Carol Vannier

Gabinho Leandro

Magal Rodolfo Fernanda

Jakes, Felix Micha Camille

Cécile Naud

Didier Simon Le Denmat

Thierry Crozes

Yves Richard

Philippe David

J F Motte

David Barral

Lati Gwen

Bruno They

Fred, Hawa Erika Yuan

Marlio, Irina Roxane Gabriel

Cris Victor

I love to write this part! This incredible act of exercising gratitude will not be free of mistakes or forgetfulness, so I apologize. My rst thanks go to my mother, Arly, this remarkable woman who

List of Figures

1.4 Sample architecture for micromagnetic modelling. a) From [START_REF] Skomski | Giant energy product in nanostructured twophase magnets[END_REF], b)From [START_REF] Schre | Modelling of exchange-spring permanent magnets[END_REF], c) From [START_REF] Skomski | Geometry Dependence of Magnetization Reversal in Nanocomposite Alloys[END_REF]. d) [START_REF] Bance | High energy product in Battenberg structured magnets[END_REF]. e) f) [START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF]. g) [START_REF] Sepehri-Amin | Development of high coercivity anisotropic Nd-Fe-B/Fe nanocomposite powder using hydrogenation disproportionation desorption recombination process[END_REF]. . . . . . . . . . . . . . . . 9

1.5 The papers cited are: Parhofer et al. [START_REF] Parhofer | Remanence enhancement due to exchange coupling in multilayers of hard-and softmagnetic phases[END_REF], Shindo et al. [START_REF] Shindo | Exchangespring behavior in sputter-deposited -Fe/NdFeB multilayer magnets[END_REF], Goute et al. [START_REF] Goute | MFM study of NdFeB and Nd-FeB/Fe/NdFeB thin lms[END_REF], Fullerton et al. [START_REF] Fullerton | Hard/soft magnetic heterostructures: model exchange-spring magnets[END_REF], Liu et al. [START_REF] Liu | High energy products in exchange-coupled nanocomposite lms[END_REF], Crew et al. [START_REF] Crew | Interdi usion in bilayer CoPt/Co lms: potential for tailoring the magnetic exchange spring[END_REF], Liu et al.

[94], Seki et al. [START_REF] Seki | Magnetic properties and microstructure of the granular lms processed by annealing FePt-based multilayers[END_REF], Zambano et al. [START_REF] Zambano | Dependence of exchange coupling interaction on micromagnetic constants in hard/soft magnetic bilayer systems[END_REF], Neu et al. [START_REF] Neu | Fully Epitaxial, Exchange Coupled SmCo 5 /Fe Multilayers With Energy Densities above 400 kJ/m 3[END_REF], Cui et al. [START_REF] Cui | Nd 2Fe 14B/FeCo Anisotropic Nanocomposite Films with a Large Maximum Energy Product[END_REF][START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF], Wang et al. [START_REF] Wang | Magnetization reversal of FePt based exchange coupled composite media[END_REF], Dai et al. [START_REF] Dai | Magnetization reversal and magnetic interactions in anisotropic Nd-Dy-Fe-Co-B/MgO/ -Fe disks and multilayers[END_REF] and Son et al. [START_REF] Son | Fabrication and temperature-dependent magnetic properties of large-area L10-FePt/Co exchange-spring magnet nanopatterns[END_REF][START_REF] Son | E ect of the soft layer thickness on magnetization reversal process of exchange-spring nanomagnet patterns[END_REF]

5.26

Hysteresis loop for samples detailed in Table 5.5 ( 0 = 6 T). . . .

5.27

Hysteresis loop for samples detailed in Table 5.6 ( 0 = 6 T) . . . . les moteurs de véhicules traditionnels d'ici 2040 [START_REF] Nakamura | The current and future status of rare earth permanent magnets[END_REF].

A n de mesurer et de comparer les performances des di érents aimants, une gure de mérite couramment utilisée est le produit énergétique ou ( ) , c'est-àdire le travail potentiel disponible qui va promouvoir une conversion énergétique plus e cace. L'évolution de cette valeur au l des ans peut être observée dans la gure 6 [2]. Cette valeur a doublé tous les 12 ans entre la découverte des aimants en acier (les fers à cheval classiques) et le développement des aimants de haute performance.

Les aimants en acier et Alnico exploitent l'anisotropie de forme, à l'échelle macroscopique dans le cas des aimants en acier (d'où la forme familière en fer à cheval été multipliés par dix [START_REF] Chen | What Happens after the Rare Earth Crisis: A Systematic Literature Review[END_REF], montre les conséquences possibles de la pénurie de matières premières. Les risques de coût et d'approvisionnement associés aux terres rares et le développement de nouveaux matériaux pouvant combler l'écart de performance entre les ferrites et le NdFeB [START_REF] Coey | Permanent magnets: Plugging the gap[END_REF] ont été un facteur déterminant dans la dé nition des principales orientations de la recherche actuelle sur les aimants permanents (Figure 7). La présente thèse porte sur une direction de recherche spéci que, à savoir le développement de nanocomposites magnétiques durs et doux.

Systèmes modèles pour les nanocomposites durs/doux

Les nanocomposites durs/doux visent à combiner le meilleur de deux matériaux : l'aimantation élevée (densité des moments dipolaires magnétiques) de la phase magnétique douce et la coercivité élevée (résistance à la désaimantation) de la phase magnétique dure (Figure 8). L'amélioration de ces deux propriétés dans un aimant permettra d'améliorer le produit énergétique maximal, dont il a été question précédemment. Cependant, la simple combinaison de ces deux classes de matériaux magnétiques ne donne généralement pas de bonnes propriétés, mais au contraire, on observe xxv Chapter 0. Résumé une dégradation de la coercivité. Le point clé pour obtenir les propriétés souhaitées réside dans le contrôle ultime des dimensions des phases, en les rendant nanométriques pour favoriser le couplage d'échange. L'étude expérimentale de Coehoorn [START_REF] Coehoorn | Meltspun permanent magnet materials containing Fe3B as the main phase[END_REF][START_REF] Coehoorn | Preparation and magnetic properties of R-Fe-B permanent magnet materials containing Fe3B as the main phase[END_REF], suivie par le modèle micromagnétique développé par Kneller et Hawig [START_REF] Kneller | The exchange-spring magnet: a new material principle for permanent magnets[END_REF], a ouvert ce sujet de recherche, qui a été étudié au cours des trois dernières décennies.

Structure de la thèse

Le premier chapitre de cette thèse passe en revue certains concepts de base du magnétisme, nécessaires à une meilleure compréhension des nanocomposites durs/doux.

Contexte de la thèse

Conclusions

Compte tenu du scénario présenté dans l'état de l'art, nous pouvons diviser la recherche sur les nanocomposites durs et doux en trois groupes principaux : (i)

General Introduction 0.1 Introduction

A permanent magnet is an object made from a material that can maintain a remnant magnetisation in the absence of an external eld. The importance of permanent magnets has increased during the last century from a material that aroused curiosity to one having a wide range of applications. These materials are key for mechanical-electrical energy conversion, and because of this they are widely used in motors, actuators and generators. For this reason, e orts to improve permanent magnet performance can be translated into more e cient energy conversion and generation. These e orts are in full agreement with the clean and renewable energy agenda, including for example, electric vehicles and wind turbines. Besides this, the demand for high-performance magnets is going to increase in the next decades considering that many countries plan to ban traditional vehicle engines by 2040 [START_REF] Nakamura | The current and future status of rare earth permanent magnets[END_REF].

In order to measure and compare the performance of di erent magnets, a key gure of merit used is ( ) , that is the potential energy available work and it is going to promote a more e cient energy conversion. The evolution of this value through the years can be observed in Figure 6 [2]. This value has doubled every 12 years between the discovery of steel magnets (the classic horseshoes) and the development of high performance magnets.

Steel and Alnico magnets exploit shape anisotropy, at the macroscopic scale in the case of steel magnets (thus the familiar horse-shoe shape of these magnets), As the most produced worldwide, a million tonnes of ferrites are shipped every year [START_REF] Coey | Permanent magnets: Plugging the gap[END_REF].

at
NdFeB is part of a family of permanent magnets discovered in 1983 based on rare-earth (RE), and transition metal (TM) compounds [START_REF] Sagawa | New material for permanent magnets on a base of Nd and Fe (invited)[END_REF][START_REF] Croat | Pr-Fe and Nd-Fe-based materials: A new class of high-performance permanent magnets (invited)[END_REF]. This family holds the record energy product value of almost 500 ∕ 3 . In 2008, China was responsible for 95% of the mining and processing of Nd [START_REF] Jones | Materials science: The pull of stronger magnets[END_REF] and 78.5% of the global production of NdFeB sintered magnets [2].

The environmental clean and renewable energy agenda will directly impact the growing demand for rare-earth-based magnets. In order to achieve functional properties at high temperatures is necessary to added to NdFeB scarce heavy rareearth (HRE), such as Dy and Tb. The market behaviour during the 2011 RE crisis, when prices increased ten-fold [START_REF] Chen | What Happens after the Rare Earth Crisis: A Systematic Literature Review[END_REF], shows the possible consequences of raw material shortage. The cost and supply risks associated with REs and the development novel materials that can ll the gap in performance between ferrites and NdFeB [START_REF] Coey | Permanent magnets: Plugging the gap[END_REF] today (Figure 7). The focus of this thesis is to deal with one speci c research direction, namely the development of hard-soft magnetic nanocomposites.

Model systems for hard-soft nanocomposites

Hard-soft nanocomposites aim to combine the best of two materials: the high magnetisation (density of magnetic dipole moments) of the soft magnetic phase and the high coercivity (resistance to demagnetision) of the hard magnetic phase (Figure 8). The improvement of these two properties in a magnet will result in the enhancement of the maximum energy product, discussed previously. However, the simple combination of these two classes of magnetic materials usually does not result in good properties, but on the contrary, the degradation of the coercivity is observed.

The key point to obtain the desired properties is in the ultimate control of the phases dimensions, making them nanometric and promoting exchange coupling. The experimental study of Coehoorn [START_REF] Coehoorn | Meltspun permanent magnet materials containing Fe3B as the main phase[END_REF][START_REF] Coehoorn | Preparation and magnetic properties of R-Fe-B permanent magnet materials containing Fe3B as the main phase[END_REF], followed by the micromagnetic model developed by Kneller and Hawig [START_REF] Kneller | The exchange-spring magnet: a new material principle for permanent magnets[END_REF], opened this research topic, which has been investigated for the past three decades.

Thesis outline

The rst chapter of this thesis reviews some basic concepts in Magnetism,

necessary

Basic concepts in Magnetism

The concepts discussed in this section are presented in many textbooks, including Simple Models of Magnetism by Skomski [START_REF] Skomski | Simple Models of Magnetism[END_REF] and Magnetism and Magnetic Materials by Coey [START_REF] Coey | Magnetism and Magnetic Materials[END_REF].

1

Chapter 1. Hard-Soft Magnetic Nanocomposites

Hysteresis loop and Micromagnetic model

An important starting point when discussing hard-soft magnetic nanocomposites is to de ne hard and soft ferromagnetic materials and how they behave under an external magnetic eld. A hard magnetic material, or a permanent magnet, tends to keep its magnetisation even in the absence of an external eld, while the soft magnetic material is a temporary magnet, loosing its global magnetisation if the external eld is removed. These characteristics can be visualized in the hysteresis loop, where the magnetisation ( ) is plotted as a function of the applied magnetic eld ( ), as depicted in Figure 1.1-a. Hard magnetic materials present a broad and ideally square M(H) loop with a large coercivity ( ) while soft magnetic materials have very narrow loops. Magnet energy landscape during magnetisation reversal. From [START_REF] Coey | Magnetism and Magnetic Materials[END_REF].

H M M s M r H c H c Energy 0 /2 H > H c H = H c H < H c H = 0
Following the loop (Figure 1.1-a), it starts in the virgin state, where the material is demagnetized and the microscopic ordering of the magnetic moments, called domains, are oriented in di erent directions resulting in zero overall magnetisation.

The external applied eld modi es the domain structure and drives the alignment until the saturation ( ). When the applied magnetic eld goes back to zero, the material maintains a certain degree of magnetisation, called remanence ( ). Increasing the eld intensity in the opposite direction will reduce the magnetisation to zero and the correspondent value of applied eld is named coercivity ( ).

The hysteresis loop is the result of complex non-equilibrium and nonlinear phenomena where the state of the systems depends of its own history. The applied eld combined with di erent energies will de ne an energy landscape with stable and metastable minimum. The energy landscape pictured in Figure 1.1-b, considers the simplest case of coherent rotation, with the moments remaining parallel and rotating in unison (where is the angle between the magnetisation and the applied eld ).

As the applied eld increases in the opposite direction of the initial magnetisation, the reversal of the magnetisation is the only way to reduce the system energy.

The various sources of magnetic energy are in competition during the magnetisation reversal process and this is going to de ne the di erent energy landscapes.

This complex analysis, that was rst investigated by Brown in 1940 [START_REF] Fuller Brown | Theory of the Approach to Magnetic Saturation[END_REF], constitutes a eld of research called micromagnetism. Even though the term was named micromagnetism, most of the studied phenomena occur at the length scale between 1 nm and 1 . The two basics assumptions of this approach are: (i) the magnetisation and the other quantities are described in the approximations of the continuous medium as a function of and (ii) the local magnetisation will be determined by the minimum energy resulting from the competition between exchange interaction, anisotropy, Zeeman energy, and magnetostatic self-interaction (de ned below). The hysteresis loop is the result of the local rotations of the magnetisation vector ( ( )) as function of the applied eld ( ). The concept of micromagnetic free energy, associated with the Gibbs free energy, involves material parameters that are temperature-dependent. This formulation, that started to be developed by Bloch in 1932 and evolved with Brown [START_REF] Brown | Micromagnetics[END_REF], can be written for a uniaxial magnet as (Equation 1.1):

= ∫ ⎧ ⎪ ⎨ ⎪ ⎩ ∇ 2 ⏟⎴⎴⎴⏟⎴⎴⎴⏟ ℎ -1 sin 2 ⏟⎴⏟⎴⏟ - 0 2 ⋅ ( ) ⏟⎴⎴⎴⏟⎴⎴⎴⏟ . -0 ⋅ ⏟ ⎴ ⏟ ⎴ ⏟ ⎫ ⎪ ⎬ ⎪ ⎭ 3 (1.1)
Each term in Equation 1.1 relates with one of the energies involved in the magnetisation reversal process, and they will be explained in the following sections.

Zeeman energy

Also named External eld energy, it is the potential energy associated with a the magnetisation of an object ( ) in anexternal magnetic eld ( )( Equation 1.2).

= -∫ 0 ⋅ 3 (1.2)
will promote the alignment of the magnetisation along the applied eld direction.

Exchange

The rst term in the Equation 1.1 is the exchange energy at the continuum level and it arises from the exchange interaction. The exchange energy between neighboring sites that can be described at the discrete level as = -

Anisotropy

The magnetocrystalline anisotropy energy, corresponding to the second term in Equation 1.1, is minimized when the magnetisation is aligned along a certain axis (or planes) called easy axis (or planes), that is determined by crystal-eld and spinorbit e ects. There are many approaches to tackle anisotropy calculations, including:

the spin-orbit coupling and crystal eld interaction and the single-ion model. In this discussion the phenomenological models were used. The simplest approach is to consider uniaxial anisotropy energy described in Equation 1.3 :

= 1 sin 2 + 2 sin 4 + 3 sin 6 (1.3)
Where is the magnetic volume, is the angle between the easy axis and the magnetisation, and 1 , 2 and 3 are the rst, second and third uniaxial anisotropy constants, respectively. This property is also going to distinguish soft and hard magnetic materials. Very soft materials typically have anisotropy energy density smaller than 5 ∕ 3 while for hard materials, the values can reach 10 ∕ 3 . Typically, in a hard magnet the lower-order terms dominate the anisotropy contribution at room temperature. In the formulation presented in Equation 1.1, only the second-order uniaxial anisotropy ( 1 ) is considered.

Magnetostatic energy

This interaction has a long-range character and is also known as dipolar energy. Magnetostatic self-interaction is the result of the eld produced by the magnetisation distribution in the sample itself ( ). A simple approach considers a magnet composed of small dipoles that interact between them creating a magnetic eld at a distance by the -ℎ dipole generating total energy described in Equation 1.4.

= 1 2 ∑ 0 ⋅ ( ) (1.4)
It is important to divide by 2 to eliminate double-counting of the dipolar bond and . In general, parallel alignment is favorable if two moments are placed with their easy axis on the same axis while the antiparallel occurs if they are positioned "side by side".

Dipolar energy is the most complicated factor in micromagnetic models.

With its non-local character, it is very di cult to determine it analytically while numerical solutions cost extremely long computational time.

Characteristic dimensions

Competition between uniaxial anisotropy, which favors magnetisation alignment with the easy axis, and the demagnetising eld, that favors the magnetic ux closure, usually generates magnetic domains. These regions, where magnetisation has uniform direction as shown in Figure 1.1, are separated by a thin structure called a domain wall, rst introduced by Bloch, and depicted in Figure 1.2.

The domain wall width is de ned by the competition between exchange energy and anisotropy. Figure 1.2 shows that inside the domains the magnetisation is aligned with the easy axis while across the wall the magnetisation is rotated through 180 . Because of this, the anisotropy will favor the magnetisation to lie in the easy direction, which tends to narrow the wall width. On the other hand, the exchange punishes a rapid change in direction, that generates magnetisation gradients, thus favoring a wide wall width. Equations 1.5, 1.6 show, respectively, expressions for the the domain wall width and the Bloch-wall width, as depicted in Figure 1.2. The domain formation is necessary to minimize magnetostatic energy but the domain wall the center of the wall (x=0) the magnetisation vector is parallel to the y axis. Adapted from [START_REF] Skomski | Simple Models of Magnetism[END_REF].

formation also costs energy to the system (Equation 1.7).

0 = √ 1 (1.5) = 0 (1.6) = 4 √ 1 (1.7)
Here is the exchange sti ness and 1 is the anisotropy measured in ∕ and ∕ 3 , respectively. In hard magnetic materials (high value of 1 ) 0 can measure some nanometers, and in soft magnetic materials, it can be hundred of times bigger.

The competition between the exchange energy and the dipolar energy denes the Exchange lentgh (Equation 1.8):

= √ 0 2 (1.8)
Which can be interpreted as the smallest length on which the magnetisation can rotate to minimise dipolar interactions since the exchange favors parallel moments. This concept is important for the discussion about exchange-spring magnets and in the analysis of coupling between two magnetic phases.

Exchange-spring magnets

Following an experimental report by Coehoorn on the attainment of ∕ values of over 0.5 and coercivity of 0.3 T in isotropic 3 --magnets containing just 15 % hard magnetic phase [START_REF] Coehoorn | Meltspun permanent magnet materials containing Fe3B as the main phase[END_REF][START_REF] Coehoorn | Preparation and magnetic properties of R-Fe-B permanent magnet materials containing Fe3B as the main phase[END_REF], Kneller and Hawig proposed an approach to signi cantly increase the energy product of permanent magnets [START_REF] Kneller | The exchange-spring magnet: a new material principle for permanent magnets[END_REF].

Their idea, previously explored in 1965 by Goto et al. [START_REF] Goto | Magnetization and Switching Characteristics of Composite Thin Magnetic Films[END_REF], was to produce a nanostructured composite material that combines a hard magnetic phase exchange coupled to a high magnetisation soft phase. It is also from this work, by Kneller and Hawig, that the concept of an exchange spring magnet and a one-dimensional model for the coupling was proposed in Figure 1.3.

In this study cited above, about exchange springs, all the quantities related to the soft phase are labelled m, due to the higher values of magnetisation. For the hard phase the label k is used, emphasizing the higher values of anisotropy. A onedimensional model was used to estimate the critical dimensions for the two phases that are disposed in alternation along x. The regions have widths of 2 and 2 .

From the same schematic, it is possible to visualize that the moments in the middle of the soft phase start to rotate to align with the external eld, while the moments of the soft phase at the interface with the hard phase remain coupled during the entire reversal process, giving the insight that if 2 is reduced, the soft phase could be fully coupled to the hard phase.

In order to estimate of the critical value for 2 , the concept of domain wall

Micromagnetic models of exchange-spring magnets

Kneller and Hawig demonstrated with a one-dimensional model of the microstructure and the micromagnetic structure how exchange coupled composite materials could achieve higher energy products for critical dimensions of the distinct phases [START_REF] Kneller | The exchange-spring magnet: a new material principle for permanent magnets[END_REF]. Several works explored di erent materials and methods to predict and improve magnetic properties, especially ( ) , for hard-soft nanocomposites. Some of these works are summarized in Table 1.1 with the available information about the soft and hard magnetic phase dimensions and content, as well the calculated ( ) , coercivity ( ) and remnant magnetisation ( ). [26], c) From [START_REF] Skomski | Geometry Dependence of Magnetization Reversal in Nanocomposite Alloys[END_REF]. d) [START_REF] Bance | High energy product in Battenberg structured magnets[END_REF]. e) f) [START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF]. g) [START_REF] Sepehri-Amin | Development of high coercivity anisotropic Nd-Fe-B/Fe nanocomposite powder using hydrogenation disproportionation desorption recombination process[END_REF].

Skomski and Coey used an analytical model to predict giant energy products via exchange hardening of hard-soft nanocomposites composed of aligned phases.

Di erent suggestions for sample architecture can be visualized in Figure 1.4-a. This investigation presents an analytic nucleation eld from micromagnetic vector equation and considers the interaction between the soft magnetic regions. With this approach was possible to suggest di erent geometries in order to optimize the coupling and increase the soft phase content.

The innovative contribution, from Schre and Fidler, it was the use of niteelement method to model exchange-spring permanent magnets, showing the correlation between the local arrangement of the magnetic moments and the magnetic properties of these magnets [START_REF] Schre | Modelling of exchange-spring permanent magnets[END_REF][START_REF] Fidler | Micromagnetic modelling -the current state of the art[END_REF]. This work highlights the in uence of the phase distribution in inclusions embedded in a hard magnetic matrix, trying to get the optimized structure regardless the experimental constrains. Skomski, using a analytical/numerical approach, explores the best shape and the "nanogeometry" (Figure 1.4-c) including discussion about the magnetostatic interaction within the soft magnetic phase, all [START_REF] Skomski | Geometry Dependence of Magnetization Reversal in Nanocomposite Alloys[END_REF].

Bance et al., using nite elements, studied Battenberg structured magnets where a soft core, an inter-di usion layer, a hard matrix and a super hard matrix are taken into account, as shown in Figure 1.4-d, using nite elements [START_REF] Bance | High energy product in Battenberg structured magnets[END_REF].

The next three following studies combine simulation and experiments, designing their modeled structures in a way to reproduce the ones fabricated and char-acterized experimentally. Fullerton et al. modeled a multilayer thin lm structure of SmCo/Fe bilayers using a one-dimensional model with a chain of spins. The optimal architecture with a SmCo layer thickness of 1.2 nm and a 4 nm thick Fe layer would produce a maximum energy product ( ) around 560 ∕ 3 (Figure 1.4-e), however, good magnetic properties would be di cult to be achieved in such a thin lm of SmCo [START_REF] Fullerton | Exchange-spring behavior in epitaxial hard/soft magnetic bilayers[END_REF][START_REF] Fullerton | Hard/soft magnetic heterostructures: model exchange-spring magnets[END_REF]. The multilayer approach was also studied by Cui et al. using , in a system where a NdFeB layer was coupled to Fe layer through a Ta spacer-layer; the experimental results were promising even though the simulation showed the coupling was due to magnetostatic instead of exchange interactions (Figure 1.4-f) [START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF]. A more recent study using nite elements, conducted by Sepehri-Amin et al., shows Fe nanospheres inside NdFeB grains. of 540 ∕ 3 is predicted for nano-spheres from 6 to 30 nm at a constant concentration of 6.7% of Fe introduced in a 200 nm NdFeB grain (Figure 1.4-g) [START_REF] Sepehri-Amin | Development of high coercivity anisotropic Nd-Fe-B/Fe nanocomposite powder using hydrogenation disproportionation desorption recombination process[END_REF].

Materials

The intrinsic magnetic properties of various candidates for hard and soft magnetic materials are listed in Table 1.2. The following sections give a brief overview the materials explored during this thesis. The initial choice of hard phase was NdFeB as it has the best properties. Because of challenges related to preparing NdFeB at the appropriated length scale the use of FePt as hard matrix was also explored. For the soft phase, FeCo and Co were chosen and the presence of Co allow element selective characterization.

NdFeB

This magnetic material, discovered in 1984 [START_REF] Sagawa | New material for permanent magnets on a base of Nd and Fe (invited)[END_REF][START_REF] Croat | Pr-Fe and Nd-Fe-based materials: A new class of high-performance permanent magnets (invited)[END_REF], presents the best performance as a room temperature permanent magnet.

2 14 has a tetragonal structure, as represented in Figure 1.5 . The Nd, as a rare earth element, is responsible for the strong magnetocrystalline anisotropy while the presence of Fe leads to a high magnetisation. There are many bulk metallurgical routes used to fabricate this material, such as rapid quenching, mechanical alloying, HDDR, followed by sintering, bonding and hot compaction [START_REF] Coey | Magnetism and Magnetic Materials[END_REF].

In the framework of this thesis, the use of NdFeB sputtered thin lms was explored. NdFeB thin and thick lms have been the object of many investigations [START_REF] Sugawara | E ects of Separation and Cap Layers on the Magnetic Properties of Arrays of Square Nd-Fe-B Thin Films[END_REF][START_REF] Yu | Nanostructured NdFeB lms processed by rapid thermal annealing[END_REF] and have applications in areas such as biology [START_REF] Pivetal | Micro-magnet arrays for speci c single bacterial cell positioning[END_REF] and micro-systems [START_REF] Dempsey | High performance hard magnetic NdFeB thick lms for integration into micro-electro-mechanical systems[END_REF].

A search in the literature of the topic revealed that most of the lms reported have thickness in the range of 100 to 1000 nm. With this in mind, a part of this work was dedicated to develop thin lms ( ≤ 50 nm) that would be compatible with the other fabrication processes used here for the model samples fabrication (Section 3. The synthesis of the hard magnetic 1 0 FePt phase requires a long-range order that cannot be achieved at room temperature. Usually, bulk material synthesis starts with an A1 precursor which is then submitted to annealing. In the case of thin 1.3: Properties of FePt ordered and disordered phases.From [START_REF] Gut Eisch | FePt Hard Magnets[END_REF] lms, the phase can be obtained during sputtering deposition on a heated substrate or by post-deposition annealing [START_REF] Ristau | On the relationship of high coercivity and L10 ordered phase in CoPt and FePt thin lms[END_REF]. X-ray di raction is commonly used to characterize the chemical order (S) of this alloy, that relates the fraction of the Pt(Fe) sites that are occupied by the correct atom [START_REF] Lyubina | Nanocrystalline hard magnetic FePt powders[END_REF].

