a), the nanoparticles exhibit well-defined flower-like structures with a mean diameter d TEM = 23.7 nm and a standard deviation σ = 6.4 nm (Fig. 3.19b). XRD patterns (Fig. 3.19d) measured on a dried ferrofluid sample confirm the presence of a spinel phase with a lattice parameter a ≃ 8.37 Å and a coherent domain size of 14 nm, which is smaller than the size determined by TEM.

Electron tomography experiments were realized at IPCMS (Strasbourg, France) in collaboration with O. Ersen and W. Baaziz, using a JEOL 2100 FEG S/TEM microscope operated at 200 kV equipped with a spherical aberration corrector on the probe-forming lens. Samples were dispersed by ultrasonication in ethanol and deposited on a holey carbon coated TEM grids. The acquisition of tilt series was acquired in TEM mode using the tomography plug-in of the Digital Micrograph software by tilting the specimen in the angular range +67.5°and -70.5°using an increment of 1.5°in the equal mode, giving thus a total number of images of 93 images. The recorded images of the tilt series were spatially aligned by cross correlating consecutive images using IMOD software. For the volume calculation, the algebraic reconstruction technique (ART) implemented in the TomoJ plugin working in the ImageJ software was used to compute the reconstructed volumes. Finally, the visualization and the analysis of the final volumes were carried out using the displaying capabilities and the isosurface rendering method in the Slicer software.

Electron tomography observations on the nanoflowers (Fig. 3.19c) show that the nanoparticles are formed by smaller (∼ 8 nm) crystallites (or "petals") aggregated around a core. 3D reconstruction also evidenced the presence of small cavities (< 2 nm) inside some petals. A total of four particles were observed by tomography with average diameter (as measured from 2D images) of 31.1 ± 0.2 nm, thus larger than the average nanoflower diameter. The analysis of the tomography images yields a mean volume of 10300 ± 1200 nm 3 . This value is 35% smaller than the volume of a sphere with similar diameter. Moreover, the surface was estimated to 4900 ± 800 nm 3 , which is 60% higher than the surface of a perfect sphere with similar diameter. Finally, the specific surface S spec = S/ρV with the density of CoFe 2 O 4 ρ = 5.29 g/cm 3 [START_REF] Cullity | Introduction to Magnetic Materials[END_REF], was calculated to 89 m 2 /g. As a comparison, Lartigue Chapter 3 et al. [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] using nitrogen adsorption measurements found S spec = 82 m 2 /g for iron oxide nanoflowers, with 29 nm in diameter. This is consistent with our findings. At the nanoscale, nanoparticles present a complex crystalline structure. Due to the chemical process during synthesis, small crystallites start to form before agglomerating in larger nanoparticles. Using HRTEM, the particle structure could be resolved (Fig. 3.20a). The Fast Fourier Transform (FFT) of the HR image (Fig. 3.20b) shows diffused spots, caused by the so-called "mosaicity" within a single nanoparticle [START_REF] Bertuit | Structure-Property-Function Relationships of Iron Oxide Multicore Nanoflowers in Magnetic Hyperthermia and Photothermia[END_REF]. Fig. 2c-f shows the FFT patterns measured from different areas of a typical nanoparticle. A spot corresponding to a specific hkl plane family (here 311 was arbitrarily chosen) and the angle between this node, and a reference horizontal axis was measured (Fig. 3.20). The angular spread is of the order of 6°for this specific nanoparticle. Similar deviation angles were found for all the nanoparticles measured by HRTEM. The nanoflowers are composed of crystallites arranged in a similar crystalline orientation but slightly tilted from one crystallite to another. This result Single phase ferrofluids is consistent with previous HRTEM observations of nanoflowers [58][43] [54] [START_REF] Thomas | One-Step Continuous Synthesis of Functionalized Magnetite Nanoflowers[END_REF], although the angular spread between the crystallites was found to be smaller in those studies (between 1°and 3°). The mosaicity of the nanoparticles can explain the smaller sizes found by XRD (d XRD < d TEM ), as diffraction is sensitive to the crystallites and not to the whole nanoflowers. SAXS experiments were carried out at PHENIX laboratory (Paris, France) on a Xeuss 2.0 equipment equipped with a GeniX source operating at λ = 1.54 Å and a Pilatus detector. Samples were conditioned in glass capillaries with a diameter of 1 mm, and two sample-todetector distances, 0.3 m and 2.5 m. In such conditions, the investigated q-range (where q is half of the diffusion angle) ranges from ≈ 4.10 -3 to 1.2 Å -1 . For experiments involving a magnetic field, a magnet was placed near the sample with the magnetic field (≈ 300 mT) oriented parallel to the capillary, and the SAXS pattern was then recorded. Figure 3.21a presents the SAXS curves obtained in the absence of any magnetic field measured for samples with volume fractions ϕ = V NP /V total of 0.014% and 0.14%. Both curves display a similar shape with variations in intensity that are in line with the differences in volume fraction. Both curves were compared with the SAXS curves corresponding to the form factor of monodisperse spheres (Fig. 3.21b and 3c). Several results can be deduced from this comparison : (i) both curves are well approximated by a form factor corresponding to a sphere [START_REF] Guinier | Small-Angle Scattering of X-Rays[END_REF] with a diameter of 27 nm; (i)i the absence of marked oscillations in the experimental curves reveals that the particles are polydisperse, a conclusion in line with TEM results; (iii) the deviation at high q of the slope of the SAXS curve from the q -4 dependence (exhibited by the envelope of the spherical form factor) suggests that the surface of the particles displays significant roughness [START_REF] Glatter | Small Angle X-ray Scattering[END_REF]; (iv) at low q the behavior of both systems is different: the particles at a volume fraction of 0.014% display a plateau that follows the form factor of spheres (Fig. 3.21b), whereas for a volume fraction of 0.14% (Fig. 3.21c) an upward deviation is observed. This reveals the presence of larger objects corresponding to associated particles in the suspension. The low slope observed in this region might be tentatively assigned to the presence of chains of particles. However, the q range on which this is observed is too limited to provide a definitive interpretation. Figure 3.22 shows the influence of a magnetic field (300 mT) on the SAXS patterns of suspensions with volume fractions of 0.014% and 0.14%. Figure 3.22a and 4b present the bidimensional scattering pattern obtained for the sample with a volume fraction of 0.014% in the absence and presence of a magnetic field, respectively. No significant differences are observed, which shows that for this sample, at the scale probed by SAXS, no visible structure appears under a magnetic field. This is confirmed by the integrated data (Fig. 3.22e) that do not exhibit any significant differences related to the application of a field. The situation is markedly different in the case of the sample with a volume fraction of 0.14%. Indeed, when compared to the bidimensional scattering pattern in the absence of a magnetic field (Fig. 3.22c), the pattern obtained under field (Fig. 3.22d) clearly exhibits anisotropic features that can be assigned to the presence of almost vertically oriented objects. This can also be noticed by looking at the integrated signal (Fig. 3.22f). Under an applied magnetic field, a structure factor appears with a peak located at ∼ 0.017 Å -1 . This corresponds to a distance of ∼ 36 nm. Considering that the MNPs have a diameter of ∼ 27 nm (as determined by SAXS), this reveals the presence in the system of aggregates of particles that are not in close contact but separated by less than 10 nm.

Evidence of particle assemblies from SAXS measurements

Furthermore, data at low q display an upward deviation that can be assigned to the existence of larger structures. Even considering the limited q-range available at low q, the slope observed for q values lower than the peak positions suggests that these structures are not only linear, since this would lead to an evolution in q -1 that is not observed here. In order to image particle assemblies, cryo-TEM observations were performed on diluted (ϕ = 0.014%) and concentrated (ϕ = 0.14%) ferrofluids. While the former shows isolated, non-interacting nanoparticles (Fig. 3.23a), self-assembly is observed in the latter, with nanoparticles forming small chains, rings and branches (Fig. 3.23b). Finally, under a 25mT magnetic field, nanoparticles form long micrometric chains aligned along the field direction (Fig. 3

.23c).

The assemblies identified in Section 3.3 were further studied and quantified. We analyzed 453 images containing assemblies, and calculated the statistical probability of appearance of a certain assembly amongst the ones observed (note that this is different from the probability of observing the corresponding self-assembly, since isolated particles were not included in the counting). The sorted assemblies are mostly a combination of small chains and rings (Fig. 3.24). We established a classification based on that of Kantorovich et al. [START_REF] Kantorovich | Temperature-Induced Structural Transitions in Self-Assembling Magnetic Nanocolloids[END_REF] The statistical analysis shows that chains are the most probable assembly to form with a 62% probability. Small rings mixed with chains or other rings have a 20% probability to form, while intertwined chains forming networks appear in 18% of the cases. A closer look at each category shows that well-defined, isolated chains are very frequent (51%). Other types of assemblies were less likely to appear, such as the double crossing chain or "Xshape" assembly at only 1% (or 5 cases), and the double ring at 2% (8 cases). The remaining 12%, a branched mix of chains and rings, do not fit into previous categories and are labeled "branches". Kantorovich et al. [START_REF] Kantorovich | Temperature-Induced Structural Transitions in Self-Assembling Magnetic Nanocolloids[END_REF] used Monte-Carlo simulations to estimate, at similar particle concentration and temperature, that the assemblies where composed of 73% of chains and 23% of rings, with ∼4% of other shapes. These values are consistent with our findings.

The number of particles per assembly was also counted. The average chain is composed of 6 nanoparticles (Fig. 3.25a) while the average rings are composed of 13 nanoparticles (Fig. 3.25b), however these averages can vary substantially. Indeed, as a chain increases its length, it becomes energetically favorable to turn into a ring. Thus the average number of particles per chain is lower than for the rings. Moreover, we measured an average distance of 5 nm between the nanoparticles for all types of assemblies. This is in agreement with the SAXS measurements.

Imaging of local magnetic configurations within nanoflower assemblies

Electron holography experiments [START_REF] Dunin-Borkowski | Off-Axis Electron Holography of Magnetic Nanowires and Chains, Rings, and Planar Arrays of Magnetic Nanoparticles: Electron Holography of Magnetic Nanostructures[END_REF] were carried out at CEMES (Toulouse, France) in collaboration with C. Gatel and M. Andersen. A lacey, carbon coated TEM grid was plasma cleaned for 20s and a 5 µL drop of the ferrofluid was deposited on the grid. The measurements were carried out at room temperature. First, we located MNP assemblies resembling the ones previously observed by cryo-TEM. We then measured the hologram of the assembly by making the transmitted electron beam interfere with a reference beam going through a hole in the grid. The same hologram was measured again after turning the grid by 180°in order to remove the phase shift contribution from the electric potential of the nanoparticles. The resulting image after treatment shows the magnetic induction lines projected in the plane of the grid.

Fifteen different assemblies were measured using electron holography. Five typical examples are presented on Fig. 3.26. Phase images of the mean inner potential are shown in the left column. We added isophase contours calculated from the magnetic contribution to the electron phase shift: induction lines are parallel to these isophase contours. On the right amplitude images extracted from the same holograms are presented. The orientation of the in-plane projected magnetization for each particle is represented by red arrows. Fig. 3.26a-b show a ring-shaped assembly, with closed, rotating magnetic induction lines. In this case the magnetic moments are aligned head-to-tails, as would be the case for a system dominated by dipolar magnetic interactions to minimize the magnetic dipolar energy. Similarly, Fig. 3.26c-d show a chain assembly with most moments aligned head-to-tail, except for one MNP in the center of the chain presenting an out-of-plane magnetization, represented by a circle. The out-of-plane particle is situated next to a smaller particle which could act as a defect in the magnetic chain. Anti-parallel coupling between two interacting chains is also observed (Fig. 3.26e-h) in agreement with Ref. [START_REF] Varón | Dipolar Magnetism in Ordered and Disordered Low-Dimensional Nanoparticle Assemblies[END_REF] showing that particles are next to each other in such configuration. In addition, anti-parallel alignment of particles can also be obtained within a chain with a projected magnetization perpendicular to the axis of the chain or perpendicular to the plan of the substrate (Fig. 3.26i-j). While dipolar magnetic interactions dominate the organization of particles in rings, it seems that individual magneto-crystalline anisotropy must be taken into account when particles are Chapter 3 arranged in chains, as evidenced by the fact that not all particles are aligned head-to-tail in this configuration. It is worth to notice that the preparation method for electron holography observations necessitates the deposition of a drop on a TEM grid, and that the subsequent solvent evaporation can alter the orientation of the nanoparticles (and therefore their magnetic moment). However the particle assemblies are very similar to the ones observed by cryo-TEM. The saturation magnetization (M s ) is 264 kA/m (see Table 3.4). This value is close to the value measured by Fu et al. [START_REF] Fu | Catalytically Active CoFe 2 O 4 Nanoflowers for Augmented Sonodynamic and Chemodynamic Combination Therapy with Elicitation of Robust Immune Response[END_REF] of M s = 264 kA/m for cobalt ferrite nanoflowers (168 nm in diameter) and lower than the bulk saturation magnetization expected to 425 kA/m [START_REF] Cullity | Introduction to Magnetic Materials[END_REF]. The cobalt molar ratio X m = 20% measured by chemical titration shows that the nanoflowers are under-stoichiometric and can be formulated as Co 0.6 Fe 2.4 O 4 . This molar ratio is in the same range as for other cobalt ferrite synthesis (Daffé et al. [START_REF] Daffé | Magnetic Anisotropies and Cationic Distribution in CoFe 2 O 4 Nanoparticles Prepared by Co-Precipitation Route: Influence of Particle Size and Stoichiometry[END_REF] with 26.4% < X m < 35.5% or Torres et al. [START_REF] Torres | Validity of the Néel-Arrhenius Model for Highly Anisotropic Co x Fe 3-x O 4 Nanoparticles[END_REF] with 18.2% < X m < 30.3%). Moreover, other studies show that a similar molar ratio in cobalt ferrite nanocubes [START_REF] Sathya | Co x Fe 3-x O 4 Nanocubes for Theranostic Applications: Effect of Cobalt Content and Particle Size[END_REF] and nanospheres [START_REF] Sharifi Dehsari | Impact of Stoichiometry and Size on the Magnetic Properties of Cobalt Ferrite Nanoparticles[END_REF] produces a high coercive field at temperatures below 10 K (µ 0 H c ∼ 1.2 T and 2 T respectively). Magnetization curves show a magnetically blocked state below the fusion temperature of the solvent. The magnetization curve at 300 K was fitted by the Langevin model weighted by a gaussian distribution of the volumes (Fig. 3.14c). The resulting magnetic volume distribution (Fig. 3.27) gives a mean volume V 0 = 8100 ± 2700 nm 3 . The average volume extracted from the electron tomography measurements correspond to the higher side of the distribution, showing that some amount of disordered spins do not contribute to the magnetic moment of the particle. Indeed, if we consider a layer of thickness d = 0.6 nm and the surface measured in tomography S = 5265 nm 2 , one obtains a volume of disordered spins V dis = dS = 2632 nm 3 . From Bishop et al. [START_REF] Bishop | Nanoscale Forces and Their Uses in Self-Assembly[END_REF], the bulk saturation magnetization will decrease resulting in a reduced M s = M bulk s [(V total -V dis )/V total ]. Considering V dis , we find that the saturation magnetization is reduced to M s = 288 kA/m, which is close to the experimental value we measured. Thus, the morphology of the nanoflowers and their high surface to volume ratio can also explain the reduction in M s . The coercive field µ 0 H c was measured between 10 and 250 K and reached 1 T at 10 K. The effective anisotropy constant K eff was determined to be 245 kJ/m 3 by extrapolating the coercive field-temperature curve to T → 0 K using the Stoner-Wohlfarth model. The nanoflowers exhibit a large magnetic anisotropy Chapter 3 which strongly contributes to the magnetic properties of the ferrofluid.

