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N

ATURE OF THE

F

IRST

-O

RDER

M

AGNETIC

P

HASE

T

RANSITION IN

G

IANT

-M

AGNETOCALORIC

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N

ATURE OF THE

F

IRST

-O

RDER

M

AGNETIC

P

HASE

T

RANSITION IN

G

IANT

-M

AGNETOCALORIC

M

ATERIALS

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op donderdag 21 april 2016 om 10:00 uur

door

Y

IBOLE

Master of Science in Condensed Matter Physics, Inner Mongolia Normal University, Hohhot, China,

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. E. Brück

copromotor: Dr. ir. N. H. van Dijk

Samenstelling promotiecommissie: Rector Magnificus, voorzitter

Prof. dr. E. Brück, Technische Universiteit Delft Dr.ir. N. H. van Dijk, Technische Universiteit Delft

Onafhankelijke leden:

Prof. dr. O. Tegusi Inner Mogolia Normal University Prof. dr. J. Aarts Universiteit Leiden

Prof. dr. ir. T. H. van der Meer

Universiteit Twente

Prof. dr. F. M. Mulder Technische Universiteit Delft

Dr. M. Lo Bue École normale supérieure de Cachan

Prof. dr. P. Dorenbos Technische Universiteit Delft, reservelid

The work presented in this PhD thesis is financially supported by the Foundation for Fundamental Research on Matter (FOM), the Netherlands, via the Industrial Partnership Program IPP I28 and co-financed by BASF New Business, carried out at the section Fun-damental Aspects of Materials and Energy, Faculty of Applied Sciences, Delft University of Technology (TUD).

Printed by: Uitgeverij BOXPress, ’s-Hertogenbosch

Copyright © 2015 by Yibole ISBN 978-94-6186-625-7

An electronic version of this dissertation is available at http://repository.tudelft.nl/.

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C

ONTENTS

1 Introduction 1

1.1 The magnetocaloric effect . . . 2

1.2 Magnetic refrigeration . . . 2

1.3 Magnetocaloric materials. . . 4

1.4 Scope and outline of this thesis. . . 6

2 Theoretical aspects 7 2.1 Theromodynamics of the magnetocaloric effect . . . 8

2.1.1 Thermodynamic potentials at play. . . 8

2.1.2 Maxwell relation and Clausius-Clapeyron equation . . . 9

2.1.3 Calorimetric method. . . 10

2.2 X-ray absorption spectroscopy and X-ray magnetic circular dichroism . . . 12

2.2.1 X-ray absorption spectroscopy. . . 12

2.2.2 X-ray magnetic circular dichroism. . . 12

2.2.3 Sum rules for the transition metal L edge . . . 14

3 Experiments and Techniques 17 3.1 Sample Preparation. . . 18

3.1.1 Synthesis by High Energy Ball Milling . . . 18

3.1.2 Metallic Flux Crystal Growth. . . 18

3.2 Structural Analysis . . . 19

3.2.1 Powder X-ray Diffraction. . . 19

3.2.2 Single Crystals X-ray Diffraction . . . 19

3.2.3 Scanning Electron Microscopy. . . 19

3.3 Magnetization Measurements . . . 19

3.4 Differential Scanning Calorimetry . . . 20

3.4.1 Commercial Differential Scanning Calorimetry . . . 20

3.4.2 In-field Differential Scanning Calorimetry. . . 21

3.5 Direct Adiabatic Temperature Change . . . 21

3.6 High-Field MCE Measurement . . . 22

3.7 X-ray Magnetic Circular Dichroism. . . 22

4 Determination of the magnetocaloric effect in (Mn,Fe)2(P,Si,B) materials 25 4.1 The case of second-order phase transitions. . . 26

4.2 Isothermal entropy change for a first-order phase transition . . . 28

4.2.1 Indirect determination of∆S from magnetization measurements . . 29

4.2.2 Indirect determination of∆S from isofield in-field DSC . . . 31

4.2.3 Direct determination of∆S from isothermal DSC measurements . . 33 vii

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viii CONTENTS

4.3 Adiabatic temperature change for a first-order phase transition . . . 34

4.3.1 Indirect determination of∆T from isofield in-field DSC. . . 34

4.3.2 Direct determination of∆T . . . 34

4.4 Conclusions. . . 35

5 Direct measurement of the magnetocaloric effect in (Mn,Fe)2(P,X) (X = As, Ge, Si) materials 37 5.1 Introduction . . . 38