The phase diagram also reveals the existence of two other phases at equilibrium, when the Pt content is below 35 % occurs the formation of Fe 3 Pt ( 1 2 ) and when the Pt content is above 55 % occurs the formation of 3 ( 1 2 ). The magnetic properties for the ordered and disordered phase can be visualized in Table 1

.3.
Many studies of hard soft nanocomposite employ 1 0 phase as the hard magnet, including self-assembled nanoparticles [START_REF] Zeng | Exchange-coupled nanocomposite magnets by nanoparticle self-assembly[END_REF][START_REF] Pousthomis | On the advantages of spring magnets compared to pure FePt Strategy for rare-earth free permanent magnets following a bottom-up approach[END_REF], multilayer thin lm [START_REF] Parhofer | Remanence enhancement due to exchange coupling in multilayers of hard-and softmagnetic phases[END_REF] and bulk magnet prepared by mechanical ball milling [START_REF] Gut Eisch | FePt Hard Magnets[END_REF]. FePt alloys can be em-Chapter 1. Hard-Soft Magnetic Nanocomposites ployed in a wide range of applications such as high-density storage media and microelectromechanical systems, including corrosive environments. The synthesis of this alloy can be performed by metallurgical processes (e.g. ball milling, cold rolling) [START_REF] Gut Eisch | FePt Hard Magnets[END_REF][START_REF] Hai | An original route for the preparation of hard FePt[END_REF], chemical routes (nanoparticles) [START_REF] Sun | Monodisperse FePt Nanoparticles and Ferromagnetic FePt Nanocrystal Superlattices[END_REF] and physical vapor deposition (sputtering [START_REF] Visokay | Direct formation of ordered CoPt and FePt compound thin lms by sputtering[END_REF], molecular-beam epitaxy [START_REF] Visokay | Direct formation of ordered CoPt and FePt compound thin lms by sputtering[END_REF], pulsed laser deposition [START_REF] Fähler | Pulsed laser deposition of hard magnetic lms[END_REF]) x.

FeCo and Co

1-( 0.65<x<0.50) is called Permendur and presents the largest magnetisation at room temperature. This material, with a body centered cubic structure, has a magnetic polarization = 2.45 and it is a great candidate to enhance magnetisation in hard-soft nanocomposites. The composition must be in this particular range to achieve such high magnetisation, which unfortunately was not available for this work, where the alloy 40 60 was used.

The other soft magnetic phase used was Co, that can be hexagonal closepacked (

) and face centered cubic ( ). The latter being stabilized in thin lms.

Its magnetic polarization is = 1.81 and non-negligible magnetocrystalline anisotropy

( 1 = 410 ∕ 3
) is manifested by the ℎ structure. This was explored by the consolidation of Co nano-rods fabricated by chemical routes, presenting a promising RE-free bulk magnet [START_REF] Ener | Consolidation of cobalt nanorods: A new route for rare-earth free nanostructured permanent magnets[END_REF].

Magnetic characterization techniques

The major hysteresis loops gives information about the global properties of a nanocomposite. Exploring how the magnetisation changes for more complex variations of the external eld can reveal subtleties related to interactions between the hard and soft phases. The techniques described below are commonly used to characterize hard-soft nanocomposites.

Recoil loops

The measurement of recoil loops consists of applying, removing and reapplying a demagnetized eld to the sample. Basically, to build a recoil loop, a negative eld should be applied, and then the magnetisation is measured while increasing the eld back up to 0 T, then the way back is repeated from 0 T to negative eld. This characterization is carried out between the second and third quadrants of the hysteresis loop. The main goal is to evaluate coupling between the constituent phases in the magnetic nanocomposites, that should be, ideally, dominated by exchange interaction. Recoil loops are commonly used to characterize exchange-coupled permanent magnets [START_REF] Goll | Magnetic and microstructural properties of nanocrystalline exchange coupled PrFeB permanent magnets[END_REF][START_REF] Shindo | Exchangespring behavior in sputter-deposited -Fe/NdFeB multilayer magnets[END_REF][START_REF] Crew | Interdi usion in bilayer CoPt/Co lms: potential for tailoring the magnetic exchange spring[END_REF][START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF] due to the direct visualization of reversal permeability ( ) already discussed in the section about exchange-spring magnets (Figure 1.3). Open recoil loops were reported to indicate a breakdown in exchange coupling with the enclosed area being proportional to the volume of decoupled soft magnetic phase. However, a recent debate about the origin of opened recoil loops suggest other reasons as domain formation besides the decoupling [START_REF] Choi | Origin of recoil hysteresis loops in Sm-Co∕Fe exchange-spring magnets[END_REF].

First Order Reversal Curves -FORC diagram

The approach presented by Pike et al. is clearly inspired by the Preisach diagram, but it di ers in the fact that it is not based on any assumption (e.g. constant interaction eld, well-de ned switching eld) [START_REF] Pike | Characterizing interactions in ne magnetic particle systems using rst order reversal curves[END_REF]. FORC analysis is applied in many areas such as geomagnetism, bio-magnetism, recording media [START_REF] Winklhofer | Identifying reversible and irreversible magnetization changes in prototype patterned media using rst-and second-order reversal curves[END_REF], assembled nanowires [START_REF] Dobrotă | What does a rst-order reversal curve diagram really mean? A study case: Array of ferromagnetic nanowires[END_REF] and permanent magnets [START_REF] Schre | First order reversal curve studies of permanent magnets[END_REF]. A negative aspect of this technique is that it requires the acquisition of thousands of data points. Its popularization became possible thanks to the progress of magnetometry techniques, in particular, higher speed of measurements.

The Classical Preisach Model (CPM) assumes that the macroscopic hysteresis loop can be described as a summation and aggregate response of a distribution of elementary hysterons. As represented in Figure 1.8, this mathematical hysteron can be adapted for the magnetic parameters and it will de ne the axis for the FORC distribution.

The First Order Reversal Curves (FORC) and the major hysteresis loop (MHL-Zero order reversal curve) can be acquired with the same equipment. The protocol for FORC measurements consists of three steps:

1-Saturate the sample in a positive eld. The major hysteresis loop determines the value of the saturation eld ( ). This value will determine the limit of maximum applied eld (indicated in Figure 1.8). 2-Apply a reversal eld . This value will determine the limit of minimum reversal eld (indicated in Figure 1.8).

3-Measure the magnetisation curve from back to the saturation eld, resulting in a curve m( , ). The grey discs in Figure 1.8 represent each data point acquired in the protocol.

After following the above protocol, the data can be displayed in di erent ways (Figure 1.9). In Figure 1.9-a the usual graph is presented, where the magnetisation is plotted as afunction of the applied eld and the dotted paths represent reversal curves. The same data can be plotted as a function of the return eld ( ), where the 3D view brings information about the magnetisation map (Figure 1.9-b). This map is visualized in Figure 1.9-c and the FORC diagram (Figure 1.9-d) can be obtained from Equation 1.10. The mixed derivative (Equation 1.10) used to obtain the FORC distribution is a way to highlight any irreversible process, so as to be more apparent to the human eye.

= - 1 2 2 ( , ) = - 1 2 ( , ) ( , ) (1.10)
A direct observation is the coercivity ( ) and interaction ( ) eld distributions that appears in the diagonal axis. Figure 1.9-d shows a single hard phase distribution for an isotropic thin lm of FePt 1 0 , with a peak around 0.8 T and a boomerang shape due to exchange interactions between the grains. A partially coupled or decoupled exchange-spring magnet can be characterized by two or more peaks in the axis and a pronounced soft signature at 0 T. FORC diagram can also be used to inspect exchange bias through a positive shift in the axis. A more detailed interpretation of the FORC diagrams can be based on di erent models, such as noninteracting single domain particles, single domain particle interactions described by a mean eld model and a Preisach model [START_REF] Pike | Characterizing interactions in ne magnetic particle systems using rst order reversal curves[END_REF], Ising-type model and others [START_REF] Panagiotopoulos | A simple approach to the First Order Reversal Curves (FORC) of two-phase magnetic systems[END_REF]. The interpretation of the FORC diagrams presented in this thesis is inspired by the approach developed by Panagiotopoulos [START_REF] Panagiotopoulos | A simple approach to the First Order Reversal Curves (FORC) of two-phase magnetic systems[END_REF] and in a number of studies related with hard-soft nanocomposite and exchange-coupled magnets [START_REF] Son | E ect of the soft layer thickness on magnetization reversal process of exchange-spring nanomagnet patterns[END_REF][START_REF] Okamoto | Temperature dependent magnetization reversal process of a Ga-doped Nd-Fe-B sintered magnet based on rst-order reversal curve analysis[END_REF][START_REF] Dai | Magnetization reversal and magnetic interactions in anisotropic Nd-Dy-Fe-Co-B/MgO/ -Fe disks and multilayers[END_REF][START_REF] Dai | Magnetic interactions in anisotropic Nd-Dy-Fe-Co-B/ -Fe multilayer magnets[END_REF][START_REF] Sakuma | Exchange Coupling Interaction in L1 0-FePd/ -Fe Nanocomposite Magnets with Large Maximum Energy Products[END_REF].

Chapter 1. Hard-Soft Magnetic Nanocomposites

A brief history of the development of hard-soft magnetic nanocomposites

This section presents the current status of research in hard-soft nanocomposites. In Figure 1.10, a mindmap presents an overview of the topic including fabrication routes and materials. Following each branch, it is possible to visualize some paths signalized with a star that correspond to methods used in this thesis.

Fabrication routes

Metallurgical synthesis

Metallurgical synthesis can be divided in three steps: alloy preparation, consolidation and processes to promote texture and increase coercivity. In this section, some examples of magnetic nanocomposites produced by these techniques will be presented. More details on advances in the bulk metallurgical synthesis of nanocomposites, including the use of novel powder consolidation techniques, can be found in a recent review by Yue et al. [START_REF] Yue | Fabrication of bulk nanostructured permanent magnets with high energy density: challenges and approaches[END_REF].

Melt spinning/Strip casting

This technique consists in the injection of molten alloy through an ori ce that falls onto a circumferential surface of a rotating roll in an inert atmosphere. The cooling rate depends on the surface velocity and can be tuned to produce nanocrystalline alloys. The rst production of NdFeB by melt spinning was reported in of 1984 [START_REF] Croat | Pr-Fe and Nd-Fe-based materials: A new class of high-performance permanent magnets (invited)[END_REF].

Melt spinning deserves to be highlighted because it was with this technique that the rst hard-soft magnetic nanocomposite samples were produced. The Fe-rich alloy properties reported by Coehoorn, Mooji and Waard in 1989, aroused scienti c interest in nanocomposite properties and their potential applications [START_REF] Coehoorn | Meltspun permanent magnet materials containing Fe3B as the main phase[END_REF][START_REF] Coehoorn | Preparation and magnetic properties of R-Fe-B permanent magnet materials containing Fe3B as the main phase[END_REF]. more th a n 4 a t% Nd, Nd2Fe 23B3 is the a s e th a t crys ta lliTe s , this pha s e wa s obto de compos e in a lloys conta ining le s s th a n d in to Fe 3B a nd Nd2Fe 14B in the te mpe rte rva l be twe e n T 1 a nd T 2.

etic properties

e s e rie s o f (Fe 3B)l_xfNd2Fe 14B) x a lloys e d in the pre vious s e ction the coe rcive fie ld s th a t we re a nne a le d in the DS C a ppa ra tus ra te o f 20 K / n f m to a te mpe ra ture 20 °C 2 is s trongly corre la te d with the a mount o f 14B th a t is forme d, i.e . with the he a t o f n a t T 2 (fig. 2). Howe ve r, for Nd-conce ntrabove 4 a t% the coe rcivity is lowe r th a n e d fro m this corre la tion. This indica te s th a t ne a ling conditions which le a d to a high ity might be s trongly de pe nde nt on the ce o f crys ta llize d pha s e s , which s hows a a t a pproxima te ly 4 at% Nd (s e e s e ction 3). ra l a nne a ling proce dure s we re us e d to optie pe rma ne nt ma gne tic prope rtie s . In fig. 3 nce ntra tion re gion for the optima l H~ is ~o M (13

/ t i J =Ii -1 0 I i t i i 1 2
.0 p.o H (I-) 5 a t% Nd in to Fe 3B a nd Nd2Fe 14B in the te mpe ra ture inte rva l be twe e n T 1 a nd T 2.

Magnetic properties

In the s e rie s o f (Fe 3B)l_xfNd2Fe 14B) x a lloys dis cus s e d in the pre vious s e ction the coe rcive fie ld o f fla ke s th a t we re a nne a le d in the DS C a ppa ra tus with a ra te o f 20 K / n f m to a te mpe ra ture 20 °C a bove T 2 is s trongly corre la te d with the a mount o f Nd2Fe 14B th a t is forme d, i.e . with the he a t o f re a ction a t T 2 (fig. 2). Howe ve r, for Nd-conce ntrations a bove 4 a t% the coe rcivity is lowe r th a n e xpe cte d fro m this corre la tion. This indica te s th a t the a nne a ling conditions which le a d to a high coe rcivity might be s trongly de pe nde nt on the s e que nce o f crys ta llize d pha s e s , which s hows a cha nge a t a pproxima te ly 4 at% Nd (s e e s e ction 3).

S e ve ra l a nne a ling proce dure s we re us e d to optimize the pe rma ne nt ma gne tic prope rtie s . In fig. 3 the conce ntra tion re gion for the optima l H~ is s hown, for fla ke s th a t we re a nne a le d is othe rma lly . Conce ntra tion de pe nde nce of coe rcive fie ld of fla ke s , a nne a le d is othe rma lly fo r 30 ra in. Th e s pa cing be twe e n contours of e q u a l/to ll ¢ is 0.025 T.

t i J =Ii -1 0 In fig. 3 the o p tim u m in Hc wa s fo u n Nd4.5Fe77.0B18.5. F ro m the hys te re s is loop in it ca n de duce d th a t the coe rcive fie ld #0H~ is T a nd th a t the e ne rgy product (BHm~x) i k J / m 3. At 2 T the ma te ria l is n o t quite s a tu The re fore , the prope rtie s might be s lightly b a fte r ma gne tiza tion a highe r fie ld.

I i t i i 1
A cha ra cte ris tic fe a tu re o f the s e ma te ria ls i high is otropic M r/ M s ra tio. F o r a n a s s e m ra n d o m ly orie nte d non-inte ra cting crys ta llite unia xia l a nis otropy M r/ M s is 0.5 if the ma g za tion is de te rmine d b y a cohe re nt ro ta tio s pins in the gra ins . The ra tio ca n be e ve n l due to d o m a in fo rm a tio n . If it is a s s ume Fe 3 B pos s e s s e s unia xia l ma gne tocrys ta llin s o t r o p y M r/ M s C a n o n ly e xce e d 0.5 due to s inte ra ctions be twe e n crys ta Uite s . If the Fe 3B ta llite s a re e xcha nge -couple d, the ma gne ti dire ction within e a ch o f the crys ta llite s is Strip casting is similar to melt spinning, but can produce much greater quantity of material. This method could be suitable for industrial fabrication of hard-soft magnetic nanocomposites [START_REF] Hirosawa | Development of Industrial Nanocomposite Permanent Magnets: A Review[END_REF] .

The recent work of Sepehri-Amin et al. presents a bulk nanocomposite containing 2 14 withproduced by strip casting followed by hydrogenation disproportionation desorption recombination (HDDR) and + -nanocrystalline alloys prepared by distinct heat treatments. Single-phase behaviour and remanence enhancement were observed in powders crystallized at low temperatures ( 600 ). In contrast, two-phase decoupled behaviour was reported for samples annealed at higher temperatures, showing impact of the temperature in the increase of the grain size of the soft phase [START_REF] Ding | High magnetic performance in isotropic -Fe+Sm 2Fe 17N x[END_REF].

This technique was also used by Neu et al. to produce high remanence and Zr. Si and Zr were the additives that had the higher ( ) , reaching 90

∕ 3 .
Moving to ball milling, 2 14 with 10 % of Fe nanocomposite was prepared using di erent diameter balls followed by annealing and quenching in water.

Both the milling and annealing conditions have an impact on the microstructure and the coupling between the phases, with the highest energy product (185 ∕ 3 ) found in the 6 h milled sample [START_REF] Mican | E ect of Milling Conditions on the Microstructure and Interphase Exchange Coupling of Nd2Fe14B/ -Fe Nanocomposites[END_REF]. and a remanence ratio of 0.9 and ( ) of 206 ∕ 3 . Microstructural analysis shows oriented 7 rod-shape grains and equiaxed FeCo grains [START_REF] Li | Novel Bimorphological Anisotropic Bulk Nanocomposite Materials with High Energy Products[END_REF][START_REF] Li | Controllably Manipulating Three-Dimensional Hybrid Nanostructures for Bulk Nanocomposites with Large Energy Products[END_REF].

Chemical synthesis

In this section, the focus will be placed on the use of chemical routes to fabricate magnetic nanoparticles (MNP) as building blocks for hard-soft nanocomposite. Fabrication can be divided into two steps: (i)Synthesis, (ii)Protection and Stabilization. Table 1.4 compares di erent synthesis routes that can be applied for MNP production. Besides the synthesis methods described in Table 1.4, other methods used for core/shell nanoparticles include microwave-assisted, and electrodeposition [START_REF] López-Ortega | Applications of exchange coupled bi-magnetic hard/soft and soft/hard magnetic core/shell nanoparticles[END_REF].

The second step concerning Stabilization and Protection, includes the following processes: surface passivation (mild oxidation) and coating with several materials, e.g. surfactant, polymer, precious-metal, carbon, silica, matrix dispersed [START_REF] Lu | Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application[END_REF]. Considering these fabrication routes, MNP can be produced with satisfactory control of structure, morphology and composition. The following overview will focus on hard-soft nanocomposite fabricated by chemical routes and highlight the signi cant and ongoing works related to rare-earth and precious metal (Pt, Pd) based material. A complete review including other materials can be found in the paper of Lopez Ortega et al. [START_REF] López-Ortega | Applications of exchange coupled bi-magnetic hard/soft and soft/hard magnetic core/shell nanoparticles[END_REF].

The fabrication of hard-soft nanocomposites by chemical methods became possible following the report of a procedure for fabrication of 1 0 FePt monodispersed particles [START_REF] Sun | Monodisperse FePt Nanoparticles and Ferromagnetic FePt Nanocrystal Superlattices[END_REF] and size-controlled synthesis of magnetite nanoparticles ( with -(>20 nm) Table 1.5: Summary result obtained from [START_REF] Zeng | Exchange-coupled nanocomposite magnets by nanoparticle self-assembly[END_REF] with samples described in Figure 1.16.

Table 1.5 summarizes the results obtained after the hard and soft nanoparticles cited were mixed under ultrasound and binary assembled. As it is shown in Figure 1.16, distinct assembly structures are formed, depending on the nanoparticle size ratio. Subsequently, the assembled particles were submitted to annealing and the outcome of this treatment is described in the last column of table 1.5. Figure 1.17 -a FePt in assemblies like Sample A (4 nm: 4nm) after annealing. The mass ratio varies from 0 to 0.20, while the coercivity drops from 1.9 T to 0.68 T and an enhancement of 15% in occurs.

Figure 1.17-c presents the hysteresis loop for the mass ratio of 0.1, where single-phase behaviour and improvement suggest that the two phases ( ∕ 3 ) are exchange-coupled for sample A. On the other hand, Figure 1.17-d depicts the hysteresis loop for Sample C, with the same mass ratio as the loop above; in this case two-phase behaviour is observed. It could be expected from the results reported in Table 1.5, either before or after annealing. Segregation during the binary assembly, together with the presence ofregions (size > 20 nm) reduces the intimate contact between the phases, disfavouring coupling. The nanocomposites produced from sample A achieve high coercivity and remnant magnetisation due to the dimensions of the formed soft phase (Fe 3 Pt <10 nm) and its intimate contact with the hard phase.

For the sample with the hysteresis loop depicted in 1.17-c, the ( ) exceeds by 37% of the pure FePt nanoparticles. This work is very signi cant because it opened many possibilities for the understanding of hard-soft nanocomposites using chemical synthesis. Further works with similar methods can be found in the literature [START_REF] Zeng | Bimagnetic Core/Shell FePt/Fe 3O 4Nanoparticles[END_REF][START_REF] Zeng | Tailoring magnetic properties of core∕shell nanoparticles[END_REF][START_REF] Liu | Building Nanocomposite Magnets by Coating a Hard Magnetic Core with a Soft Magnetic Shell[END_REF].

One of the rst works reporting the use of rare-earth-based MNP for hardsoft nanocomposite, investigated a system constituted of ( 1- ) 5 ∕ 3 4 (x∼ 0.1) core/shell structure, where the Fe 3 O 4 acted to stabilize the nanoparticles in air.

HRTEM and X-ray Laue di raction were carried out to characterize the structure of the 5 and 3 4 , revealing particles with 5 nm -20 nm dimensions, from pure hard magnetic phase to the core/shell MNP. Although only modest values of coercivity (0.25 T) were achieved, exchange coupling between the two phases was evidenced by an increase in the blocking temperature of the nanocomposite compared to

Pousthomis et al. reported an investigation using binary assemblies of

FeCo and

FePt, the same materials that will be explored in this thesis. In order al. [START_REF] Son | Fabrication and temperature-dependent magnetic properties of large-area L10-FePt/Co exchange-spring magnet nanopatterns[END_REF][START_REF] Son | E ect of the soft layer thickness on magnetization reversal process of exchange-spring nanomagnet patterns[END_REF]. This section will summarize some relevant works using Physical Vapor Deposition applied to the investigation of hard-soft magnetic nanocomposites. Figure Some of the papers cited in this timeline will be discussed in details. Overall, the progress made in thin lm deposition and optimization contributed the understanding of exchange-spring magnets. The nanometric control of the microstructure, exibility and reproducibility, makes this approach suitable for the design of model samples.

One of the rst works using thin lms to study hard-soft nanocomposites was reported by Parhofer et al. in 1996 [49]. This work consists of NdFeB (1.5d)/Fe(d)/ NdFeB(1.5d) trilayers deposited by sputtering, varying from 7 to 110 nm and keeping the volume content of Fe constant. The idea was to use the knowledge accumulated about the deposition of the hard magnetic material to explore the exchange spring concept. Structural and chemical characterization was carried out using X-ray di raction (XRD), Rutherford backscattering spectroscopy (RBS) and Atomic Force Microscopy (AFM). With these techniques, the authors were able to identify peaks corresponding to the 2:14:1 phase with signi cant texture, in an Nd rich alloy thin lm (Fe:Nd ratio = 3.8) and a considerable surface roughness (around 50% of the thickness). This indicates e cient exchange coupling between the layers. The decrease in the ( ) when the thickness increases above 20 nm occurs due to the degradation of the coercivity [START_REF] Fullerton | Exchange-spring behavior in epitaxial hard/soft magnetic bilayers[END_REF][START_REF] Fullerton | Hard/soft magnetic heterostructures: model exchange-spring magnets[END_REF].

Moving to the SmCo/Fe nanocomposites, it was observed that even though ent Fe layer thickness. From [START_REF] Fullerton | Hard/soft magnetic heterostructures: model exchange-spring magnets[END_REF] the SmCo has an epitaxial growth as described previously In Figure 1.27-Right, the Fe layer is polycrystalline with (110) texture. In the hysteresis loop of the sample with 2.5 nm thick Fe layers, it is possible to observe single-phase behaviour and a drop of coercivity from 3 T to 1.7 T comparing to the hard phase alone. When the thickness of Fe increases to 20 nm, the hysteresis loop changes drastically, showing a two-phase behaviour that can be explained by the partial coupling between the two phases.

Neu et al. used pulsed layer deposition (PLD) for the epitaxial growth of 5 ∕ ∕ 5 trilayer to study the coupling as a function of Fe layer thickness [START_REF] Neu | Fully epitaxial, exchange coupled SmCo 5/Fe/SmCo 5trilayers[END_REF][START_REF] Sawatzki | Largely enhanced energy density in epitaxial SmCo 5/Fe/SmCo 5exchange spring trilayers[END_REF]. For Fe thickness up to 6 nm, they obtained fully coupled nanocomposite. However, even with 12.6 nm thick Fe, an energy product of 312 ∕ 3 is achieved.

The applicability of epitaxial growth to form fully coupled phases in a nanocomposite was explored again achieving an energy product surpassing 400 ∕ 3 (Figure 1. 28-c). This work also uses pulsed laser deposition on Cr-bu ered MgO [START_REF] Kazakova | Frontiers of magnetic force microscopy[END_REF] at 500 in a stack architecture of [ 5 ∕ ] 5 with a constant total thickness. Figure 1.28-a presents the thickness of the individual Fe layer ( ) and Sm-content in the 5 layers as a function of the multilayer index n [START_REF] Neu | Fully Epitaxial, Exchange Coupled SmCo 5 /Fe Multilayers With Energy Densities above 400 kJ/m 3[END_REF]. In Figure 1.28-b it is possible to observe a reversible exchange spring behavior for n=1 ( = 23 nm). For ≥ 2 the layers are completely coupled, the kink pre- data of remanence and coercivity. From [START_REF] Neu | Fully Epitaxial, Exchange Coupled SmCo 5 /Fe Multilayers With Energy Densities above 400 kJ/m 3[END_REF] sented in n=2 was explained as di erence in the coercivity of the 5 lms. When increases the coercivity of the 5 layers starts to reduce due to the coupling with the soft layer and the Sm depletion (observed in Figure 1.28-a). On the other hand, an enhancement of the remanence is observed compared with the pure 5 lm [START_REF] Neu | Fully Epitaxial, Exchange Coupled SmCo 5 /Fe Multilayers With Energy Densities above 400 kJ/m 3[END_REF]. The authors also report that the interdi usion of Co into the Fe layers leads to an increased saturation polarization in the interdi used zone due to the even higher magnetic moment of the Fe-Co alloy.

A very high energy product was also achieved by the insertion of Ta as spacer layer in a to 0.95 T. Despite this, the remanence decreases and a kink appears around 0 T in the in-plane measurement. This behaviour is similar for the lms with spacer layer of 10 nm to 250 nm, with a smooth magnetisation decrease in the positive eld and a kink in the in-plane curve near to zero-eld. On the other hand, with Ta = 400 nm, the coercivity is recovered to 1.34 T while the two-phase behaviour is also visible in the out of plane measurement. Finally, Figure 1.29-h shows the coercivity evolution as a function of the thickness of the Ta spacer layer with the benchmark of the single layer lm.

In order to understand the di erences between M(H) loops in-plane and outof-plane, micromagnetic simulations were carried out showing that the magnetostatic interaction was responsible for the coupling once the spacer layer was introduced. In other words, the exchange coupling, as a short-range interaction, decays with a few nanometers of spacer layer, however the thin lm under a out-of-plane magnetic eld is coupled by magnetostatic energy. When the spacer layer reaches 400 nm even the dipolar interaction is not enough to keep the magnetic coupling between hard and soft layers [START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF].