Distribution of magnetic properties from FORC diagrams

Experimental parameters

FORC diagrams were measured at the IPGP-IMPMC Mineral Magnetism Analytical Facility (Paris, France) with a magnetometer (µ-VSM) from Princeton Measurements Corporation equipped with a cryostat. For stable single domain particles, in first approximation, the integrated FORC distribution along the vertical axis can be interpreted as the distribution of the interaction field of particles, and the marginal FORC distribution as the coercivity distribution of the system [66] [155]. FORC diagrams were each constructed from 134 individual FORCs measured with a field step of 15 mT, at a temperature of 100 K, and with an averaging time of 0.3 s. The measurement time for each FORC diagram was about one hour. They were subsequently analyzed with the FORCinel software [START_REF] Harrison | FORCinel: An Improved Algorithm for Calculating First-Order Reversal Curve Distributions Using Locally Weighted Regression Smoothing: FORCINEL ALGORITHM[END_REF], with a variable smoothing factor [START_REF] Egli | VARIFORC: An Optimized Protocol for Calculating Non-Regular First-Order Reversal Curve (FORC) Diagrams[END_REF]. The variable smoothing considerably reduces the noise levels by applying larger smoothing factors to the background, while preserving the areas along Single phase ferrofluids the axes with relatively small smoothing factors. Three FORC diagrams were measured on each sample. First, 20 µL of the liquid ferrofluid was enclosed in a polycarbonate gelcap and centered between the coils. The sample was cooled in zero-field to 100 K, and a first FORC diagram was measured (ZFC measurement). Then, the sample was reheated to room temperature, cooled in a field of 1.8 T, and a second FORC diagram was measured (FC measurement). Finally, the VSM head to which the sample is attached was turned by 90°, and a third FORC diagram was measured (FC90 measurement).

In order to further investigate the macroscopic magnetic properties of the ferrofluid, FORC diagrams were measured on both the concentrated sample (ϕ = 0.14%) and the diluted sample (ϕ = 0.014%) studied with the previous methods. For stable single domain particles, in first approximation, the FORC distribution along the horizontal axis, (marginal FORC distribution, Fig. 3.29a) can be interpreted as the coercivity distribution of the system H c , and the FORC distribution along the vertical axis (Fig. 3.29b) as the distribution of the interaction fields of particles H u [START_REF] Roberts | First-Order Reversal Curve Diagrams: A New Tool for Characterizing the Magnetic Properties of Natural Samples[END_REF] [START_REF] Egli | Theoretical Aspects of Dipolar Interactions and Their Appearance in First-Order Reversal Curves of Thermally Activated Single-Domain Particles[END_REF].

FORC diagrams for the concentrated ferrofluid.

The ZFC FORC diagram form a tear-drop shape typical of interacting single domain particles48 (Fig. 3.28a, d). The average diameter of 23.7 nm (determined from TEM) is expected to yield a single domain behavior since the critical diameter for CoFe 2 O 4 is D c = 40.7 nm [START_REF] Torres | Validity of the Néel-Arrhenius Model for Highly Anisotropic Co x Fe 3-x O 4 Nanoparticles[END_REF]. However, due to the complex structure of the nanoflowers and the mosaicity between crystallites, a multi domain magnetic configuration might have been energetically favorable, but we find that it is not the case here.

In the FC configuration, the shape of the FORC contours is more elliptical with little spread on the vertical axis (Fig. 3.28b, e), while the FC90 FORC diagram is again characterized by a tear-drop shape, but more extended along the vertical axis and less along the horizontal axis than in the ZFC configuration (Fig. 3.28c, f). A lobe extending from the main peak in the negative H u region is also visible.

The features can be tracked using the sets of individual FORCs on which the FORC function is superimposed. For the FC configuration, the FORC function is the strongest for measuring fields very close to the reversal field, which translates on the FORC diagram as a main peak with little spread on the vertical axis (Fig. 3.28b). On the contrary, the FC90 and to a lesser extend the ZFC FORCs are slightly more slanted, and FORC functions extend around measuring fields larger and smaller than the reversal field of each FORC (Fig. 3.28a,c). This causes a more extended spread of the main FORC peaks along the vertical axis.

Because nanoflowers tend to form assemblies like rings and chains, their collective behavior is expected to be modified by this ordering and one could expect that the magnetic response of the assemblies becomes that of elongated particles for which shape anisotropy dominates. For instance, in the FC configuration, the field is applied along the easy magnetization axis of the chains, and therefore, individual magnetic moments switch direction for larger fields. By contrast, the FC90 configuration is equivalent to a measurement along the hard magnetization axis of these chains and should lead to magnetic moments switching over higher fields, as observed in [START_REF] Carvallo | Magnetic and Structural Properties of Biogenic Magnetic Nanoparticles along Their Production Process for Use in Magnetic Hyperthermia[END_REF] [START_REF] Carvallo | Magnetic and Structural Properties of Biogenic Magnetic Nanoparticles along Their Production Process for Use in Magnetic Hyperthermia[END_REF], which is not the case here. The ZFC FORCs have shapes intermediate between those measured in FC and FC90.

Chapter 3

Analysis of marginal and vertical profiles.

When comparing ZFC and FC marginal profiles, there is a sharp increase in the µ 0 H c for which the FORC distribution is maximum (+25%), as well as an increase in the Full Width at Half Maximum (FWHM) of the marginal distribution (+10%) (Fig. 3.29a). The FC90 marginal profile displays a decrease of the position of the H c peak maximum by 14% and 30% compared to the ZFC and FC configurations, respectively. The maximum of the interaction field distribution, inferred from the vertical profiles, is fairly constant for all configurations and its width increases slightly between ZFC and FC (+10%) (Fig. 3.29b). The vertical distribution of the FC90 profile shows a 50% and 33% increase of the FWHM compared to the ZFC and FC profiles, respectively. FORC diagrams for the diluted sample.

The volume fraction of ϕ = 0.014% of the diluted sample corresponds to that on the cryo-TEM images of Figure 3.23a. At this concentration, MNPs are isolated. The ZFC FORC Single phase ferrofluids diagram of this sample (Fig. 3.30) is similar both in shape and in marginal or vertical profiles (Fig. 3.31) to that of the more concentrated sample. Indeed, the dipolar energy is much weaker than the magnetic anisotropy energy in cobalt ferrites. Thus, the magnetic properties of the material are related to the intrinsic properties of the nanoparticles rather than to their collective behavior. However, when comparing the FC marginal profiles of both concentrations, we can see that the more diluted sample has a distribution of coercivities centered at lower field values. This is an evidence of chaining in an applied field in the concentrated sample. At low concentrations, the nanoparticles are less able to form chains, being further apart. Consequently, the magnetic properties of the FC sample are dependent both on magnetic anisotropy of cobalt ferrites and on structural properties.

Cryo-TEM observations allow a deeper interpretation of the FORC diagrams for ϕ = 0.14%. Indeed, in ZFC measurements, MNPs are dispersed in small chains or isolated, and the field necessary to align the moments in the direction of the applied field is directly linked to the dipolar interactions felt by the particles. The assemblies being small and not interacting with each other, the coercivity distribution is slightly narrower and reaches a maximum at fields lower than the FC one. In the FC case, the applied field of µ 0 H = 1.8 T before cooling aligns all the particles in long chains. These chains observed by cryo-TEM are 500 nm to 1 µm long, however the field applied on the sample was only µ 0 H = 20 mT, which is much smaller than the field applied in the FORC measurement. Thus, we can estimate that the chains formed under the FC configuration during the FORC measurements could be much longer or more rigid, and the particles composing the chains experience a high dipolar interacting field and are strongly coupled together. Therefore, the coercivity distribution broadens and reaches a higher maximum compared to the measurements in ZFC configuration.

Simulations of FORC diagrams

Simulation parameters In order to improve the qualitative analysis of FORC diagrams, we carried out simulations using the FORCulator software [START_REF] Harrison | FORCulator: A Micromagnetic Tool for Simulating First-Order Reversal Curve Diagrams[END_REF]. The FORCulator algorithm solves the LLG equations with a damping factor of 0.9, for a specific configuration of N monodisperse nanoparticles with diameter d in a box of 500x500x500 nm. The nanoparticles can be either randomly distributed in space or form chains. Each specific chain configuration depends on the following parameters: the number of chains (N chain ), the number of particles per chain (N NP ), the distance between particles in a chain e, the rigidity of the chain or collapse factor (c, 0 ≤ c ≤ 1 with c = 0 for a perfectly straight chain) and the general orientation of the chains along the axis x, y, z of the simulation box, ([xyz]). The applied field during the calculation is oriented along the z axis. Polydispersity is taken into account in the model by introducing a lognormal distribution of switching fields with mean β and polydispersity σ. The values chosen here are σ = 0.3 and β = 2. They were determined by fitting the experimental FORC marginal distribution of the sample measured in ZFC configuration with a lognormal function. The anisotropy easy axis can be randomly distributed in space or aligned with the axis of the chains. For each configuration, 200 individual FORCs were calculated with a field step of 10 mT and µ 0 H b = 1000 mT and µ 0 H u = ± 100 mT. In order to increase the quality of the data, N avg configurations were averaged together to obtain the final FORC diagram. The total number . The easy axis of each particle are either aligned with the direction of the chain (labeled aligned) or randomly oriented (labeled random). The different experimental configurations are ZFC with aligned easy axis (a, g, m), ZFC with random easy axis (b, h, n), FC with aligned easy axis (c, i, o), FC with random easy axis (d, j, p), FC90 with aligned easy axis (e, k, q) and FC90 with random easy axis (f, l, r). of particles simulated (N NP * N chain * N avg ) is always equal to 5000 at minimum to ensure good statistics. One simulation typically lasted from 15 to 20 hours. Based on our cryo-TEM observations, a ZFC configuration was modeled by considering N chain = 5 chains of N NP = 10 nanoparticles each, separated by e = 2 nm. The chains are randomly oriented in space ([xyz] = [0 0 0]) and the rigidity c = 0.6 to simulate the mix between chains, rings and networks observed in cryo-TEM images. A total of N avg = 100 configurations were simulated. In the FC configuration, the chain length was increased to N NP = 50 particles with the interparticle distance kept to e = 2 nm as well. The number of chains N chain = 5 is not large enough to introduce interactions between the chains. The collapse factor was reduced to c = 0.02 to obtain almost parallel chains, all oriented along the direction of the applied field ([xyz] = [0 0 1]). A total of N avg = 20 configurations was simulated. For the FC90 configuration, we used the same parameters as in the FC configuration but the chains are oriented in a direction perpendicular to that of the applied field ([xyz] = [1 0 0]). The FORCulator software was originally built to simulate FORC diagrams of magnetite at room temperature, therefore our simulations are set at 300 K and the saturation magnetization is set to that of magnetite. However, it is possible to fix the value of individual moments to that of CoFe 2 O 4 by artificially modifying the size of individual particles.

Individual particles of cobalt ferrites have a cubic anisotropy, however the organization in chains that is observed experimentally causes the effective anisotropy to be uniaxial. Therefore, we chose to run our simulations with uniaxial anisotropy particles, as is also often done in other micromagnetic simulations (e.g., [START_REF] Usov | Magnetic Nanoparticles with Combined Anisotropy[END_REF]). The number of particles per chain in the ZFC configuration N NP = 10 was chosen as a compromise between the mean number of particles per chain N NP = 5 and per ring N NP = 12 found in cryo-TEM images (Fig. 3.23). Despite all these limitations, the simulations of FORC diagrams are nonetheless useful as a first approach for a qualitative study of the variations in FORC diagrams depending on the configuration.

Using FORCulator software [START_REF] Harrison | FORCulator: A Micromagnetic Tool for Simulating First-Order Reversal Curve Diagrams[END_REF], the ZFC FORC diagram was calculated with two different orientation of the anisotropy easy axis : aligned with the axis of the chain (Fig. 3.32ag-m) and randomly oriented for each particle (Fig. 3.32b-h-n). There is a better agreement in the shape and main features with the experimental FORC diagram in the case of the random easy axis, which is compatible with the electron holography observations. However, the main peak is shifted to lower coercivities (Fig. 3.33a). This might be due to the simulation operating at a higher temperature than the experiments (300 K vs 100 K) and is also observed on the subsequent simulated diagrams.

For the FC FORC diagram, setting the anisotropy easy axis in the direction of the chain should be similar to the corresponding experimental conditions (Fig. 3.32c-i-o). The FORC diagram obtained by simulation is indeed fairly similar to the measured one: the tear-drop shape is no longer observed, instead, the FORC contours are more elliptical, with a tail extending to high coercive fields (Fig. 3.32o). On the contrary, the FORC diagram in FC configuration with randomly distributed easy axis (Fig. 3.32d-j-p) does not resemble the experimental FC FORC diagram. The simulated ZFC and FC marginal profiles (Fig. 3.33a) show a similar trend in increasing maximum and FWHM as the experimental profiles. Likewise, the coercive field of the maximum of FC FORC distributions is higher than that of the FC90 distribution (Fig. 3.33a).

Finally, FC90 FORC diagrams were modelled with anisotropy easy axis either randomly oriented (Fig. 3.32f-l-r) or oriented in the direction of the chain (Fig. 3.32e-k-q). It is interesting to note that the agreement with experiment is much better in the case of the random orientation (Fig. 3.32r). It could be explained by the fact that in this configuration, due to Chapter 3 the cubic magnetocrystalline anisotropy of cobalt ferrite, the anisotropy easy axis is aligned with the field but there are two other easy axis available for the magnetic moment to orient itself, both perpendicular to the axis of the chain. This decreases the coercivity of the entire chain, as seen in the experimental data. In any case, the comparison between ZFC and FC90 simulated FORC distribution profiles is not in very good agreement with the experimental similar comparison, since both horizontal profiles are centered on similar values of coercive fields and the FWHM of FC90 is larger than that of the ZFC profile. Moreover, the shapes of the vertical profiles (Fig. 3.33b) are different from the shapes of the experimental ones, with a decrease in the values of interactions fields for FC and FC90 profiles. Indeed, the FC interaction field distribution presents a maximum at -10 mT, which corresponds to the magnetic field created by a chain of 50 nanoparticles with magnetic moments aligned in the same direction.

Conclusion on Co_24_F

We investigated a ferrofluid composed of cobalt ferrite nanoflowers with various experimental techniques in order to probe structural and magnetic properties from the nanoscale organization to the macroscopic collective magnetic properties. The main results are the following.

Firstly, individual MNPs have a rough and large surface-to-volume ratio, which reduces saturation magnetization compared to bulk cobalt ferrite. The flower-shaped particles are composed of crystallites interconnected by crystalline distortions at the interfaces. A low stoichiometry in cobalt determined by chemical titration induces an anisotropy constant larger than that of the bulk material.

Secondly, when studying collective properties, cryo-TEM observations show that the diluted sample contains non interacting nanoparticles while the concentrated one has a wide variety of assemblies, with a majority of small chains. However, both samples exhibit similar magnetic properties in FORC measurements, because the anisotropy energy greatly exceeds the magnetic dipolar energy, an observation which is also consistent with electron holography results. Simulated FORC diagrams are in fairly good agreement with the experimental ones.

Thirdly, when a magnetic field is applied to the ferrofluid, the nanoparticles in the concentrated sample form long micrometric chains, as evidenced by cryo-TEM and SAXS measurements, while the diluted sample does not show this chaining effect. For both volume fraction, FC FORC diagrams are shifted to higher coercive fields compared to ZFC diagrams. This shift is stronger for the concentrated sample as the chains contribute to the increase of coercivity. Simulations based on uniaxial anisotropy and an easy axis of magnetization aligned parallel with the chain axis fail to explain the magnetic properties obtained experimentally.

Chapter 3 varies slighty between configurations, with a FWHM of 100, 90 and 120 mT for ZFC, FC and FC90 respectively. All the values are reported in table 3

Sample Mn_21_F

The FORC diagrams were measured using the following parameters:

t avg = 200 ms, µ 0 H b = ± 80 mT, µ 0 H max c = 50 mT, µ 0 H sat = 500 mT, µ 0 H step = 2 mT and N FORC = 118.
For sample Mn_21_F, the FORC diagrams are centered at low coercive fields (< 10 mT). All three FORC diagrams, ZFC at ϕ=0.1% (Fig. 3.35a), ZFC at ϕ=1% (Fig. 3.35b) and FC at ϕ=0.1% (Fig. 3.35c) have similar features. The pattern exhibits high positive intensity close to H c and H u = 0, with a small negative contribution in µ 0 H u < 0 and µ 0 H c = 15 mT. This negative contribution is within the noise of the experiment and can be neglected. As the FORC diagram is "stuck" to the y-axis, for comparison, a Half-Width Half Maximum was extracted from the profiles (see Table 3.9). The ZFC FORC diagrams between volume fraction ϕ = 0.1 and 1% have an slight increase of dispersion in the interaction field distribution (HWHM = 6.9 and 8.2 mT respectively). On the contrary, for the FC, HWHM decreases to 5.6 mT. ZFC FC FC90 µ 0 H max u (mT) -0.2 -0.2 -1.2 FWHM (mT) 9.0 6.9 13.1 Table 3.10: Maximum and FWHM of coercive and interaction fields distribution extracted from FORC diagrams of sample Fe_27_F.