5.2 Magnetocaloric effect at intermediate magnetic field. . . 38

5.2.1 Magnetocaloric effect in MnFeP0.45As0.55 . . . 38

5.2.2 Magnetocaloric effect in Mn1.20Fe0.80P0.75Ge0.25. . . 41

5.2.3 Magnetocaloric effect in (Mn,Fe)2(P,Si) . . . 43

5.2.4 Discussion of intermediate magnetic field data . . . 48

5.3 Field dependence of the magnetocaloric effect in (Mn,Fe)2(P,Si) . . . 51

5.3.1 Preliminary data. . . 51

5.3.2 Field dependence of the entropy change. . . 53

5.3.3 Field dependence of the adiabatic temperature change . . . 55

5.3.4 Discussion of high field data. . . 55

5.4 Conclusions. . . 57

6 Insight into the magnetic and electronic structure of (Mn,Fe)2(P,Si,B) com-pounds by X-ray magnetic circular dichroism 59 6.1 Introduction . . . 60

6.2 Experimental and calculation details . . . 61

6.3 XAS and XMCD results at the L-edge of Mn and Fe . . . 63

6.4 Comparison of the experimental results with theoretical calculations . . . 66

6.5 Derivation of quantitative moments for the spin and orbital moments . . . 68

6.6 Moment evolution across the ferromagnetic phase transition. . . 69

6.7 Conclusions. . . 73

7 Structural and magnetic properties of single-crystalline (Mn,Fe)2(P,Si) 75 7.1 Introduction . . . 76

7.2 Single crystal growth and experimental details . . . 76

7.3 Crystal structure characterization. . . 80

7.4 Magnetic properties of antiferromagnetic single crystals . . . 82

7.5 Magnetic properties of ferromagnetic single crystals . . . 82

7.6 Conclusions. . . 87 Summary 89 Samenvatting 91 References. . . 93 Acknowledgements 107 List of Publications 109 Curriculum Vitæ 111

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1

I

NTRODUCTION

The balance between human well-being, economic growth and a sustainable future is the main challenge for the 21st century. The International Energy Agency (2012) claimed that the world energy demand will increase by 35% from 2010 to 2035 [1]. While the level of world energy demand increases, the environmental degradation and climate changes turn into serious issues, and are driving the trend towards a cleaner and more efficient use of the energy systems. At present, refrigeration represents a large portion of the total worldwide energy consumption, approximately 15% [2]. Since the 1930s, modern refrigerators use the mechanical vapor compression/expansion technology. Although this technology has been improved in many aspects over the years and is now mature, the low energy efficiency and the use of gas refrigerants are strong drawbacks making it less appealing for future use. Refrigerants that contains hazardous chemicals that contribute to a large degree to the ozone layer depletion have been prohibited by the Montreal Protocol that sets targets for the consumption of ozone-depleting substances (and will gradually phase them out by 2030) [3]. These ozone-depleting refrigerants have however been gradually replaced by refrigerants presenting a strong greenhouse effect, about ten thousands times stronger than that of carbon dioxide, which have also been partially limited by Kyoto Protocols for the emissions of greenhouse gases [4]. These international agreements thus open the way for new refrigeration technologies. This thesis searches after such a pathway by looking for new refrigerants based on a totally different technology. Advanced magnetic materials, known as magnetocaloric materials, employed for the emerging magnetic refrigeration technology will be explored from both fundamental and applied points of view. In this chapter, we will first give a general background on the magnetocaloric effect, magnetic refrigeration and giant magnetocaloric materials.

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2 1.INTRODUCTION

1.1.

THE MAGNETOCALORIC EFFECT

T

HEmagnetocaloric effect (MCE) is the thermal response of a magnetic material to a change in external magnetic field. Under adiabatic conditions, it manifests itself as a change in temperature. The MCE is intrinsic to all magnetic materials. This effect was experimentally discovered by Weiss and Picard, who in 1917 observed a 0.7 K tempera-ture change in nickel when exposed to a magnetic field change of 1.5 T in the vicinity of its Curie temperature (TC= 627 K) [5].

The first successful applications of the magnetocaloric effect took place at very low temperatures. Soon after the discovery of the MCE, Debye and Giauque in the late 1920s independently showed the principle to achieve ultra-low temperatures (below 1 K) using adiabatic demagnetization of paramagnetic salts [6,7]. This large MCE in paramagnetic salts can occur even in the absence of any magnetic transition but is restricted to very low temperatures. This pioneering application of the MCE led to the Nobel prize in chem-istry in 1949 for Giauque and it is still one of the most common techniques in use to reach T <2 K. The MCE of a paramagnet decreases exponentially with the temperature, so that this effect becomes negligible above T ≈ 20 K.