The investigation about spacer layer and coupling between hard and soft

Thesis context

The achievement of a high performance magnetic hard-soft nanocomposite will depend on three pillars schematized in Figure 1.32, namely (i) the nanometric size of the soft phase, (ii) the quality of the interface between soft and hard phases and (iii) the proximity of soft and hard phases. However, for experimental or even more fundamental reasons, it becomes clear that these three constraints can hardly all be satis ed at the same time and that a subtle trade-o between all three will have to be made.

Hard-soft nanocomposite magnets

Small dimensions soft phase The limitation of the soft phase dimensions to tens of nanometres will require a ne optimization of size, shape and distribution of soft elements to prevent a deterioration of the hard phase. On the other hand, the reduction in the size of the soft phase may favour its di usion into the hard phase, ruining the interface and creating a gradient of composition. A possible solution to face such a challenge would be the introduction of a di usion barrier, as reported in studies involving multilayer thin lms. However, this strategy, in turn, would impair exchange coupling between the phases, considering that exchange interactions take place on the scale of a few nanometres.

Sharp interface

Phases in intimate contact

Considering the great potential of hard-soft nanocomposites for applications in the eld of permanent magnets, it is crucial to tackle the mentioned technological bottlenecks by improving our understanding of the critical parameters in such systems. While the improvement of metallurgical manufacturing routes is essential for large-scale production of nanocomposites, the fabrication of model thin lm based samples that can be compared to micromagnetic models will be extremely is relevant.

The work presented in this thesis is located at the intersection between the model samples fabricated by thin lm deposition methods and the use of nanofabrication (e-beam lithography) (Figure 1.33). The combination of these two techniques, allows for the exploration of how the distribution of a nanometric soft magnetic phase into a hard magnetic matrix will impact the magnetisation reversal of the nanocomposite.

In the framework of this thesis, nanocomposite samples were produced and 40 thoroughly characterized structurally and magnetically. The structural information was used to provide precise information for micromagnetic modelling. The results from experimental characterization could then be compared to the results from numerical simulations. The knowledge accumulated in this process will feed into attempts to map the critical parameters for the further developments of hard-soft nanocomposites.

E-beam lithography

Nanofabrication is used in many elds, including electronics, photonics, magnetism and life sciences. The emergence of electron beam lithography (EBL), during the 1980s, was an important step in this domain. EBL uses an adapted scanning electron microscope with a high voltage gun used as an extremely sharp pen able to draw a nanometric pattern in a wafer coated with an energy-sensitive polymer (i.e., polymethyl methacrylate -PMMA) [START_REF] Vieu | Electron beam lithography: resolution limits and applications[END_REF]. After this the resist is developed and the sample is suitable for further processing such as reactive ion etching, selective ion implantation, electroplating, and physical vapor deposition (PVD), the last one will be explored in this work. Although all the described steps are critical to obtaining suitable lithography, the essential part is the exposure chamber. This system contains many subsystems to control complicated tasks, and they are described in Figure 2.2 [START_REF] Groves | Electron beam lithography[END_REF].

Starting from the hardware part, the electron gun, from where the electrons are emitted, can be made by di erent technologies such as thermionic or eld emis- sion. The most common electron gun for this application is called a thermal eld emission cathode. These cathodes are heated up to high temperature, avoiding gas absorption leading to stable operation with a small size of the source. However, the quality of the source limits the lithography resolution; the nal result also depends on the electromagnetic lens system that focuses, blanks and corrects the beam along the column. Additionally, the system needs a high precision stage to keep a precise positioning between the beam and the sample. The high vacuum system is indispensable in the electronic beam technique, requiring an airlock to load and unload the sample without interfering with the column vacuum.

Before starting the lithography, it is necessary to transfer the pattern data and use speci c software to convert that design into commands for the e-beam scan of the sample. All this framework is connected with a feedback process and the input of detectors and the stage positioning system. It is necessary to optimize each step described in Figure 2.1 in order to get suitable lithography. The following list describes these optimizations: Spin coat resist: The speed, acceleration, time, and polymer concentration determine the thickness obtained. Regardless of the parameters used, the resist must be baked in order to evaporate excess solvent. Usually, the resist thickness must be three times that of the deposited lm. Additionally, the choice for PVD establishes the number of resist layers necessary to have good lift-o . Figure 2.3 shows the different pro les of lm deposition on top of a patterned resist, for lms deposited by evaporation and sputtering, respectively [START_REF] Chen | Nanofabrication by electron beam lithography and its applications: A review[END_REF]. The di erent deposition methods have di erent directionality (evaporation is unidirectional while sputtering is multi-directional), which can render di cult the solvent penetration during the lift-o process. The combination of two layers of resist which have slightly di erent sensitivity can overcome this problem, generating a prole con guration called an undercut (Figure 2.4 ). This pro le permits the solvent to penetrate between the resist and the thin lm. Exposure: Some preparation steps consist of designing the pattern, transfering the le and converting for the e-beam machine using the correct parameters as mean-eld and sub eld (determines what is going to be scanned by the beam and what is going to be moved by the stage). Besides this, it is necessary to prepare the column to align the beam, correcting the focus and astigmatism. These correction procedures and positioning and sample alignment changes for each system. To allow this procedure, in the present study, alignment marks were fabricated prior to e-beam lithography.

Once all the parameters mentioned above are adjusted, the exposure can start. If it is the rst time the pattern is being performed with this resist and substrate preparation, it is necessary to do a dose test. The dose corresponds to the product of the exposure time and e-beam current divided by the exposed surface. The choice of the right dose is necessary to grant the resist polymer modi cation in the right places. An underdose can prevent the resist from being removed in the development step while an overdose can prevent the resist around the exposure area from being removed during the lift-o .

Development:

The developer is a solvent that dissolves only the resist modi ed by the e-beam. The development time is a very critical parameter, that must be optimized in order not to let resist residues or overreact with the exposed areas. It is necessary to wash the sample with a conventional solvent, such as isopropyl alcohol, to stop the development process.

Deposition: This step consists of the thin lm growth, covering the resist and the developed areas. As described in the spin-coat section, the choice of the deposition method is going to determine the choice of resist parameters. It is crucial to determine the deposition rate and be sure of the deposited thickness.

Lift-o :

The goal of this process is to remove the resist below the deposited lm. The resist and the temperature must be compatible with the resist and thin lm.

The time should also be optimized and ultrasound cleaning steps are also needed.

The samples developed in this project were fabricated in the Institut NEEL cleanroom facilities, including the e-beam exposure processed in the Nanobeam NB5.

Magnetron Sputtering

Sputtering is the result of energetic ion collisions with a chosen material, named the target,that acts as a cathode, in order to remove atoms or molecules that are then deposited on a substrate that acts as an anode. In this work, a magnetron sputtering in direct current (DC) and radio-frequency (RF) modes was used, and it is going to be described in more detail.

The sputtering process usually happens in a previously evacuated vacuum chamber (about 10 -9 bar). An inert working gas, typically argon, lls this chamber, and it is the medium where the glow discharge is started and maintained. Accelerated free electrons will ionize argon atoms; hence, the + ions are going to be attracted by the target (cathode). The collision of + ions with the target results in the ejection of atoms through momentum transfer. These atoms travel through the plasma and are deposited on the anode, where a substrate is placed, and the lm grows. nets below the target generate a magnetic eld con guration that traps the electrons around it and increase the e ciency of Ar ionization. In the rst con guration, the target is connected with a power source (DC or RF), and this promotes the sputtering process and the thin lm deposition. In the second con guration (Figure 2.6), the substrate is connected to an RF power source that is going to generate a self-bias on the substrate even if it is not conductive. This negative self-bias happens thanks to an impedance match between the substrate and the source. It will attract the Argon ions and give rise to an etching process, removing material previously deposited on the substrate and cleaning the surface for the next steps.

A magnetron sputtering deposition or etching requires the evaluation of some interdependent parameters such as base vacuum pressure in the chamber, Argon pressure and ow rate, power applied in the target (or substrate in case of etching), the distance between the target and substrate, and the deposition/etching rate. The system used to fabricate the samples presented in this work is available at Institut NEEL.

The magnetron sputtering machine, named DP850 was produced by Aliance Concept. It has a base pressure from 10 -6 to 10 -8 bar, can hold eight targets (diameter of 3 inches) that can be powered by DC or RF sources. Additionally, there are two substrate holders (diameter of 4 inches) with the possibility to be heated (up to 800 ), with variable distance from the target (5 to 10 cm) and etched when connected to an RF source.

E-gun evaporator

Evaporation is considered one of the simplest and best established deposition methods. It consists of heating a target material and its vapor deposits over a substrate. In the case of an e-gun evaporator, an electron beam is directed at the target crucible and transfers energy to heat it. Figure 2.7 shows the schematic of a vacuum chamber in which is placed the target and the substrate. The system has a tungsten lament as an electron source, and a coil system bends the e-beam to reach the target.

Tube furnace and Rapid Thermal Annealing

Sample heat treatment was performed in a homemade tube furnace. This furnace consists of a tube cavity enclosed by heating coils. It works from 200 to 1250 , with a three heating zone system, each one with three PID controllers. The tube has a diameter of 70 mm of diameter and 500 mm long heating zone, with ± 2 . It is equipped with a load lock and vacuum system that can reach pressure of 10 -10 bar.

All the equipment was designed and built by Richard Haettel. The maximum sample size is 6 × 10 2 .

Firstly, the temperature is set, and while it stabilizes, the sample is placed in the load lock. Once the desired vacuum is achieved in the load lock, the sample can be inserted in the furnace for a given time. Once removed to the load lock, the sample cools naturally.

Rapid Thermal Annealing (RTA) was also used for the ex-situ heat treatment of some samples. The process was carried out in the RTP JetFirst 100 made by SEMCO.

In this system a halogen lamp illuminates and heats the substrate under an inert atmosphere (Ar) or under vacuum (10 -8 bar). The temperature control is done using a thermo-couple touching the back surface of the sample substrate. The heating process as well the cooling process can be controlled using ramp functions from 1 ∕ to 400 ∕ .

RTA has as advantages the heat treatment of 4 inch wafers and the control of the heating and cooling ramps. On the other hand, the heat treatment carried out in the tube furnace is more reproducible for small samples and has better vacuum system.

Transmission Electron Microscopy (TEM) 2.5.1 Transmission Electron Microscope and measurement

The discovery of the wave behaviour of electrons, at the beginning of 20th century, opened the path for the formulation of de Broglie's equation (Equation 2.1).

From this equation, it is possible to estimate the electron wavelength ( ) in for a given energy ( ) in eV.

= 1.22 1∕2 (2.1)
Considering the typical energy of an electron beam in a TEM, which is approximately 100 keV; the result is a ∼ 4 . This wavelength shows the great potential to use electronic microscopy, even though this value is not directly translated in resolution due to problems with lenses and aberrations.

This technique requires careful sample preparation (Section 2.5.2) in order to make the specimen thin enough to be transparent for the accelerated electrons.

The interaction between the incident beam and the specimen generates a variety of signals that are described in Figure 2.8-Left. In this work, the combination of Characteristic X-rays (Energy-dispersive Spectrometry -EDX) with Scanning Transmission Electron Microscopy (STEM) was used to obtain chemical maps of nanometric samples. Energy-loss spectrometry (EELS) can also be used to acquire chemical information. Figure 2.8-Right depicts a cross-section view of a TEM, including the electron gun, the condenser system, the objective system, the projector system, and the image recording system. Although not shown in this picture, the instrument also needs a sophisticated vacuum and cooling systems. The instrumentation starts from the electron gun, the basics of which where previously described in section 2.1. The next system is also called the illumination system, where several condenser lenses make the beam either parallel or convergent. The sample holder/stage and the objective system are indispensable parts of the microscope, the rst because of the possibility to move and align the sample, and the latter for all the focus and image formation adjusts. Finally, the projector lens redirects the beam to the uorescent screen or the image recording system (usually a CCD camera in the column).

The details given in this section provide a basic overview of this powerful tool for structural and chemical characterization. The operation of this complex system requires constant practice and careful alignment using several lenses to minimize aberrations and distortions. The interpretation of the images is also a great challenge, and usually, it is not straightforward. Additional information can be found in several textbooks [START_REF] Williams | Transmission Electron Microscopy[END_REF]. Some of TEM images presented in this thesis were obtained at Institut Neel using a CM300-Phillips at 300 kV with Gatan CCD camera operated by Thibaut Devillers and me. The other images were acquired at CEA-Grenoble by Aurélien Masseboeuf and Hanako Okuno using a Titan Themis operated at 200 kV, probe corrected tted with a SuperX detector for EDX analysis.

Sample preparation

A TEM sample must be electron transparent and a representative part of the investigated material. There are many techniques to prepare a suitable TEM sample; however this choice depends on the kind of material and the information that is pursued. Ideally, the sample preparation should not generate artefacts that a ect the measurement. In this section, two methods are going to be described for continuous thin lm and patterned samples, respectively. Figure 2.9 illustrates the TEM preparation for cross-section observation of a continuous thin lm. The procedure consists in:

1-Take a piece around 25

2 of the sample.

2-Cut into two similar parts.

3-Glue the two pieces with lm surface facing each other. This "sandwich" is prepared using epoxy resin.

4-Using a diamond saw, cut it in lamellas around 700 thick.

5-Using diamond paper and a precise polishing machine, polish the lamella on both sides until reaching a thickness of 30 . Usually the lamella is glued with wax to a at Pyrex surface.

6-Glue a standard TEM copper ring on top of the lamella using the epoxy resin and then unglue from the Pyrex using an acetone bath. Introduce the copper ring with the lamella in the Precision Ion Polishing System (PIPS). This equipment allows to nish the polishing process with Ar ions reaching the sample at grazing incidence (3 KeV ±7 ) until it opens a hole in the centre of the lamella. The pro le view of this hole, reveals a very thin region around it. This is the interesting observation region as it is thin enough to be crossed by the TEM beam. Selected samples were prepared using the Focused Ion Beam (FIB) approach.

The equipment used works similarly to a Scanning Electron Microscope (SEM) but includes an ion mill tool and a gas injection system. The main ion used is Ga+, and it can produce a well-controlled beam. for the samples analyzed in this thesis includes the following steps:

• Deposit a protective layer using ion-beam induced deposition. The gas injection system provides the material to cover the targeted surface. Pt is the chosen element for this layer, but other elements such as C and W can also be used.

• In order to bulk-out the material around the targeted area, it is necessary to dig trenches until a thin cross-section lamella stands alone.

• A U-Cut is performed, liberating the lamella from all the side connections.

• The lift-out procedure is executed by attaching a probe using static electricity or depositing a thin layer to glue them.

• The mounting step consists in bringing the sample attached to the probe to the TEM Copper sample holder. A deposition is necessary to attach the sample to the sample holder.

• An additional thinning step is necessary to reach the target thickness of around 50 -100 nm in the desired area.

Scanning Electronic Microscopy

Scanning electronic microscopy (SEM) is a well-established technique to characterize di erent materials. In this microscope, an electron beam replaces the light source, and it is possible to explore electron-matter interactions and to investigate di erent aspects of the material such as topography and chemical composition.

The underlying architecture of an SEM consists of an electron gun (tungsten lament, 6 , FEG) and a column with di erent coils used to condense, focus, and move the beam in the scanning process, all of this under high vacuum.

The rst important aspect is the penetration of electrons into the sample which is determined by the electron energy (acceleration voltage) and the material itself, resulting in an interaction volume. The energy carried by this primary beam can be lost into inelastic scattering, emitting secondary electrons (SE). The SE created close to the surface can escape into the vacuum, and their detection provides information about the surface structure that provides an image with topographical contrast.

A backscattered electrons (BSE) signal is detected from electrons that had an elastic scattering and it is proportional to 2 . Hence, the image built by the BSE signal provides qualitative information about the chemical composition of the specimen.

Another aspect of SEM explored in the project is the composition analysis based on x-ray photons emitted by the specimen as another result of the electronmatter interaction. The Energy-dispersive X-ray spectroscopy (EDX) allows the estimation of material composition for a wide range of chemical elements.

The Zeiss Ultra Plus Field Emission Scanning Electron Microscope (FESEM)

and SEM LEO 1530 (FESEM), with a typical lateral resolution of 1 nm, operating in 5 keV (for images) and 20 keV (For EDX analysis), were available for the development of this project.

Atomic Force Microscopy -AFM

The basic idea behind AFM is the use of a sharp tip close to the specimen surface, and from this interaction, extract information about the surface properties with nanometric resolution. This technique has its origin in Scanning Tunneling Microscopy (STM), with the improvement that it could be used not only with a conductive material but with insulating material as well. In STM the tunneling current between tip and sample is the measured quantity, while in AFM the key is the precise quanti cation of the force between the tip and the sample.

The basic setup for an AFM system is depicted in Figure 2.11-Left. The tip at the end of a cantilever interacts with the sample, and the cantilever bending is monitored by a laser re ection on a position-sensitive diode (PSD). This system of detection based in beam de ection is the most used in commercial AFM and has a typical detection limit of ∆ = 0.2

. The signal measured by the PSD is going to be the input for a feedback loop that controls the scanner and the cantilever. Depending on the operation mode, an excitation of the cantilever can also be applied. The position of

x,y scanner combined with the de ection signal are treated to form 2D image of the The force between tip and sample can be measured in a static mode using the deflection of the cantilever on which a tip is mounted. The cantilever acts as a spring and its deflection is proportional to the tip-sample force. If the stiffness of the cantilever spring k (spring constant) is known, the force between tip and sample can be determined by measuring the bending of the cantilever. Hooke's law gives F = -kz, where F is the force and z is the distance the cantilever spring is bent relative to its equilibrium position without the sample present. Figure 1.6 shows a typical silicon cantilever used as a force sensor in atomic force microscopy with a sharp tip (probe) at its end. The deflection of the lever is measured for instance using a laser beam reflected from the back of the cantilever into a split photodiode as shown in Fig. 1.7.

In the static mode of operation, the surface contour is mapped while scanning by changing the z-position of the tip in such a way that the tip-sample force and, correspondingly, the tip-sample distance are kept constant. The tip position maintaining a constant tip-sample distance is recorded as topography signal. In other words: the feedback loop maintains a constant force between the tip and the sample i.e. constant bending of the cantilever, as shown in Fig. 1 force interacts unless they are long-range forces (e.g., electric, magnetic), (ii) closer distance leads to attractive force, and (iii) very small distances generate strong repulsive force [START_REF] Voigtländer | Atomic Force Microscopy[END_REF]. The choice of a interaction regime will de ne the system operation mode.

Atomic force microscope (AFM) can also be classi ed as Static or Dynamic mode concerning the cantilever excitation. Besides this, the predominant force between the tip and sample determines if the system operates in contact or non-contact regime, relating to the sketch shown in Figure 2.11-Right. For the Static Mode, the cantilever is described as a spring, and Hooke's law ( = -) relates the cantilever sti ness (k), the force between the tip and the sample (F) and the cantilever bending with respect to the equilibrium position (z). Based on this model a set-point of the force tip-sample is determined and it is related to the cantilever de ection measured in a PSD. The topography image is formed from the contour at constant tip-sample force that is usually set at the contact regime.

In the Dynamic mode, the cantilever base is excited by a piezoelectric driving at a frequency ( ) close to its resonance frequency ( 0 ). During the scanning, while it interacts with the sample, the resonance frequency changes and amplitude ( ) is modi ed, that must be measure together with the phase ( ). If the excitation oc-curs in a small amplitude limit the AFM is operating in Amplitude Mode. In this mode the change in amplitude varies linearly with the tip-sample force. In other words, the tip-sample interaction can be described as an additional spring in the oscillator system. Figure 2.12 compares the excitation curve of amplitude and phase for a free cantilever and under tip-sample interaction.

1.0

1.0

Free cantilever Tip-sample interaction Figure 2.12: Comparison between amplitude and phase for a free cantilever and cantilever under tip-sample interaction.

The Tapping mode is also called intermittent contact mode because the amplitude excited in the cantilever in this mode is large (50 nm), which results in operation in the contact and non-contact regime. The driving frequency is very close to the resonance. Although there are many similarities with the Amplitude Modulation, in this mode, the linear approach is not applicable, once an anharmonic tip-sample force leads to the coexistence of two vibrational modes. The most considerable disadvantage of this method is that there is no easy description of the tip-sample interaction.

However, the amplitude variation has a linear relationship with the tip-sample distance, and this can be used as a clear signal for the feedback loop. This mode is the most applied under ambient conditions with the advantage of being a contact mode without risk of damaging the sample surface. The AFM topography images presented in this thesis were acquired in Tapping mode.

An alternative is the Frequency Modulation mode that is used when the sys-tem Q-factor is high, which happens when the measurement is performed under vacuum. In this mode, the cantilever oscillates at the resonance frequency, the amplitude is kept at a constant value, and a phase-locked loop (PLL) uses the measured frequency to control the tip-sample distance via a z-feedback loop.

Magnetic Force Microscopy -MFM

MFM was demonstrated for the rst time in 1987 [START_REF] Martin | Magnetic imaging by ''force microscopy'' with 1000 Å resolution[END_REF] [START_REF] Sáenz | Observation of magnetic forces by the atomic force microscope[END_REF] and it has an intimate relation with AFM. The setup and instrumentation are the same as the used in AFM, except for the probe that must be made or coated with a magnetic material.

Essentially, this tip is going to be sensitive to the force generated by the interaction between its magnetic moment and the sample stray eld at a given distance. However, this is a three dimensional force and the cantilever geometry only allows de ection in one particular direction, which can be described as interaction with a force gradient.

The cantilever de ection measurement, as in the AFM, is key, and these techniques can be easily combined (Figure 2.13).

x, y scanner x, y scanner x, y scanner As depicted in Figure 2.13, the rst pass, operated in tapping mode for example, obtains information about the topography. The probe is then lifted to a chosen distance (usually dz 50 nm), where the van der Walls forces are negligible compared to long range such as the magnetic force. The second pass can be divided in two categories: DC and AC. In the DC mode, the dz is kept constant and the cantilever is static, being de ected by the action of magnetic force. In the AC mode, the cantilever is excited around a resonance frequency. The interaction with the sample stray eld results in a change in the amplitude and a phase lag. When a color code is associated with the signal obtained from the magnetic interaction, the magnetic domain structure can be visualized when it is plotted as a function of x,y positions.

MFM has a spatial resolution of tens of nanometers and sensitivity of 10 pN, does not require a di cult sample preparation and has exibility to work in di erent environments. Besides these advantages, it is possible to apply an in situ magnetic eld to investigate di erent magnetisation states and explore a variety of magnetic coatings, changing the moment and coercivity of the tip [START_REF] Kazakova | Frontiers of magnetic force microscopy[END_REF]. the reversal of the lower 5 layer (Figure 2.14-e-f) and the complete reversal of the trilayer (Figure 2.14-i) [START_REF] Neu | Imaging the Magnetization Processes in Epitaxial Exchange Coupled SmCo 5 /Fe/SmCo 5 Trilayers[END_REF]. This images can be related with the global magnetic measurements and support the comprehension of exchange-spring behaviour.

In-situ pulsed magnetic eld

Motivated by the idea of changing the remnant states of samples under observation in the MFM and study the magnetisation reversal process, an in-situ pulsed magnetic eld setup was employed. This setup was initially developed at Institut Neel The new designed sample holder is attached at the microscope and has a good mechanical coupling. It needs to be made of insulating material to avoid any risk of electrical discharge between the coil and the microscope, and it is necessary to ground the sample to avoid charge accumulation. As with the magnetic force, the electric eld gradient generates a long range interaction, which disturbs the measurement.

The setup works as shown in Figure 2.15, where the sample holder has two positions. The lower position, where the sample is positioned precisely in the middle of the coils, then it is moved up in order to engage and be scanned. With the current coils, it is possible to apply 3 T in plane and 6 T out of plane with a resolution of 20 mT.

Scanning Magneto Optical Kerr E ect

The scanning polar MOKE system, used for preliminary magnetic characterization in this work, was developed by Andre Dias at Institut NEEL. This equipment allows a high-throughput measurement of hysteresis loops with a large applied eld (10 T). The Kerr e ect corresponds to a change in polarization of light re ected on a magnetic material. The e ect can be explored in di erent geometries, and the one chosen for this system is the Polar Kerr e ect. It means that the linearly polarized light reaches the surface with normal incidence, and the material is also magnetized in the perpendicular direction. Usually, the polarization rotation after the re ection is less than a degree and in some cases there is also an ellipticity component. of the Sm being off-set by 3 cm with respect to the centre of the Co base. Deposition was made on thermally oxidised Si substrates of diameter 100 mm and Ta was deposited as both buffer (10 nm) and capping (5 nm) layers. The substrate holder was stationary during deposition. Films were deposited at room temperature and subsequently annealed ex-situ at 450 C for 10 minutes.

Local hysteresis loops were measured using a scanning polar MOKE system schematised in Figure 1. The system is equipped with a bipolar pulsed current source coupled with a Cu-coil of inner (outer) diameter ⇠3 (10) mm. The length of individual field pulses is of the order of 16 µs, and the delay between positive and negative field pulses is about 10 ms. The centre of the coil is hollow, to allow the incident and reflected light beams to pass through. The film under measurement is scanned in-plane below the coil using an x-y stage (minimum step size = 2 µm) and the coil to sample distance is set to 100 µm. Full details of the scanning MOKE system will be published elsewhere.

To characterize the magnetic properties of the compositionally graded SmCo film using our MOKE system, we set the system to measure every 5 mm in the x and y directions and adjusted the charge of the capacitors to provide an effective magnetic field of 6 T at the level of the magnetic layer. While maximum fields of 10 T are achievable at the level of the substrate, limiting the field to lower The schematic shows the trajectory of the incident beam and re ected beam, from the laser to the detector. The wafer with the deposited thin lm is positioned on an XY stage that allows us to scan the sample surface. The light goes through the bipolar coil system that can be moved close to the surface using a Z stage. The re ected light goes through a Wollaston prism where it is separated in its orthogonal polarization components. The rotation angle related to the Kerr e ect can be then recovered thanks to the di erence in signal from the two photo-detectors positioned to capture the intensity of each component [START_REF] Dias | Preparation and characterisation of compositionally graded SmCo lms[END_REF].

Vibrating-sample magnetometer and Superconductive Quantum Interference Device

This section described the equipment used for the global magnetic characterization of the samples. As this description combines two techniques, the rst step is to explain the Vibrating-Sample Magnetometer (VSM). The sample is immersed in a uniform magnetic eld, and then sinusoidally vibrated [START_REF] Smith | Development of a Vibrating-Coil Magnetometer[END_REF]. According to Faraday's induction law, this vibrating sample acts as a magnetic dipole and can generate electromotive force that can be picked up by a wound coil of wire. In other words, the voltage generated in this pick-up coil is going to be proportional to the sample magnetisation.

In the simplest VSM models, there is an electromagnet that generates the uniform eld, a motor that is coupled with the sample holder, a pick-up coil system, and a lock-in ampli er that has as input the sinusoidal signal associated with the sample movement and as output the voltage proportional to the sample magnetisation. However, this system has sensitivity around 10 -6 emu and can reach a maximum applied eld of around 3 T.