Sample Co_53_F

The FORC diagrams were measured using the following parameters: Table 3.11: Maximum and FWHM of coercive and interaction fields distribution extracted from FORC diagrams of sample Co_53_F. Sample Co_16_F has a similar coercive field distribution as Co_24_F. Indeed, from the marginal profile on Figure 3.38a, we can see an increase towards higher coercive field between the ZFC and FC configuration. Additionally, the FC90 configuration yields a similar coercive field distribution as the ZFC configuration. As previously shown, this can be evidence of cubic magnetocrystalline anisotropy of the spinel phase of CoFe 2 O 4 . The vertical profile (Fig. 3.38d) or interaction fields distribution shows that each configuration has similar interactions, with a FWHM such that FWHM FC ≤ FWHM ZFC ≤ FWHM FC90 . However, the maximum of the peak is not modified between each configuration and stays centered at µ 0 H u = 0 T. No anisotropic mean field affects the magnetic nanoparticles. Sample Co_53_F does not exhibit any significant different between the ZFC, FC and FC90 FORC diagrams, both for coercive field (Fig. 3.38c) or interaction field (Fig. 3.38f) distribution. The magnetic nanoparticles are not affected by the external magnetic field before freezing, or at least it is not translated on their macroscopic magnetic properties. Moreover, despite the very high polydisersity nature of the nanoflowers, the ZFC FORC shape of sample Co_53_F is quite narrow compared to Co_16_F and Co_24_F. Chapter 3

t avg = 200 ms, µ 0 H b = ± 250 mT, µ 0 H max c = 1.35 T, µ 0 H sat = 1.8 T, µ 0 H step =

Size effect in cobalt ferrites nanoflowers

Soft magnetic material and structuration

The comparison between Co_24_F, Co_16_F or Co_53_F with Fe_27_F and Mn_21_F shows the large difference in anisotropy between a hard and soft magnetic material. The FORC diagrams are not centered at the same coercive fields. In the next chapter, we will exploit this effect by studying a mix of soft and hard magnetic materials in binary ferrofluids. FORC diagram will allow us to disentangle both magnetic contribution from each other, which is not possible in classical magnetometry like SQUID.

For samples Fe_27_F and Mn_21_F, the FC FORC diagram is less dispersed and more point-like than the ZFC, whereas the FC90 FORC pattern is much wider (Fig. 3.38b). Contrary to previous hard magnetic nanoparticles, the FC coercive field distribution moves to lower fields compared to the ZFC, while the FC90 coercive field distribution gets broader towards higher fields. This result can be compared to a previous study on maghemite nanoparticles by Carvallo et al. [START_REF] Carvallo | Magnetic and Structural Properties of Biogenic Magnetic Nanoparticles along Their Production Process for Use in Magnetic Hyperthermia[END_REF]. In this study, the magnetic nanoparticles were extracted and purified from magnetotactic bacteria and coated in DOPC. Cryo-TEM observations on an aqueous suspension of the nanoparticles showed the presence of rings and networks. Moreover, FORC diagrams in ZFC, FC and FC90 configuration were measured. The variation of coercive and interaction field distribution behaves the same way as for sample Fe_27_F, and completely different than Co_16_F or Co_24_F. Indeed, the FC90 H c distribution is shifted to higher fields (Fig. 3.39a), which is consistent with the Stoner-Wohlfarth model. In this case, the magnetite nanoparticles behave as uniaxial magnetic moments and the cubic magnetocrystalline anisotropy of the material does not influence its macroscopic magnetic properties. A disorder layer inducing uniaxial surface anisotropy could be responsible for this behaviour.

Finally, the shift to lower field of the FC coercive field distribution compared to the ZFC one is surprising. Indeed, in the Stoner-Wohlfarth model, we expect to see a increase of coercivity for uniaxial particles with easy axis aligned with the direction of the field. The clusters present in Fe_27_F and Mn_21_F could be the cause of this deviation from the model, however, the same effect is observed for the magnetosome in [START_REF] Carvallo | Magnetic and Structural Properties of Biogenic Magnetic Nanoparticles along Their Production Process for Use in Magnetic Hyperthermia[END_REF] and cryo-TEM did not show any signs of aggregation. Nonetheless, the conditions for FORC measurements are different than cryo-TEM as the sample stays liquid for a longer time before freezing in a FORC experiment. Thus, if aggregation forms slowly, cryo-TEM could possibly not see them (due to rapid freezing) while the suspension measured by FORC would contain clusters.

Discussion

In the ferrofluid, the behavior of magnetic nanoparticles is influenced by their magnetic properties, particularly their anisotropy energy. Hard magnetic materials like CoFe 2 O 4 possess a large anisotropy energy, which results in the magnetic moments remaining aligned with the easy axis, behaving as stable, rigid dipoles. At room temperature, the nanoparticles experience Brownian motion, and when the measurement time exceeds the Brownian relaxation time τ B = 3ηV H /k B T , where η is the fluid viscosity and V H is the hydrodynamic volume, the particles exhibit superparamagnetic behavior.

On the other hand, soft magnetic materials like MnFe 2 O 4 and Fe 2 O 3 have lower anisotropy energy, making their magnetic moments less stable over time due to thermal fluctuations. In this case, it becomes essential to consider the Néel relaxation time τ N = τ 0 exp(KV m /k B T ), where τ 0 is a characteristic time of 10 -9 s and V m is the magnetic volume.

The effective anisotropy constants calculated in Table 3.5 are only applicable at low temperatures. The temperature dependence of K eff is still not well understood, although some empirical laws have been attempted based on experimental data [START_REF] Yoon | Temperature Dependence of Magnetic Anisotropy Constant in Manganese Ferrite Nanoparticles at Low Temperature[END_REF] or using the law of approach to saturation [START_REF] Rosensweig | Ferrohydrodynamic Fluids for Direct Conversion of Heat Energy[END_REF] [START_REF] Kahmann | Determination of the Effective Anisotropy Constant of Magnetic Nanoparticles -Comparison between Two Approaches[END_REF]. Direct measurements of K(T ) on single crystals have been implemented by orienting the crystalline easy and hard axis with the magnetic field [START_REF] Guragain | Effect of Terbium Ion Substitution in Inverse Spinel Nickel Ferrite: Structural and Magnetic Study[END_REF]. However, for powders or ferrofluids, such measurements are not feasible, and the only available information is that K eff decreases as temperature increases.

Based on the values of K eff at T → 0 K, it can be estimated that the anisotropy energy of CoFe 2 O 4 nanoparticles is much larger than that of MnFe 2 O 4 or Fe 2 O 3 at room temperature. As a result, the magnetic moments of CoFe 2 O 4 nanoparticles remain stable for a longer time, allowing for magnetic dipolar interactions to occur. The formation of chains is possible as the interacting dipoles can order themselves due to their stable orientation over time.

In contrast, for MnFe 2 O 4 and Fe 2 O 3 nanoparticles, the magnetic moments oscillate around their easy axis orientations, and interactions occur without long-lasting order. As a result, the magnetic nanoparticles attract and repulse each other in random orientations, leading to the formation of clusters, as observed in the cryo-TEM experiments.

Moreover, it is interesting to compare the magnetic and structural properties of Co_16_F and Co_24_F. The anisotropy constant calculated for sample Co_16_F K eff ≈ 450 kJ/m 3 is significantly larger than the bulk value of CoFe 2 O 4 . This discrepancy could be attributed to various factors, such as the presence of magnetic dipolar interactions or the influence of cubic magnetocrystalline anisotropy. These complexities may lead to deviations from the predictions of the Stoner-Wohlfarth model. However, an important difference between both samples is the mean magnetic moment derived from the Langevin fit (Fig. 3.15). By Chapter 3 comparing the dipolar coupling ratio λ = µ 0 µ 2 /d 3 k B T for both samples, we find λ = 6.3 for Co_16_F and λ = 8.7 for Co_24_F. Both samples have magnetic moments large enough to induce self-assembly (λ ≥ 2), but their different dipolar coupling ratios have a significant impact on the resulting structures. As Co_24_F is composed of larger nanoparticles with a mean magnetic moment of 21 ×10 -19 Am2, exhibits stronger magnetic interactions. As a result, more chains are formed in this sample compared to clusters. On the other hand, Co_16_F comprises smaller nanoparticles but a mean magnetic moment of 10 ×10 -19 Am2, resulting in weaker magnetic interactions. Consequently, both chain formation and aggregation are observed, as seen in the cryo-TEM images.

These insights into the magnetic behavior of different nanoparticles help to explain the observed differences in their self-assembly behavior in the ferrofluid. The stability of magnetic moments and the magnitude of anisotropy energy play a crucial role in determining the formation of chains or clusters in the system. Understanding these magnetic properties is vital for controlling and engineering the self-assembly of magnetic nanoparticles for various applications, including in nanotechnology and biomedicine.

Conclusion

The ferrofluids synthesized using the polyol process are nanoflowers with diameters ranging from 15 to 30 nanometers. The cobalt ferrite samples were under stoechiometric in Co. The saturation magnetization value was discovered to be lower than the bulk value. Cryo-TEM was used to image the microstructure. Cobalt ferrite nanoparticles assemble into small chains and networks, while manganese ferrite nanoflowers aggregate into clusters of hundreds of nanoparticles.

A ferrofluid composed of cobalt ferrite nanoflowers with interesting self-assembling properties was further investigated. It was found that the nanoflowers exibihit a single domain magnetic behaviour. Moreover, the anisotropy energy exceeds the magnetic dipolar energy. Finally, we make a connection between magnetic properties and stuctural properties, including single particle characteristics and self-assembly.

Our results can help constrain future simulations involving interacting nanoparticles, as well as provide new insights on the properties of similar ferrofluids under static external magnetic field. Future work can focus on the dynamics of chain formation and the influence of alternative fields on these chains. In addition, as the anisotropy energy greatly exceeds the magnetic dipolar energy in this study, similar measurements would be of interest on a material with reduced anisotropy, such as magnetite. Chapter 4

Introduction

I showed in the previous chapter that the remarkable property changes in ferrofluids originate from magnetic interactions at the nanoscale. Nanoparticles can spontaneously arrange themselves into chains and rings due to strong dipole-dipole interactions. This intricate behavior has applications in modeling new ferrofluids that show novel magnetic responses to external magnetic fields, with implications for biomedical applications, mechanical properties, and optics.

In order to synthesize and model new materials having desired properties, understanding and manipulating these nanoscale structures, and thus studying the interactions between nanoparticles is essential. As experimental ferrofluids are polydisperse by nature, some theoretical studies have focused on systems where nanoparticles have two differing sizes, known as bidisperse systems [START_REF] Ivanov | Phase Separation in Bidisperse Ferrocolloids[END_REF][160] [161][162]. This represents a first approximation of polydisperse ferrofluids. Another way to create a binary system is to use two different magnetic components thus creating a magnetically bidisperse system (such as one ferrimagnet and one paramagnet, or one hard ferrimagnet and one soft ferrimagnet). Such a binary ferrofluid serves as a fundamental model for studying interactions between particles within ferrofluids, allowing better, more realistic constraints on future theoretical models. Moreover, these combinations lay the foundation for crafting complex materials with significant implications for emerging magneto-optical applications [START_REF] Zhang | Enhancement of the Field Modulation of Light Transmission through Films of Binary Ferrofluids[END_REF].

In this chapter, I begin by presenting a study of a non-interacting binary sphere ferrofluid carried out by a former PhD student of the team. This will allow me to introduce the main results and the poisoning effect, before presenting the experimental results obtained during this thesis. Next, the magnetic and structural properties of a binary ferrofluid composed of nanoflowers of CoFe 2 O 4 and MnFe 2 O 4 mentioned in the previous chapter are investigated by means of FORC magnetometry and chemically selective microscopy. Another binary ferrofluid with maghemite nanoflowers for the soft magnetic component is also measured and its properties are compared to previous results. Finally, a more complex case of binary ferrofluid is briefly discussed.

Details on the preparation and measurements of binary ferrofluids 4.2.1 Definition of the concentration ratios in a binary ferrofluid

In the following, FF a and FF b are the two single phase ferrofluids that are mixed to produce the binary ferrofluid. The volume fraction in phase a is defined as:

ϕ a = V a NP V a liq = N a NP V a single NP V a liq (4.1)
with V NP the volume of nanoparticles in the ferrofluid, V liq the total volume of ferrofluid, N NP the number of nanoparticles in the ferrofluid and V single NP the volume of one nanoparticle.

Binary ferrofluids

For any volume of binary ferrofluid V Bin produced by mixing together a volume V a and V b of single phase ferrofluid FF a and FF b respectively (V Bin = V a + V b ), we have the volume fraction of the binary ferrofluid ϕ Bin :

ϕ Bin = ϕ a V a + ϕ b V b V Bin (4.2)
By taking ϕ a = ϕ b = ϕ and V b = xV a , we have:

ϕ Bin = ϕV a + ϕxV a V a + xV a = ϕ (4.3)
For every binary ferrofluid, we keep ϕ a = ϕ b = ϕ so that ϕ Bin = ϕ. For example, mixing FF a with ϕ a = 0.1% and FF b with ϕ b = 0.1% will result in a binary ferrofluid FF Bin with ϕ Bin = 0.1%. The volume of FF a and FF b in the binary ferrofluid will determine the ratio r ≡ V a : V b so that making a binary ferrofluid is quick and easy if the single phase ferrofluids have the same volume fraction. For a ratio r = 1:1, equal volumes of FF a and FF b are mixed, for a ratio r = 1:2, a volume V of FF a and 2V of FF b are mixed, etc.

It is important to note that the ratio r does not compare numbers of nanoparticles per unit volume together. The volume fraction is related to the number of particles per unit volume ϕ N such that:

ϕ = N NP V single NP V liq = ϕ N V single NP (4.4)
with N NP the number of nanoparticles, V liq the total volume and V single NP the volume of one nanoparticle.

Since the ratio r is defined as the volumetric ratio between FF a and FF b , a binary ferrofluid r = 1:1 will not necessarily contain equal amounts of nanoparticles from FF a and FF b . Indeed, ϕ depends on the volume of one nanoparticle, and as each synthesis yields different sizes, ϕ N ̸ = ϕ and r ̸ = ϕ a N : ϕ b N .

Analysis protocol of magnetometric measurements

Magnetization curves obtained by SQUID magnetometer are normalized by the mass of nanoparticles used for the measurement. The resulting magnetization M is thus first obtained in Am 2 /kg and needs to be converted to A/m with the density ρ. When one mixes together two ferrofluids with volume fraction ϕ, one needs to be careful about the quantities used. As it is more precise to use scales for mixing the ferrofluids, the mass fraction ϕ m must be considered to obtain a binary ferrofluid with a given ratio in volume. The conversion between ϕ and ϕ m is defined as:

ϕ m = ϕρ (1 -ϕ)ρ water + ϕρ (4.5)
where ρ is the density of the material (5.29 g/cm 3 for CoFe 2 O 4 , 5.0 g/cm 3 for MnFe 2 O 4 and 5.24 g/cm 3 for Fe 2 O 3 [START_REF] Cullity | Introduction to Magnetic Materials[END_REF]), and ρ water = 1 g/cm 3 the density of water.

Chapter 4

In order to compare the magnetization curve of the reference ferrofluids with the magnetization curve of a theoretical binary ferrofluid calculated from both references, we use:

M (H) T h. = aM a + bM b a + b (4.6)
where M (H) T h. is the calculated magnetization curve for a theoretical ferrofluid and M a and M b the magnetization curves for reference ferrofluid FF a and FF b , respectively. In the notations for each binary ferrofluid, the parameters a and b correspond to the ratio of each single phase ferrofluid mixed to produce the binary ferrofluid. For example, for a ratio 1:2, a = 1 and b = 2. For this, it is essential that the M (H) curves are interpolated on the same H, so that they can be summed correctly.

Finally, it is useful to define a relative error ∆A to compare a parameter A Exp. obtained from magnetic measurements on a binary ferrofluid with a calculated parameter A T h. obtained from the theoretical binary magnetization curve:

∆A = A Exp. -A T h. A T h. (4.7)
This error ∆A will be used to compare coercivity, remanence or area of M (H) for example.