To get a significant MCE at room temperature one should take advantage of the en-tropy anomaly inherent to a magnetic transition. This MCE related to a magnetic phase transition can be described in an entropy-temperature plot. In Fig. 1.1, the entropy lines for a ferromagnetic-paramagnetic transition are represented without and with ex-ternal magnetic field. The application of a magnetic field favors the development of the magnetic phase with the largest net magnetization. At the ferro-to-paramagnetic tran-sition, the S(T ) lines will be shifted to higher temperatures by the magnetic field in a similar way as the magnetization versus temperature curves. Depending on whether the magnetic field is applied in adiabatic or in isothermal conditions, the magnitude of the MCE can be quantified by two parameters: an adiabatic temperature change∆Tad

or an isothermal entropy change∆S. The MCE of a magnetic material is maximized in the vicinity of the magnetic phase transition. To be used as magnetic refrigerant in room-temperature magnetic refrigeration, the MCE materials must therefore present a ferro-to-paramagnetic phase transition temperature near room temperature.

Other kinds of magnetic transitions can also lead to a significant MCE, in particular those leading to the development of a large difference in magnetization between the two phases at play (ferri-paramagnetic, antiferro-ferromagnetic etc.). They are however barely used in magnetic refrigeration prototypes and are not studied here.

1.2.

MAGNETIC REFRIGERATION

M

AGNETICrefrigeration (MR) near room temperature is based on the MCE. A mag-netic refrigeration cycle is analogous to that used in vapor compression technol-ogy, but instead of pressure, a change in external magnetic field is used as driving force. The schematic sketch of a single stage magnetic refrigeration cycle is shown in Fig. 1.1. A magnetic refrigeration device usually consists of: a magnetic refrigerant, a perma-nent magnet to generate the field changes, hot/cold heat exchangers and a heat transfer medium. Starting from a temperature just above the TCin zero magnetic field (T0), the

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in-1.2.MAGNETIC REFRIGERATION 3 S N S N Tot al Ent ropy , S Temperature, T 1 T0 T0+ ΔTad 2 3 T0- ΔTad 4 B = 0 B > 0 Heat rejection Heat load ∆S ∆Tad

Figure 1.1: S-T diagram representing a Brayton cycle for first-order magnetic transition materials (ferro-paramagnetic). There are two adiabatic processes (1 and 3) and two isofield processes (2 and 4).

crease of its temperature. The second step is to expel the heat from the MCE material to the surroundings under isofield conditions by a heat transfer medium (typically water with additives). The third step is an adiabatic removal of the magnetic field, which will cool down the MCE material below its initial temperature. Finally, the MCE material is brought in thermal contact (heat exchanger) with the system to be cooled to provide its cooling power.

The cycle illustrated in Fig.1.1corresponds to the Brayton MR cycle, which is at the basis of the current MR prototypes. From the schematic representation, one can note that the temperature span of such a cycle is from T0-∆Tad(-∆B) to T0+∆Tad(+∆B), and

is directly proportional to the∆Tad of the MCE material. The largest∆Tad currently

achievable is of the order of 3 K for∆B = 1 T. Therefore, to ensure a temperature span of 16 K or more (between 20◦C room temperature and the mandatory 4C in the fridge),

cycles that allow an amplification of the MCE are used. The most common approach is the Active Magnetic Regenerative Refrigeration cycle [8]. It basically consists of a cas-cade of Brayton cycles along one direction of the MCE refrigerant bed by only partial heat transfers [9]. However, in such a regenerative cycle, part of the MCE is used for the amplification of the∆Tad. As a result, the total cooling power of the MR machine

de-creases. On the other hand, the amount of heat transferred to the hot and cold reservoirs (δQ = T dS) is proportional to the ∆S of the MCE material. The T ∆S achievable by MCE material is smaller than the latent heat of transformation/vaporization of the refriger-ant gazes used in conventional gas compression refrigeration. But, this is expected to be

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4 1.INTRODUCTION

overcome by higher efficiency in MR systems.

Near room temperature magnetic refrigeration only started in 1976 by the work of Brown using Gd plates as refrigerant [9]. He proposed a regenerative process allow-ing for a much larger temperature span than the observed MCE (∆Tad) of the material.