In order to overcome the applied eld typically limitation, the electromagnet can be replaced by superconducting coils that can reach 10 T. They are cooled to cryogenic temperatures during the operation to guarantee no electrical resistance state in their wires. Thanks to this property, larger electrical currents can be applied, generating the larger applied magnetic eld.

To achieve higher sensitivity, the Superconductive Quantum Interference Device (SQUID) is exploited. A SQUID uses the Josephson e ect to measure small changes in magnetic ux. The Josephson e ect concerns tunneling of Cooper pairs through an insulating barrier placed in a superconducting material. The superconducting current crosses the resistive barrier without a voltage drop when it is smaller than the critical current. Figure 2.17 shows the current vs. voltage curve in a Josephson tunnel junction. When a bias current ( ) is applied, the operating point can be placed between the superconducting and resistive behaviours if a magnetic ux is coupled with the SQUID loop, depending on the ux direction and intensity a proportional screening current is created inside the loop. In the case where is bigger ).

Reference 2f

Lock-in V includes detection coils based on a 2 order gradiometer that is going to capture the magnetic ux generated by the oscillating sample. An essential step of this kind of measurement is to center the sample in the gradiometer, using a linear motor, to get the highest signal. This signal is going through a ux transformer to be coupled with the SQUID loop. Finally, the measured voltage is associated with the measured magnetisation.

A MPMS3 SQUID magnetometer produced by Quantum Design was used to carry out the global magnetic measurements in this thesis. This equipment has sensitivity of 10 -8 emu, temperature range of 1.8 K to 400 K and maximum applied eld of 7 T.

Measurement and corrections

The measurement was carried out in samples prepared in Silicon substrate with 100 nm of 2 (Thermal Oxidized layer). This substrate has a diamagnetic contribution that can be corrected according to Equation 2 This chapter describes the protocols developed for sample fabrication, including all optimization needed to obtain our hard-soft nanocomposites. It is important to note that this is the rst time that this fabrication approach is used. On the one hand, this opens new possibilities, on the other hand, it brings the need for extra care and rigor in execution and characterization.

The general strategy is shown in Figure 3.1, where the soft magnetic nanostructure is fabricated by e-beam lithography, and the hard magnetic matrix is deposited on top afterwards. The nanostructures are deposited using e-gun evaporation, whereas the matrix is deposited using magnetron sputtering. This approach allows each material to be developed in parallel, increasing the dynamism and getting faster to the nal goal. However, the most challenging step is to combine both techniques considering that all the materials involved are sensitive to oxidation. A combination of Au protection followed by a surface recovery with Argon etching was thus implemented. This is the key point to combine both techniques, e-beam lithography and sputtering deposition, and produce nanocomposite samples.

The Figure 3.2 shows the process owchart that is going to be discussed in detail in the following sections.

Nano-rods

The soft magnetic nanostructures, produced by e-beam lithography, are curcial for the development of the hard-soft nanocomposites. As described in Chapter 1, the dimensions of the soft magnetic phase are the critical parameter for the coupling between the two phases. The optimal dimensions are obtained from micromagnetic simulations, based on the domain width of the hard phase that are usually tens of nanometers. With e-beam lithography, as described in Chapter 2, it is possible to produce structures with these characteristics, but a bottleneck of these technique is the was to optimize the design and make it reproducible. In this step, the dimensions, the resist thickness, the electronic dose, and the bu er layer behaviour, were systematically varied until an optimal condition was achieved. Besides providing samples for local measurements such as MFM, the small surface was used to explore the minimum width achievable with this e-beam system.

Moving on, the rst attempt to get a large surface was not successful, as can be observed in detail with the bad lift-o and gnarled rods obtained by the continuous surface attempt. Finally, a patterned surface seemed more promising to achieve larger surfaces without compromising the lift-o and rod dimensions.

Figure 3.5 shows the nal choice for the nano-rod arrays and their respective dimensions.These four di erent arrangements were chosen to to explore low versus high density, shape anisotropy, and small versus large width. It is important to point out that these are not optimized structures with respect to maximized remanence and energy product. The idea is to explore the limits of electronic lithography techniques and produce well controlled samples that could be modeled by micromagnetic simu-w=24 nm l=200 nm d=200 nm w=24 nm l=200 nm d=52 nm w=30 nm l=400 nm d=80 nm w=120 nm l=400 nm d=130 nm This rectangular shape is intentionally chosen to know the orientation of the nanorods with naked eyes. The choice of the individual area is related to the limits imposed by lithography, where the exposure of a micrometric area avoids the e ects of prox-imity and facilitates the lift-o . In addition, this choice will determine a micrometric surface for the nanocomposite samples that will, consequently, be suitable for local measurements (MFM) and for micromagnetic models. On the other hand, the choice of total surface is related to the guarantee of a minimum signal for the global magnetic characterization by VSM-SQUID. Although e-beam lithography is considered as a slow method for this kind of fabrication, one total surface (54 thousands arrays units) is written in one hour. Figure 3.7 shows a the tilted view, displaying the topography and the absence of any resist residues. Summarizing the processed described, three di erent materials were used to prepare 10 nm thick nano-rod arrays. 40 60 and Co, as soft magnetic material, and Pt as non-magnetic material. The two rst were covered with Au 3 nm layer to prevent oxidation.

Hard magnetic phase

Once the development of the nanostructures has been described, it is time to address the optimization of the hard phase in which the soft nano-rods will be embedded. The owchart depicted in Figure 3.8 shows the process used to select the hard magnetic phase best adapted to making nanocomposites. The rst criterion to be met was the satisfactory magnetic properties, i.e. single phase behaviour and high coercivity. These properties must be reproducible in lms thinner than 50 nm. The thickness limit criterion eliminated NdFeB thin lms and the magnetic characterization of these lms are discussed in section 4.2.1. The second criterion established was maintaining the magnetic properties when the lm was micro-patterned (5 × 5 2 )

and nally, if these micro-patterns could be thinner than 25 nm. Both, the nanofabrication process and the annealing conditions, had to be optimized in order to get the properties suitable for the nanocomposite fabrication. The details of these processes as well as the results obtained for each material, are going to be described in Chapter Even if the magnetic properties are the critical criterion for choosing the phase, in this chapter, the focus will be on describing the manufacturing steps. Details on the magnetic characterization of the samples will be discussed in the Chapter 4.

NdFeB thin lms

NdFeB thin lms were prepared by magnetron sputtering deposition using two distinct strategies. The rst one consisted in investigating the best magnetic properties that could be obtained from the deposition system (as function of the target, the deposition rate, the deposition temperature and the annealing conditions). In the second strategy, the lms were produced with the constrains imposed by integration with the nano-rod fabrication, such as oxidation of the bu er layer and the impossibility of heating the substrate during the deposition. Both processes were done with the same NdFeB single alloy target, in which composition was 36.2 % of Nd, 62.4 % of Fe and 1.4 % of B. from the special sample holder, used to t a 5 cm (2 inches) wafer and allowing it be directly exposed to the infrared lamp that heats the substrate. This ensured a homogeneous and reproducible heating process and stable deposition temperature. As described in the rst strategy box, a two-steps annealing process was employed, optimizing in a range of deposition and post-annealing temperatures. At this point, the annealing was performed using Rapid Thermal Annealing (RTA) and the thin lm schematic shows the sample architecture. On the other hand, in the second strategy box, the lms were deposited at room temperature and the impact of bu er layer thickness was investigated, after it was submitted to natural oxidation. The Tube furnace and RTA were used for the annealing.

FePt thin lms

The FePt thin lms were developed, mainly by Yuan Hong, in the framework of a joint study of graded composition lms (Hong et al., in prep) and coatings for high coercivity MFM probes (Annex). The idea of studying compositionally graded lms was to nd the best composition and annealing conditions to give high coercivity.

My contribution to this study concerned structural (TEM and AFM) and magnetic characterizations (VSM and MFM). The coating of MFM probes and the hard phase for the nanocomposite require a homogeneous lm with the equiatomic composition that leads to 1 0 -phase. The rst step towards homogeneous lms was the target design with the magnetic properties investigation via scanning MOKE. Figure 3.10 presents a schematic of ve target designs. The samples were submitted to the which led to the use of the bilayer resist approach, using PMMA/MMA and PMMA layers. It is necessary to improve the original bilayer recipe to match the resist thickness with the deposited thin lm and guarantee a clear lift-o without lateral "wings," or other resist residues. Figure 3.13 demonstrates an evolution of this process to get cleaner and sharper micro-patterns, passing through samples that had lateral residues and rough surface. in other words, it was possible to detect a soft magnetic phase even though soft magnetic nano-rods were not included in the material. The presence of a soft phase would be extremely problematic for the hard-soft nanocomposite analysis, once the main goal is to investigate how the hard magnetic phase is a ected by the di erent soft phase arrays. A hard phase micropatterned FePt lm with only hard magnetic phase is the benchmark to be compared with the other samples. Because of this, three di erent shapes of hard micro-pattern, treated by di erent annealing conditions, were tested to obtain the best and most stable magnetic properties. This approach will be detailed in the magnetic characterization chapter. Figure 3.14 shows the chosen shapes in which corner curvature radius was modi ed from the original "sharp" edge (r = 30 nm), going through r =1 and ending in a circle with r = 2.5 . This work was developed in collaboration wit F. Orlandini-Keller. properties of the hard magnetic phase, benchmark samples of micro-patterned FePt were produced without nano-rods inclusions and with non-magnetic nano-rods (Pt).

The following chapter will present the properties of the building blocks for the hardsoft nanocomposites.

Soft magnetic nano-rods

The development of nano-rods was described in Section 3.1, including a number of di erent steps with the ultimate goal of large patterned surface with enough magnetic signal to be characterized by VSM-SQUID. The result of this optimization was the fabrication of FeCo and Co nano-rod micrometric arrays repeated over a milimetric surface. These nano-rods were coated with Au to avoid oxidation.

same protection strategy was adopted in this work.

The nano-rod arrays were also characterized by AFM and MFM, the probe chosen was a low coercivity CoCr(20 nm)/Pt homemade coating with lift height of 15 nm. Figure 4.2 depicts the topography, the virgin magnetic state and the remnant state after application of a in-plane eld (3 T -along the rods). The saturated state remnant after the 3 T applied eld evidences that no rods ipped at 0 T and reinforce the presence of contamination to justify the shoulder presented in Figure 4.1-left and right. The study of how the magnetic moments are organized in the virgin state is of interest in itself and a number of works report the study of such magnetic con gurations via a two-dimensional Ising model considering thermal arti cial spins [START_REF] Arnalds | A new look on the two-dimensional Ising model: thermal arti cial spins[END_REF].

However this issue is not the focus of this thesis.

Hard magnetic thin lms 4.2.1 NdFeB thin lms

During the description of sample preparation (Section 3.2.1) two strategies were described for the preparation of the hard magnetic matrix. The rst to optimize NdFeB thin lm properties, depositing in di erent temperatures and post-deposition ex-situ annealing performed in an RTA and exploring di erent bu er layers. The second strategy was to apply the constrains of the integration of the hard matrix with the nano-rods, as the deposition at room temperature on prior oxidized bu er layers followed by ex-situ annealing for .

NdFeB thin lms-Strategy 1

The optimization process generated many samples and the MOKE was chosen for fast characterization for a comparative study. The samples that presented good potential were selected for further investigation using VSM-SQUID. The discrepancies between these two techniques were discussed previously in Section 2.10.2, and can be associated with the di erent characteristics between the sample surface probed by MOKE and the volume probed by VSM-SQUID. Additionally, there are some aspects of the demagnetisation curve that are just revealed in the in-plane VSM-SQUID measurement that is not accessible in the polar Scanning MOKE system. Figure 4.3 shows a table with the hysteresis loops obtained from MOKE for the NdFeB thin lms. (last row) and with 1 minute annealing at a heating rate of 50 ∕ . The results for 2 minutes treatment can be visualized in Annex A.2. The in uence of the choice of bu er layer on the magnetic properties of NdFeB is reported in many studies [START_REF] Jiang | Structure and magnetic properties of NdFeB thin lms with Cr, Mo, Nb, Ta, Ti, and V bu er layers[END_REF][START_REF] Hannemann | E ect of Cr and Ta bu ers on hard magnetic Nd2Fe14B lms[END_REF][START_REF] Okumoto | E ect of underlayer structure on the crystallographic and magnetic properties of Nd-Fe-B thin lms[END_REF][START_REF] Serrona | E ect of Mo and Ti bu er layers on the structure and magnetic properties of Nd-Fe-B lms prepared on Mo, W, Ta, Nb and Si substrates[END_REF][START_REF] Chen | E ect of heat treatment on microstructure and magnetic properties of anisotropic Nd-Fe-B lms with Mo or Ti bu er layer[END_REF]. We also observe that changing the bu er layer from Ta to Mo a ects the magnetic layer. As it is shown by Jiang et al., when the annealing conditions are optimized, lms with a Mo bu er layer reach better of values of coercivity (i.e. Observing again the table in Figure 4.3, the rst column depicts the hysteresis loops of as deposited NdFeB lms for deposition temperature from 500 to 700 . From these loops we observe a two phase behaviour for samples deposited above 650 , which is attributed to a partial formation of the hard magnetic phase 2:14:1 during deposition. Following all samples annealed ex-situ post-deposition, the degradation of magnetic properties occurs above 550 . The post-deposition annealing temperature is below the deposition one to cover a wider range in case of discrepancy between the temperature calibration in the sputtering and RTA.

In the table presented in

The two-step process was optimized to nd the best annealing conditions as reported in many studies [START_REF] Serrona | Magnetic and structural properties of NdFeB thin lm prepared by step annealing[END_REF][START_REF] Su | Systematic Investigation of the In uence of Preparation Process and Target Composition on Structure and Magnetic Properties of Nd-Fe-B Thin Films[END_REF][START_REF] Lileev | Properties of hard magnetic Nd-Fe-B lms versus di erent sputtering conditions[END_REF]. A direct comparison between these studies and our work is not possible because the di erences between lm composition, thickness, the annealing time and furnace speci cations. The criteria to choose the best heat treatment, for the samples deposited on Ta, was to have high coercivity and single phase behaviour. Accordingly, the best combination was a deposition temperature of 500-550 and annealing at 500 . Figure 4.6 shows hysteresis loops obtained by VSM-SQUID for in-plane and out-of-plane applied eld.

When measured by VSM-SQUID, especially in-plane, the best samples selected from table in Figure 4.3, present a two-phase behaviour, with a small "shoulder" around 0 T. As mentioned previously, the presence of any soft magnetic phase prohibits the use of the lm for the fabrication of hard-soft nanocomposites. From Figure 4.6, we can also observe a change in the lm texture when changing the deposition temperature. The di erence between the in-plane and out-of-plane loops reveals that the lm deposited at 550 is more textured.

NdFeB thin lms-Strategy 2

The second strategy described in Section 3.2.1, consists in a natural oxidation of the bu er layer before the deposition of NdFeB. It is important to test this because during nanocomposite fabrication, the bu er layer is exposed to air. Figure 4.7 presents MOKE hysteresis loops for lms deposited at room temperature and with an oxidised bu er layer of Ta or Mo, varying in thickness between 5 and 50 nm. It is concluded that the best properties were achieved with bu er layer of 5 nm. This may happen because the 50 nm bu er layer can "store" more oxygen, that can, during the heat treatment oxidize NdFeB layer. It is known that the bu er layer roughness, that tends to increase with the increase of the thickness, can also in uence the magnetic layer properties. However, the study of Chen et al. [START_REF] Chen | E ects of bu er layer and substrate temperature on the surface morphology, the domain structure and magnetic properties of c-axis-oriented Nd2Fe14B lms[END_REF], that discussed this, does not take into account any bu er layer oxidation.

More detailed measurements done using VSM-SQUID are presented in Figure 4.8. Besides the results of the heat treatment performed using a RTA with bu er layer of Ta or Mo, the ex-situ annealing was also carried out in the tube furnace with diverse time and temperature for a Ta bu er layer of 5 nm. The heat treatment in a tube furnace was studied due to the better vacuum system and reproducibility.

After exploring di erent heat treatments and bu er layers, we concluded that the NdFeB thin lm did not reach the requirements to be a hard magnetic phase for the model nanocomposite samples. The best results obtained with an oxidized bu er layer, depicted in Figure 4.8, shows that some soft magnetic phase is always present (Left curves). In the case of samples treated in the tube furnace, the coercivity varied from 0.4 T to 0.7 T with also a soft magnetic component. Following the unsuccessful optimization process described here, it was decided to study the use of FePt as the hard magnetic layer. RE-based hard magnetic phase are more susceptible to degradation than Pt-based phase, being more resistant to corrosion and the lithogra-phy processes.

FePt thin lms

FePt thin lms were produced by sputtering using composite targets. The process described in Section 3. From target A to E, the quantity or size of Pt pieces were changed, increasing the concentration of Pt in the corresponding lms. Note in Figure 4.9 the pieces were distributed along the "sputtering ring", in other words, the pieces were placed where the Ar ions preferentially hit the target. According to the results displayed in Figure 4.9, measured using MOKE, the highest coercivity is found in lms produced by target C. Following the investigation about the magnetic properties of lms deposited from target C, three pieces along the radial direction were selected to be measured by VSM-SQUID. Figure 4.10 shows the hysteresis loops for each piece and their respective po-sition with respect to the center of a 5 cm (2 inch) wafer. The normalized hysteresis loops prove the homogeneity of the thin lm produced from target C, considering the curves are practically identical. As the lms are deposited at room temperature and later submitted to annealing, an isotropic FePt lm is expected. The high coercivity, around 1 T, and the single phase behaviour indicates the formation of the 1 0 phase. As mentioned in Section 3.2.2, the FePt thin lm was developed in the framework of a high-throughput study of graded lms. In this chapter more details of the structural and magnetic characterizations will be explored.

FePt thin lms -micro-patterning

As discussed previously, it was not possible to produce a large and continuous surface of soft magnetic nano-rods, especially, for the high density patterns. This large surface covered by nano-rod arrays were feasible when they had micrometric dimensions and they were displayed with some microns between them (Figure 3.6).

An additional step of micro-lithography was necessary to minimize the amount of hard phase without contact with soft phase generating a inhomogeneous material that would be very di cult to investigate regards the interaction between the phases involved. This process was detailed in Section 3.2.3.

The rst micro-patterns produced by UV lithography presented good magnetic properties, but the shape was not reproducible, since the corner curvature edge dimensions were at the limit of this technique (sub microns). When e-beam lithography was used, sharp corner edges were achieved (r = 30 nm), however the magnetic properties became unstable. Considering that the edges could be the origin of the twophase behaviour and the heat treatment could also play a role in the magnetic properties, an investigation was designed to nd the best conditions. The micro-pattern optimization study was carried out with samples with three di erent corner curvature radius (as depicted in Figure 3.14 -r: 0 , 1.0 and 2.5 0 ), using three di erent temperatures ( 450 , 500 and 550 ) during three distinct times ( 10 min, 30 min and 60 min). This study produced 27 samples for each thickness (25 nm and 50 nm) that were characterized by hysteresis loops at VSM-SQUID, where the two-phase behaviour and coercivity were compared. As the arrows indicate in Figure 4.12 the samples with radius of 30 nm and 2.5 presented a pronounced peak around 0 T, con rming the presence of soft phase. The same analysis were done for all the hysteresis loops collected from the All the micro-patterned samples were prepared on the same substrate, being submitted to the same fabrication process at the same time. Considering this, the open question about them was: why were the magnetic properties better for the samples with corner curvature radius of 1 ? Comparing the roughness of the di erent shapes, a small di erence was found, where 1.9 nm, 1.9 nm and 1.4 nm were measured for the samples with corner curvature radius of 30 nm, 1 , and 2.5 , respectively.

This characteristic is not expected to explain the di erence in the hysteresis loops for the respective samples. The other information extracted from the AFM measurements was the thickness pro le at the feature edge where the resist could be poorly liftedo . This graph, depicted in 4.13, shows that all the shapes has some residual resist with thickness between 10 and 15 nm. The sample that presents the best magnetic properties is the one with the biggest quantity of residual resist. Moving to the MFM images, the samples were saturated in-plane in the direction indicated by the black arrow. Their similar domain structure, with the contrast typical of an isotropic lm and do not explain the discrepancy in their hysteresis loops. The other MFM contrast observed is on the edges of the micro-pattern related with the saturated state, being bright on the right and dark on the left.

Most of the studies reported about micro-patterned FePt thin lms have a top-down approach, etching a deposited lm through a lithography mask [START_REF] Seki | Dot size dependence of magnetic properties in microfabricated L10-FePt (001) and L10-FePt (110) dot arrays[END_REF][START_REF] Wang | Dot Size Dependence of Magnetization Reversal Process in <formula formu-latype="inline"><tex Notation="TeX">L1 0 </tex></formula>-FePt Dot Arrays[END_REF][START_REF] Kurosu | Improvement of Magnetic Properties in Microfabricated FePt and Fe Nano-Composites Upon Post-Annealing[END_REF], they see an e ect of the dot size, obtaining better results in the micrometric dots, however the dot shape is not explored. Results obtained from a deposition-last process were reported by Noh et al. [START_REF] Noh | Hyper ne FePt patterned media for terabit data storage[END_REF], but the dot size of 30 nm and thickness of 7 nm are not comparable to the samples developed in this thesis.

Since the current analysis allowed us to nd the best conditions for the hard matrix, the FePt micro-pattern with corner curvature radius of 1 was chosen nanocomposite fabrication. However, the clear explanation why this samples is the best still missing. A valid question is if the M(H) loops, and in particular the soft shoulder, is representative of individual loops or rather the e ect of some low coercivity patterns.

Chapter 5

Hard-soft nanocomposites

Bilayer -FePt/FeCo

This section presents the results obtained for an FePt/FeCo bilayer fabricated under the same conditions as the one already described in Section 3.3. This means that the soft magnetic layer of FeCo was prepared by evaporation, covered with a Au layer to prevent oxidation, then later etched to remove the Au prior to deposition of the FePt layer. The main goal was to evaluate the etching process for surface recovery described in Section 3.4. The apparent single phase behaviour, visible in Figure 5.1 suggests that exchange coupling between the two layers was established and that the Au layer was successfully removed. The single phase behaviour could also be associated with dipolar coupling, because of this the measurements were performed in-plane. As demonstrated by Cui et al., any spacer-layer between the hard and soft magnetic layer would weaken the exchange coupling and this could be visualized as a kink in the in-plane hysteresis loop (mentioned in Figure 1.29 in Section 1.2.1) [START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF].

FeCo nano-rods in a -patterned FePt (25 nm) -

Case study

In this section a detailed case study of samples consisting of FeCo or Pt nanorods embedded in a 25 nm thick micro-patterned FePt matrix will be presented.

Structural characterization

The nano-rod array fabrication and characterization were previously presented and discussed in Sections 3.1 and 4.1, respectively. Figure 5.4 recalls the four di erent nano-rod arrays embedded in the FePt micro-patterned hard matrix and how the samples were named. Table 5.1 shows the dimensions corresponding to each nano-rod array and extra information about the Pt rods and bilayers that will be compared in the following discussion. Note that all these samples were produced in the same batch, which means they were on the same substrate, their lithography, deposition, lift-o and annealing were all carried out at the same time. Plan-view SEM images shows the nal shape chosen after the results obtained from the hard layer micro-patterning and annealing optimisation process (Sec- Summarizing, the examination of these images indicates that in 25NC3, which has the narrowest nano-rods (width = 24 nm), Co and Fe di use from the nano-rods into the hard magnetic matrix, with the Co seen to remain concentrated in a shell around the original interface with the nano-rods. On the other hand, in 25NC4, which has the widest nano-rods (width = 120 nm) the bulk of the nano-rod material remains in place, though there may be some di usion at the edges of the rods.

The formation of voids during annealing is attributed to the Kirkendall e ect [START_REF] Resnick | NUCLEATION OF VOIDS IN METALS DURING DIFFUSION AND CREEP[END_REF], in which a di erence in di usion rates between two distinct materials promotes interface motion and pore formation. In the samples studied here, the formation of voids in the positions of the narrowest FeCo nano-rods, indicates a higher rate of diffusion of Co (and Fe) atoms into FePt, compared to Pt di usion into FeCo. The size dependence of the nanoscale Kirkendall e ect was explored in a study by Railsback et al. [START_REF] Railsback | Size-Dependent Nanoscale Kirkendall E ect During the Oxidation of Nickel Nanoparticles[END_REF], where nanoparticles of 26 nm had asymmetric single void formation while particles with 96 nm of diameter had multiple voids forming a porous structure. In other words, the nanostructure size impacts void formation and indeed it is explored in nanotechonology to generate hollow particles and wires [START_REF] Fan | Formation of Nanotubes and Hollow Nanoparticles Based on Kirkendall and Di usion Processes: A Review[END_REF].

As a result of di usion, the model architecture of the as-deposited nanocomposites is modi ed during the annealing step which is necessary to form the hard magnetic FePt phase. Considering the dimensions of 25NC2 it is likely that the same di usion and void/shell formation happens in this sample. However, due to the laborious preparation and scarce time to access the TEM, these samples were not investigated. Nevertheless, concentration of the di used atoms in a shell at the original nano-rod matrix interface in the samples with the narrowest nano-rods, and limitation of di usion to the edges of the widest nano-rods, allow the study of the in uence of the original soft feature size on magnetisation reversal in these hard-soft nanocomposites. In other words, despite the di usion, the soft magnetic region is still limited to nanostructure dimensions. In the discussion below, we will make the over-simpli ed assumption that the volume content of soft magnetic material in the nanocomposites is equivalent to that of the as-fabricated nanocomposites, before annealing.

Magnetic characterization

Hysteresis loops of the four hard-soft nanocomposites are compared with those of a reference array of hard FePt micro-patterns and the continuous hard-soft bilayer in Figure 5.11. The M(H) loop of 25NC1, which has the lowest soft phase volume ratio (1.8%), is comparable to that of the array of hard FePt micro-patterns. While the volume ratio of the soft phase is too low to expect any signi cant in uence on remanence, it is noteworthy that the presence of nanoscaled soft rods/shells, which could serve as nucleation sites for magnetisation reversal in the hard phase, did not have any signi cant in uence on the coercivity of 25NC1. The M(H) loops of the other hard-soft NCs are signi cantly modi ed compared to that of the array of hard FePt micro-patterns, while they nevertheless maintain a higher coercivity than the continuous hard-soft bilayer, and none of them show an obvious soft phase shoulder. The evolution in coercivity and remanence with soft phase content of the nanocomposites and the bilayer is plotted in Figure 5.12-left. The inverse behaviour of coercivity and remanence with increasing volume content of soft phase, classically seen in hard-soft nanocomposites, is also found here. The estimation of the error bar can be found in Annex A.4.