Dipolar coupling constant for a binary ferrofluid

The dipolar coupling constant λ (see Eq. 1.10) can also be defined for a binary ferrofluid using:

λ = µ 0 µ a µ b 4π da+d b 2 3 k B T (4.8)
with µ a and µ b the mean magnetic moment and d a and d b the nanoparticle diameter in single phase ferrofluid FF a and FF b , respectively. If one of the initial ferrofluid has a λ > 2, but the other does not, it can result in a λ < 2 for the binary. Thus, the dipolar coupling between nanoparticles can be lessened in the binary ferrofluid. In conclusion, this study shows that the binary ferrofluid does not behave as the average of single phase ferrofluids. The hard magnetic material becomes softer in the presence of the soft manganese ferrite nanoparticles, and vice-versa, the soft magnetic material becomes harder in the binary ferrofluid. Indeed, the magnetic interactions between neighbouring nanoparticles inside the liquid gives rise to novel magnetic response.

Based on this work, I continued the study of binary ferrofluids, by exploring the poisoning effect, where a hard magnetic material presenting self-assembly is "poisoned" by the presence of soft magnetic material. The aim is thus to investigate this effect with samples with strong magnetic dipolar interactions and the modification of their magnetic and self-assembly properties in the binary ferrofluid.

We analyzed three binary ferrofluids composed of single phase ferrofluids presented in Chapter 3:

• Binary FF 1 : Co_16_F + Mn_21_F

• Binary FF 2 : Co_16_F + Fe_27_F Chapter 4

Bulk magnetic properties

All measurements by SQUID magnetometer and FORC diagrams were done at 100 K in order to fully saturate cobalt nanoparticles at 1.7 T (the maximum magnetic field available on the electro-magnet in the FORC diagram set-up) while staying below the blocking temperature of manganese ferrite nanoparticles.

All FORC diagrams were plotted with the FORCinel software with smoothing factor: S c0 = 5, S c1 = 8, S b0 = 5, S b1 = 8 and λ = 0. Unlike the previous binary ferrofluid in Section 4.3, the theoretical magnetization curves overlap well with the experimental ones. Small differences can be seen around H = 0 but they are not large enough to be truly visible with this experimental method. The reason for this difference is not immediately obvious, and we will try to understand why we do not get the same result for this new binary ferrofluid.

Zero Field Cooled conditions

Field Cooled conditions

By applying an external magnetic field (2 T) on the ferrofluid at room temperature in the SQUID magnetometer before cooling the sample, we measured magnetization curve in FC configuration on samples Co_16_F, Mn_21_F (Fig. 4.6a) and binary ferrofluids with 1:1, 1:2 and 3:1 ratios (Fig. 4.6b).

As seen previously in Chapter 3, cobalt ferrite nanoflowers align in chains parallel to the direction of the magnetic field and coercivity increases. Manganese ferrite nanoflowers on the other hand do not exhibit a significant modification of their magnetic properties in FC configuration.

The M (H) measured on binary ferrofluids show an increase in coercivity and remanence compared to the ZFC ones. However, due to the bulk nature of SQUID magnetometry, the change in coercivity or remanence is difficult to attribute to either cobalt ferrite nanoflowers or manganese ferrite nanoflowers. In the following section, FORC diagrams can be used to discriminate the impact of each component on magnetic properties. Furthermore, the theoretical curve no longer overlaps with the experimental curve (Fig. 4.7). The theoretical M (H) measured on binary ferrofluids with ratios 1:1, 1:2 and 3:1 are significantly different from the experimental curves. For ratio 1:1 and 1:2, M (H) T h. is more open (larger coercivity and remanence) than M (H) Exp. , while for ratio 3:1, M (H) T h. is less open (weaker coercivity and remanence) than M (H) Exp. . In order to understand the origin of this difference between the theoretical and experimental curves, it is necessary to be able to probe the cobalt ferrite and manganese ferrite nanoparticles individually. To do this, we use FORC diagrams, which allow us to disentangle the contributions of both magnetic materials.

Disentangling hard from soft magnetic contributions

Experimental parameters

The following FORC diagrams were measured at 100 K and ϕ = 0.1% with two different set of measuring parameters adapted either for CoFe 2 O 4 or MnFe 2 O 4 nanoparticles. The binary ferrofluids were thus measured twice, once with a broad range of fields to probe the hard magnetic material and once with a smaller window of fields to zoom on the soft magnetic material. 3.8 and Table 3.9 for samples Co_16_F and Mn_21_F, respectively.

Using these results, we can analyze the modification of magnetic properties on both components in binary ferrofluids with varying ratio of CoFe 2 O 4 :MnFe 2 O 4 . On Figure 4.8ce-g, FORC diagrams of the binary ferrofluids measured using the set of parameters 1 to probe the soft magnetic component (MnFe 2 O 4 nanoparticles) are plotted, with ratios 1:1, 1:2 and 3:1 respectively. On Figure 4.8d-f-h, FORC diagrams of the binary ferrofluids measured using the set of parameters 2 to probe the hard magnetic component (i.e. CoFe 2 O 4 nanoparticles) are plotted, with ratios 1:1, 1:2 and 3:1 respectively. At low fields, the contribution from the soft magnetic material is visible and the shape of the FORC diagram remains centered on H u = 0 for all ratios, like in the single phase 123 Chapter 4 ferrofluid. The intensity of the this peak decreases with increasing CoFe 2 O 4 nanoparticle content in the binary ferrofluid. Indeed, on Figure 4.8g for ratio 3:1, the intensity of this peak is more than 20 times smaller than in the single phase ferrofluid of reference. Similarly, the intensity of the FORC peak in the high field region originating from the hard magnetic component decreases with increasing MnFe 2 O 4 nanoparticle content in the binary ferrofluid. However, at first sight for both magnetic components, the FORC diagrams have the same shape and general position on the H u and H c axis in the binary ferrofluids. To observe and quantify more precise modification of magnetic behaviour, I plotted the marginal and vertical profiles obtained from the 2D FORC diagrams, corresponding to the coercive field and interaction field distribution, respectively. Conversely, the FORC diagram centered at low fields (∼ 10 mT) corresponding to manganese ferrite nanoflowers show differences between the binary ferrofluids (Fig. 4.8c-e-g) and the reference ferrofluid (Fig. 4.8a). From the marginal (Fig. 4.9a) and vertical profiles (Fig. 4.10a), as the amount of cobalt ferrite nanoparticles increases in the binary ferrofluid, the coercive and interaction field distributions become wider and more dispersed towards higher fields.

From both types of profiles (Fig. 4.9 and 4.10), I calculated a Full Width Half Maximum (FWHM) for each binary ferrofluids and single phase ferrofluids. The relative change in FWHM between binary and reference ferrofluide ∆FWHM is plotted as a function of cobalt ferrite nanoparticles content in the ferrofluids on The FORC diagrams measured in FC configuration for single phase ferrofluids and binary ferrofluids with ratios 1:1, 1:2 and 3:1 are presented on Figure 4.12. For manganese ferrite nanoflowers (Fig. 4.12a), the FORC diagram is similar to the ZFC one, while for cobalt ferrite nanoflowers (Fig. 4.12b), the FORC diagram peak is shifted to higher coercive fields (Fig. 4.8b). In the binary ferrofluid, the FORC peak at low fields is shifted to negative interaction field value for ratios 1:1 (Fig.

Binary ferrofluids

The marginal and vertical profiles are plotted on Figures 4.13 and 4.14 respectively. From the profiles at low fields, we still observe an increase in FWHM of coercive (Fig. 4.13a) and interaction (Fig. 4.14a) field distribution of manganese ferrite nanoparticles, similar to what was observe in the ZFC case. Furthermore, the interaction field distributions are shifted towards negative fields proportionally with the amount of cobalt ferrite in the binary ferrofluid (Fig. 4.14a), as seen on the FORC diagram.

Secondly, for the cobalt ferrite particles the H c distribution shifts towards small fields (Fig. 4.13b) for binary ferrofluid with ratio 1:2. In the case of binary ferrofluids with ratios of 1:1 and 3:1, there is no significant modification of the coercive field distribution except for a small increase of FWHM towards high coercive fields. The interaction field distribution also shifts towards negative fields with decreasing cobalt ferrite content. Additionally, the interaction field distribution of the hard magnetic component is modified only through the shift to negative peak with decreasing cobalt ferrite content (Fig. 4.15c), while FWHM and I max increase greatly for the soft magnetic component (Fig. 4.15d), the latter up to +8000% in FC configuration. In order to enlighten these modifications of magnetic properties in the binary ferrofluids, observation of the assemblies formed by the nanoparticles in the ferrofluids is essential. The differences between ZFC and FC configurations especially need to be adressed to understand why the magnetic properties of cobalt ferrite are not modified in a similar fashion. There is a need for element-sensitive microscopy to disentangle the CoFe 2 O 4 from the MnFe 2 O 4 nanoflowers in assemblies produced in the binary ferrofluids. When an external magnetic field is applied on the ferrofluid, long chains form as shown on Figure 4.17. In this case, a pattern of alternating CoFe 2 O 4 and MnFe 2 O 4 nanoflowers is observed. Moreover, the "body" of the chain seems to be mainly composed of cobalt ferrite nanoparticles, where manganese ferrite nanoparticles insert themselves as cluster inclusions. For the 1:1 ratio, the number of cobalt ferrite nanoparticles is greater than that of manganese ferrite nanoparticles. This is due to the difference in diameter (and therefore volume) of the Co_16_F and Mn_21_F samples; the volume fraction in the 1:1 binary ferrofluid is the same, but the number of particles per volume is not. Despite this, for each ratio 1:1, 1:2 and 3:1, the chains are composed of both types of particles and formed by alternating small clusters of each particle. As the quantity of cobalt decreases (ratio 1:2, Fig. 4.17b), the clusters of manganese ferrite gain in size inside the chains. Conversely, with ratio 3:1 (Fig. 4.17c), the chains and agglomerates are mainly cobalt ferrite nanoparticles with small defect-like inclusions of manganese ferrite nanoparticles.

Influence of structuration on magnetic properties

According to the chemical mapping images, particles form clusters in binary ferrofluids. At the interface of two clusters composed of different particles, the magnetic environment due to magnetostatic interactions is modified compared to the single phase ferrofluid. Moreover, cobalt ferrite particles possess a very high magnetic anisotropy, which stabilizes their magnetic moment in a given direction for a prolonged period of time. Conversely, the low anisotropy of manganese ferrite nanoparticles causes magnetic moments to oscillate around the easy axis of magnetization rapidly over time. So, when the two nanoparticles are in contact, the presence of an unstable magnetic moment will not greatly alter the magnetic orientation of a cobalt particle. The manganese particle, on the other hand, will be subjected to a very strong, stable interaction field, resulting in a change in its orientation and hence in the macroscopic magnetic properties of the binary ferrofluid. However, these changes are visible at the manganese scale, and conventional SQUID magnetometry is unable to detect them very accurately through the strong signal from the cobalt ferrite. It is through FORC diagrams that these modifications become more apparent.

When ferrofluids are subjected to an external magnetic field, however, changes in magnetic properties become very significant and detectable even by SQUID magnetometry. Thanks to chemical mapping, we can link this result to the structuration of nanoparticles in binary ferrofluids. The magnetic field, by aligning the particles in chains, creates an alternation of cobalt ferrite and manganese ferrite. In this configuration, the interactions between the two types of nanoparticles are much stronger and anisotropic. In fact, an easy axis of magnetization induced by the shape of the chain leads to interactions between particles with a head-to-tail preferential orientation. In the case of MnFe 2 O 4 nanoflowers, the magnetic environment is completely altered compared to the single phase ferrofluid, thanks to the presence of particles with significant anisotropy and oriented in the same direction. Cobalt ferrite nanoparticles are also subjected to a change in magnetic configuration. Manganese ferrite particles act as defects in the cobalt ferrite chains. The poisoning effect is clearly observed, with the hard magnetic material becoming softer in the presence of the soft magnetic material.

The magnetic properties of manganese ferrite are modified by the presence of cobalt ferrite. The soft magnetic material becomes harder, and coercivity increases proportionally with the amount of hard magnetic material. This result is similar to that observed in [START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF], Chapter 4 however, the effect is less significant than for 6 nm spheres. Indeed, cobalt ferrite shows no change in its magnetic properties in the presence of manganese ferrite, in contrast with the previous study. In the previous binary ferrofluids, magnetic anisotropy was the determining factor inducing novel magnetic properties. However, one can also modify the magnetic moment of the particles mixed to create a new binary ferrofluid. This is comparable to a bidisperse ferrofluid, simulated in [START_REF] Ivanov | Phase Separation in Bidisperse Ferrocolloids[END_REF], as the change of volume induces a change of magnetic moment in such system.

Binary ferrofluid of CoFe

From samples Co_16_F and Fe_27_F, we can obtain a binary ferrofluid combining both a hard and soft magnetic material as well as "large" particles (high magnetic moment in Co_16_F: <µ> = 12 µ B ) and "small" particles (low magnetic moment in Fe_27_F: <µ> = 4.5 µ B ). The main magnetic properties of both samples are summarized in Table 4.2. The binary ferrofluid 2 has a dipolar coupling parameter λ = 1.13.

Element-selective magnetometry

In order to understand the changes in magnetic properties in the binary ferrofluid 2, we measured chemically selective magnetization curves using an X-ray spectroscopy technique, RIXS-MCD (see Section 4.3). Such element-selective hysteresis were measured at 220 K on the single phase ferrofluid Co_16_F and on the binary ferrofluids with ratios 1:1 and 1:5 at ϕ=0.1% (Fig. 4.18a) and ϕ=1% (Fig. 4.18b) at Co edge in ZFC conditions. Magnetization curves at the Fe edge were not measured since both CoFe 2 O 4 and Fe 2 O 3 components would be probed. From these results, no modification of magnetic properties is observed for the cobalt ferrite nanoflowers, whatever the amount of maghemite nanoflowers present in the binary ferrofluid.

Separation of magnetic contributions Experimental parameters

The following FORC diagrams were measured at 100 K and ϕ = 0.1% with two different sets of parameters adapted either for CoFe 2 O 4 or Fe 2 O 3 nanoparticles. The binary ferrofluids were thus measured twice, once with a broad range of fields to probe the hard magnetic material and once with a smaller window of fields to zoom on the soft magnetic material. In FC configuration, the coercive field distribution of the cobalt ferrite nanoparticles (Fig. 4.20b) decreases towards lower fields with a shift of ∆I max = -3%, while the FWHM increases by 5%. The interaction field distribution also shift to negative fields and FWHM decreases by 19% (Fig. 4.21b. For the Fe 2 O 3 nanoflowers, the trend is similar to the ZFC configuration with an increased FWHM (+62%) in addition to a shift to higher fields (∆I max = + 11%) (Fig. 4.20d). The interaction field distribution also moves to negative fields (Fig. Here, the differences between M (H) Exp. and M (H) T h. are again observed but for they are more significant for some ratios (e.g. 2:1 and 1:2) than others (e.g. 1:3).

To analyze the modifications of magnetic properties observed experimentally with respect to theoretical ones, the parameters H c , M r and the area under the magnetization curves are calculated for different ratios assuming linear additivity and they are reported together with the experimental ones as a function of CoFe 2 O 4 content on Figure 4.23a, b and c respectively.

First, the changes in area and remanence are linear for theoretical M (H) with increasing CoFe 2 O 4 content, while the coercivity is following a more complex relation that resemble f (x) = tanh(x).

By comparing the area variations with increasing cobalt ferrite content in ZFC and FC configurations (Fig. 4.23a), we observe that the linear trend is respected. Likewise, the remanence in ZFC configuration follows the theoretical line, but not in FC configuration (Fig. Binary ferrofluids (corresponding to ratio 1:2). Binary FF 2 obeys to a similar behaviour for ∆M r and ∆H c (red points) with an increase of 125% and 60% respectively compared to the theoretical values.

From STXM chemical maps, we can attribute the modifications of magnetic properties in binary FF 1 to the changes in structuration and magnetic environments for CoFe 2 O 4 and MnFe 2 O 4 nanoflowers. As the magnetic properties in binary FF 2 have similar variations than binary FF 1, one reckons that the poisoned chains observed in binary ferrofluid 1 might also appear in binary ferrofluid 2. In order to validate this assumption, the sample needs to be observe by element-selective microscopy. However, maghemite nanoflowers lack a cation that can help identify them from cobalt ferrite nanoflowers, like manganese in sample Mn_21_F. As the stoichiometry in CoFe 2 O 4 nanoparticles is low on cobalt atoms, this renders the experiment more complicated and might require longer exposition time (difficult because of carbon contamination).