Following Brown’s proof of concept, a large number of MR prototypes have been built in laboratories all around the world, establishing magnetic refrigeration as a competi-tive cooling technology for commercial application [10,11]. MR is an environmentally friendly alternative to conventional vapour compression technology mostly for two rea-sons [10,12,13]. It uses a solid magnetic refrigerant, so that it does not release any gases that cause ozone depletion or a direct greenhouse effect, meeting the current require-ments for international agreerequire-ments. In addition, it has the potential for a higher energy efficiency in comparison with the compression refrigeration [10,14], which is of partic-ular interest in view of the increase in global energy demand.

1.3.

M

AGNETOCALORIC MATERIALS

A

LTHOUGHmany aspects are involved in the development of the magnetic refrigera-tion technology, magnetocaloric materials play an essential role in it. In particular, as shown in the previous section, developing MCE materials that present a large∆Tad

and∆S is crucial to build an efficient MR system. Considering the current

state-of-the-art permanent magnets (Bmax≈ 1.4 T) , the cooling performance should be achieved for

moderate magnetic fields (∆B ≤ 1 T).

Historically, the interest in room-temperature magnetic refrigeration has been pri-marily boosted by the discovery in 1997 by Pecharsky and Gschneidner of a giant mag-netocaloric effect (GMCE) in Gd5Si2Ge2materials, which present a MCE about 50 larger

than that of Gd metal [15]. Within a few years after that, several other material sys-tems were reported that show a GMCE near room temperature. The most promising systems are presented in Table1.1: Fe2P-based (Mn,Fe)2(P, X) (X = As, Ge, Si, B) [16–21],

La(Fe,Si)13and their hydrides [22,23], (Mn,As) and MnAs1-xSb1-x[24,25], MnCoGeBx[26],

FeRh (which can also be considered as one of the pioneering GMCE materials) [27], Heusler alloys [28–31] and some other materials (see reviews [12,32,33]).

To make a distinction between these different material families, it is important to establish a classification depending on the phase transitions at play. In this thesis, the following terminology will be used. A distinction between first-order and second-order transitions will be made depending if a latent heat is present or not, respectively. As the latent heat amplifies the entropy anomaly at the magnetic phase transition, it results in a giant magnetocaloric effect (GMCE) at the first-order magnetic transition (FOMT).

For systems with a FOMT, a second classification level can be introduced depending on whether it is associated to a change in crystalline structure as in magneto-structural transitions, or if the lattice symmetry remains unchanged as in magneto-elastic transi-tions. In Table1.1, one can note that both types are equally represented among GMCE materials. However, at the present time, only two GMCE materials systems, (Mn,Fe)2(P,Si)

and La(Fe,Si)13, are produced at pre-industrial scale and both are based on a

magneto-elastic FOMT. This preference can be explained by the easier possibility to tune the in-tensity of the phase transition (latent heat) by chemical composition in magneto-elastic rather than in magneto-crystalline phase transition.

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1.3.MAGNETOCALORIC MATERIALS 5

Materials Type of Frist–order phase transition Low TCrystal structureHigh T Magnetic structureLow T High T Ref

Gd5Si2Ge2 Magneto-structural Orthorhombic Gd 5Si4-type

Monoclinic

Gd5Si2Ge2-type FM PM [15]

MnAs Magneto-structural HexagonalNiAs-type OrthorhombicMnP-type FM PM [24] Ni2MnGa Magneto-structural TetragonalMartensite AusteniteCubic FM FM [29]

MnCoGeB Magneto-structural Orthorhombic TiNiSi-type Hexagonal Ni

2In-type FM PM [26]

(Mn,Fe)2(P,Si) Magneto-elastic HexagonalFe 2P-type

Hexagonal

Fe2P-type FM PM [18]

La(Fe,Si)13 Magneto-elastic NaZnCubic 13-type

Cubic

NaZn13-type FM PM [22]

FeRh Magneto-elastic CsCl-typeCubic CsCl-typeCubic AFM FM [27]

Table 1.1: Overview of the current giant MCE materials and their main characteristics.

Among systems with a magneto-elastic FOMT, a third classification level can be made for the distinction between isotropic cell volume discontinuity, like the∆V in the cubic La(Fe,Si)13and FeRh systems, and the anisotropic change in cell parameters∆c/a in the

hexagonal (Mn,Fe)2(P, Si) system. This distinction has at first glance only little influence

on the GMCE performance. It is however relevant for other parameters, such as the evo-lution of the microstructure and structural properties across the phase transition.