To check the potential in uence on magnetisation reversal of the topographical features produced in the FePt matrix by depositing it on an array of nano-rods (indents on the bottom surface and associated bumps on the top surface), we fabricated a fth nanocomposite (25NC5) consisting of non-magnetic Pt nano-rods in a hard magnetic micro-patterned FePt matrix. The M(H) loop of this sample is compared with that of the hard-soft nanocomposite with comparable starting nano-rod arrays (25NC4) and the reference array of hard FePt micro-patterns in Figure 5.12-right. The M(H) loop of 25NC5 is comparable to the latter, and has a signi cantly higher coercivity than the hard-soft nanocomposite. This indicates that the topographical features 5.1 ( 0 = 6 T).

produced in the FePt matrix should not act as a source of coercivity reduction in the hard magnetic matrix.

In order to explore more details of the reversal process in nanocomposites The images were obtained using an MFM probe coated with a hard magnetic layer of FePt and with coercivity higher than 0.5 T (for details about probe fabrication and characterization see Annex A.5). The magnetic eld was applied using the pulsed eld system described in Section 2. inal nano-rods is clearly identi ed in the topographic image, since the FePt deposit followed the topography imposed by the underlying nano-rods (as already shown in the TEM cross-section images). Up to three types of magnetic contrast can be seen in the MFM images. A rst contrast situated at the top and bottom edges of the micropatterns (i.e. along the edges which are perpendicular to the direction of the applied magnetic eld -hereafter referred to as the "edge contrast" and indicated in Figure In the case of 25NC2, 25NC3 and 25NC4, we can also see an additional ne contrast, which manifests itself as a periodic set of somewhat fuzzy but discernible horizontal lines. The spacing of the lines is correlated with the length of the original underlying soft nano-rods, and we attribute this contrast to the stray eld produced by the arrays of underlying nano-rods (nano-shells in the case of di used nano-rods).

While the size of the individual nano-rods is the same in 25NC1 as in 25NC3, the lower density of nano-rods in 25NC1 could explain. The absence of this third type of contrast in this sample. The diagram in Figure 5.16 presents the superposition of the contrast originated from the burried soft nano-rods and the domains from the FePt matrix. The impact of applying a negative eld of growing strength on the remnant MFM images shown in the remaining columns will be discussed.

For all samples the edge contrast of the micro-pattern becomes weaker before practically disappearing after application of a eld of -1 T. A relatively high intensity of ipped contrast is observed following application of a eld of -3 T. The eld of -1 T is close to the coercivity of the hard micro-patterns and 25NC1, while it is higher than that of 25NC2, 25NC3 and 25NC4. The observed evolution in the edge contrast can be attributed to the reversal of at least the edges of the hard matrix. As the edges of the nanocomposites are free of nano-rods, their reversal in 25NC2, 25NC3 and 25NC4 should belong to the high eld end of the broad wing-like features seen in the FORC diagrams of these samples, which do indeed reach up to an applied eld of 1 T. The periodic horizontal line contrast of 25NC2 and 25NC3 is not evident in the image taken after application of a eld of -500 mT and it then reappears for higher negative elds.

A possible explanation is schematized in Figure 5. [START_REF] Zeng | Exchange-coupled nanocomposite magnets by nanoparticle self-assembly[END_REF], where two states are proposed, a rst with the rods antiparallel like they appear when not in a hard magnetic matrix (Figure 4. In this case study, a set of complementary magnetic characterization techniques to probe the in uence of the size and volume of the soft magnetic nano-rods on the magnetic behavior of our model nanocomposites was used. Major hysteresis loops revealed how a low volume fraction (1.8%) of narrow rods (24 nm) does not a ect the loop of the nanocomposite compared to a reference hard micro-patterned lm. Increasing the volume fraction of soft nano-rods does result in a drop in coercivity, with comparable values found for nanocomposites 25NC3 and 25NC4, having 8 vol % narrow rods (24 nm) and 11 vol % wide rods (120 nm), respectively. The shape of the demagnetization curves of these samples are somewhat di erent, the former being convex, the latter concave. FORC analysis then allowed us to extract more information about switching eld distributions in nanocomposites and micro-patterned hard lms. In particular, it revealed the presence of an uncoupled soft magnetic phase in both 25NC3 and 25NC4, that was not evident in the major hysteresis loops. Differences in the switching eld distributions of 25NC3 and 25NC4 in higher elds are attributed to di erences in the extent of coupling between the hard matrix and the embedded nano-rods. While the above discussed techniques are global in nature, MFM allows to probe magnetic con gurations in a local manner. Thanks to the fact that we patterned both the soft rods (at the nanoscale) and the hard matrix (at the microscale), it is possible to distinguish switching of these distinct phases. MFM imaging in di erent remnant states allowed us to "see" how the wide rods of 25NC4 switch in smaller elds than the narrow rods of 25NC3.

Micromagnetic simulations

To support our experimental observations and analysis, we have initiated collaborations to model magnetization reversal in our nanocomposites. This work is still on-going, and I will present encouraging results obtained to date. A rst set of results were obtained by J. Fischbacher and T. Schre (Danube University Krems) using a nite element (FE) method (FEMME). In this study the in uence of the size and volume fraction of the soft magnetic inclusions, as well as the e ect of di usion between the hard and soft phases, on demagnetization curves were simulated. To assess the eventual in uence of the topography of the hard matrix induced by deposition on an array of nanorods, we also prepared a nanocomposite containing non-magnetic nanorods. Experimental details of the preparation and characterization of this sample type are given below, and simulations of such structures are included here. A second set of results were obtained by L. Ranno (Institut NEEL), using a nite di erence (FD) method (MuMax). In this study both demagnetization and recoil curves were simulated for the two samples dealt with in the case study (25NC3 and 25NC4), which allows comparison with experimental MFM images.

Finite Element

In the FE simulations, one nano-rod in a hard magnetic matrix was considered. Magnetisation reversal curves were calculated for hard-soft nanocomposites and a reference hard magnetic layer. Simulations of nanocomposites were made considering the model architecture prior to annealing (hereafter referred to as "planned"), and the nal architecture produced during annealing (hereafter referred to as "result"), the latter taking into account the e ect of di usion. In the ner structures (NC1, NC2 and NC3), di usion is considered to lead to transformation of soft FeCo nano-rods into soft FeCoPt nano-shells, resulting in the creation of voids at the original positions of the nano-rods. In the coarsest structure (NC4), the formation of voids at the surface of the soft nano-rod is considered. The non-magnetic Pt nano-rod of NC5 is treated as a void. Schematic diagrams of the modelled structures are compared in Figure 5.17. The topography of the hard matrix (bumps on top of the nano-rods)

is not considered. The size of the FePt grains was set at approximately 25 nm and an isotropic easy axes distribution was assumed. Neighbouring grains were in direct contact (no grain boundary phase) and perfectly coupled. The mesh size at interfaces and surfaces was 1.5 nm. The material parameters used for these simulations are listed in Table 5.2. The anisotropy constant and order parameter of L1 0 FePt were deduced by adjusting the simulation parameters for a reference hard magnetic layer to match the experimental hysteresis loop of a micro-patterned FePt lm.

K (MJ/m³) J (T) A (pJ/m)

FePt (S = 0. Simulated demagnetisation curves of non-di used and di used nanocomposites are compared with reference hard magnetic layers in Figure 5.18. For sample "25NC1" (Figure 5.18-a), all three demagnetization curves practically overlap, indicating that a very small volume of soft inclusion (1.8 %), di using or not, does not a ect reversal of the hard matrix. This is in good agreement with our experimental observation. In the other hard-soft nanocomposites which have a higher volume of soft phase (6.7-11.5%), the coercivity of the nanocomposite is reduced with respect to that of the reference hard layer, but di usion does not signi cantly modify the simulated demagnetization curves. The in uence of the size and constituent material of the nano-rods on the simulated demagnetization curves is shown in Figure 5.19-left.

The overall tendency agrees with the corresponding experimental demagnetization curves shown on Figure 5.19-right. These preliminary results support our experimen-tal ndings, and suggest that the di usion we observed may not impact so strongly on the magnetization reversal process.

Finite Di erence

In the FD simulations, an array of ideal (non-di used) soft nano-rods in a hard magnetic matrix was simulated, as schematized in Figure 5.20. The material parameters used for these simulations are listed in A snapshot image of the averaged reduced magnetization con guration of the sample with coarse structures (25NC4), at the coercive eld, is shown in Figure 5.22. Such a magnetization con guration corresponds to what would be measured during MFM imaging at this eld. Based on this con guration, the expected MFM image for a scan height of 50 nm was simulated with the MFM probe modelled as a monopole. In the resultant image (Fig 5 .22), we can identify a periodicity which corresponds to the soft nano-rod array. This result supports our claim to be able to "see" reversal of the soft nanorods using MFM. Recoil curves are now being calculated, to allow simulation of MFM images in remnant state, which could then be directly compared to our MFM images.

Though preliminary, the simulation results presented here are very encouraging as they support our analysis of magnetization reversal in our hard-soft magnetic nanocomposites probed using both magnetometry and MFM. We will now pursue these collaborations and a joint publication will be prepared in the near future.

Pt nano-rods in a -patterned FePt (25 nm)

As mentioned in the Case study, nanocomposites were prepared replacing the soft magnetic nano-rods by non-magnetic nano-rods. The main idea was to produce samples under the protocol developed during this thesis and evaluate the impacts of the fabrication process, as well as the roughness, possible surface degradation induced in solvent baths and during annealing. At rst, Au was the material chosen, considering that it would not alloy with either Fe or Pt. However when deposited by evaporation to form nano-rods in the developed resist, the Au dewets [START_REF] Leroy | How to control solid state dewetting A short review[END_REF] which changes the nano-rods shape drastically. Because of this, Pt was used as a nonmagnetic material and the possible alloy formation would be well known by the Fe-Pt phase diagram. Another relevant comparison is the MFM contrast of the samples with magnetic and non-magnetic nano-rods. For this example, the MFM images obtained after saturation in-plane of samples 25NC3 and 25NC4 with FeCo nano-rods, presented in the Case study, were compared with the current Pt nano-rod nanocomposites (Figure 5.25). It is expected that non-magnetic inclusions in a magnetic material would create a cavity e ect and magnetostatic energy would be minimized with magnetic ux closure generatin an anomaly in the stray eld probed by the MFM tip. However, from the images shown in Figure 5.25 it can be seen that the periodic contrast that seen in NC3-Pt and NC4-Pt is much weaker than in the soft magnetic nano-rods images. This comparison supports the analysis of the remnant state reported in the Study case.

FeCo nano-rods in a -patterned FePt (50 nm)

The samples presented in this section were prepared following the same protocol, only increasing the thickness of the micro-patterned FePt hard matrix from 25 to 50 nm. While the rods have the same dimension, the volume content of soft phase is reduced as indicated in the legend of Figure 5.26 and in Table 5.5 . In general, the coercivity is less a ected that for the nanocomposites with 5.5 ( 0 = 6 T).

Sample

25 nm thick matrix, due to the lower volume content of the soft nano-rods. However, sample NC4, which has the widest rods (w = 120 nm) presents a "shoulder" around 0 T, indicating that part of the soft phase is decoupled. A slight reduction of coercivity is also observed in this same sample. Considering that the impact of the soft nanoinclusions is much more clear with the 25 nm thick FePt matrix, the following samples prepared with Co nano-rods were prepared with 25 nm thick hard matrix.

Co nano-rods in a -patterned FePt (25 nm)

In this section, Co nano-rods embedded in a micro-patterned FePt 25 thick lm matrix will be presented. Table 5.6 presents the information related with the samples presented. Conclusions and prospects

Conclusions

Considering the scenario presented in the state of the art, we can divide research in hard-soft nanocomposites in three main groups: (i) bulk production routes (metallurgical, chemical), (ii) the understanding of the critical parameters with model samples and (iii) micromagnetic simulations proposing optimal structures or modelling the nanocomposites reported. This work is a rst step in the investigation of soft nano-rods produced by e-beam lithography embedded in hard magnetic matrix. The use of nanofabrication aimed to the ultimate control of the soft magnetic inclusions in size and position while the characterizations revealed the structural and magnetic properties. These properties were correlated and discussed at the light of micromagnetic simulations.

One of the biggest challenges in executing this project was to fabricate the samples. The integration of soft magnetic nano-rods made by e-beam lithography with a hard magnetic matrix deposited by sputtering, was successfully performed despite the di culties faced in combining these di erent fabrication techniques. Many steps were needed to optimize fabrication and to solve unexpected problems. In the case of e-beam lithography of the nano-rods, the biggest bottleneck was the so-called proximity e ect, because of which the lowest achievable distance between objects is limited, especially if they have very small dimensions. The lowest inter-rod distance achieved in this study was 50 nm. The proximity e ect also limits the surface area that can be patterned, which led us to fabricate repeat arrays of nano-rods so as to produce samples with a large overall surface area (mm 2 ) suitable for magnetometry measurements. Individual arrays have a surface area of 5 × 5 m 2 , and are separated from neighbouring arrays by a gap of 5 µm. To maximise the soft phase content, the hard magnetic matrix was micro-patterned, so as to limit its coverage to just above the arrays of soft nano-rods. The micro-patterning of the hard magnetic matrix introduced new problems, for instance a two phase behaviour in the hard phase. Thanks to extensive optimisation, hard-soft magnetic nanocomposites consisting of soft nano-rods (four di erent architectures) embedded in a hard magnetic matrix were successfully produced by nanofabrication. Nevertheless, the highest volume content of soft phase achieved was only 11 % because of the constraints discussed above, which necessarily limits the enhancement of ( ) that can be achieved with respect to the hard phase alone. It also limits the absolute value of ( ) that can be achieved compared to other material combinations and other fabrication routes. For this reason, we do not use ( ) as a gure of merit for our model samples. Rather we study the impact of sample architecture on magnetisation reversal in our nanocomposites.

The fact that nanofabrication a ords control over the size, shape and position of the soft phase greatly facilitates local structural characterization (SEM, TEM). More importantly, it brings speci c advantages to the study of magnetisation reversal, on the one hand allowing component speci c (hard µ-pad vs soft nano-rod) pattern recognition in MFM imaging and on the other allowing simulation geometries which match very well to the real systems under study. Another group recently reported the use of nanoimprint lithography, but while they nano-patterned a bi-layer consisting of a soft layer deposited on a hard layer [START_REF] Son | E ect of the soft layer thickness on magnetization reversal process of exchange-spring nanomagnet patterns[END_REF], we succeeded to bury our nano-patterned soft phase in a hard matrix. Soft-in-hard structures are predicted to be the most promising nanocomposite architectures [START_REF] Skomski | Geometry Dependence of Magnetization Reversal in Nanocomposite Alloys[END_REF], and decoupling the in-plane dimensions of the hard and soft features a ords the speci c advantages outlined above.

With regard to the materials explored, FeCo and Co were used as the soft phase, while NdFeB and FePt were investigated as candidates for the hard phase. Nd-FeB was eliminated due to the degradation of its magnetic properties when deposited as a very thin lm (Sections 3.2.1 and 4.2.1). FePt, however, proved to be a robust choice, as single hard phase behaviour could be achieved in a reproducible fashion in lms as thin as 25 nm. The fabrication protocol for FePt lms used in this project was established in an extensive study of both compositionally graded and homogeneous lms, carried out in collaboration with Y. Hong (Sections 3.2.2, 4.2.2 and A.5). The micro-patterning process and optimization of the heat treatment of micro-patterned lms was made in collaboration with F. Orlandini-Keller (Sections 3.2.3 and 4.2.3).

The as-deposited and subsequently micro-patterned FePt was in the disordered A1 0 state, and an annealing step was required to produce coercive L1 0 FePt.

Kirkendall-type di usion was observed in the annealed nanocomposites with the narrowest nano-rods (24 nm). This di usion process generated voids in the original position of the nano-rods, and resulted in the formation of FeCo-rich regions of thickness close to about 20 nm surrounding the voids. In the samples with 120 nm wide nanorods, FeCo essentially remained in place, though some voids were observed at the edges of the nano-rods. This indicates that there is a relationship between the size of the nano-rods and the di usion that occurs in the nanocomposites (Section 5.2.1).

Note that one of the fundamental premises of obtaining a nanocomposite with good magnetic properties is to maintain the nanometric dimensions of the soft phase, a conclusion from various micromagnetic models (Sections 1.1.2 and 1.1.3). However, this requirement is confronted with the limitations imposed by fabrication techniques.

Based on extensive bibliographic research (Section 1.2), reports of problems related to di usion during annealing to form the hard phase are very common and inherent to many fabrication techniques [START_REF] Le Breton | A structural investigation of SmCo5/Fe nanostructured alloys obtained by high-energy ball milling and subsequent annealing[END_REF][START_REF] Xiong | Atom probe study on the bulk nanocomposite SmCo/Fe permanent magnet produced by ball-milling and warm compaction[END_REF][START_REF] Pousthomis | On the advantages of spring magnets compared to pure FePt Strategy for rare-earth free permanent magnets following a bottom-up approach[END_REF]. In some cases it promotes positive changes in the structure, for example enhancing the energy product [START_REF] Zeng | Exchange-coupled nanocomposite magnets by nanoparticle self-assembly[END_REF][START_REF] Neu | Fully Epitaxial, Exchange Coupled SmCo 5 /Fe Multilayers With Energy Densities above 400 kJ/m 3[END_REF]. In other cases, the choice of materials or sample architecture is made in order to avoid the impact of di usion as much as possible [START_REF] Sakuma | Exchange Coupling Interaction in L1 0-FePd/ -Fe Nanocomposite Magnets with Large Maximum Energy Products[END_REF][START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF]. Based on an analysis of the samples produced in the framework of this thesis it was possible to establish a clear trade-o between the size of soft magnetic nano-rods and the ease of di usion. This observation was possible thanks to the use of high resolution and chemically sensitive TEM imaging (Section 2.5).

Although the results of structural characterization are of enormous importance for the study of hard-soft magnetic nanocomposites, the main focus of investigation in this thesis is the magnetic properties and the understanding of magnetisation reversal. The impact of increasing the soft phase content on the decrease of coercivity and increase of remanence, was assessed using major hysteresis loops (Section 5.2.2) measured by VSM-SQUID magnetometry. Further global investigation of the coupling between the hard matrix and the soft nano-rods according to their size was performed using First Order Reversal Curves which revealed very distinct signatures for samples with di erent soft phase dimensions (Section 5.2.2). These measurements also revealed the presence of both coupled and uncoupled soft magnetic phases, the latter not obvious in major hysteresis loops. Local magnetic measurements, investigating a micrometric unit of the nanocomposites, were performed using an MFM microscope combined with a home-made in-situ pulsed eld system (Section 2.8.1).

The evolution in magnetic contrast as a function of the remanent state provides a visual signature of switching of both the hard matrix and the soft nano-rods, thus revealing how magnetization reversal of nanocomposites depends on the size of the soft-nano-rods (Section 5.2.2).

To complement the experimental study, a collaboration was established with researchers specialized in simulations. A rst set of simulations indicates that the di usion observed in nanocomposites with the narrowest nano-rods, does not significantly modify reversal with respect to the originally planned nanostructure. What is more, good agreement is achieved between measured and simulated demagnetisation curves as a function of the size and volume content of soft nano-rods. A second set of simulations support our analysis of contrast observed in MFM imaging. These simulation also reveal how reversal starts in the soft nano-rods, and that the nano-rod size impacts domain propagation. Although the simulation results are preliminary, the good agreement achieved between two di erent models and the experimental results

show a promising path for the study of hard-soft nanocomposites (Section 5.2.3).

Prospects

Model hard-soft magnetic nanocomposites

While the original nanofabrication approach developed here will hardly be used for the manufacture of hard-soft nanocomposites for use in applications, it can be further used in the study of model nanocomposites. As a rst example, it would be interesting to study in more detail the in uence of the size of FeCo nano-rods on di usion into an FePt matrix. A concrete suggestion would be to study di usion in nanocomposite samples in which the width of the soft nano-rods is varied in a progressive manner in a given sample. As all rods would be buried under the same lm and annealed under exactly the same conditions of temperature and time, we would eliminate eventual sample to sample variations and could thus carefully establish the critical minimum nano-inclusion width to avoid di usion in FeCo/FePt nanocomposites. High resolution TEM imaging with chemical analysis would be the ideal characterization approach for this study. I have already prepared arrays of soft nano-rods with nanorod widths varying in the range 24-120 nm (Figure 6.1) that could be used for such a study. The same approach could also be used to probe di usion in nanocomposites combining other materials. high coercivity and single phase behaviour can be prepared in our magnetron system [START_REF] Akdogan | Preparation, Characterization, and Modeling of Ultrahigh Coercivity Sm-Co Thin Films[END_REF]. I thus began investigating the potential to use SmCo as the hard matrix in a nanocomposite, in collaboration with F. Orlandini-Keller. The rst step concerned the fabrication of SmCo lms having a graded composition, using an asymmetric target (Figure 6.2). The motivation here was to use a high throughput approach (fabrication of graded lms, magnetic characterization using scanning MOKE) to quickly optimize the composition of the SmCo lm. Once the optimum area was identi ed, a study of the in uence of both annealing conditions and micro-patterning on the magnetic properties of the SmCo lm was begun. This study is being continued by F.

Orlandini-Keller in the framework of the ANR SHAMAN project, and the aim will be to fabricate nanocomposites consisting of Fe or FeCo soft nano-rods in a hard SmCo matrix. to carry out element selective magnetic measurements using XMCD. These measurements were planned together with partners of the ANR SHAMAN project (A. Rogalev and Fabrice Wilhelm, ESRF) and we have provided them with FeCo/FePt samples reported in the case study. These measurements will be carried out as soon as the beamline is operational, hopefully before my defense! With these experiments we expect to see 2-phase reversal in the Co loops of our nanocomposites, a rst switching event at low eld corresponding to uncoupled Co, and a second switching event corresponding to Co which is coupled to the hard matrix. The details of the loops are expected to vary with the nanorod size.

Beyond hard-soft magnetic nanocomposites

Quantum computing

The soft magnetic nano-rod arrays developed in the framework of this thesis aroused the interest of a colleague from Institut NEEL, M. Urdampilleta, working in the eld of quantum computing. Essentially, he is interested to exploit nanomagnets, which produce extremely high magnetic eld gradients (10 9 T/m), in combination with a microwave magnetic eld, to manipulate spin qubits. This would be an alternative to the use of electron spin resonance, presently used for this purpose. Arrays of nanomagnets would allow the manipulation of assemblies of spin qubits, which is hardly achievable with electron spin resonance. I have already simulated the magnetic elds and eld gradients expected from nano-magnet arrays designed together with M. Urdampilleta (Figure 6.3), and I am in the process of transferring to him the experimental protocols I developed for the fabrication of magnetic nano-rod arrays.

Biology and medicine

The extremely high magnetic eld gradients produced by nano-rods are also of potential interest for use in biology. Indeed, our group has extensive experience in the development of micro-scaled magnets for both very fundamental and applied bio-related studies. Examples of the former include studies of the in uence of high magnetic eld gradients on cell development, and of the in uence of magnetically induced mechanical forces on cell and embryo development. Examples of the latter include cell and protein manipulation for diagnostics. Decreasing the size of magnets used in such studies from the micro-scale to the nanoscale with result in a three-orders of magnitude increase in the magnetic eld gradients achievable. As the lengthscale of interaction will drop o as the size of the magnets is downscaled, the high eld gradients will be experienced at the nanoscale, and thus we envisage that nanomagnets could be used to act on tiny biological objects (DNA strands, molecules. . . ) or just at the surface of larger species (cells, embryos. . . ). The potential to collaborate with biologists will now be explored.

1 2 1. 2 6 1. 3

 2263 Évolution du produit énergétique ( ) (à température ambiante) au 20 siècle. From [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv 2 Orientations actuelles de la recherche sur les aimants permanents. . . xxv 3 Schéma du principe des nanocomposites magnétiques durs/doux. . . xxvi 4 Diagramme des piliers d'un aimant nanocomposite dur-doux et des dé s.xxx 5 Schéma de ce contexte de thèse. . . . . . . . . . . . . . . . . . . . . . xxxi 6 Evolution of the energy product ( ) (at room temperature) in the 20th century. From [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . xxxviii 7 Current directions in permanent magnet research. . . . . . . . . . . . xxxix 8 Schematic of the principle behind hard + soft magnetic nanocomposites. xl 1.1 a) Hysteresis loop with schematic magnetic domains con guration. b) Magnet energy landscape during magnetisation reversal. From [21]. . Schematic of a 180 Bloch wall. The wall is located in the y-z plane, and the center of the wall (x=0) the magnetisation vector is parallel to the y axis. Adapted from [20]. . . . . . . . . . . . . . . . . . . . . . . . Left: Schematic one-dimensional model of exchange-coupled composite material. Right: Hysteresis loops for the distinct magnets. Adapted from [10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 14 5 -

 25 crystalline structure obtained by VESTA[START_REF] Momma | VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data[END_REF]. . . . . . . . .13 1.6 Research in NdFeB lms. . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Equilibrium phase diagram of the Fe-Pt system. Insert of the schematic crystallographic structures. From [45, 46] . . . . . . . . . . . . . . . . 14 xi List of Figures 1.8 Hysteron and data distribution for FORC diagram. . . . . . . . . . . . 17 1.9 FORC analysis. a) magnetisation data as function of applied eld( ). b) 3D view of the magnetisation data as a function of the reversal eld ( ) and applied eld ( ). c) Surface colormap obtained from (b). d) FORC diagram processed. Data obtained from 1 0 FePt thin lm. . . . 18 1.10 Hard-soft nanocomposite mindmap. . . . . . . . . . . . . . . . . . . . 19 1.11 a) Concentration dependence of the coercive eld of akes. b) Hysteresis loop of crystallized 4.5 77.0 18.5 [8] . . . . . . . . . . . . . . 20 1.12 Left: HRTEM images of the interface betweenparticles and the stoichiometric NdFeB grains. Right: EDX spectra from stoichiometric NdFeB phase (dashed line) andphase (solid line). From [69]. . 21 1.13 a)Hysteresis loops of HDDR processed NdFeB, before (red) and after (blue) NdCu di usion, parallel and perpendicular to the c-axis. HAADF-STEM b)low and c-d) high magni cation of Fe grain, 2 14 grains and grain boundary. From [28] . . . . . . . . . . . . . . . . . . . . . . 22 1.14 a) 3D atom probe analyses of a SmCo/Fe nanocomposite magnet with maps of Sm, Co, Fe and O and b) composition pro les along the length direction. c) Magnetic hysteresis loop of the same sample. From [14]. 23 1.15 Schematic of the sample preparation with a) ball milling of SmCo raw materials and Fe powder, b) compression of the milled powders and temperature gradient deformation and c) nal bulk nanocomposite with oriented SmCo nanorods and Fe(Co) equiaxed grains. d) Longitudesectional bright-eld TEM image with arrows indicating the rod shaped grains. e) Hysteresis loop of sample made at the optimum conditions [80]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.16 Top: TEM images of components for nanocomposite fabrication from Refs. FePt [51] and Fe 3 O 4 [83]. Bottom: TEM images showing binary nanoparticle assemblies [16]. . . . . . . . . . . . . . . . . . . . . . . . 26 1.17 a) HRTEM for sintered FePt/Fe 3 Pt obtained from Sample A. b) , and of the ∕ 3 nanocomposites annealed like Sample A, as a function of the mass ratio. Hysteresis loops for ∕ 3 nanocomposites with mass ratio of 0.1 c) Sample A. d) Sample C. [16]. . . . 27 xii List of Figures 1.18 Left: TEM images of Pd nanoparticles (dark points, d ∼ 5 nm) surrounded by -2 3 particles in a molar ratio of Fe/Pd = 80/20. Right: Schematic illustration of FePd/Fe nanocomposite with di erent FePd:Fe volume ratio [18]. . . . . . . . . . . . . . . . . . . . . . . 28 1.19 Hysteresis loops of FePd/Fe nanocomposites: (Left) formed at various annealing temperatures. (Right) with various hard/soft phase volume fraction formed by annealing at 723 K [18]. . . . . . . . . . . . . . . . 28 1.20 Left: FORC diagram of FePd/Fe (44/56) nanocomposites formed by annealing at (a) 773 K and (b) 823 K. Right: ( ) dependence on annealing temperature for nanocomposites with di erent volume ratio [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.21 Schematic illustration of 5 ∕ nanocomposite. From[88]. . . . . 29 1.22 XRD patterns of 5 ∕ (x %) nanocomposite wit x = 0, 5, 10 and 20. b) HAADF-STEM image. c) Elemental map of the 5 ∕ (10 %). From[88]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.23 Hysteresis loops of the 5 -Fe (x %) nanocomposites. a) ( x = 0 -20) at 300 K. Inset. the change of and with the di erent contents in the Fe nanocomposites. b) (x = 10) before and after 1.5 GPa compaction at 300 K. From [88]. . . . . . . . . . . . . . . . . . . . . . 30 1.24 a) TEM image of sample after annealing (33% Pt). (b)STEM-HAADF and the corresponding (c) STEM-EDX chemical mapping of (b) Fe, (d) Pt, (e)Co. f) Evolution of ( ) as a function of the Pt in the FeCo/Pt composites (red dots) and the FePt references (black squares) [15]. . . 31 1.25 Timeline with relevant studies employing Physical Vapor Deposition.