Instead, an electron-based microscopy technique like EELS or EDX would be faster and more precise way of performing chemical mapping on the ferrofluid. However, the range in field of view allowed by EELS is limited, and it would be time consuming to image large areas with enough assemblies and nanoparticles to gather statistically significant information. We have done some EELS tests on specimens prepared with binary ferrofluids and we find that the carbon contamination is very important due to the method of preparation (citrate molecules surrounding the nanoparticles are composed mainly of carbon and cannot be remove or the stability is lost, which prevents the emergence of self-assembly). Instead of scanning a whole area to obtain a chemical map, it is possible to record a spectra on a few pixels, particle per particle. This is very tedious and not suited for large number of nanoparticles, but technically possible.

Further investigations are necessary to conclude on the binary FF 2 and its comparison to binary FF 1. In particular, the role of magnetic anisotropy or magnetic moment in the poisoning effect is not yet obvious.

Discussion on binary ferrofluid 3

As the sample Co_53_F is very polydisperse, its magnetic properties are complex and it acts by itself as a bidisperse ferrofluid, with large nanoflowers of > 50 nm in diameter and small 8-10 nm petals. Thus, when mixed with another type of nanoflowers with different composition, the magnetic interactions become difficult to apprehend and the interpretation of the magnetometry precarious. Further analysis of the magnetic properties of the CoFe 2 O 4 nanoflowers is necessary before being able to understand the impact of the MnFe 2 O 4 nanoparticles on new magnetic properties in the binary. For example, the sizes of some nanoflowers in Co_53_F (70-100 nm) might indicate the presence of multi-domain states in a fraction of the nanoparticles. With such magnetic structure, the magnetic moment is zero even with large magnetic anisotropy. This would impact the self-assembly properties of the nanoparticles, which has to be properly investigated, both in the single phase ferrofluid and in the binary ferrofluid.

Conclusion

In this chapter, a study of binary ferrofluids was presented. Starting from previous measurements done in our team before the thesis, the poisoning effect on small nanospheres without self-assembly was established by FORC diagrams and element-selective magnetometry. To continue this work, I studied a binary ferrofluid of similar chemical composition, CoFe 2 O 4 mixed with MnFe 2 O 4 , but with nanoflowers of larger diameters and a large enough dipolar constant in order to observe self-assembly. The mean magnetic moments of both component are of the same order of magnitude, which allows us to focus on the impact of magnetic anisotropy only. This binary ferrofluid was investigated through bulk magnetometry, FORC diagrams allowing the separation of soft from hard magnetic contribution and chemical-sensitive microscopy to observe the structuration in the binary ferrofluid. We find that the magnetic properties of the MnFe 2 O 4 component are deeply modified by the presence of CoFe 2 O 4 nanoparticles when no field is applied on the fluid and the assemblies are oriented randomly. Indeed, in this configuration, the nanoflowers form clusters of intermediate sizes (100-200 nm in dimension). Those self-assembled clusters are composed of smaller aggregates of either CoFe 2 O 4 or MnFe 2 O 4 nanoflowers. Therefore, while some nanoparticles are in close contact with other of different chemical composition inside the clusters, many others only see the same magnetic environment as in the single phase ferrofluid (being in the center of an aggregate). I suggest that the difference in environment does not have the same impact on CoFe 2 O 4 and MnFe 2 O 4 nanoparticles. Indeed, while CoFe 2 O 4 has a large magnetic anisotropy and thus a stable magnetic dipole, MnFe 2 O 4 has a weaker magnetic anisotropy which induces Néel relaxation at a timescale preventing stable magnetic interactions to form. Thus, in the binary ferrofluid, CoFe 2 O 4 nanoparticles magnetic moments act as an effective magnetic field that orients and "stabilize" the magnetic moments of the MnFe 2 O 4 nanoparticles. Their coercivity increases as this effective field becomes a new local magnetic anisotropy. When averaged on all nanoparticles, aggregates and clusters, there is no preferential direction and the interaction field measured in FORC diagrams remains centered at zero. Chapter 4 However, when a magnetic field is applied, the CoFe 2 O 4 and MnFe 2 O 4 nanoparticles form long, anisotropic chains. In this configuration, interaction field distribution is shifted towards negative fields, which is the evidence of a mean magnetic field affecting the soft magnetic component. Meanwhile, the hard magnetic component experience a new magnetic environment by being "poisoned" by the soft magnetic component, that are placed at regular intervals inside the chains. This poisoning effect reduces the coercive field distribution of CoFe 2 O 4 , which becomes softer. Interestingly, this effect only occurs for a high enough fraction of MnFe 2 O 4 nanoflowers in binary FF 1. Simulations are needed to understand what are the limitations of the poisoning effect with respect to the concentration of each component.

Moreover, a binary ferrofluid with two components of different magnetic anisotropy and different mean magnetic moments (CoFe 2 O 4 and Fe 2 O 3 nanoflowers) was studied. The results are not yet completely understood, but the main idea is that the poisoning effect seems to be at play as well. Indeed, this binary ferrofluid exhibits novel magnetic behaviour that differs significantly from a non-interacting theoretical binary ferrofluid. From FORC diagrams and bulk magnetometry, we find that the new magnetic interactions leads to an increase of bulk coercivity and coercive field distribution for the soft magnetic material, as in previous binary ferrofluids. However, this effect is dependent on the ratio of CoFe 2 O 4 :Fe 2 O 3 nanoparticles. We were unfortunately not able to perform an analysis of structuration properties on this binary ferrofluid, which would give great insight on the non-linear modifications of the magnetic properties observed by SQUID magnetometry. Moreover, the hard magnetic material is not modified in the ZFC configuration for the ratios measured by element-selective magnetometry, which is consistent with previous results on other binary ferrofluids.

Finally, a study on a more complex binary ferrofluid was initiated. The CoFe 2 O 4 nanoflowers are now larger than before (50-100 nm), and mixed with smaller MnFe 2 O 4 nanoflowers (21 nm). The objective was to investigate and quantify the influence of particle size on magnetic properties, both in the single phase and binary ferrofluids. However, the sample presents a very polydisperse range of sizes, which makes the interpretation of the data hazardous. Further experiments on the single phase ferrofluid are necessary to understand the modification of the magnetic properties in the binary ferrofluid. As for the soft magnetic component, the poisoning effect could still be involved as the coercive field distribution was increased when in the binary ferrofluid.

General conclusion and prospects

Summary

Ferrofluids are colloidal suspensions of magnetic nanoparticles. Due to the reduced size ( ∼ 5-25 nm), each nanoparticle behaves as a single magnetic domain and can be approximated as a unique magnetic dipole. If the magnetic moment of nanoparticles is large enough, magnetic dipolar interactions are stronger than thermal energy. Because nanoparticles are free to move in the liquid, they can assemble into microstructures, a process called self-assembly. These microstructures can take a variety of forms, from chains, rings or more complex networks. Self-assembly depends on the magnetic properties of each individual nanoparticle, which are influenced by its shape, size or composition. In addition, two single-phase ferrofluids with different magnetic nanoparticles can be physically mixed together and are called binary ferrofluids. Due to the new interactions taking place between nanoparticles, new collective magnetic properties arise, creating a tunable magnetic material. This is of interest both for applications and for theoretical models, as it allows the discovery of novel interaction mechanisms. When a ferrofluid with high magnetic moment nanoparticles is mixed with a ferrofluid with low magnetic moment nanoparticles, it has been theorized that a "poisoning effect" occurs, in which assemblies of high magnetic moment nanoparticles are "poisoned" and shortened by the low magnetic moment nanoparticles.

In this thesis, I experimentally studied ferrofluids made of flower-shaped nanoparticles composed of cobalt ferrite, manganese ferrite, and maghemite. The objectives of the thesis were (i) to understand the relationship between structuration and magnetic properties through investigating ferrofluids with different types of magnetic dipolar interactions by changing the size, shape, and composition of the magnetic nanoparticles, and (ii) to analyze quantitatively the poisoning effect in binary ferrofluids showing self-assembly and understand its consequences on the modification of magnetic properties. The originality of the work lies in the use on experimental investigations from the nanoscale to the macroscopic scale, using advanced experimental techniques rarely employed in ferrofluid studies to date.

I have used TEM declined as different forms, in particular, cryo-TEM, for which I developed preparation and measurement protocols. This was an opportunity to make an incursion into the field biogenic iron nano-oxides (magnetosomes, 40 nm in size), which also raise the same question of the relationship between structuration and magnetic properties. The results have been published in JMMM [START_REF] Carvallo | Magnetic and Structural Properties of Biogenic Magnetic Nanoparticles along Their Production Process for Use in Magnetic Hyperthermia[END_REF] and I helped to supervise the internship of A. Fondet for the cryo-TEM part of the work.

Chapter 3 presents the results obtained on single phase ferrofluids. The ferrofluids synthesized by the polyol process are composed of spherical crystallites assembled into a flower-shaped multi-core nanoparticle called nanoflower. The magnetic saturation value was found to be lower than the bulk value. The Langevin model was used to calculate the mean magnetic moment, and the Stoner-Wohlfarth model was used to estimate the magnetic anisotropy. The microstructure was imaged by cryo-TEM. Cobalt ferrite nanoparticles assemble into small chains and networks, while manganese ferrite nanoflowers aggregate into clusters of hundreds of nanoparticles. This structural difference is explained by the value of the magnetic anisotropy. In fact, since cobalt ferrite nanoparticles have a large magnetic anisotropy even at room temperature, the Néel relaxation time is very long and the magnetic moment is stable enough to give rise to interactions with preferential orientation. On the contrary, manganese ferrite nanoparticles have low magnetic anisotropy and their magnetic moments oscillate at a frequency too high to allow magnetic interactions to form chains.

A ferrofluid composed of cobalt ferrite nanoflowers with interesting self-assembling properties was further investigated. The 3D morphology of the individual nanoparticles was resolved by electron tomography, providing values for the volume and surface area of the nanoflower. We were able to relate the reduced saturation magnetization to the amount of disordered spins present in the surface. In addition, the self-assembly process was quantified by analyzing 450 cryo-TEM images and classifying the different shapes observed into 10 categories. The most frequently observed assemblies were chains (62%) and rings (20%). The ferrofluid was also observed at a lower volume fraction and the nanoparticles were isolated, no self-assembly was present.

To understand the magnetic interactions taking place at the nanoscale, electron holography was performed on nanoflowers assembled into chains, rings, and double chains. This technique allowed observing the orientation of the magnetic moments of each nanoparticle within the assembly. In rings, the magnetic moments were found to be oriented head-to-tail and in a closed loop. In double chains, the magnetic moments were antiferromagnetically coupled. Finally, in a chain, anti-parallel coupling and out-of-plane orientation were observed instead of the expected head-to-tail orientation. We attribute this type of configuration to the large magnetic anisotropy competing with the dipolar magnetic interactions. Moreover, the collective magnetic properties of the ferrofluid were investigated by FORC diagrams at low temperature (frozen phase) in two different interaction regimes (dilute, concentrated) and three different configurations. First, when no field was applied before cooling the liquid (zero field cooled, or ZFC), the self-assembled ferrofluid showed similar properties to the dilute ferrofluid showing isolated nanoparticles. The coercive field distribution is completely related to the magnetic anisotropy and the magnetic interactions do not affect the properties of the ferrofluid. The FORC diagram also confirmed the single domain nature of the nanoflowers. Second, a magnetic field was applied before the sample was cooled (Field Cooled, or FC), which produced long, parallel, field-aligned chains in a concentrated ferrofluid, while the dilute ferrofluid did not exhibit any chains. In this configuration, the coercive field distribution increased to higher fields. This is explained by the Stoner-Wohlfarth model, where non-interacting randomly oriented magnetic dipoles have lower coercivity than field-aligned magnetic dipoles. In addition, we found that the effect of increased coercive field distribution is stronger when the nanoparticles are chained because the magnetic interactions couple the nanoparticles together and the magnetic field required to switch the magnetization is larger. Finally, a magnetic field was applied before cooling, and after the sample was cooled, the sample holder was rotated 90°and the FORC diagrams were measured with a magnetic field perpendicular to the cooling one. In this configuration, the coercive field distribution was lower than before, and no model explained this effect. To understand this result, I simulated FORC diagrams with different nanoparticle structures and found it could not be explained by considering an uniaxial anisotropy with easy axis aligned with the axis of the chains. The introduction of disorder on the orientation of the easy axis was our attempt to approximate cubic anisotropy. These results will be the subject of a paper soon to be submitted to ACS Nano.

In Chapter 4, I studied binary ferrofluids consisting of a hard magnetic material and a soft magnetic material. The first binary ferrofluid consisted of nanoflowers of CoFe 2 O 4 and MnFe 2 O 4 , both with magnetic dipolar interactions strong enough to produce self-assembly. The binary ferrofluid was prepared with three different CoFe 2 O 4 :MnFe 2 O 4 ratios. The magnetic properties were measured using FORC diagrams in both ZFC and FC configurations. X-ray microscopy was used to obtain chemical maps of the binary ferrofluids in ZFC and FC configurations.

In the ZFC configuration, the MnFe 2 O 4 component in the binary ferrofluid is found to have broader coercive and interaction field distributions due to the existence of new magnetic interactions with respect to the pure phase. However, the CoFe 2 O 4 component in the binary ferrofluid did not show different magnetic properties. The chemical map indicated that the nanoparticles were clustered into large aggregates composed of both nanoparticles. In the FC configuration, the MnFe 2 O 4 component still exhibited the same effect, but in this case the magnetic properties of the CoFe A second binary ferrofluid was also investigated. The same CoFe 2 O 4 nanoflowers as in the previous binary ferrofluid were mixed with γ-Fe 2 O 3 nanoflowers. We were not able to use chemical mapping and only measured the magnetic properties using FORC diagrams and SQUID magnetometry. From the FORC diagrams, a similar effect as described above was observed: in the ZFC configuration, the γ-Fe 2 O 3 component in the binary ferrofluid exhibited a broadened coercive and interaction field distribution, while the magnetic properties of the CoFe 2 O 4 component were not modified. In the FC configuration, the coercive field distribution of the CoFe 2 O 4 nanoparticles is slightly shifted to lower fields. However, further investigations using SQUID magnetometry and different CoFe 2 O 4 :Fe 2 O 3 ratios showed more complicated results. The change in magnetic properties of the binary ferrofluid is not linearly related to the CoFe 2 O 4 content.

As a general behaviour, the poisoning effect in a binary ferrofluid composed of a hard self-assembled and a soft magnetic material will cause the soft magnetic material to become harder. It is remarkably different than the case of binary CoFe 2 O 4 -MnFe 2 O 4 ferrofluids showing no self-assembly [START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF], where it was previously found that the hard component becomes softer. In our case, this effect is present only for FC configuration and for a specific ratio.

Prospects

During this thesis, experimental methods were applied to address open questions in the field of ferrofluids, in particular those regarding self-assembly and magnetic properties. While many were partially answered, others remain or new ones appeared. In this last section, I will explore unresolved questions, preliminary work not included in the manuscript, and emerging ideas to further the state of knowledge on magnetic nanoparticles and ferrofluids.

Nanoflowers

The crystalline and atomic structure of cobalt ferrite nanoflowers was studied in Chapter 3 using XMCD and HRTEM. However, the relationship between these results and the magnetic properties (e.g. saturation magnetization M s and coercivity H c ) was not fully clear and deserves further investigation. For example, to relate the reduced value of M s to potential defects between the petals of the nanoflowers, it would be interesting to image the particles and the interface between petals with a higher resolution. In addition, I also measured by HRTEM other nanoflowers samples of my PhD work although the results are not shown here. A careful quantitative comparison between these different nanoflowers could provide a connection between the morphology (diameter or number of petals per flower) and the magnetic properties (M s or H c ). The differences in coercivity and magnetic anisotropy between cobalt ferrite nanoparticles need to be further analyzed. Finally, since tomography has proven to be a valuable tool for understanding the morphology of nanoflowers, new observations will be made on other samples in the near future, continuing the collaboration with O. Ersen and W. Baaziz at IPCMS. These results could help to constrain future micromagnetic simulations on flower-shaped nanoparticles, which will be carried out in collaboration with V. Dupuis at PHENIX laboratory.

Self-assembly and chain formation under magnetic field

Since the SAXS measurements were performed with a laboratory equipment, the resolution did not allow us to observe a q-range lower than 4.10 -3 Å -1 , which in real space corresponds to objects smaller than a few hundred nanometers. The chains formed under magnetic field in this work can reach 1 µm. Therefore, it would be interesting to measure ferrofluids exhibiting chain formation under an applied magnetic field on a SAXS beamline in a synchrotron (for example SWING beamline at SOLEIL synchrotron) that allows a lower q-range to observe the chains. Since SAXS is an averaged measurement over many nanoparticles, one could obtain valuable information about the average length of the chains, the distance between nanoparticles in the chain, etc. This would require some preparation work as no magnetic field environment is proposed at the SWING beamline, but a simple electromagnet respecting the geometry of the experiment could be implemented.

In order to continue the analysis of the magnetic properties at the nanoscale, another electron holography experiment will be performed, pursuing our collaboration with C. Ga-tel and E. Snoeck at the CEMES laboratory. Specimens of cobalt ferrite nanoflowers will be prepared under an external magnetic field of 5 mT and 50 mT. The orientation of the magnetic induction lines inside the chains of nanoparticles will be imaged, as was done previously on assemblies in the same ferrofluid. The aim is to quantify the magnetic field required to align the magnetic moments with the direction of the field, and to relate this information to the magnetic anisotropy and macroscopic magnetic properties of the ferrofluid.

Complementary to holography, STXM measurements combined with XMCD can provide a map of magnetic moment for chains of nanoparticles in remanence [START_REF] Chevrier | Collective magnetotaxis of microbial holobionts is optimized by the three-dimensional organization and magnetic properties of ectosymbionts[END_REF]. While initial tests were conducted during the thesis, these measurements are currently challenging due to the very low remanence value at room temperature. In the future, a cryostat will be installed on the HERMES beamline, allowing for low-temperature measurements and ultimately a larger remanence. In addition, the spatial resolution of the STXM line is currently ∼30 nm, which limits observation of our nanoparticles. In order to overcome this limitation, ptychography could be used instead of STXM [START_REF] Mille | Ptychography at the Carbon K-edge[END_REF]. Ptychography is a coherent diffraction imaging technique that measures diffraction patterns at many overlapping points on a sample and then uses an algorithm to reconstruct amplitude and phase images of the object and probe. It is presently under development in Extremely Brillant Source synchrotrons (SOLEIL-II and ESRF-ESB). During the thesis, we tried to implement ptychography measurements, but we only noticed an improvement in absorption contrast and not in spatial resolution. This outcome may be attributed to the characteristics of the samples, in particular the surfactants, as we encountered major difficulties with carbon contamination. Nevertheless, it is essential to closely follow ptychography due to the potential for rapid progress resulting from improvements in detector sensitivity and reconstruction algorithms. Future developments of the sample environment versatility make this technique appealing to many fields.

In addition, the crystalline orientation of the same nanoparticles, measured in electron holography, could be determined using Nano Beam diffraction (NBD). I did some tests with NBD on chains and rings during my thesis. Although it is a long and difficult process, because each nanoparticle must be aligned with the beam to determine its zone axis, and the angle of the sample holder must be rigorously recorded, this experiment is possible and could provide more information about the nature of the magnetic anisotropy (uniaxial or cubic). NBD could also indicate the direction of the easy axis in the unit cell of a nanoparticle [START_REF] Alphandéry | Assemblies of Aligned Magnetotactic Bacteria and Extracted Magnetosomes: What Is the Main Factor Responsible for the Magnetic Anisotropy?[END_REF], which is not straightforward since all measurements of magnetic anisotropy are performed on bulk material.

A liquid cell in the TEM [START_REF] Jonge | Resolution and Aberration Correction in Liquid Cell Transmission Electron Microscopy[END_REF] could also be a useful tool for future work. By observing the dynamics of self-assembly in real time, we could gain valuable insight into the time scale and mechanisms of self-assembly. In addition, the magnetic field applied during the imaging using the electromagnetic lens of the TEM would allow direct observation of chain formation, which could complement SAXS measurements and macroscopic magnetometry measurements.

Dynamical magnetic properties

All magnetometry measurements in this thesis were performed in a static regime, with a DC magnetic field. However, much of the research on ferrofluids focuses on the dynamic magnetic properties through AC susceptibility measurements. In order to compare our samples with state-of-the-art ferrofluids and recent models [START_REF] Ivanov | How Particle Interactions and Clustering Affect the Dynamic Magnetic Susceptibility of Ferrofluids[END_REF], proper measurements of the dynamic magnetic susceptibility need to be performed. In addition, E. Bertuit and I started magnetic hyperthermia measurements at the PHENIX laboratory during the thesis. Although the results are still inconclusive and require further investigation, the ferrofluids composed of nanoflowers show great potential for heating efficiency. New important insights into ferrofluids for biomedical applications could be obtained by exploring the relationship between particle interactions, dynamic susceptibility, heating efficiency and flower-shaped nanoparticles. As a new magnetic material with tunable magnetic properties, binary ferrofluids are of great interest for hyperthermia experiments. In a future work, it would be interesting to study the heating efficiency of single-phase ferrofluids and binary ferrofluids, and try to produce binary ferrofluids with optimized heating efficiency.

Binary ferrofluids

The current study of binary ferrofluids requires further investigation because some magnetic properties are not fully understood. In the case of self-assembled CoFe 2 O 4 -MnFe 2 O 4 binary ferrofluids, simulations of configurations of nanoparticles can be performed to try to reproduce the FORC diagrams and the results of SQUID magnetometry at different ratios CoFe 2 O 4 :MnFe 2 O 4 .

In addition, X-ray microscopy can provide magnetic information as well as element selectivity. By combining XMCD and STXM, we can measure the remanent magnetization of the nanoparticles while discriminating between CoFe 2 O 4 and MnFe 2 O 4 nanoparticles. During this work, an attempt was made on large microscopic chains of CoFe 2 O 4 nanoflowers. However, the remanence at room temperature was too low and indistinguishable from the background noise. The current setup at the HERMES beamline allows the application of a magnetic field during the measurements. A second attempt can be made under field to enhance the XMCD signal by saturating the magnetization. Other compositions of nanoparticles may also be more suitable for this experiment, for example nanowires made of a soft magnetic material (FeNi alloys) have recently been successfully measured on the beamline [START_REF] Álvaro-Gómez | Micromagnetics of Magnetic Chemical Modulations in Soft-Magnetic Cylindrical Nanowires[END_REF].

Finally, the optimization of element-selective magnetization curves measured by RIXS-MCD is feasible. Currently, measuring one hysteresis curve takes 12 to 15 hours, limiting the number of samples measured during a single week of beamtime. However, the upgrade of SOLEIL and ESRF will increase the flux and reduce the measurement time. Additionally, replacing the liquid cell in between samples is a time-consuming and restrictive process, and the maximum magnetic field strength available (∼500-800 mT) is not sufficient to fully saturate the magnetization. Currently, F. Choueikani (DEIMOS beamline) is developing a flow-through liquid cell for use in transmission in the soft X-ray range. Our team assisted with the commissioning process but we encountered some leaking issues at room temper-

4. 5 . 1

 51 Element-selective magnetometry . . . . . . . . . . . . . . . . . . . 4.5.2 Separation of magnetic contributions . . . . . . . . . . . . . . . . . 4.5.3 Varying the CoFe 2 O 4 :Fe 2 O 3 ratio . . . . . . . . . . . . . . . . . . . 4.5.4 Comparison with the previous binary ferrofluid . . . . . . . . . . . 4.6 Binary ferrofluid of CoFe 2 O 4 and MnFe 2 O 4 nanoflowers with polydispersity 4.6.1 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Discussion on binary ferrofluid 3 . . . . . . . . . . . . . . . . . . . 4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1 Figure 1 . 1 :

 111 Figure 1.1: Different types of magnetism. From[START_REF] Jeong | Superparamagnetic Colloids: Controlled Synthesis and Niche Applications[END_REF]

Figure 1 . 2 :

 12 Figure 1.2: Magnetic domains in a ferromagnetic or ferrimagnetic material : reduced saturation magnetization. From [17].

Figure 1 . 3 :

 13 Figure 1.3: Magnetization curve M(H) with hysteresis: the features characterizing the hysteresis are the remnant magnetization M r (residual magnetism), the coercive field H c (field necessary to demagnetize the material) and saturation magnetization M s .

Figure 1 . 5 :

 15 Figure 1.5: Schematic of atomic positions in the crystal structure of spinel ferrites showing the rhombohedral unit cell of edge equals to the lattice parameter a.

Figure 1 . 6 :

 16 Figure 1.6: Magnetic dipole-dipole interaction E dip in µ 0 µ 2 /4πd 3 units for four different configurations of two dipole moments with moment µ separated by a distance d: antiparallel, head-to-tail, parallel and opposite.

Figure 1 . 7 :

 17 Figure 1.7: Diagram of the variables used for anisotropy and Zeeman energies. The applied magnetic field H makes an angle ϕ with the axis of easy magnetization, and the magnetic moment an angle θ with the easy axis.

Figure 1 . 8 :

 18 Figure 1.8: (a) Néel relaxation: the magnetic moment (red) orients itself independently from the crystallographic matrix (blue) and (b) Brownian relaxation : the nanoparticle physically rotates, which also causes the rotation of the magnetic moment.

Figure 1 . 9 :

 19 Figure 1.9: (a) Relaxation times τ B , τ N and τ as a function of size for magnetite nanoparticles [28] at room temperature, and (b) example of reversible magnetization curve following the Langevin model for superparamagnetic nanoparticles.

Figure 1 . 10 :

 110 Figure 1.10: Water treatment using MNPs [8].

Chapter 1 1. 5

 15 Current research on magnetic nanoparticles and ferrofluids 1.5.1 Magnetic nanoparticles

Figure 1 . 12 :

 112 Figure 1.12: (a) Approximation of a log normal distribution by two sizes of different fractions. From [88]. (b) Average size of clusters formed by the large particles as a function of the volume fraction of the small particles ϕ S . The volume fraction of the large particles is fixed to ϕ L = 0.05. From [89].

Figure 1 . 13 :

 113 Figure 1.13: Sketch showing (a) the chain-destabilization caused by the presence of small particles between the large particles in a chain and (b) the poisoning effect -the chainshortening due to small particles attached to the edge of a chain. (c) The change of the magneto-viscous effect forced by the presence of small particles -expressed using the small particle influence parameter SPIP -plotted against shear rate in the presence of an external magnetic field . Data points of A, B, and C denote respectively bidisperse ferrofluids with ϕ L = 25, 5 and 3%. The dotted lines represent a linear fit for the sample set A and an exponential fit for sample sets B and C. From [91].

Chapter 2 Figure 2 . 1 :

 221 Figure 2.1: XRD diffraction of ferrites on theoretical powders.

2

 2

  .

Figure 2 . 2 :

 22 Figure 2.2: Schematic representation of a TEM in (left) imaging and (right) diffraction mode (from [97]).

Figure 2 . 3 :

 23 Figure 2.3: HRTEM image of a spherical shaped nanoparticle of CoFe 2 O 4 where the atomic columns are visible as dark and bright dots.

Figure 2 . 4 :

 24 Figure 2.4: Protocol of grid preparation fror cryo-TEM adapted from [101]

Figure 2 . 5 :

 25 Figure 2.5: (a) Schematic representation of a TEM in electron holography mode [62], (b) Conventional TEM image, (c) hologram with fringes in inset, (d) magnetic phase shift and (e) MIP phase shift reconstructed from hologram.

Figure 2 . 6 :

 26 Figure 2.6: Residual fields in MPMS3

Figure 2 . 7 :

 27 Figure 2.7: Illustration of (a) FORCs and (b) resulting FORC diagram, from [106]

Chapter 2 Figure 2 . 8 :

 228 Figure 2.8: Single particle with switching field B sw in a mean interaction field B int : (a) hysteresis and (b) FORC diagram. FORC diagrams of (c) interacting particles with narrow size distribution, (d) non-interacting particles with broad size distribution and (e) simulated interacting Ni nanopillar arrays with broad size distribution. From [106].

Figure 2 . 9 :

 29 Figure 2.9: Illustration of sample environment in a VSM.

Chapter 2 Figure 2 . 10 :

 2210 Figure 2.10: Interface of the software FORCulator [69] with nanoparticles arranged in chains.

Figure 2 .

 2 Figure 2.11: (a) Example of SAXS pattern [84], (b) illustration of a SAXS set-up with an applied magnetic field and (c) form factor for a theoretical sample composed of monodisperse spherical nanoparticles [84].

Figure 2 .

 2 Figure 2.12: (a) Illustration of XMCD for a single-electron system in a ferromagnetic material. (b) XAS and XMCD spectra for the Co L 2,3 edge, showing the right (µ+) and left (µ-) handed polarization, along with their sum (absorption spectrum) and the difference spectrum (XMCD). From [111].

Chapter 2 Figure 2 . 13 :

 2213 Figure 2.13: Multiplet calculations of XMCD for (a) Fe 3+ (T d ), Fe 3+ (O h ) and Fe 2+ (O h ) ions and for (b) Co 2+ (O h ) and Co 2+ (T d ) ions. From [113].

Figure 2 . 14 :

 214 Figure 2.14: (a) Schematic of the two-photon process in 1s2p RIXS. Example of (b) RIXS and (c) RIXS-MCD map measured on cobalt ferrite nanospheres at the Co edge, from [116].

2

 2

  .15) was designed to withstand low temperatures (∼ 20 K) and high vacuum environments. It is made of copper and is attached to a cold finger, inserted inside a cryostat, and placed between two poles of an electro-magnet aligned with the incident beam. The head of the cell is a squared cavity filled with ferrofluid through a hole sealed by a Viton O-ring and a non magnetic screw. This window is closed by Kapton foil (50 µm thick) and Stycast glue.

Figure 2 . 15 :

 215 Figure 2.15: Liquid cell for RIXS-MCD measurements, from [117].

Figure 2 . 16 :

 216 Figure 2.16: Chemical map obtained by X-ray microscopy.

Figure 3 . 1 :

 31 Figure 3.1: (a-c-e-g-i-k-m-o): TEM images of the eight ferrofluid samples (scale bar = 100 nm) with synthesis conditions (i.e. temperature as a function of time in inset, (b-d-f-h-j-l-n-p): corresponding diameter distribution histogram fitted by either a gaussian or a lognormal function.

Figure 3 . 2 :

 32 Figure 3.2: Powder XRD pattern measured with a Co anode on (a) cobalt ferrite samples Co_17_S, Co_24_F, Co_16_F and Co_53_F, (b) manganese ferrite samples Mn_21_F and (c) magnetite sample Fe_27_F.

Chapter 3 Figure 3 . 3 :

 333 Figure 3.3: Size distribution of sample Co_53_F before size sorting treatment.

Figure 3 . 4 :

 34 Figure 3.4: Supernatant of centrifuged sample Co_53_F.

Figure 3 . 5 :

 35 Figure 3.5: Pellet of centrifuged sample Co_53_F.

Figure 3 . 6 :

 36 Figure 3.6: Pellet of magnetically decanted sample Co_53_F.

Figure 3 . 7 :

 37 Figure 3.7: Pellet of magnetically decanted and centrifuged sample Co_53_F.

Figure 3 . 8 :

 38 Figure 3.8: Representative cryo-TEM images of CoFe 2 O 4 , MnFe 2 O 4 and Fe 2 O 3 nanoflowers at different volume fractions ϕ.

Figure 3 . 9 :

 39 Figure 3.9: Cryo-TEM images of sample Co_24_F (a) with and (c) without external magnetic field. TEM images of sample Co_24_F with air-dried method of preparation (b) with and (d) without external magnetic field.

Figure 3 . 10 :

 310 Figure 3.10: Magnetization as a function of temperature for samples Mn_13_S and Mn_21_F.

Chapter 3 Figure 3 . 11 : 3

 33113 Figure 3.11: Magnetization curves measured with the SQUID magnetometer at different temperatures for samples (a) Co_13_S ϕ = 0.1%, (b) Co_17_S ϕ = 0.1%, (c) Co_24_F ϕ = 0.014%, (d) Co_16_F ϕ = 0.005% and (e) Co_53_F ϕ = 0.06%.

Figure 3 . 14 : 3 Figure 3 . 15 :

 3143315 Figure 3.14: Magnetization curves M(H) at 300 K (black) and weighted Langevin best fit (red) with resulting parameters <µ> and σ with for samples (a) Co_16_F, (b) Mn_21_F, (c) Co_24_F and (d) Fe_27_F.