6 4. 7 = 4 2 5. 17

 674217 . . . . . 32 1.26 Left: Out of plane hysteresis loop of 27 nm (NdFeB)/24 nm (Fe)/27 nm (NdFeB) trilayer compared to a 80 nm NdFeB single layer. Right: Reduced remanence R(d) and coercivity as a function of the Fe-interlayer thickness d (out of plane measurements). From [49]. . . . . . . . . . . 33 xiii List of Figures 1.27 Left:Dark-eld cross-sectional TEM image and the electron di raction patter of a (11 20)oriented SmCo/Co superlattice. Center: Maximum energy product ( ) of a series of SmCo-Co as a function of Co layer thickness. Right: Room-temperature hysteresis loops of a single SmCo lm and SmCo-Fe bilayers with di erent Fe layer thickness. From [37] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.28 a)Thickness of the individual Fe layers and Sm-content in the individual 5 layers as a function of multilayer index n. b) Hysteresis loops for n=1,2,3,4 and 5. c) ( ) as a function of layer index n and an estimation based on interpolated data of remanence and coercivity. From [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.29 Hysteresis loops of a) Ti(20 nm)/NdFeB (100 nm)/Nd(10 nm)/Ti (20 nm)/ and Ti(20 nm)/NdFeB (100 nm)/Nd(10 nm)/Ta (x nm /Fe (10 nm)/ Ti (20 nm) b) x = 0 nm, c) 2 nm, d) 10 nm, e) 50 nm, f) 250 nm and g) 400 nm. h) The coercivity dependence of Ta thickness [19]. . . 1.30 The MFM images of the micron-sized soft magnetic disk. a) Schematic illustration of lithography-patterned arrays of Fe disks onto a continuous NdDyFeCoB layer with MgO spacer layer. b) Optical image of the disk array. c) and d) The in-eld MFM images of the coupled and decoupled samples. e) and f) MFM images at 160 K. [65]. . . . . . . . 1.31 a) AFM, MFM and TEM images of a nano-disk array [99].b) Hysteresis loops for samples of FePt/Co(0, 3 and 7 nm) with out-of-plane texture measured at room temperature [99].c) FORCs and d) FORC diagrams for the same samples listed in (b) [99] . . . . . . . . . . . . . . . . . .1.32 Diagram of Hard-soft nanocomposite magnet pillars and challenges. . 1.33 Schematic of this thesis context. . . . . . . . . . . . . . . . . . . . . . 2.1 Schematic process of nanofabrication. . . . . . . . . . . . . . . . . . . 2.2 Schematic of electronic beam lithography equipment. . . . . . . . . . 2.3 Schematic of di erent deposition pro les.Left: Directional (Evaporator). Right: Multi-directional (Sputtering). . . . . . . . . . . . . . . . . 2.4 Schematic of an undercut resist pro le. . . . . . . . . . . . . . . . . . 2.5 Schematic of magnetron sputtering: deposition con guration. . . . . . xiv List of Figures 2.6 Schematic of magnetron sputtering: etching con guration. . . . . . . 2.7 Schematic e-gun evaporator. . . . . . . . . . . . . . . . . . . . . . . . 2.8 Left:Schematic of the signal generation from the interaction of a highenergy electron beam with thin specimen. Adapted from [105]. Right: TEM basic layout [From CreativeCommons]. . . . . . . . . . . . . . . 2.9 Schematic of cross-section sample preparation.From [106] . . . . . . .2.10 a) Schematic of Focused Ion Beam machine. SEM image of b) Crosssection of the lamella . c) Lamella attached to Copper ring. . . . . . . 2.11 Left: Basic setup of AFM system. Right: Qualitative sketch of the force between the tip and sample as a function of the distance between them. Adapted [107]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Comparison between amplitude and phase for a free cantilever and cantilever under tip-sample interaction. . . . . . . . . . . . . . . . . . 2.13 Operation mode AFM/MFM: 1 pass in tapping mode to obtain topography and 2 pass DC and AC mode to obtain magnetic contrast. . . . 2.14 Zero-eld MFM images of S 5 ∕ ∕ 5 trilayer a) in fully saturated state, after having applied elds b) -0.50 T, c) -0.54 T, d) -0.56 T, e) -0.58 T, f) -0.70 T, g) -0.74 T, h) -0.80 T and i) -1.0 T along the easy magnetisation direction, from [111] . . . . . . . . . . . . . . . . . . . 2.15 From the left; Top view pulsed eld system coupled in the microscope and in-plane and out-of-plane coils. Schematic and image of sample holder mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16 Schematic diagram of scanning polar MOKE system incorporating a bi-polar pulsed magnetic eld.From [112]. . . . . . . . . . . . . . . . . 2.17 Current vs. voltage curve in a Josephson tunnel junction. Adapted from [114]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.18 Schematic for VSM-SQUID equipment. . . . . . . . . . . . . . . . . . 2.19 Correction for diamagnetic contribution. . . . . . . . . . . . . . . . . 3.1 Schematic overall protocol developed for sample preparation. . . . . . 3.2 Flowchart of sample preparation. . . . . . . . . . . . . . . . . . . . . . 3.3 Flowchart of nano-rods optimization process. . . . . . . . . . . . . . . xv List of Figures 3.4 SEM (Secondary electron) images of the optimization nano-rods fabrication process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 SEM (Secondary electron) images of nal nano-rod arrays. . . . . . . 3.6 Fabrication of large surface sample (schematic and top view SEM Secondary Electrons). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Tilted view -SEM Secondary Electrons. Left: Low magni cation nanorod arrays. Right: Nano-rods in detail. . . . . . . . . . . . . . . . . . . 3.8 Flowchart of hard magnetic phase development. . . . . . . . . . . . . 3.9 NdFeB sample preparation details and lm schematic. . . . . . . . . . 3.10 FePt composite target design. . . . . . . . . . . . . . . . . . . . . . . . 3.11 Schematic of the hard phase deposition with and without the micropatterning over the nano-rod arrays. . . . . . . . . . . . . . . . . . . . 3.12 Micro patterning of hard magnetic phase above soft nano-rod arrays, using UV lithography -top view SEM Secondary Electrons. . . . . . . 3.13 Micro-pattern development process for hard matrix (no soft nano-rod arrays) using e-beam lithography. . . . . . . . . . . . . . . . . . . . . . 3.14 FePt micro-pattern with di erent corner curvature radius (r = 0 , 1 and 2.5 , respectively). . . . . . . . . . . . . . . . . . . . . . . 3.15 Etching and deposition of hard magnetic matrix. . . . . . . . . . . . . 4.1 Left: M(H) loop for a Co nano-rod (w=40 nm, l=400 nm) array with di erent applied eld directions. Right: Comparison between distinct nano-rod dimensions and continuous lm of FeCo ( in-plane and parallel). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 FeCo (10 nm) /Au (3 nm) nano-rods (w=40 nm, l=400 nm d=60 nm): a)Topography obtained by AFM.b) Magnetic phase contrast in the virgin state. c) After in-plane applied eld (3 T) . . . . . . . . . . . . . . 4.3 Study of two step process in NdFeB thin lms. Measured by pulsed MOKE. Maximum 0 = 4 . . . . . . . . . . . . . . . . . . . . . 4.4 Study of two-step process in NdFeB thin lms.Left: Mo bu er layer. Right: Ta bu er layer. Maximum 0 = 6 . . . . . . . . . . . . . 4.5 Study of two-step process in NdFeB thin lms. Ta bu er layer. a) Bright eld. b) Dark eld. . . . . . . . . . . . . . . . . . . . . . . . . . xvi List of Figures 4.6 Study of two-step process in NdFeB thin lms. Maximum 0 = Study of annealing of NdFeB thin lms with Ta and Mo bu er layers performed at RTA -1 min. Measured by pulsed MOKE. Maximum 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Study of heat treatment of NdFeB thin lms deposited on oxidized on Ta or Mo bu er layers. Left: Annealing carried out in a RTA. Right: Annealing carried out in a tube furnace. Maximum 0 = 6 . . . 4.9 Target design and their respective hysteresis loops and coercivity maps. Measured by pulsed MOKE. Maximum 0 = 4 . . . . . . . . . . 4.10 M(H) curves for three di erent pieces of an FePt deposited lm from target C. Maximum 0 = 6 . . . . . . . . . . . . . . . . . . . . . 4.11 Raw data from VSM-SQUID measurement of micro-patterned FePt thin lm.Left: Thickness of 25 nm and Right: Thickness of 50 nm. . . . . . 4.12 ∕ curves for patterned samples of 25 nm thick of FePt. Annealing conditions: 500 -60 minutes. . . . . . . . . . . . . . . . . . . . . 4.13 Top: Topography image of 25 nm thick FePt micro-pattern with different corner curvature radius. Middle: Thickness pro le graph. Bottom: MFM phase contrast. The black arrow indicates the direction of the applied eld and the lines identify was the pro le thickness were acquired. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Hysteresis loop (in-plane) of FePt/FeCo bilayer with di erent thickness of FePt layer and di erent annealing time. A: 10 min and B: 60 min at 500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 FORC diagrams and their respective raw data. a) FePt 24 nm/FeCo 6 nm -A, b) FePt 24 nm/FeCo 6 nm -B. c) FePt 50 nm/FeCo 6 nm -A. . 5.3 TEM cross-section images of bilayer FePt 24 nm/FeCo 6 nm. a-b) Labeled layers. c) FePt crystals without sharp interface contrast with FeCo (dotted square). d) Sharp contrast (full arrows) and di use (dotted arrow). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 SEM top view SE images of nano-rod arrays embedded in ans FePt micro-pattern, 25NC1, 25NC2, 25NC3 and 25NC4. Scale bar = 1 . Information about the sample name. . . . . . . . . . . . . . . . . . . . xvii List of Figures 5.5 TEM cross section images of 50NC2 before annealing. a-b) One embedded nano-rod. c) Five embedded nano-rods. d) Dark eld image of three embedded nano-rods. . . . . . . . . . . . . . . . . . . . . . . . . 5.6 TEM cross section images of nano-rods after annealing. a-b ) 50NC2. c-d) 50NC4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 TEM cross section images from HAADF of nano-rods after annealing. Top: NC3. Bottom: NC4. . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 TEM cross section images from NC3 after annealing. a) HAADF. b) Co map. c) O map. d) Pt map. e) Si map. f) Fe map. . . . . . . . . . . . . 5.9 TEM cross section images from nano-rods in NC3 after annealing. a) HAADF. b) O map. c) Si map. d) Co map. e) Pt map. f) Fe map. . . . . 5.10 TEM cross section images from nano-rods in NC4 after annealing. a) HAADF. b) Co map. c) O map. d) Fe map. e) Si map. f) Pt map. . . . . 5.11 Hysteresis loop for samples detailed in Table 5.1 ( 0 = 6 T). . . . 5.12 Left: and as function of FeCo vol %. Right: Hysteresis loop for samples detailed in Table 5.1 ( 0 = 6 T). . . . . . . . . . . . . . . 5.13 FORC diagrams a) Hard micro-pattern. b) NC3. c)NC4. d) Bilayer. . . 5.14 FORC-raw data with ∕ (H) a) Hard micro-pattern. b) NC3. c)NC4. 5.15 (First column) AFM topography view of nanocomposites. MFM phase contrast in virgin and di erent remnant states. The micro-patterns have dimensions of approximately 5 × 5 2 . . . . . . . . . . . . . . 5.16 Detailed view and schematic of MFM phase contrast of 25NC3 and 25NC4. The micro-patterns have dimensions of approximately 5 × 5 Sample structures simulated to 25NC1, 25NC2, 25NC3, 25NC4 and 25NC5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.18 M(H) curve simulated to 25NC1, 25NC2, 25NC3, 25NC4 and 25NC5. .5.19 Left: M(H) curve obtained by micromagnetic simualtion. Right: M(H) curves measured from the nanocomposites. . . . . . . . . . . . . . . . 5.20 Model details of sample 25NC3 and 25NC4. . . . . . . . . . . . . . . . 5.21 M(H) curve and average magnetisation con guration of 25NC3 and 25NC4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii List of Figures 5.22 Simulated magnetisation con guration of 25NC4, expected MFM image based on the simulation and comparison with experimental MFM image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.23 SEM top view (SE images) of nano-rods for NC2 a) Au and c) Pt. Nanorods for NC4 b) Au and d) Pt. . . . . . . . . . . . . . . . . . . . . . . . 5.24 Hysteresis loop for samples detailed in Table 5.4. . . . . . . . . . . . . 5.25 MFM images of 25NC3, 25NC4, 25NC3-Pt and 25NC-Pt. . . . . . . . .

5. 28 FORC

 28 diagrams a) 25NC2-Co. b) 25NC3-Co. c) 25NC4-Co. Note the soft nano-rods are made of Co. . . . . . . . . . . . . . . . . . . . . . . 6.1 SEM images of nano-rods with di erent widths. Summary of the study of SmCo as hard magnetic matrix. . . . . . . . . . . . . . . . . . . . . 6.2 Summary of the study of SmCo as hard magnetic matrix. . . . . . . . 6.3 Nanomagnets (grey rectangle) architecture with respect the quantum dots (brown circles) and their respective magnetic eld map. The gradients are extracted at the position of the quantum dot (dashed black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1.1Au etching calibration curve established using AFM. . . . . . . . . . . A.2.1Polar MOKE curves of NdFeB layers deposited and annealead at different temperatures ( 0 =4 T). . . . . . . . . . . . . . . . . . . . . A.3.1dM/dH plots for micro-patterned FePt -50 nm and R = 30 nm . . . . . A.3.2dM/dH plots for micro-patterned FePt -50 nm and R = 1.0 . . . . A.3.3dM/dH plots for micro-patterned FePt -50 nm and R = 2.5 . . . . A.3.4dM/dH plots for micro-patterned FePt -25 nm and R = 30 nm . . . . . A.3.5dM/dH plots for micro-patterned FePt -25 nm and R = 1 . . . . . A.3.6dM/dH plots for micro-patterned FePt -25 nm and R = 2.5 . . . . A.5.1Left: Probe holder used for the deposition of hard magnetic and auxiliary layers, in magnetron sputtering system. Right: Probe holder used for probe magnetisation in a superconducting coils. . . . . . . . . . . xix Résumé Introduction Un aimant permanent est un objet fabriqué à partir d'un matériau qui peut maintenir une aimantation résiduelle en l'absence de champ extérieur. L'importance des aimants permanents s'est accrue au cours du siècle dernier, passant d'un matériau qui suscitait la curiosité à un matériau ayant un large éventail d'applications. Ces matériaux sont essentiels pour la conversion de l'énergie mécanique en électrique et réciproquement, et pour cette raison, ils sont largement utilisés dans les moteurs, les actionneurs et les générateurs. C'est pourquoi les e orts visant à améliorer les performances des aimants permanents peuvent se traduire par une conversion et une production d'énergie plus e caces. Ces e orts sont tout à fait dans la lignée de l'agenda des énergies propres et renouvelables, incluant par exemple les véhicules électriques et les éoliennes. En outre, la demande d'aimants à haute performance va augmenter dans les prochaines décennies étant donné que de nombreux pays prévoient d'interdire

FePtFigure 1 :

 1 Figure 1: Évolution du produit énergétique ( ) (à température ambiante) au 20 siècle. From [2].

Figure 2 :

 2 Figure 2: Orientations actuelles de la recherche sur les aimants permanents.

Figure 3 :

 3 Figure 3: Schéma du principe des nanocomposites magnétiques durs/doux.

Figure 4 :Figure 5 :

 45 Figure 4: Diagramme des piliers d'un aimant nanocomposite dur-doux et des dé s.

FePtFigure 6 :

 6 Figure 6: Evolution of the energy product ( ) (at room temperature) in the 20th century. From [2].

Figure 7 :

 7 Figure 7: Current directions in permanent magnet research.

Figure 8 :

 8 Figure 8: Schematic of the principle behind hard + soft magnetic nanocomposites.

Figure 1 . 1 :

 11 Figure 1.1: a) Hysteresis loop with schematic magnetic domains con guration. b)

  ferromagnetism favoring the parallel spins ( ). In other words, exchange energy penalty occurs with rapid uctuation in magnetisation direction. The constant is named exchange sti ness, and it is proportional to the Curie temperature ( ) and to the exchange constant ( ). The typical value of for a ferromagnet with above room temperature is around 10 pJ/m.

Figure 1 . 2 :

 12 Figure 1.2: Schematic of a 180 Bloch wall. The wall is located in the y-z plane, and

width (Equation 1 . 6 ) 9 ≃ √ 2 ( 1 . 9 )Figure 1 . 3 :

 16921913 Figure 8.35 Hysteresis behaviour of a spring magnet (a) optimized two-phase nanostructure, (b) overcoupled nanostructure, (c) hard phase alone and (d) constricted loop due to two independent phases (after E. F. Kneller and R. Hawig, IEEE, Trans. Mag. 27, 3588 (1991).)

Figure 1 . 4 :

 14 Figure 1.4: Sample architecture for micromagnetic modelling. a) From [25], b)From

  Figure 1.5:

2 14

 2 crystalline structure obtained by VESTA[START_REF] Momma | VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data[END_REF].

17

 17

Figure 1 . 6 :

 16 Figure 1.6: Research in NdFeB lms.

Chapter 1 .Figure 1 . 7 :

 117 Figure 1.7: Equilibrium phase diagram of the Fe-Pt system. Insert of the schematic crystallographic structures. From[START_REF] Massalski | Binary phase diagrams[END_REF][START_REF] Gut Eisch | FePt Hard Magnets[END_REF]

Chapter 1 .Figure 1 . 8 :

 118 Figure 1.8: Hysteron and data distribution for FORC diagram.

Figure 1 . 9 : 1 0

 191 Figure 1.9: FORC analysis. a) magnetisation data as function of applied eld( ). b) 3D view of the magnetisation data as a function of the reversal eld ( ) and applied eld ( ). c) Surface colormap obtained from (b). d) FORC diagram processed. Data obtained from 1 0 FePt thin lm.

Figure 1 . 10 :

 110 Figure 1.10: Hard-soft nanocomposite mindmap.

Figure 1 .

 1 11-a shows the relation between coercivity and composition. The optimum in was found for 4.5 77.0 18.5 and the M(H) loop can be visualized in Figure 1.11-b R . Coe hoorn e t a t / Fe 3 B containing pe rm ane nt m agne ts 103

Fig. 4 .

 4 Fig. 4. Hys te re s is lo o p of crys ta llize d Nd4.s Fe 77B18.5.

  during 30 min. The te mpe ra ture whe re the optim u m wa s fo u n d ra nge d fro m 640 to 680 ° C. The pos ition of the a re a o f optima l He ca n be e xpla ine d fro m the following cons ide ra tions . Above 5 a t% Nd no Nd2Fe ]4B is fo u n d . Ins te a d,

Fig. 3

 3 Fig.3. Conce ntra tion de pe nde nce of coe rcive fie ld of fla ke s , a nne a le d is othe rma lly fo r 30 ra in. Th e s pa cing be twe e n contours of e q u a l/to ll ¢ is 0.025 T.

Figure 1 .

 1 Figure 1.11: a) Concentration dependence of the coercive eld of akes. b) Hysteresis loop of crystallized

Figure 1 .

 1 Figure 1.12: Left: HRTEM images of the interface betweenparticles and the stoichiometric NdFeB grains. Right: EDX spectra from stoichiometric NdFeB phase (dashed line) andphase (solid line). From [69].

70 30

 70 in ltration. In this case, the soft phase consisted of sphericalinclusions of diameter 200 nm, and the nanocomposite had a coercivity of 0.85 T. The hysteresis loops obtained parallel and perpendicular to the c-axis of aligned as HDDR-processed 11.48 82.52 6.0 (in red) and after

70 30Figure 1 .

 701 Figure 1.13: a)Hysteresis loops of HDDR processed NdFeB, before (red) and after (blue) NdCu di usion, parallel and perpendicular to the c-axis. HAADF-STEM b)low and c-d) high magni cation of Fe grain,

8 88 4

 84 -based composite alloys and evaluate the e ect of the addition of Cu, Si,

3

 3

Figure 1 .

 1 Figure 1.14: a) 3D atom probe analyses of a SmCo/Fe nanocomposite magnet with maps of Sm, Co, Fe and O and b) composition pro les along the length direction. c) Magnetic hysteresis loop of the same sample. From [14].

Chapter 1 .Figure 1 . 15 :

 1115 Figure 1.15: Schematic of the sample preparation with a) ball milling of SmCo raw materials and Fe powder, b) compression of the milled powders and temperature gradient deformation and c) nal bulk nanocomposite with oriented SmCo nanorods and Fe(Co) equiaxed grains. d) Longitude-sectional bright-eld TEM image with arrows indicating the rod shaped grains. e) Hysteresis loop of sample made at the optimum conditions [80].

Chapter 1 . 4 3 Figure 1 .

 1431 Figure 1.16: Top: TEM images of components for nanocomposite fabrication from Refs. FePt [51] and Fe 3 O 4 [83]. Bottom: TEM images showing binary nanoparticle assemblies [16].

Figure 1 .

 1 Figure 1.17: a) HRTEM for sintered FePt/Fe 3 Pt obtained from Sample A. b) , and of the ∕ 3 nanocomposites annealed like Sample A, as a function of the mass ratio. Hysteresis loops for ∕ 3 nanocomposites with mass ratio of 0.1 c) Sample A. d) Sample C. [16].

5

  MNPs[START_REF] Hong | Exchange coupled magnetic nanocomposites of Sm(Co1-xFex)5 / Fe3O4 with core/shell structure[END_REF].Sakuma et al.[START_REF] Sakuma | Exchange Coupling Interaction in L1 0-FePd/ -Fe Nanocomposite Magnets with Large Maximum Energy Products[END_REF] reported on the fabricaton of 1 0 FePd / -het-Chapter 1. Hard-Soft Magnetic Nanocomposites erostructured nanocomposites. This work is relevant because of the clever choice of FePd as hard magnetic phase, which avoids the formation of Fe rich alloys, and the use of advanced magnetic characterization as First Order Reversal Curve (FORC) diagrams. The heterostructures were fabricated via interfacial atom di usion between Pd andafter the reduction of -2 3 . The volume ratio of the phases impacts on the shape of the nal heterostructure, as shown in Figure 1.18.

Figure 1 .

 1 Figure 1.18: Left: TEM images of Pd nanoparticles (dark points, d ∼ 5 nm) surrounded by -2 3 particles in a molar ratio of Fe/Pd = 80/20. Right: Schematic illustration of FePd/Fe nanocomposite with di erent FePd:Fe volume ratio [18].

Figure 1 . 19 :

 119 Figure 1.19: Hysteresis loops of FePd/Fe nanocomposites: (Left) formed at various annealing temperatures. (Right) with various hard/soft phase volume fraction formed by annealing at 723 K [18].

Figure 1 .

 1 Figure 1.21 presents a schematic for the fabrication of Fe nanoparticles stabilized in a 5 matrix. This innovative work combines the non-trivial manufacturing of soft magnetic inclusion embedded in a rare-earth based matrix with compaction techniques. The process became possible due to the stabilization of Fe nanoparticle together with precipitated ( ) 3 nanorods and ( ) 2 nanoplates. The Fe nanoparticles were mixed in ethanol under soni cation and then submitted to annealing. An additional compaction step was performed to improve the exchange coupling between the phases [88].

Figure 1 . 21 :

 121 Figure 1.21: Schematic illustration of 5 ∕ nanocomposite. From[88].

Figure 1 .

 1 Figure 1.22: XRD patterns of 5 ∕ (x %) nanocomposite wit x = 0, 5, 10 and 20. b) HAADF-STEM image. c) Elemental map of the 5 ∕ (10 %). From[88].

Figure 1 . 23 :

 123 Figure 1.23: Hysteresis loops of the 5 -Fe (x %) nanocomposites. a) ( x = 0 -20) at 300 K. Inset. the change of and with the di erent contents in the 5 -Fe nanocomposites. b) (x = 10) before and after 1.5 GPa compaction at 300 K. From [88].

Chapter 1 .

 1 Figure 1.24: a) TEM image of sample after annealing (33% Pt). (b)STEM-HAADF and the corresponding (c) STEM-EDX chemical mapping of (b) Fe, (d) Pt, (e)Co. f) Evolution of ( ) as a function of the Pt in the FeCo/Pt composites (red dots) and the FePt references (black squares) [15].

Figure 1 . 25 :

 125 Figure 1.25: Timeline with relevant studies employing Physical Vapor Deposition. The papers cited are: Parhofer et al.[49], Shindo et al.[56], Goute et al. [92], Fullerton et al. [37], Liu et al. [93], Crew et al.[57], Liu et al. [94], Seki et al. [95], Zambano et al. [96], Neu et al. [17], Cui et al. [97, 19], Wang et al. [98], Dai et al. [65] and Son et

Chapter 1 .

 1 Hard-Soft Magnetic Nanocomposites 1.25 presents a timeline with the evolution and combination of di erent materials, layer architecture and analysis techniques.