Chapter 3 Figure 3 . 16 :

 3316 Figure 3.16: Magnetization curve of samples Mn_21_F and Fe_27_F at ϕ=0.1% and 100 K.

Figure 3 . 19 :

 319 Figure 3.19: (a) TEM image of the CoFe 2 O 4 nanoflowers. (b) Diameter distribution fitted by a lognormal function, giving d TEM = 23.7 nm and standard deviation σ = 6.4 nm. (c) Example of 3D reconstruction of a nanoflower obtained by electron tomography. (d) XRD pattern measured on a dried ferrofluid sample with indexed diffraction peaks corresponding to the spinel phase of CoFe 2 O 4 .

Figure 3 .

 3 Figure 3.20: (a) HRTEM image of a nanoflower, (b) Fast Fourier Transform (FFT) of the whole image, (c)-(f) FFT of different areas in the particle with the angle measured between the same hkl diffraction peak and the reference horizontal axis

Figure 3 .

 3 Figure 3.21: (a) Radial integration of the SAXS pattern measured for volume fractions ϕ = 0.014% and ϕ = 0.14%. Comparison between the experimental curve and the calculated form factor of monodisperse spheres for volume fractions (b) ϕ = 0.014% and (c) ϕ = 0.14%.

Chapter 3 Figure 3 . 22 :

 3322 Figure 3.22: Bidimensional scattering patterns for volume fraction (a) ϕ = 0.014% without magnetic field and (b) with magnetic field, (c) ϕ = 0.14% without magnetic field and (d) with magnetic field. (e) Radial integration for volume fraction ϕ = 0.014% and (f) ϕ = 0.14%.

Figure 3 . 23 :

 323 Figure 3.23: Representative cryo-TEM images at (a) ϕ = 0.014%, (b) ϕ = 0.14% and (c) with an external magnetic field H applied before freezing (scale bar = 100 nm).

Chapter 3 Figure 3 . 24 :

 3324 Figure 3.24: Statistical analysis on cryo-TEM images with the associated percentage of occurrence (scale bar = 50nm).

Figure 3 . 25 :

 325 Figure 3.25: Distribution of the number of particles per (a) chain and (b) ring from cryo-TEM images. N is the total number of chains or rings.

Figure 3 . 26 :Figure 3 . 27 :

 326327 Figure 3.26: Electron holography images. (a-c-e-g-i) magnetic induction lines as a heat map and (b-d-f-h-j) TEM images of the corresponding assemblies with added direction of the projected magnetization on each particle (red arrows).

Figure 3 . 28 :

 328 Figure 3.28: FORC diagrams measured on ferrofluid at 100 K and ϕ = 0.14% in (a-d) ZFC, (b-e) FC and (c-f) FC90 configurations. VARIFORC smoothing parameters: Sc0, Sc1, Sb0, Sb1, λc, λb = 7, 10, 7, 10, 0, 0.

Figure 3 .

 3 Figure 3.29: (a) Marginal FORC profile and (b) vertical from FORC diagrams for ZFC (random easy axis), FC (aligned easy axis) and FC90 (random easy axis) configurations.

Figure 3 . 30 :

 330 Figure 3.30: FORC diagrams measured on the sample at 100 K and ϕ = 0.014% in (a-d) ZFC, (b-e) FC and (c-f) FC90 configurations. VARIFORC smoothing parameters: Sc0, Sc1, Sb0, Sb1, λc, λb = 10, 12, 10, 12, 0, 0.

Figure 3 . 31 :

 331 Figure 3.31: Marginal (left) and vertical (right) profiles extracted from experimental FORC diagrams at ϕ = 0.14% and ϕ = 0.014%, for ZFC, FC and FC90 configurations.

Chapter 3 Figure 3 . 32 :

 3332 Figure 3.32: (top) Example of particle configuration used in the FORCulator simulations with the uniaxial anisotropy easy axis represented as a red line. (middle) Resulting calculated FORCs and (bottom) FORC diagrams (VARIFORC smoothing parameters: Sc0, Sc1, Sb0, Sb1, λc, λb = 5, 8, 5, 8, 0, 0). The easy axis of each particle are either aligned with the direction of the chain (labeled aligned) or randomly oriented (labeled random). The different experimental configurations are ZFC with aligned easy axis (a, g, m), ZFC with random easy axis (b, h, n), FC with aligned easy axis (c, i, o), FC with random easy axis (d, j, p), FC90 with aligned easy axis (e, k, q) and FC90 with random easy axis (f, l, r).

Figure 3 . 33 :

 333 Figure 3.33: (a) Marginal and (b) vertical profiles extracted from FORC diagrams simulated with FORCulator in configurations ZFC with random orientation of easy axis, FC with easy axis aligned with the chains and FC90 with random orientation of easy axis.

Figure 3 . 35 :

 335 Figure 3.35: FORC diagrams measured at 100 K on sample Mn_21_F in (a) ZFC and ϕ = 0.1%, (b) ZFC and ϕ = 1% and (c) FC and ϕ = 0.1%.

  15 mT and N FORC = 137. Finally, sample Co_53_F measured in ZFC configuration (Fig. 3.37d) shows a FORC diagram with a different shape than previous CoFe 2 O 4 samples. A negative component appears below µ 0 H u = 0 and near the maximum of intensity in µ 0 H c . This component is more intense in the FC configuration (Fig. 3.37b) and less intense in the FC90 configuration (Fig. 3.37c). All three FORC diagrams have very similar features.

Figure 3 . 37 :

 337 Figure 3.37: FORC diagrams of sample Co_53_F with ϕ = 0.06% measured at 100 K in (a) ZFC, (b) FC and (c) FC90.

Figure 3 . 38 :

 338 Figure 3.38: (a-b-c) Coercive and (d-e-f) interaction field distribution for samples (a-d) Co_16_F, (b-e) Fe_27_G and (c-f) Co_53_F.

Figure 3 . 39 :

 339 Figure 3.39: (a) Coercive and (b) interaction fields distribution extracted from FORC diagrams measured on purified magnetosomes (from [156]).

4. 3

 3 Binary ferrofluid of CoFe 2 O 4 and MnFe 2 O 4 nanospheresIn a previous thesis[START_REF] Daffe | Anisotropies and Magnetic Couplings of Texturable Ferrofluids[END_REF], a binary ferrofluid composed of CoFe 2 O 4 and MnFe 2 O 4 6 nm nanospheres (dipolar coupling constant λ < 1) and ratio CoFe 2 O 4 :MnFe 2 O 4 = 1:1 was investigated. Because my work on binary ferrofluids was initiated as the continuation of this study, the main results of this work[START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF] are summarized below.Cryo-TEM observations on the binary ferrofluid at ϕ=0.2% (Fig.4.1a) showed dispersed nanoparticles with few clusters composed of 5-10 nanospheres. By performing EDX on a

Figure 4 . 1 : 4 Figure 4 . 2 :

 41442 Figure 4.1: Cryo-TEM images of the CoFe 2 O 4 -MnFe 2 O 4 binary ferrofluid: large scale, low magnification bright field TEM image showing the long range particle dispersion (a), high magnification high-angle annular dark field scanning TEM (HAADF-STEM) image of a five particle assembly (b) and EDX elemental map showing the distribution of Fe, O, Co and Mn (c-f) in the five particles shown in (b). From[START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF]

Figure 4 . 4 :

 44 Figure 4.4: Normalized magnetization curves of (a) samples Co_16_F and Mn_21_F and (b) binary ferrofluids with different CoFe 2 O 4 :MnFe 2 O 4 ratios, at 100 K and ϕ = 0.1% in ZFC configuration.

  , 4.5b and 4.5c respectively.

Figure 4 . 5 :

 45 Figure 4.5: Experimental magnetization curves of binary ferrofluids with ratios (a) 1:1, (b) 1:2 and (c) 3:1 with theoretical magnetization curves of CoFe 2 O 4 and MnFe 2 O 4 single phase ferrofluids (black) in ZFC configuration.

Chapter 4 Figure 4 . 6 :

 446 Figure 4.6: Normalized magnetization curves of (a) samples Co_16_F and Mn_21_F and (b) binary ferrofluids with different CoFe 2 O 4 :MnFe 2 O 4 ratios, at 100 K and ϕ = 0.1% in FC configuration.

Figure 4 . 7 :

 47 Figure 4.7: Experimental magnetization curves of binary ferrofluids with ratios (a) 1:1, (b) 1:2 and (c) 3:1 with theoretical magnetization curves of CoFe 2 O 4 and MnFe 2 O 4 single phase ferrofluids (black) in FC configuration.

1 .Figure 4 . 8 :

 148 Figure 4.8: FORC diagrams in ZFC configuration of samples (a) Mn_21_F, (b) Co_16_F, and binary ferrofluids with CoFe 2 O 4 :MnFe 2 O 4 ratio (c-d) 1:1, (e-f) 1:2 and (g-h) 3:1. (a-c-e-g) are measured with parameters 1 and (b-d-f-h) with parameters 2.

Figure 4 . 9 :

 49 Figure 4.9: Coercive field distribution extracted from ZFC FORC diagrams at (a) low fields corresponding to MnFe 2 O 4 nanoflowers and (b) high fields corresponding to CoFe 2 O 4 nanoflowers.

Figure 4 . 10 :

 410 Figure 4.10: Interaction field distribution extracted from ZFC FORC diagrams at (a) low fields corresponding to MnFe 2 O 4 nanoflowers and (b) high fields corresponding to CoFe 2 O 4 nanoflowers.

Figure 4 . 11 :

 411 Figure 4.11: FWHM variation from the reference ferrofluid for binary ferrofluids 1:2, 1:1 and 3:1 in coercive field distribution (circle) and interaction field distribution (square).

Figure 4 . 11 .Figure 4 . 12 :

 411412 Figure 4.12: FORC diagrams in FC configuration of samples (a) Mn_21_F, (b) Co_16_F, and binary ferrofluids with CoFe 2 O 4 :MnFe 2 O 4 ratio (c-d) 1:1, (e-f) 1:2 and (g-h) 3:1.

  4.12c) and 3:1 (Fig. 4.12g), but not for ratio 1:2 (Fig. 4.12e). For all ratios, the FORC diagram is wider both in H c and H u compared to the single phase ferrofluid of MnFe 2 O 4 nanoparticles. At high fields, the FORC diagrams of the hard magnetic component are more noisy than the CoFe 2 O 4 ferrofluid. The intensities also decrease with decreasing CoFe 2 O 4 content, from most intense in ratio 3:1 (Fig. 4.12h), to intermediate in ratio 1:1 (Fig. 4.12d), to less intense in ratio 1:2 (Fig. 4.12f). The shape of the FORC diagrams appears similar to the single phase ferrofluid, but the variations in coercive and interaction fields are difficult to quantify from the 2D diagrams only.

Figure 4 . 13 :

 413 Figure 4.13: Coercive field distribution extracted from FC FORC diagrams at (a) low fields corresponding to MnFe 2 O 4 nanoflowers and (b) high fields corresponding to CoFe 2 O 4 nanoflowers.

Figure 4 . 14 :

 414 Figure 4.14: Interaction field distribution extracted from FC FORC diagrams at (a) low fields corresponding to MnFe 2 O 4 nanoflowers and (b) high fields corresponding to CoFe 2 O 4 nanoflowers.

Figure 4 . 15 :

 415 Figure 4.15: ∆FWHM and ∆I max variation from the reference ferrofluid for binary ferrofluids 1:2, 1:1 and 3:1 in coercive field distribution (a-b) and interaction field distribution (c-d) for (a-c) CoFe 2 O 4 and (b-d) MnFe 2 O 4 nanoparticles.

Chapter 4 Figure 4 . 17 :

 4417 Figure 4.17: Composite made from element-selective X-ray microscopy. Blue/purple nanoparticles are MnFe 2 O 4 , green nanoparticles are CoFe 2 O 4 . Binary ferrofluid in FC configuration with ratios (a) 1:1, (b) 1:2 and (c) 3:1. Scale bar = 200 nm.

Figure 4 .

 4 Figure 4.17a (ratio 1:1) shows a 8 µm long chain and an elongated agglomerate of over

Figure 4 . 18 :

 418 Figure 4.18: Element-selective magnetization curves measured at the Co edge (blue) and binary ferrofluids at (a) ϕ = 0.1% and (b) ϕ = 1% with ratio (red) 1:1 and (orange) 1:5.

1 .

 1 Parameters for Fe 2 O 3 : N FORC = 118, t avg = 300 ms, µ 0 H max c = 50 mT, µ 0 H step = 2 mT, µ 0 H sat = 500 mT and µ 0 H b = ± 80 mT; 2. Parameters for CoFe 2 O 4 : N FORC = 134, t avg = 300 ms, µ 0 H max c = 1.35 T, µ 0 H sat = 1.8 T, µ 0 H step = 15 mT and µ 0 H b = ± 230 mT. Distribution of magnetic properties The FORC diagrams of samples Fe_27_F and Co_16_F are plotted on Figure 4.19a and b respectively for ZFC configuration, and Figure 4.19e and f respectively for FC configuration. The FORC diagrams of the binary ferrofluid 2 composed of a 1:1 mixture of both samples are plotted on Figure 4.19c-d for ZFC configuration and 4.19g-h for FC configuration.As previously seen for binary ferrofluid 1, this binary ferrofluid present no modification of magnetic properties for the cobalt ferrite nanoparticles in ZFC configuration. The coercive field distribution (Fig.4.20a) and interaction field distribution (Fig.4.21a) are the same in the single phase and binary ferrofluid. However, the FORC diagram of Fe 2 O 3 nanoparticles is significantly modified in the binary ferrofluid (Fig.4.19a-c). The FORC peak is much more extended, presenting a 15% increase of FWHM in H c distributions (Fig.4.20c) and a 215% increase of FWHM in H u distributions (Fig.4.20c).

Figure 4 . 20 :

 420 Figure 4.20: Coercive field distribution extracted from FORC diagrams on the binary ferrofluid 2 in (a-c) ZFC configuration and (b-d) FC configuration.

Figure 4 . 21 :

 421 Figure 4.21: Interaction field distribution extracted from FORC diagrams on binary ferrofluid 2 in (a-c) ZFC configuration and (b-d) FC configuration.

  4.21d).

4. 5 . 3 Figure 4 . 22 :

 53422 Figure 4.22: Magnetization curves of samples Co_16_F (CoFe 2 O 4 ), Fe_27_F (γ-Fe 2 O 3 ) and binary ferrofluid 2 with various CoFe 2 O 4 :Fe 2 O 3 ratios in (a) ZFC and (b) FC configurations. The modification of magnetic properties was further investigated by SQUID magnetometry with various CoFe 2 O 4 :Fe 2 O 3 ratio. On Figure 4.22a, magnetization curves measured on binary ferrofluid 2 are plotted for ratios 1:10, 1:5, 1:3, 1:3, 1:1, 2:1, 3:1 and 10:1. As the amount of CoFe 2 O 4 increases, the coercivity and remanence increases and the doublewaisted shape of the magnetization curves tends to resemble the single phase ferrofluide of cobalt ferrite nanoflowers. Hysteresis with ratios 1:3, 1:2, 1:1, 2:1 and 3:1 were also measured in FC configuration (Fig. 4.22b) and all the magnetization curves have a larger coercivity and remanence than in ZFC configuration. When the experimental magnetization curve M (H) Exp. is compared to the theoretical one M (H) T h. using Eq. 4.6, non-linear changes are observed. On Figure A.1, the M (H) Exp. measured in ZFC configuration is compared to its M (H) T h. for all ratios (1:10, 1:5, 1:3, 1:3, 1:1, 2:1, 3:1 and 10:1 on Fig. A.1a, b, d, e, f, g and h respectively). Interestingly, even in ZFC configuration, some differences between M (H) Exp. and M (H) T h. are observed. The same comparison is presented on Figure A.2 for FC configuration for all ratios (3:1, 2:1, 1:1, 1:2, 1:3 on Fig. A.2a, b, c, d and e respectively).Here, the differences between M (H) Exp. and M (H) T h. are again observed but for they are more significant for some ratios (e.g. 2:1 and 1:2) than others (e.g. 1:3).

  4.23b). The remanence decreases with decreasing CoFe 2 O 4 content but not linearly. For coercivity (Fig.4.23c), both ZFC and FC configurations give experimental variations consistent with theoretical ones.

Figure 4 . 23 :

 423 Figure 4.23: Variation of (a) area of magnetization curve, (b) remanence and (c) coercivity for binary ferrofluid 2 at various CoFe 2 O 4 :Fe 2 O 3 ratios. In red, the experimental values are plotted and in black, the expected values from theoretical magnetization curve are plotted, for ZFC and FC configurations.

Figure 4 . 25 :

 425 Figure 4.25: FORC diagrams measured in ZFC configuration: samples (a) Mn_21_F, (b) Co_53_F, binary ferrofluid with ratio 1:1 (c) at low fields with parameters 1 and (d) at high fields with parameters 2, in FC configuration: samples (e) Mn_21_F, (f) Co_53_F, binary ferrofluid with ratio 1:1 (g) at low fields with parameters 1 and (h) at high fields with parameters 2.

2 O 4

 24 component were also modified. The coercive field distribution shifted to lower fields due to the magnetic interactions with the MnFe 2 O 4 nanoparticles. From chemical mapping, we observed long parallel chains with alternating CoFe 2 O 4 and MnFe 2 O 4 nanoparticles. The soft magnetic material acts as defects in the oriented chains and lowers the coercivity of the CoFe 2 O 4 nanoparticles.

Figure A. 2 :

 2 Figure A.2: Experimental magnetization curves (red) of binary ferrofluid 2 and theoretical magnetization curves (black) calculated from samples Co_16_F and Fe_27_F in FC configuration with CoFe 2 O 4 :γ-Fe 2 O 3 ratios (a) 3:1, (b) 2:1, (c) 1:1, (d) 1:3 and (e) 1:2.

  1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Magnetism in bulk magnetic materials . . . . . . . . . . . . . . . 8 1.2.1 Historical origin of studies on magnetism . . . . . . . . . 8 1.2.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.3 Magnetic domains and magnetization curve . . . . . . . . 10 1.2.4 Magnetocrystalline anisotropy . . . . . . . . . . . . . . . 12 1.2.5 Spinel ferrites . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Magnetic properties of nanoparticles . . . . . . . . . . . . . . Ferrofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4.2 Synthesis and colloidal stability . . . . . . . . . . . . . . . 22 1.4.3 Applications of ferrofluids . . . . . . . . . . . . . . . . . . 23 1.5 Current research on magnetic nanoparticles and ferrofluids . . . . 24 1.5.1 Magnetic nanoparticles . . . . . . . . . . . . . . . . . . . . 24 1.5.2 Previous studies on ferrofluids . . . . . . . . . . . . . . . . 26 1.5.3 Binary ferrofluids . . . . . . . . . . . . . . . . . . . . . . . 27 1.6 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

	Chapter 1

. . 14 1.3.1 Critical diameter . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.2 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . 15 1.3.3 Magnetic dipolar interactions . . . . . . . . . . . . . . . . 16 1.3.4 Quasi-static models . . . . . . . . . . . . . . . . . . . . . . 17 1.3.5 Dynamical magnetic properties . . . . . . . . . . . . . . . 19 1.3.6 Applications of MNPs . . . . . . . . . . . . . . . . . . . . 21 1.4

Table 1 . 1 :

 11 Properties of magnetite (Fe 2 O 3 ), cobalt ferrite (CoFe 2 O 4 ) and manganese ferrite (MnFe 2 O 4

	3 )

a estimated for nanocubes and nanospheres

[START_REF] Li | Correlation between Particle Size/Domain Structure and Magnetic Properties of Highly Crystalline Fe3O4 Nanoparticles[END_REF]

.

  3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Sample description and basic characterization . . . . . . . . . . . 3.2.1 Synthesis, size distribution and molar ratio. . . . . . . . . Structuration properties . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . Brief summary of investigated samples . . . . . . . . . . . . . . . 3.6 Cobalt ferrite nanoflowers . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Conclusion on Co_24_F . . . . . . . . . . . . . . . . . . . 3.7 Distribution of magnetic properties in other single phase ferrofluids 3.7.1 Results of FORC diagrams . . . . . . . . . . . . . . . . . . 3.7.2 Size effect in cobalt ferrites nanoflowers . . . . . . . . . . 3.7.3 Soft magnetic material and structuration . . . . . . . . . . 3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In this chapter, we focus on the structuration and magnetic properties of eight ferrofluids. These ferrofluids are composed of either CoFe 2 O 4 , MnFe 2 O 4 , or γ-Fe 2 O 3 nanoparticles, and can have spherical or flower-shaped morphologies with varying diameters. Initially, conventional laboratory experiments such as XRD, AAS, TEM and SQUID are conducted to gain insights into the crystalline, chemical and magnetic properties of the nanoparticles.

	Chapter 3

3.2.2 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Saturation magnetization . . . . . . . . . . . . . . . . . . 3.2.4 Size sorting of sample Co_53_F . . . . . . . . . . . . . . . 3.3 3.4.1 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . 3.4.2 Magnetic moment distribution . . . . . . . . . . . . . . . 3.4.3 Remanence ratio . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Cation occupancy in the unit cell . . . . . . . . . . . . . . 3.5

Table 3 . 1 :

 31 nm. List of the ferrofluid samples studied in this thesis.

	Name	Composition d 0 (nm) Shape
	Co_13_S	CoFe 2 O 4	12	sphere
	Mn_13_S	MnFe 2 O 4	12	sphere
	Co_17_S	CoFe 2 O 4	17	sphere
	Co_24_F	CoFe 2 O 4	24	flower
	Co_16_F	CoFe 2 O 4	16	flower
	Mn_21_F	MnFe 2 O 4	21	flower
	Fe_27_F	Fe 2 O 3	27	flower
	Co_53_F	CoFe 2 O 4	53	flower

Table 3 .

 3 2 (except for Fe_27_F since the technique cannot discriminate between Fe 2+ and Fe 3+ ions).

	Single phase ferrofluids

Table 3 . 2 :

 32 Molar ratio X m for the ferrofluids measured by AAS and correct formulation M x Fe 3-x O 4 for the ferrite.

Table 3 .

 3 3. For cobalt ferrite, the theoretical value of a = 8.38 Å, for Chapter 3 bulk manganese ferrite a = 8.50 Å and for magnetite a = 8.39 Å.

	Sample	a (Å)	d XRD (nm)
	Co_17_S 8.388 ± 0.001 13.2 ± 0.5
	Co_16_F 8.387 ± 0.004 11.5 ± 0.6
	Co_24_F 8.372 ± 0.002 13.9 ± 1.4
	Co_53_F 8.390 ± 0.001 12.7 ± 1.2
	Mn_21_F 8.438 ± 0.007 12.2 ± 1.3
	Fe_27_F 8.358 ± 0.001 16.7 ± 1.2

Table 3 . 3 :

 33 Cell parameter a and coherent domain size d XRD derived from Equations 3.2 and 2.1 with diffraction peaks (

Table 3

 3 M s values of 230, 344, 264, 332, and 400 kA/m, respectively. Manganese ferrite samples, (Mn_13_S and Mn_21_F), have M s values of 310 and 295 kA/m, respectively. Sample Fe_27_F, consisting of magnetite/maghemite nanoparticles, has an M s value of 275 kA/m.

	.4. The the-

Table 3 .

 3 . Further investigations are required to fully understand the specific mechanisms contributing to the observed reduction in M s for each sample.

	Sample M s (kA/m)
	Co_13_S	230
	Co_17_S	344
	Mn_13_S	310
	Co_16_F	332
	Co_24_F	264
	Co_53_F	400
	Mn_21_F	295
	Fe_27_F	275

4: Saturation magnetization values for each ferrofluid measured by SQUID magnetometer

Table 3 .

 3 [START_REF] Chen | Spatial, Temporal, and Dose Control of Drug Delivery Using Noninvasive Magnetic Stimulation[END_REF] summarizes the results of the fitting process for the magnetization curves obtained from SQUID magnetometry on diluted ferrofluids. The table includes the chosen

	Single phase ferrofluids

Table 3 . 6 :

 36 Parameters of magnetic moment distribution fitted using Equation 3.10.

Table 3 . 8 :

 38 .8. Maximum and FWHM of coercive and interaction fields distribution extracted from FORC diagrams of sample Co_16_F.

		ZFC FC FC90		ZFC FC FC90
	µ 0 H max c	(mT) 720 880 670	µ 0 H max u	(mT) 10	-5	2
	FWHM (mT) 510 637 500	FWHM (mT) 100 93 124

Table 4 . 2 :

 42 2 O 4 and γ-Fe 2 O 3 nanoflowers Sample M s (kA/m) <µ> (10 4 µ B ) M r /M s (%) µ 0 H c (mT) K eff (kJ/m 3 ) Magnetic properties of samples Co_16_F and Mn_21_F. Coercivities and remanences are given for T = 100 K.

	λ

Remerciements

Table 3.5: Effective anisotropy constant determined using the Stoner-Wohlfarth model on cobalt ferrite ferrofluids. This is consistent with the fact that the magneto-crystalline anisotropy of cobalt ferrite is cubic, with an anisotropy constant K 1 = 220 kJ/m 3 [START_REF] Cullity | Introduction to Magnetic Materials[END_REF]. From Table 3.5, only two samples have a K eff consistent with this value: Co_13_S and Co_24_F. The other cobalt ferrite nanoparticles have larger K eff ≥ 400 kJ/m 3 . However, it is essential to consider that the experimental anisotropy constant, determined using Equation 3.6, represents an effective anisotropy constant. This effective constant takes into account the contributions from shape anisotropy and surface anisotropy, which can modify the total magnetic anisotropy energy of the nanoparticle. Moreover, interactions between particles modify their macroscopic magnetic properties and samples with aggregation and clusters (like Co_53_F) do not fit the Stoner-Wohlfarth model.

While this method of determination of K eff is easy to measure and analyze, it does not take into account the temperature dependence of the magnetic anisotropy. At room temperature, the anisotropy will have decreased, and to consider the influence of Néel relaxation on self-assembly and aggregation, we need to have an estimated value for K eff at 300 K, when the ferrofluid is liquid. Then, Law of Approach to Saturation (LAS) is used in the following Section.

Single phase ferrofluids

Cation occupancy in the unit cell

Cobalt ferrite crystallizes in an inverse spinel structure, where the divalent cation Co 2+ is in an octahedral (O h ) B-site and 50% of trivalent cations Fe 3+ are in tetrahedral (T d ) A-sites and 50% in B-sites. However, for nanoparticles, synthesis can induce non-stoichiometric Co x Fe 3-x O 4 materials, in which vacancies can modify the A-and B-sites occupations. To probe the site occupations of samples Co_24_F and Co_16_F, X-ray spectroscopy was performed on powders at the DEIMOS beamline in SOLEIL synchrotron. X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD) spectras were measured on the samples. The occupancy of Co 2+ , Fe 2+ and Fe 3+ ions in A-and B-sites are reported in Table 3.7. Co 2+ ions are predominantly situated in B-sites. Fe ions are distributed between Aand B-sites, with a small fraction of Fe 2+ ions in B-sites, replacing the vacancy left by the under-stoichiometric amount of Co ions. In [START_REF] Daffé | Small CoFe2O4 Magnetic Nanoparticles in Ferrofluids, Influence of the Synthesis on the Magnetic Anisotropies[END_REF], nanospheres (5-6 nm) produced by the polyol process had all Co 2+ ions in B-sites and no Fe 2+ ions in B-sites. This discrepancy After reviewing the different properties of each samples, one specific ferrofluid (sample Co_24_F) was investigated further for a better understanding of its magnetic properties, both at the nanoscale for the individual flower-shaped particle, and as a collective ensemble of interacting magnetic nanoparticles. This study is presented in Section 3.6.

Single phase ferrofluids

Distribution of magnetic properties in other single phase ferrofluids

In this section, we start by presenting results obtained from FORC diagrams. Similar measurements as those presented in Section 3.6 were done on samples Co_16_F, Mn_21_F, Fe_27_F and Co_53_F. We then compare these experimental observations of collective magnetic properties with the structuration properties measured by Cryo-TEM in Section 3.3. All the FORC diagrams presented below were plotted using the FORCinel software with smoothing factor S c0 = 5, S c1 = 8, S b0 = 5, S b1 = 8 and λ = 0.

Results of FORC diagrams Sample Co_16_F

The FORC diagrams were measured using the following parameters: Table 3.9: Maximum and FWHM of coercive and interaction fields distribution extracted from FORC diagrams of sample Mn_21_F.

Sample Fe_27_F

The FORC diagrams were measured using the following parameters: The results explained in the previous part were obtained with nanoparticles with no self-assembly in a binary ferrofluid. Here, I focus on a binary ferrofluid composed of larger nanoparticles with dipolar coupling λ > 2. The nanoparticles used for this binary ferrofluid are samples Co_16_F and Mn_21_F previously presented in chapter 3. Their main magnetic properties are summarized in Table 4.1, where coercivity and remanence were measured at 100 K. According to Eq. 4.8, λ = 4 for this binary ferrofluid. Sample M s (kA/m) <µ> (10 I start by presenting the magnetic properties measured by bulk magnetometry (SQUID) and the FORC diagrams which enable to separate the soft and hard magnetic contributions. The structuring properties of nanoparticles in the binary ferrofluid are then analysed using the chemically selective microscopy (STXM) technique. Finally, I discuss the influence of structuration on magnetic properties. Having quantified the changes in magnetic properties in binary ferrofluids, we now turn our attention to structuration properties. To this end, we use the dry deposition method described in chapter 3, which enables to obtain nanoparticle assemblies that are supposedly similar to those that form naturally in the liquid phase.

Binary ferrofluids

Structuration probed with element-selectivity microscopy

The specimen were measured at the HERMES beamline in SOLEIL synchrotron. By illuminating the sample at different energies corresponding to the Co, Mn and Fe edges, it is then possible to obtain a chemical map of the assemblies. To obtain a FC configuration, a magnetic field of around 20 mT is applied during the drying phase.

Binary samples were measured at the Co, Mn and Fe edges with ratios of 1:1, 1:2 and 3:1 already characterised by SQUID magnetometer and FORC diagrams. For each ratio, 6 to 7 zones are observed and representative images of these zones are shown in Figure 4.16 for the ZFC configuration and Figure 4.17 for FC configuration. Whether measured by FORC diagrams or element-selective magnetometry, the cobalt ferrite nanoparticles in binary ferrofluids 1 and 2 keep the same magnetic properties in ZFC configuration, while the soft magnetic material (MnFe 2 O 4 or Fe 2 O 3 ) becomes harder due to the new magnetic interactions applied on the nanoparticles coming from the hard magnetic material. In SQUID magnetometry, the different ratios measured on binary FF 2 show a complex picture. The relative variations of parameters ∆Area, ∆M r and ∆H c are summarized on Figure 4.24a, b and c respectively for binary FF 1 and 2. In ZFC, while binary FF 1 does not exhibit important variations on any parameters (grey points), binary FF 2 on the contrary presents a large increase of ∆Area and ∆H c at small CoFe 2 O 4 fractions (black points).

When the ferrofluids are measured in FC configuration, novel magnetic properties arise and the cobalt ferrite nanoparticles have modified magnetic properties. From FORC diagrams, we have seen that for binary FF 1, the coercive field distribution decreases for ratio 1:2. This effect is also visible for ∆M r and ∆H c on The binary ferrofluid 3 is composed of a polydisperse sample (Co_53_F) with sizes ranging from 8 nm (petals of flowers) to 100 nm (large flowers, not stable in solution). Therefore, the magnetic properties could be difficult to interpret due to the various types of interactions taking place in the single phase ferrofluid, as well as the interactions with the soft magnetic material mixed to form a binary ferrofluid (sample Mn_21_F). The objective was to explore the modification of sizes on binary ferrofluids. The FORC diagrams measured on this binary ferrofluid are presented below.

Magnetic properties Experimental parameters

The following FORC diagrams were measured at 100 K and ϕ = 0.06% with two different set of parameters adapted either for CoFe 2 O 4 or MnFe 2 O 4 nanoparticles. The binary ferrofluids were thus measured twice, once with a broad range of fields to probe the hard magnetic material and once with a smaller window of fields to zoom on the soft magnetic material.

FORC diagrams

From the FORC diagrams (Fig. 4.25), we can observe similar effects as before. In ZFC configuration, for the CoFe 2 O 4 component, the coercive field distribution shows a small shift to lower coercive fields (Fig. 4.26a), similarly to what was observed in the binary ferrofluid studied in [START_REF] Daffé | Bad Neighbour, Good Neighbour: How Magnetic Dipole Interactions between Soft and Hard Ferrimagnetic Nanoparticles Affect Macroscopic Magnetic Properties in Ferrofluids[END_REF]. The MnFe 2 O 4 component in the binary ferrofluid exhibits a large increase in coercive field (Fig. 4.26c) and interaction field distribution (Fig.