Figure 1 .

 1 Figure 1.26: Left: Out of plane hysteresis loop of 27 nm (NdFeB)/24 nm (Fe)/27 nm (NdFeB) trilayer compared to a 80 nm NdFeB single layer. Right: Reduced remanence R(d) and coercivity as a function of the Fe-interlayer thickness d (out of plane measurements). From [49].

Figure 1 . 27 :

 127 Figure 1.27: Left:Dark-eld cross-sectional TEM image and the electron di raction patter of a (11 20)oriented SmCo/Co superlattice. Center: Maximum energy product ( ) of a series of SmCo-Co as a function of Co layer thickness. Right: Roomtemperature hysteresis loops of a single SmCo lm and SmCo-Fe bilayers with di er-

Figure 1 .

 1 Figure 1.28: a)Thickness of the individual Fe layers and Sm-content in the individual 5 layers as a function of multilayer index n. b) Hysteresis loops for n=1,2,3,4 and 5. c) ( ) as a function of layer index n and an estimation based on interpolated

2 14 ∕

 14 Figure 1.29: Hysteresis loops of a) Ti(20 nm)/NdFeB (100 nm)/Nd(10 nm)/Ti (20 nm)/and Ti(20 nm)/NdFeB (100 nm)/Nd(10 nm)/Ta (x nm /Fe (10 nm)/ Ti (20 nm) b) x = 0 nm, c) 2 nm, d) 10 nm, e) 50 nm, f) 250 nm and g) 400 nm. h) The coercivity dependence of Ta thickness[START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF].

Chapter 1 .

 1 Hard-Soft Magnetic Nanocomposites magnetic layers continues with NdDyFeCoB/MgO/Fe multilayers and microdisks prepared by magnetron sputtering onto a Si wafer. The thickness of the MgO spacer layer varies between 20 nm and 70 nm, in order to produce well coupled and decoupled hard and soft magnetic layers, considering the magnetostatic coupling.

Figure 1 . 30 :Figure 1 .

 1301 Figure 1.30: The MFM images of the micron-sized soft magnetic disk. a) Schematic illustration of lithography-patterned arrays of Fe disks onto a continuous NdDyFeCoB layer with MgO spacer layer. b) Optical image of the disk array. c) and d) The in-eld MFM images of the coupled and decoupled samples. e) and f) MFM images at 160 K. [65].

Figure 1 . 32 :

 132 Figure 1.32: Diagram of Hard-soft nanocomposite magnet pillars and challenges.

Figure 1 . 33 :

 133 Figure 1.33: Schematic of this thesis context.

Figure 2 . 1 :

 21 Figure 2.1: Schematic process of nanofabrication.

Figure 2 .

 2 Figure2.1 shows the approach used, in this thesis, to fabricate arrays of soft magnetic nano-rods. It consists, rstly, in the wafer preparation, spin-coating the polymer, also called the resist. Next, the sample is introduced in the exposure chamber, where the pattern is written. Once the exposure is complete, the sample is developed with a speci c solvent that will dissolve only the polymer-modi ed by interaction with the e-beam. Subsequently, the PVD process of e-gun evaporation or magnetron sputtering (see Sections 2.3 and 2.2) is performed to deposit the metallic layers. Finally, the sample is treated to lift-o under the action of a solvent; this time, the solvent dissolves all the resist coating, revealing the nal metallic nanostructures in the sample[START_REF] Chen | Nanofabrication by electron beam lithography and its applications: A review[END_REF].

Figure 2 . 2 :

 22 Figure 2.2: Schematic of electronic beam lithography equipment.

Figure 2 . 3 :

 23 Figure 2.3: Schematic of di erent deposition pro les.Left: Directional (Evaporator). Right: Multi-directional (Sputtering).

Figure 2 . 4 :

 24 Figure 2.4: Schematic of an undercut resist pro le.

Figure 2 . 5 :

 25 Figure 2.5: Schematic of magnetron sputtering: deposition con guration.

Figure 2 .

 2 Figure 2.5 shows a schematic of a magnetron sputtering chamber. The mag-

Figure 2 . 6 :

 26 Figure 2.6: Schematic of magnetron sputtering: etching con guration.

  Di erent materials have a distinct melting point and conductivity, therefore, a di erent applied current is required. The e-gun evaporator used for sample fabrication in this work is available at Institut Neel cleanroom (Ti, Co, Au and Pt depositions) and PTA-Minatec (Ti, Au, FeCo and Co depositions), and is commercialized by Plassys (MEB550). Both equipments are very similar, except by the man-machine interface and vacuum system. A quartz crystal microbalance provides real-time information about the deposited thickness.

Figure 2 . 7 :

 27 Figure 2.7: Schematic e-gun evaporator.

Figure 2 . 8 -

 28 Figure 2.8-Left, also shows that the interaction between the beam and the specimen can generate elastic and inelastic scattering. A unique form of elastic scat-

Figure 2 . 8 :

 28 Figure 2.8: Left:Schematic of the signal generation from the interaction of a highenergy electron beam with thin specimen. Adapted from [105]. Right: TEM basic layout [From CreativeCommons].

Figure 2 . 9 :Figure 2 .

 292 Figure2.9: Schematic of cross-section sample preparation.From[START_REF] Devillers | Etude des propriétés physiques des phases de Ge(1-x)Mn(x) ferromagnétiques pour l'électronique de spin[END_REF]

Fig 2 .

 2 [START_REF] Kneller | The exchange-spring magnet: a new material principle for permanent magnets[END_REF] shows a schematic view of this equipment. The preparation performed by J.F. Motte, at CEA-Grenoble in a Zeiss NVISION

  Fig. 1.5 Qualitative behavior of the force between tip and sample as function of tip-sample distance

. 7 .Figure 2 . 11 :

 7211 Figure 2.11: Left: Basic setup of AFM system. Right: Qualitative sketch of the force between the tip and sample as a function of the distance between them. Adapted [107].

Figure 2 . 11 -

 211 Figure 2.11-Right qualitatively depicts the force between the tip and a given sample. It presents three di erent regimes: (i) when the tip is far from the surface, no

Figure 2 . 13 :

 213 Figure 2.13: Operation mode AFM/MFM: 1 pass in tapping mode to obtain topography and 2 pass DC and AC mode to obtain magnetic contrast.

Figure 2 .

 2 Figure 2.14: Zero-eld MFM images of S 5 ∕ ∕ 5 trilayer a) in fully saturated state, after having applied elds b) -0.50 T, c) -0.54 T, d) -0.56 T, e) -0.58 T, f) -0.70 T, g) -0.74 T, h) -0.80 T and i) -1.0 T along the easy magnetisation direction, from[START_REF] Neu | Imaging the Magnetization Processes in Epitaxial Exchange Coupled SmCo 5 /Fe/SmCo 5 Trilayers[END_REF]

Figure 2 .

 2 Figure 2.14 depicts MFM images at remnant state of trilayer of hard-soft nanocomposite magnet of 5 ∕ ∕ 5 . The investigation carried out by Neu et al. relates the MFM images with the demagnetizing process showing the domain evolution from nucleation (Figure 2.14-b), increase of the domain size (Figure 2.14-d),

  by D. Givord and O. Fruchart. All the electronics was already prepared, and the coils were fabricated by R. Haettel. During this thesis, S. Le Denmat designed and built a new sample holder and supports to attach the coils to the microscope. The electronic includes, basically a IGBT transistor and an electrochemical capacitor. The intensity of the magnetic eld applied is controlled by the charge accumulated in the capacitor, and the applied eld varies linearly with the voltage in the capacitor.

Figure 2 . 15 :

 215 Figure 2.15: From the left; Top view pulsed eld system coupled in the microscope and in-plane and out-of-plane coils. Schematic and image of sample holder mechanism.

FIG. 1 .

 1 FIG. 1. Schematic diagram of a scanning polar MOKE system incorporating a bi-polar pulsed magnetic field source.

Figure 2 . 16 :

 216 Figure 2.16: Schematic diagram of scanning polar MOKE system incorporating a bipolar pulsed magnetic eld.From [112].

Figure 2 . 17 :

 217 Figure 2.17: Current vs. voltage curve in a Josephson tunnel junction. Adapted from [114].

Figure 2 . 18 :

 218 Figure 2.18: Schematic for VSM-SQUID equipment.

Figure 2 .

 2 Figure 2.18 presents a schematic of VSM-SQUID equipment. The system

Figure 2 .Figure 2 . 19 : 1 68 3. 2 72 3. 2 . 1 73 3. 2 . 2 74 3. 2 . 3 75 3. 3 78 3. 4

 22191682722173227423753784 Figure 2.19 shows the typical measurement before and after the correction.

Figure 3 . 1 :

 31 Figure 3.1: Schematic overall protocol developed for sample preparation.

Figure 3 . 2 :Figure 3 . 3 :

 3233 Figure 3.2: Flowchart of sample preparation.

Figure 3 .

 3 Figure 3.3 shows a schematic for the nano-rods development. The rst step

Figure 3 . 4 :

 34 Figure 3.4: SEM (Secondary electron) images of the optimization nano-rods fabrication process.

Figure 3 .

 3 Figure 3.4 pictures the di erent stages of development of the nano-rod arrays. The rst two images show the rst design tried with an unrealistic aspect ratio (1:5000 -width = 40 nm and length = 200 ), resulting in a frustrated lift-o and resist collapse. Later on, reducing the length to 400 nm, it was possible to achieve a clean lift-o over a micrometric surface.

Figure 3 . 5 :Figure 3 . 6 :

 3536 Figure 3.5: SEM (Secondary electron) images of nal nano-rod arrays.

Figure 3 .

 3 Figure 3.6 presents a schematic of the large surface fabrication after adapting the dose for this situation. The arrays shown in Figure 3.5 are repeated thousands of times to reach a signal that can be measured by VSM-SQUID. The nano-rod arrays units with individual surface area of 5 × 5 2 cover a total surface of 3.0 × 1.8 2 .

Figure 3 . 7 :

 37 Figure 3.7: Tilted view -SEM Secondary Electrons. Left: Low magni cation nanorod arrays. Right: Nano-rods in detail.

4 .Figure 3 . 8 :

 438 Figure 3.8: Flowchart of hard magnetic phase development.

Figure 3 . 9 :

 39 Figure 3.9: NdFeB sample preparation details and lm schematic.

Figure 3 .

 3 Figure 3.9 presents the details about the NdFeB sample preparation starting

Figure 3 . 11 :Figure 3 . 12 :

 311312 Figure 3.11: Schematic of the hard phase deposition with and without the micropatterning over the nano-rod arrays.

Figure 3 .

 3 Figure 3.13: Micro-pattern development process for hard matrix (no soft nano-rod arrays) using e-beam lithography.

Figure 3 . 14 :

 314 Figure 3.14: FePt micro-pattern with di erent corner curvature radius (r = 0 , 1 and 2.5 , respectively).

1 4 . 2

 142 Soft magnetic nano-rods . . . . . . . . . . . . . . . . . . . . . . Hard magnetic thin lms . . . . . . . . . . . . . . . . . . . . . 4.2.1 NdFeB thin lms . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 FePt thin lms . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 FePt thin lms -micro-patterning . . . . . . . . . . . . . . . In this chapter the di erent characterizations performed on the two subsystem, namely, soft and hard magnetic phases. It contains structural characterization (AFM and TEM) and local and global magnetic measurements (VSM-SQUID and MFM).

Figure 4 . 2 :

 42 Figure 4.2: FeCo (10 nm) /Au (3 nm) nano-rods (w=40 nm, l=400 nm d=60 nm): a)Topography obtained by AFM.b) Magnetic phase contrast in the virgin state. c) After in-plane applied eld (3 T)

Figure 4 .

 4 3 it is possible to observe the evolution of the sample behavior for the di erent deposition temperatures and post-deposition ex-situ annealing performed with RTA. The samples were a multilayer lm -

Figure 4

 4 compared with the lms with Ta bu er layer. Although this promising result, the loops acquired by VSM-SQUID reveal remarkable two-phase behaviour, suggesting that the properties of the sample surface di ered from its volume, as can be visualized in Figure4.4-left.The hysteresis loops for the sample submitted to the same heat treatment in Figure4.4-left, but with a Ta bu er layer instead, is presented in 4.4-right, in this case a better agreement with the behaviour showed in MOKE and VSM-SQUID. The

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

 4344445 Figure 4.3: Study of two step process in NdFeB thin lms. Measured by pulsed MOKE. Maximum 0 = 4

Figure 4 . 6 :

 46 Figure 4.6: Study of two-step process in NdFeB thin lms. Maximum 0 = 6

Figure 4 . 7 : 4 Figure 4 . 8 :

 47448 Figure 4.7: Study of annealing of NdFeB thin lms with Ta and Mo bu er layers performed at RTA -1 min. Measured by pulsed MOKE. Maximum 0 = 4

2 . 2 Figure 4 . 9 :

 2249 Figure 4.9: Target design and their respective hysteresis loops and coercivity maps. Measured by pulsed MOKE. Maximum 0 = 4 .

Figure 4 .

 4 Figure 4.10: M(H) curves for three di erent pieces of an FePt deposited lm from target C. Maximum 0 = 6 .

Figure 4 .

 4 Figure 4.11 shows an example of the VSM-SQUID raw data obtained from the micro-pattern . The samples were measured after a heat treatment at 500 during 10 minutes. All graphs depicted in 4.11 present a diamagnetic component coming from the silicon substrate, as discussed in Section 2.10.1. Once the signal of the patterned lm decreases, this component becomes visible, appearing in the hysteresis loop. Even with this distortion, it is possible to note pronounced two phase behaviour in the 25 nm thick lms, especially in the r= 30 nm and r= 2.5samples. On the other hand, in the 50 nm thick lms, a single phase behaviour and 1 T coercivity is observed for all the samples. In order to eliminate the diamagnetic contribution from the substrate and be able to visualize clearly the phases presents in the samples, ∕ was plotted in Figure4.12.

Figure 4 . 11 :

 411 Figure 4.11: Raw data from VSM-SQUID measurement of micro-patterned FePt thin lm.Left: Thickness of 25 nm and Right: Thickness of 50 nm.

Figure 4 .

 4 Figure 4.12: ∕ curves for patterned samples of 25 nm thick of FePt. Annealing conditions: 500 -60 minutes.

Figure 4 . 13 :

 413 Figure 4.13: Top: Topography image of 25 nm thick FePt micro-pattern with di erent corner curvature radius. Middle: Thickness pro le graph. Bottom: MFM phase contrast. The black arrow indicates the direction of the applied eld and the lines identify was the pro le thickness were acquired.

5. 1 95 5. 2 99 5. 2 . 1 99 5. 2 . 2 105 5. 2 . 3 113 5. 3 119 5. 4 122 5. 5

 19529921992210523113311941225 Bilayer -FePt/FeCo . . . . . . . . . . . . . . . . . . . . . . . . . FeCo nano-rods in a -patterned FePt (25 nm) -Case study . . Structural characterization . . . . . . . . . . . . . . . . . . . Magnetic characterization . . . . . . . . . . . . . . . . . . . Micromagnetic simulations . . . . . . . . . . . . . . . . . . . Pt nano-rods in a -patterned FePt (25 nm) . . . . . . . . . . . FeCo nano-rods in a -patterned FePt (50 nm) . . . . . . . . . Co nano-rods in a -patterned FePt (25 nm) . . . . . . . . . . . 123 This chapter presents the results and discussions related with the hard-soft nanocomposites. The building blocks presented in Chapter 4 (soft magnetic nanorods, micro-patterned hard magnetic layer) were integrated, resulting in FePt/FeCo bilayer (Section 5.1) and FeCo, Co and Pt nano-rods embedded in FePt matrix. The FeCo nano-rods embedded in FePt matrix, which were investigated in more detail are presented as Case study (Section 5.2).

FePt 24 Figure 5 . 1 :Figure 5 . 2 :Figure 5 . 3 :

 24515253 Figure 5.1: Hysteresis loop (in-plane) of FePt/FeCo bilayer with di erent thickness of FePt layer and di erent annealing time. A: 10 min and B: 60 min at 500 .

Figure 5 . 4 : 99 Chapter 5

 54995 Figure 5.4: SEM top view SE images of nano-rod arrays embedded in ans FePt micropattern, 25NC1, 25NC2, 25NC3 and 25NC4. Scale bar = 1 . Information about the sample name.

tion 4 . 2 . 3 )Figure 5 . 5 :

 42355 Figure 5.5: TEM cross section images of 50NC2 before annealing. a-b) One embedded nano-rod. c) Five embedded nano-rods. d) Dark eld image of three embedded nanorods.

Figure 5 . 6 :Figure 5 . 7 :

 5657 Figure 5.6: TEM cross section images of nano-rods after annealing. a-b ) 50NC2. c-d) 50NC4.

Figure 5 .Figure 5 . 8 :Figure 5 . 9 :

 55859 Figure 5.8 shows chemical maps for 25NC3. Even though the topography reveals the prior existence of a nano-rod in that region, the absence of any chemical signal indicates that there is no material present at the original nano-rod position. Considering the nanocomposite structure, Fe should be present everywhere as it is in both the FePt matrix and the FeCo nano-rods. The distinction between matrix and rod should be visible with Pt (only matrix) and Co (only rod). It can be clearly seen that Co

Figure 5 . 10 :

 510 Figure 5.10: TEM cross section images from nano-rods in NC4 after annealing. a) HAADF. b) Co map. c) O map. d) Fe map. e) Si map. f) Pt map.

Figure 5 . 11 :

 511 Figure 5.11: Hysteresis loop for samples detailed in Table5.1 ( 0 = 6 T).

Figure 5 .

 5 Figure 5.12: Left: and as function of FeCo vol %. Right: Hysteresis loop for samples detailed in Table5.1 ( 0 = 6 T).

FirstFigure 5 . 13 :Figure 5 . 14 : 107 Chapter 5 .

 5135141075 Figure 5.13: FORC diagrams a) Hard micro-pattern. b) NC3. c)NC4. d) Bilayer.

8 . 1 Figure 5 .

 815 Figure 5.15: (First column) AFM topography view of nanocomposites. MFM phase contrast in virgin and di erent remnant states. The micro-patterns have dimensions of approximately 5 × 5

5. 16 )Figure 5 . 16 : 5 2

 165165 Figure 5.16: Detailed view and schematic of MFM phase contrast of 25NC3 and 25NC4. The micro-patterns have dimensions of approximately 5 × 5

  2), a second with domain formation inside the rods following the domain structure of the hard matrix. The periodic line contrast is observed in all the images of 25NC4, and closer inspection of sections of the images taken after -250 mT and -500 mT, outlined by white boxes, indicates that the sign of this contrast has been inverted, the schematic in Figure5.16 suggests the mechanism for the observed contrast. Based on the eld values at which the periodic horizontal line contrast of 25NC2, 25NC3 and 25NC4 are seen to switch, we associate the contrast with the soft phase component that is well-coupled (25NC2 and 25NC3) or partially coupled (25NC4) to the hard matrix.

Figure 5 . 17 :

 517 Figure 5.17: Sample structures simulated to 25NC1, 25NC2, 25NC3, 25NC4 and 25NC5.

Figure 5 .

 5 Figure 5.18: M(H) curve simulated to 25NC1, 25NC2, 25NC3, 25NC4 and 25NC5.

Figure 5 . 19 :

 519 Figure 5.19: Left: M(H) curve obtained by micromagnetic simualtion. Right: M(H) curves measured from the nanocomposites.

Figure 5 . 20 :

 520 Figure 5.20: Model details of sample 25NC3 and 25NC4.

Figure 5 .Figure 5 .

 55 Figure 5.21 shows snapshot images of reduced magnetization con gurations (blue = +1, red = -1), averaged over the depth of the nanocomposites, at di erent values of applied eld, together with demagnetization curves constructed from such a set of simulations. The demagnetization curves of the nanocomposites is comparedto that of a continuous FePt lm. Observation of a series of magnetic con gurations at di erent heights within the nanocomposites (data not shown here) clearly indicates that magnetization reversal begins in the soft nano-rods and then propagates to the hard matrix. Reversal of entire nano-rods is evident in the averaged snapshots of the sample with the coarser rods (25NC4). While the coercivity of the nanocomposites are comparable, and signi cantly lower than that of the reference hard layer, the slope of the demagnetization curves of the nanocomposites are distinct. The demag-

  Convoluted with MFM tip (lift = 50 nm)Repeated side by side to be similar to the sample

Figure 5 . 22 :

 522 Figure 5.22: Simulated magnetisation con guration of 25NC4, expected MFM image based on the simulation and comparison with experimental MFM image.

Figure 5 .

 5 [START_REF] Brown | Micromagnetics[END_REF] shows the di erence betwen the nano-rods prepared with Au and Pt.

Figure 5 . 23 : 4 :

 5234 Figure 5.23: SEM top view (SE images) of nano-rods for NC2 a) Au and c) Pt. Nanorods for NC4 b) Au and d) Pt.

Figure 5 . 24 :

 524 Figure 5.24: Hysteresis loop for samples detailed in Table 5.4.

Figure 5 . 25 :

 525 Figure 5.25: MFM images of 25NC3, 25NC4, 25NC3-Pt and 25NC-Pt.

Figure 5 . 26 :

 526 Figure 5.26: Hysteresis loop for samples detailed in Table5.5 ( 0 = 6 T).

Figure 5 . 27 : 123 Chapter 5 6 :Figure 5 . 28 :Figure 5 . 27 -

 52712356528527 Figure 5.27: Hysteresis loop for samples detailed in Table 5.6 ( 0 = 6 T)

Figure 6 . 1 :

 61 Figure 6.1: SEM images of nano-rods with di erent widths. Summary of the study of SmCo as hard magnetic matrix.

Figure 6 . 2 :

 62 Figure 6.2: Summary of the study of SmCo as hard magnetic matrix.

Figure 6 . 3 :

 63 Figure 6.3: Nanomagnets (grey rectangle) architecture with respect the quantum dots (brown circles) and their respective magnetic eld map. The gradients are extracted at the position of the quantum dot (dashed black line).

  En outre, l'état de l'art est présenté avec les principales voies de fabrication, les matériaux et les techniques de caractérisation utilisés dans ce domaine. Un comportement monophasé, suite à une optimisation du processus de recuit, a pu être obtenu dans des lms de FePt de 25 nm d'épaisseur. Une étude de l'e et de la micro-structuration sur les propriétés magnétiques a ensuite été réalisée, et une forme optimisée a été identi ée.Ensuite, dans le chapitre 5, les résultats obtenus pour divers nanocomposites sont présentés. Il s'agit notamment de bicouches FeCo / FePt, de nano-bâtonnets FeCo intégrés dans des micro-plots de FePt, de nano-bâtonnets de Co intégrés dans des micro-plots de FePt et de nano-bâtonnets de Pt intégrés dans des micro-plots de FePt. Outre les principales boucles d'hystérésis, des analyses plus poussées par FORC,

	Pour con rmer nos observations et analyses expérimentales, nous avons ini-
	tié des collaborations pour modéliser le retournement de l'aimantation dans nos na-
	nocomposites. Ces travaux sont toujours en cours, et je présenterai les résultats en-
	courageants obtenus à ce jour. Une première série de résultats a été obtenue par J.
	Les techniques expérimentales utilisées pour fabriquer les échantillons mod-

èles, ainsi que les méthodes de caractérisation utilisées dans cette thèse sont présentées dans le chapitre 2. Ce chapitre décrit à la fois les équipements commerciaux et les équipements développés sur mesure à l'Institut NEEL.

Le chapitre 3 présente la préparation des échantillons, y compris l'optimisation de la lithographie électronique pour fabriquer des nano-bâtonnets magnétiques doux, la préparation des matériaux magnétiques durs candidats (NdFeB et FePt) et les étapes de micro-modélisation de la matrice. Ce chapitre résume les protocoles de préparation des échantillons développés au cours de cette thèse. De nombreux processus d'optimisation ont été nécessaires pour parvenir à une méthode robuste et intégrer les di érentes techniques présentées, en particulier pour la lithographie par faisceau d'électrons des nanostructures, où les exigences de l'échantillon ont repoussé les limites de cette voie de fabrication. A n de tester si le protocole de préparation aurait un impact sur les propriétés magnétiques de la phase magnétique dure, des échantillons de référence de FePt micro-modelé ont été produits sans inclusion de nano-tige et avec des nano-tige (Pt) non magnétiques. Le chapitre 4 compile les résultats des di érents éléments de base, c'est-àdire les propriétés magnétiques des réseaux de nano-bâtonnets magnétiques doux et des couches magnétiques dures. Ce chapitre présente un résumé des caractérisations magnétiques et structurales réalisées pour les blocs élémentaires des nanocomposites durs/doux. On est partis des réseaux de nano-bâtonnets magnétiques doux, dont des boucles M(H) et des images MFM ont été présentées. La matrice magnétique dure a ensuite été étudiée. Malgré une étude d'optimisation approfondie, tous les lms minces de NdFeB ont montré une signature d'une certaine phase magnétique douce xxvii Chapter 0. Résumé inutilisable pour le nanocomposite. AFM, MFM, TEM avec cartographie EDX ont été e ectuées pour certains échantillons spéci ques. Dans cette étude de cas, un ensemble de techniques complémentaires de caractérisation magnétique a été utilisé pour sonder l'in uence de la taille et du volume des nano-bâtonnets magnétiques doux sur le comportement magnétique de nos nanocomposites modèles. Des boucles d'hystérésis majeures ont révélé comment une fraction de faible volume (1,8 %) de bâtonnets étroits (24 nm) n'a ecte pas l'hystérésis du nanocomposite par rapport à un lm dur de référence à micro motifs. L'augmentation de la fraction volumique des nano-bâtonnets doux entraîne une baisse de la coercitivité, avec des valeurs comparables pour les nanocomposites 25NC3 et 25NC4, ayant respectivement des bâtonnets étroits (24 nm) de 8 % volumique et des bâtonnets larges (120 nm) de 11 % volumique. La forme des courbes de désaimantation de ces échantillons est quelque peu di érente, la première étant convexe, la seconde concave. L'analyse FORC nous a ensuite permis d'extraire plus d'informations sur la distribution des champs de retournement dans les nanocomposites et les lms durs micro-structurés. En particulier, elle a révélé la présence d'une phase magnétique douce non couplée dans 25NC3 et 25NC4, qui n'était pas évidente dans les boucles d'hystérésis principales. Les di érences dans la distribution des champs de retournement de 25NC3 et 25NC4 sont attribuées à des di érences dans l'étendue du couplage entre la matrice dure et les nano-bâtonnets intégrées.

Alors que les techniques discutées ci-dessus sont de nature globale, le MFM permet de sonder les con gurations magnétiques de manière locale. Grâce au fait que nous avons structuré à la fois les nano-bâtonnets doux (à l'échelle nanométrique) et la xxviii Chapter 0. Résumé matrice dure (à l'échelle microscopique), il est possible de distinguer la retournement de ces phases distinctes. L'imagerie MFM dans di érents états de rémanents nous a permis de "voir" comment les nano-bâtonnets larges de 25NC4 commutent dans des champs plus petits que les nano-bâtonnets étroits de 25NC3.

Fischbacher et T. Schre (Université du Danube Krems) en utilisant une méthode par éléments nis (FEMME). Dans cette étude, l'in uence de la taille et de la fraction volumique des inclusions magnétiques douces, ainsi que l'e et de la di usion entre les phases dure et douce, sur les courbes de désaimantation ont été simulés. Pour évaluer l'in uence éventuelle de la topographie de la matrice dure induite par le dépôt sur un ensemble de nano-bâtonnets, nous avons également préparé un nanocomposite contenant des nano-bâtonnets non magnétiques (Pt). Les détails expérimentaux de la préparation et de la caractérisation de ce type d'échantillon sont donnés ci-dessous, et les simulations de telles structures sont incluses ici. Une deuxième série de résultats a été obtenue par L. Ranno (Institut NEEL), en utilisant une méthode de di érence nie (FD) (MuMax). Dans cette étude, les courbes de désaimantation et de recul ont été simulées pour les deux échantillons traités dans l'étude de cas (25NC3 et 25NC4), ce qui permet de les comparer aux images MFM expérimentales.

Les conclusions et perspectives nales sont présentées dans le chapitre 6.

  Résumé les échantillons. L'intégration de nano-bâtonnets magnétiques doux fabriqués par lithographie par faisceau électronique avec une matrice magnétique dure déposée par pulvérisation cathodique a été réalisée avec succès malgré les di cultés rencontrées pour combiner ces di érentes techniques de fabrication. De nombreuses étapes ont été nécessaires pour optimiser la fabrication et résoudre des problèmes inattendus.Dans le cas de la lithographie par faisceau d'électrons des nano-bâtonnets, la plus grande di culté était ce qu'on appelle l'e et de proximité, en raison duquel la plus petite distance possible entre les objets est limitée, surtout s'ils ont de très petites dimensions. La distance la plus faible entre les bâtonnets obtenus dans cette étude était de Toutefois, cette exigence est se heurte aux limites imposées par les techniques de

	Chapter 0. Résumé
	taille des nano-bâtonnets doux (Section 5.2.2).
	Pour compléter l'étude expérimentale, une collaboration a été établie avec
	des chercheurs spécialisés dans les simulations. Une première série de simulations in-
	lithographie par nano-impression, mais alors qu'ils ont nano-structuré une bicouche fabrication. Sur la base de recherches bibliographiques approfondies (section 1.2), dique que la di usion observée dans les nanocomposites avec les nano-bâtonnets les
	constituée d'une couche douce déposée sur une couche dure [11], nous avons réussi les rapports sur les problèmes liés à la di usion pendant le recuit pour former la plus étroits, ne modi e pas de manière signi cative le retournement de l'aimantation
	à enfouir notre phase douce nano-structurée dans une matrice dure. Les structures phase dure sont très courants et inhérents à de nombreuses techniques de fabrication par rapport à la nanostructure initialement prévue. De plus, un bon accord est obtenu
	douces dans la matrice dure devraient être les architectures nanocomposites les plus [13, 14, 15]. Dans certains cas, elle favorise des changements positifs dans la struc-entre les courbes de désaimantation mesurées et simulées en fonction de la taille des
	prometteuses [12], et le découplage des dimensions dans le plan des caractéristiques ture, par exemple en améliorant le produit énergétique [16, 17]. Dans d'autres cas, le nano-bâtonnets doux. Une deuxième série de simulations vient appuyer notre anal-
	dures et douces o re les avantages spéci ques décrits ci-dessus. choix des matériaux ou des architecture d'échantillons est fait a n d'éviter autant que yse du contraste observé dans l'imagerie MFM. Ces simulations révèlent également
	comment le retournement commence dans les nano-bâtonnets doux, et que la taille
	des nano-bâtonnets a un impact sur la propagation du domaine. Bien que les résul-
	tre la taille des nano-bâtonnets magnétiques douces et la facilité de di usion. Cette tats des simulations soient préliminaires, le bon accord obtenu entre deux modèles
	observation a été possible grâce à l'utilisation de l'imagerie TEM à haute résolution et di érents et les résultats expérimentaux montrent une voie prometteuse pour l'étude
	chimiquement sensible (Section 2.5). des nanocomposites durs/doux (Section 5.2.3).
	Bien que les résultats de la caractérisation structurale soient d'une impor-
	tance énorme pour l'étude des nanocomposites magnétiques durs et doux, le princi-
	pal objet de recherche de cette thèse est les propriétés magnétiques et la compréhen-
	sion du retournement de l'aimantation. L'impact de l'augmentation de la teneur en
	phase douce sur la diminution de la coercitivité et l'augmentation de la rémanence
	a été évalué en utilisant des boucles d'hystérésis majeures (Section 5.2.2) mesurées
	par magnétométrie VSM-SQUID. Une étude globale plus poussée du couplage entre
	la matrice dure et les nano-bâtonnets doux en fonction de leur taille a été réalisée
	en utilisant des courbes d'inversion du premier ordre qui ont révélé des signatures
	très distinctes pour des échantillons ayant des dimensions de phase douce di érentes
	(Section 5.2.2). Ces mesures ont également révélé la présence de phases magnétiques
	douces couplées et non couplées, ces dernières n'étant pas évidentes dans les boucles
	d'hystérésis complètes. Des mesures magnétiques locales, portant sur une unité mi-
	crométrique des nanocomposites, ont été e ectuées à l'aide d'un microscope MFM
	combiné à un système de champ pulsé in situ fait maison (Section 2.8.1). L'évolution
	du contraste magnétique en fonction de l'état rémanent fournit une signature visuelle
	du retournement à la fois de la matrice dure et des nano-bâtonnets doux, révélant
	ainsi comment le retournement de l'aimantation des nanocomposites dépend de la
	xxxiv xxxv

les voies de production massive (métallurgique, chimique), (ii) la compréhension des paramètres critiques avec des échantillons modèles et (iii) les simulations micromagnétiques proposant des structures optimales ou modélisant les nanocomposites présentés. Ces travaux constituent une première étape dans l'étude des nano-bâtonnets doux produits par lithographie par faisceau électronique et intégrés dans une matrice magnétique dure. L'utilisation de la nanofabrication visait à contrôler en dernier ressort la taille et la position des inclusions magnétiques douces, tandis que les caractérisations ont révélé les propriétés structurales et magnétiques. Ces propriétés ont été corrélées et discutées à la lumière des simulations micromagnétiques.

L'un des plus grands dé s dans la réalisation de ce projet a été de fabriquer xxxi Chapter 0. 50 nm. L'e et de proximité limite également la surface qui peut être structurée, ce qui nous a conduit à fabriquer des réseaux répétitifs de nano-bâtonnets a n de produire des échantillons avec une grande surface globale (mm 2 ) adaptée aux mesures magnétométriques. Les matrices individuelles ont une surface de 5 × 5 m 2 , et sont séparées des matrices voisines par un espace de 5 µm. A n de maximiser la teneur en phase douce, la matrice magnétique dure a été micro-structurée, de manière à limiter sa couverture juste au-dessus des matrices de nano-bâtonnets doux. La micro-structuration de la matrice magnétique dure a introduit de nouveaux problèmes, par exemple un comportement biphasé dans la phase dure. Grâce à une optimisation poussée, des nanocomposites magnétiques durs/doux constitués de nano-bâtonnets doux (quatre architectures di érentes) intégrés dans une matrice magnétique dure ont été produits avec succès par nanofabrication. Néanmoins, le plus grand volume de phase douce atteint n'a été que

de

11 % en raison des contraintes évoquées ci-dessus, ce qui limite nécessairement l'amélioration de ( ) qui peut être obtenue par rapport à la seule phase dure. Cela limite également la valeur absolue de ( ) qui peut être obtenue par rapport à d'autres combinaisons de matériaux et d'autres voies de fabrication. C'est pourquoi nous n'utilisons pas ( ) comme gure de mérite pour nos échantillons modèles. Nous étudions plutôt l'impact de l'architecture des échantillons sur le retournement de l'aimantation dans nos nanocomposites. Le fait que la nanofabrication permette de contrôler la taille, la forme et la position de la phase douce facilite grandement la caractérisation structurelle locale (MEB, MET). Plus important encore, elle apporte des avantages spéci ques à l'étude du retournement de l'aimantation, d'une part en permettant la reconnaissance de motifs spéci ques aux xxxii Chapter 0. Résumé composants (µ-plots dur contre nano-bâtonnets doux) dans l'imagerie MFM et d'autre part en permettant des géométries de simulation qui correspondent très bien aux systèmes réels étudiés. Un autre groupe a récemment fait état de l'utilisation de la En ce qui concerne les matériaux explorés, le FeCo et le Co ont été utilisés comme phase douce, tandis que le NdFeB et le FePt ont été étudiés comme candidats pour la phase dure. Le NdFeB a été éliminé en raison de la dégradation de ses propriétés magnétiques lorsqu'il est déposé sous forme de lm très mince (sections 3.2.1 et 4.2.1). Le FePt, cependant, s'est avéré être un choix judicieux, car le comportement d'une seule phase dure pouvait être obtenu de manière reproductible dans des lms aussi minces que 25 nm. Le protocole de fabrication des lms de FePt utilisés dans ce projet a été établi dans le cadre d'une étude approfondie des lms homogènes et à gradient de composition, réalisée en collaboration avec Y. Hong (sections 3.2.2, 4.2.2 et A.5). Le processus de micro-structuration et l'optimisation du traitement thermique des lms micro-structurés ont été réalisés en collaboration avec F. Orlandini-Keller (Sections 3.2.3 et 4.2.3). Le FePt tel qu'il a été déposé, puis micro-structuré, se trouvait dans un état désordonné A1 0 , et une étape de recuit était nécessaire pour produire du FePt coercitif L1 0 . Une di usion de type Kirkendall a été observée dans les nanocomposites recuits avec les nano-bâtonnets les plus étroits (24 nm). Ce processus de di usion a généré des vides dans la position d'origine des nano-bâtonnets, et a entraîné la formation de régions riches en FeCo d'une épaisseur proche de 20 nm environ autour des vides. Dans les échantillons comportant des nano-bâtonnets de 120 nm de large, le FeCo est essentiellement resté en place, bien que certains vides aient été observés aux bords des nano-bâtonnets. Cela indique qu'il existe une relation entre la taille des nano-bâtonnets et la di usion qui se produit dans les nanocomposites (Section 5.2.1). Notons que l'une des conditions sine qua non pour obtenir un nanocomposite avec de xxxiii Chapter 0. Résumé bonnes propriétés magnétiques est de maintenir les dimensions nanométriques de la phase douce, une conclusion de divers modèles micromagnétiques (Sections 1.1.2 et ??).

possible l'impact de la di usion

[START_REF] Sakuma | Exchange Coupling Interaction in L1 0-FePd/ -Fe Nanocomposite Magnets with Large Maximum Energy Products[END_REF][START_REF] Cui | Hard magnetic properties of spacer-layer-tuned NdFeB/Ta/Fe nanocomposite lms[END_REF]

. Sur la base d'une analyse des échantillons produits dans le cadre de cette thèse, il a été possible d'établir un compromis clair en-

HRE reduction in "NdFeB" magnets LRE substitution in "NdFeB" magnets Metallic RE free magnets Ferrite magnets Hard-soft nanocomposite magnets RE lean magnets

			Chapter 0. General Introduction
		Dy	Tb
	RE
	substitution
	Jan-Teller		Ce
	distortion
		Magnet	La
	MnAl	research today
	MnBi		SmFe Ti 11
	FeNi	16 2 Fe N	NdFe TiN 11
			have
	been a driving factor in de ning the main directions in permanent magnet research
			xxxviii

Hard-Soft Magnetic Nanocomposites 1.1 Basic concepts in Magnetism . . . . . . . . . . . . . . . . . . . 1

		Chapter 0. General Introduction
	the State of the Art is presented with the main fabrication routes, materials and char-
	acterization techniques used in this eld.
	The experimental techniques used to fabricate the model samples, as well
	as the characterization methods used in this thesis are presented in Chapter 2. This
	chapter describes both commercial equipment and bespoke equipment developed at Institut NEEL. Chapter 3 presents sample preparation, including optimization of e-Chapter 1
	beam lithography to fabricate soft magnetic nano-rods, the preparation of candidate
	hard magnetic materials (NdFeB and FePt) and micro-patterning steps of the matrix .
	Chapter 4 compiles results of the individual building blocks, i.e. magnetic
	properties of soft magnetic nano-rod arrays and the hard magnetic layers. Finally, re-
	sults obtained with FePt lms with the optimized composition are presented together
	with a description of its patterning.
	Then, in chapter 5, results obtained for various nanocomposites are pre-
	sented. These include, FeCo / FePt bilayers, FeCo nano-rods embedded in FePt micro-1.1.1 Hysteresis loop and Micromagnetic model . . . . . . . . . . 2
	patterns, Co nano-rods emdedded in FePt micro-patterns and Pt nano-rods embed-1.1.2 Exchange-spring magnets . . . . . . . . . . . . . . . . . . . . 7
	ded in FePt micro-patterns. Besides the major hysteresis loops, FORC analysis, AFM,
	MFM, TEM with EDX mapping were performed for select samples in the case study. 1.1.3 Micromagnetic models of exchange-spring magnets . . . . . 8
	Preliminary micromagnetic simulations were executed with the sample parameters 1.1.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
	and their results will also be discussed in this chapter. The nal considerations, con-1.1.5 Magnetic characterization techniques . . . . . . . . . . . . . 15
	clusions and perspectives are presented in Chapter 6.
	for a deeper understanding about hard-soft nanocomposites. Besides this,
	xlii	xl xli

1.2 A brief history of the development of hard-soft magnetic na- nocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1

  .2.1 Fabrication routes . . . . . . . . . . . . . . . . . . . . . . . .

19 1.3 Thesis context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Table 1 .

 1

	Hard phase	Soft phase	Struct. type	Soft dim. (nm)	Hard dim. (nm)	Content soft (vol %)	( ) ( ∕ 3 )	(kA/m) Hc	(T) Mr	Ref
	2	17 3	65	35	Multilayer	9	2.4	78.9	1000	NA	NA	[29]
	2		Fe		Grain/matrix	15	20	81.3	318	472	1.51 T [30]
	2		Fe		isotropric Multilayer	10	20	42.9	301	771	1.51	[31]
	2		Fe		textured Multilayer	15	20	NA	486	1275	1.75	[31]
			Fe		Multilayer	5	10	NA	405	NA	NA	[32]
			Fe		Multilayer	10	10	NA	390	NA	NA	[32]
			Co		Multilayer	5	10	NA	339	NA	NA	[32]
			Co		Multilayer	10	10	NA	389	NA	NA	[32]
			Fe		Multilayer stacks	8	1	85	800	500	NA	[33]*
					textured
			Fe		Multilayer stacks	8	8-x	85	700	NA	NA	[33]*
					textured
	2		Fe		textured Multilayer stacks	8	1-x	85	500	NA	NA	[33]*
			Fe		Multilayer stacks	14	14	50	300	NA	NA	[33]*
					isotropic
			Fe		Multilayer stacks	14	14	50	250	NA	NA	[33]*
					isotropic
	2	17 3	65	35	Battenberg	9.5	2.25/4.25	42	400	NA	NA	[27]**
	2
	2		65	35	Battenberg	9.5	4.25	42	380	NA	NA	[27]**
	MnBi	Co		Gain/matrix	20	20	22	406	544	1.48	[34]
	MnBi	FeCo		Gain/matrix	20	20	14	226	567	1.08	[34]

2 14 ∕ 3 ∕ -magnets calculated from demagnetisation curves for a mean grain size varying from 10 nm to 30 nm and also evaluates a core-shell 9 Chapter 1. Hard-Soft Magnetic Nanocomposites 1: Selection of studies with modeled hard-soft nanocomposites with various materials, structures and techniques.* 473 K ** 450 K structure, both depicted in Figure 1.4-b. The work of Skomski as well as that by Bance et al. explores soft nano-

Table 1 .

 1

	Chapter 1. Hard-Soft Magnetic Nanocomposites

2: Soft and hard magnetic materials and their properties.

Table 1 . 4

 14

	Synthesis	Comment	Reaction	Size	Shape	Yield
	method		period	distribution	control
	Co-precipitation	Very simple,	minutes	relatively	not good	high/
		ambient conditions		narrow		scalable
	Thermal	Complicated,	hours -days	very	very good	high/
	decomposition	inert atmosphere		narrow		scalable
	Microemulsion	Complicated,	hours	relatively	good	low
		ambient conditions		narrow
	Hydrothermal	Simple,	hours	very	very good medium
	synthesis	high pressure		narrow

3 4

)

[START_REF] Sun | Size-Controlled Synthesis of Magnetite Nanoparticles[END_REF]

: Comparison of chemical synthesis methods for MNP,

[START_REF] Lu | Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application[END_REF]

.

(Figure

1

.16)

. This method allowed a size tuning from 3 to 10 nm. Thermal annealing is necessary to convert the face-centred cubic (fcc) to the face-centred tetragonal (fct) structure, reaching 0.6 T of coercivity. On the other hand, Fe 3 O 4 particles were synthesized with a size distribution of 4 nm, with possible size increment by seed-mediated growth. The two components were then used for the production of exchanged-coupled nanocomposite magnets by nanoparticle self-assembly

[START_REF] Zeng | Exchange-coupled nanocomposite magnets by nanoparticle self-assembly[END_REF]

. Figure 1.16 presents how these studies were combined. Sample Fe 58 Pt 42 Fe 3 O 4

Table 5 .

 5 1: Samples description.

	-

Table 5 .

 5 2: Constants values used in the simulation.

	74) [98]	2.88	1.43	9.4
	FeCo [135]	0.	2.45	35.0
	(Fe,Co) 3 Pt [136]	0.	1.57	20.0
	nonmagnetic	0.	0.	0.

Table 5

 5 Neighbouring grains were in direct contact (no grain boundary phase) and perfectly coupled. The mesh size at interfaces and surfaces was 2 nm. In this model the topography of the hard phase surface was taken into account.

		Ku (MJ/m³) Js (T) A (pJ/m)
	FePt (S = 0.74)	29	1.4	20
	FeCo	0.001	2.0	20

.3. The size of the FePt grains was set at approximately 20 nm and an isotropic easy axes distribution was assumed.

Table 5 .

 5 3: Constants values used in the simulation.

	z= 30 nm	z= 15 nm	z= 0 nm
	25NC3
	25NC4
			FePt grains
			FeCo
	Cross-section		Air

FePt -50 nm nano-rod width w (nm) Inter nano-rod distance d (nm) nano-rod length l (nm) vol % soft magnetic phase Nano-rod material -patterned hard layer

		-	-	-	n.a.	-
	50NC1	24	200	200	0.9%	FeCo
	50NC2	30	90	400	3.4%	FeCo
	50NC3	24	52	200	4.0%	FeCo
	50NC4	120	130	400	5.7%	FeCo
	Continuous bilayer	-	-	-	11.0%	FeCo

Table 5 .

 5

5: Samples description.

14

Acknowledgments

Finally I thank Nanoscience and LANEF for my funding. Also, ANR for funding the SHAMAN project and all colleagues involved.

Scanning MOKE vs. VSM-SQUID

The Scanning MOKE provides a surface measurement while the VSM-SQUID gives a volume measurement that, together with the volume of the magnetic content in the sample, leads to the magnetisation in tesla (T) (or ∕ 3 ). The latter requires approximately 40 minutes to measure a typical hard magnet hysteresis loop (sample size ∼ 4 4

2 ) and the former can scan a four inches wafer in 4 hours. However, the Kerr signal cannot be directly used to estimate magnetisation and any di erence between the magnetic properties of the surface and the volume will generate discrepancy in these measurements. For these reasons, the Scanning MOKE is used for a quick screening and VSM-SQUID for a more reliable and accurate measurement.

same annealing conditions in the tube furnace at 500 during 10 minutes.

FePt thin lms -micro-patterning

As mentioned in the section on the optimization of nano-rods (Section 3.1), it is not possible to produce a continuous surface due to the limitations of e-beam lithography for high density of structures with small dimensions. Therefore, nanorod array units are spaced 5 of each other. Figure 3.11 displays a schematic of the hard phase deposition with and without the micro-patterning. As can be visualized, a second lithography step is necessary to avoid the dilution of the soft magnetic phase as well as regions of hard phase without soft inclusions, resulting in non-homogeneous material. Following this strategy, each array is equally covered by hard phase lm and the samples can be characterized individually and globally.

The rst try consisted of using UV laser lithography, considering its fastness and the need for micro-metric resolution. However, this technique does not provide enough control of the alignment, and the nal shape of the micro-pattern is not reproducible. Figure 3.12 shows di erent results obtained with the same UV lithography protocol. From this experience, it was decided that e-beam lithography would be more suitable micro-pattern the hard matrix.

As described in the e-beam lithography section, the resist choice also depends on the deposition method chosen. The sputtering deposition is not directional,

Bilayer-FeCo/FePt

Nanocomposite samples with bilayer structure were produced using the same protocol described, what includes evaporation of FeCo and Au protective layer, etching to surface recovery, deposition by magnetron sputtering of the FePt and annealing to form the hard magnetic matrix. In order to combine hard and soft materials, it is rst necessary to remove the Au protective layer on top of the soft phase. In this process consists an Ar plasma is used for etching the surface of the nano-rods, so as to remove the Au protective layer, prior to deposition of the hard matrix. The whole process is carried out under vacuum in the magnetron sputtering chamber. Additional EDX analysis was performed to verify the absence of Au in the etched samples.

Surface recovery -Hard on Soft

This chapter summarizes the sample preparation protocols developed during this thesis. Many optimization processes were necessary to reach a robust method and integrate the di erent techniques presented, specially for the e-beam lithography of the nanostructures, where the sample requirements pushed the limits of this fabrication route. In order to test if the preparation protocol would impact the magnetic This section presents the results obtained from the characterization of the soft magnetic nano-rods. Figure 4.1 shows M(H) curves for distinct nano-rod dimensions and applying the magnetic eld in di erent directions. In Figure 4.1-left it is possible to observe the e ect of the applied eld direction on a given Co nano-rod array. When is parallel to the easy (longer) axis, the shape anisotropy leads to a coercivity of = 0.180 T, when the applied eld is parallel to the hard axis the coercivity is close to 0 T. It is important to remark that for both measurements the applied eld ( ) is in plane and due to the very small detected signal, the diamagnetic contribution from the substrate was removed (according to the procedure described in Section 2.10.1). The fact that the sample has a very small signal, approximately 1.0 10 -6 . . . , can make any contamination signal dominates the measurement. This may account for the soft "shoulder" signature around 0 T, observed in the Figure 4.1-left and right.

In Figure 4.1-Right, the graph also shows the impact of shape anisotropy.

The continuous thin lm shows soft behavior while the the nano-rods present a coercive eld that increases with the rod aspect ratio (l/w). The rods with w=30 nm present coercivity of 0.120 T while rods with w= 120 nm has = 20 mT (both nanorods arrays have the same length (400 nm)). According to their results, the oxidation on the top surface is the most critical and the addition of a Au protection layer was enough to prevent rod degradation [START_REF] Laureti | Size Dependence of Exchange Bias in Co/CoONanostructures[END_REF]. The This chapter presents a summary of the magnetic and structural characterizations carried out in the building blocks for the hard-soft nanocomposites. Starting from the soft magnetic nano-rod arrays, where M(H) loops and MFM images were presented. Moving to the hard magnetic matrix, despite an extensive optimization study, all NdFeB thin lms showed a signature of some soft magnetic phase. Single phase behaviour, following an optimization of the annealing process could be achieved in 25 nm thick FePt lms. A study of the e ect of micro-patterning on the magnetic properties was then carried out, and an optimised shape was identi ed. The next chapter presents the extensive characterization of the building blocks assembled.

T. A drop in coercivity is expected according to Equation 5.1, which predicts the nucleation eld [START_REF] Fullerton | Hard/soft magnetic heterostructures: model exchange-spring magnets[END_REF], considering a bilayer system of a hard and a soft magnetic phase, where the thickness of the soft magnetic layer is smaller than the domain width of the hard phase ( ≤ ℎ ). It is considered that the anisostropy of the soft magnetic phase ( ) is much smaller than the anisotropy of the hard magnetic phase ( ℎ ) ( ≪ ℎ )

and the magnetisation of the soft magnetic phase ( ) is approximately twice the magnetisation of the hard phase ( ℎ ) ( ∼ 2 ℎ ). For the studied system, the change in the thickness of the FePt should lead to a reduction ( %) of 17.4% in the nucleation eld. However the coercivity value drops by 42 %, suggesting that other factors also impact the reversal process such as defects and inhomogenities or the evolution of anisotropy of the hard phase. From the FORC diagrams the switching eld distribution can be visualized for each bilayer nanocomposite. The presence of one peak around their respective coercivity values is a indicative of single phase behavior associated with the exchangecoupling of the layers. In Figure 5.2 -a, the absence of acquisition points around 0 T prevents a full analysis of the process, thus the existence of a secondary phase cannot be excluded. A similar problem is faced in Figure 5.2-c. Figure 5.2-b presents the sample that was annealed during 60 minutes and even though the coercive eld distribution is sharper, the degradation of the coercivity drag the peak to 65 mT, suggesting that the microstructure might be more complex than a simple bilayer.

Figure 5.3 presents the cross-section images prepared by the Polishing + Ion milling method described in Section 2.5.2. The pictures show regions with and without the sharp interface and also gives information about the FePt lm microstructure.

The hard magnetic layer is one or two grains deep, as depicted in Figure 5.3b-c and some of the crystals do not have a sharp interface contrast with FeCo (dotted square).

This investigation reveals regions in the sample FePt 24 nm/FeCo 6 nm -B where

A.2 NdFeB thin lm

A.3 Micro-patterned FePt optimization

A.4 Error bar -Case study measurements

Table 1 shows the coercivity values considering the in uence of the correction of the diamagnetic contribution from the substrate. The variation considers an error of 10 % in the diamagnetic correction.

The error bar for the magnetisation was calculated based in the error associ- ated to the volume estimation of the magnetic content. For this estimation, the critical point in is the surface measurement, once the thickness is the same considering that the deposition happened at the same time. The surface determination was not trivial to measure because sometimes the sample would break during the cutting process, remembering they were originally on the same wafer. The error for the surface was obtained from Equation 1.

Where is the sample surface, is the sample width, is the sample length.

A.5 High coercivity MFM probes

The main motivation for the in-house fabrication of high coercivity MFM probes were the elevated price and non reliability of the commercial probes. The high in the probe before the MFM scanning. When a reversal eld of 0.2 T is applied the image became blurry and at -1.0 T the contrast had still not inversed, suggesting that the probes coercivity is bigger then 1 T. When -7.0 T is applied, the contrast is ipped and sharp. After +7.0 T is applied, the initial contrast is totally recovered.

Magnetic holography is being performed in collaboration with A. Masseboeuf applying a magnetic eld parallel to the tip direction.