Several studies pointed out that the GMCE originates from a complex interplay be-tween magnetic, lattice and electronic properties. Most of the FOMTs shown in Table 1.1result from mechanisms specific to that particular system. To mention only a few: In Gd5Si2Ge2, Ge and Si play a key role in the magneto-structural transition due to the

de-velopment of induced magnetic moments on Ge(Si) in the ferromagnetic state and their influence on the chemical bounding between Gd slabs [34]. In FeRh, the mechanism responsible for the FOMT is still controversial, but the strong hybridization between Fe and Rh is an important factor, as well as the instability of the Rh magnetic moment at the FOMT [35,36]. In (Mn,Fe)2(P,Si), the reduction of the itinerant magnetic moments of the

Fe site across the ferromagnetic transition is expected to play a major role [37]. These complex mechanisms that give rise to the GMCE are still the object of many controver-sies and deserve more works.

Despite the significant improvements of the MCE performances achieved in the last two decades, mainly due to the discovery of GMCE materials with an enhanced MCE (both∆S and ∆Tad) at moderate field values, some other pre-conditions still have to

be ensured before they can successfully be used in a commercial magnetic refrigerator. These are the cost of raw materials and production, environmental concerns (not toxic), magnetic anisotropy, corrosion and stability, etc. (see reviews [10]). Furthermore, a few problems intrinsic to FOMT still hinder their use in MR applications. These include

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hys-6 1.INTRODUCTION

teresis, dynamics of the phase transition, cyclability of the MCE and an increase in brit-tleness due to cell changes at the FOMT.

1.4.

SCOPE AND OUTLINE OF THIS THESIS

T

HEaim of the present work, of characterizing advanced magnetocaloric materials in the (Mn,Fe)2(P,Si) system, is twofold. From the application point of view, an

ad-vanced characterization and optimization of the GMCE is preferred in order to design new magnetic refrigerants. From a more fundamental point of view, a better knowledge of the underlying mechanism responsible for the giant magnetocaloric effect is aimed to gain. This latter question is closely related to the origin of the anisotropic magneto-elastic FOMT in this system: “what are the mechanisms at play?” and “how does the FOMT develop?”. This thesis contains seven chapters, including this introduction. The content of the subsequent chapters are:

Chapter 2 aims to provide some theoretical aspects related to the magnetocaloric

ef-fect as well as the X-ray absorption spectroscopy and X-ray magnetic circular dichroism used later in the thesis.

Chapter 3 presents a brief description of the sample preparation, experimental

tech-niques and characterization methods. A description of the crystal growth, the in-field Differential scanning calorimetry, the direct ∆Tad measurements and the X-ray

mag-netic circular dichroism experiments will be shown.

Chapter 4 is devoted to the determination of the MCE, the quantification of∆S and

∆Tadin (Mn,Fe)2(P,Si,B) materials by means of various direct and indirect methods. The

results from the different methods will be compared and discussed.

Chapter 5 focuses on a systematic study of the direct∆Tadmeasurements on three

generations of (Mn,Fe)2(P,X) with X = As, Ge, Si materials. In the first part, by using a

cyclic∆Tcyclicprobe, it has been highlighted that the MCE in this series of materials can

be cycled. This is an important pre-condition for a material aimed to be used in applica-tions where the field continuously oscillates. In addition, these first results point out the role played by the non-magnetic elements in the control of the latent heat of the FOMT. In the second part, the concept is explained of how to employ the field dependence of the MCE in (Mn,Fe)2(P,Si) materials to optimize the MCE in intermediate magnetic field.

Chapter 6 explores the magnetic and electronic properties of (Mn,Fe)2(P,Si,B)

mate-rials across their first-order magnetic phase transition by X-ray magnetic circular dichro-ism. The experimental spectra, charge-transfer multiplet simulations and first-principle calculations made it possible to obtain the element-selective magnetic moments of Mn and Fe across the FOMT.

Chapter 7 presents the study of the structural and magnetic properties of

single-crystalline (Mn,Fe)2(P,Si). Ferromagnetic Mn0.83Fe1.17P0.72Si0.28crystals have been grown

for the first time and are studied for their magnetocrystalline anisotropy. The magnetic properties of single-crystalline antiferromagnetic Mn0.96Fe0.94P0.80Si0.20are also studied

for comparison. A new magnetic behavior, related to the magnetization process at the ferro-to-paramagnetic FOMT, is observed and discussed.

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2

T

HEORETICAL ASPECTS

Some theoretical aspects of the magnetocaloric effect (MCE) and X-ray magnetic circu-lar dichroism will be given in this chapter. The thermodynamic concepts frequently used for the description of the MCE are presented. Direct measurements of the magnetocaloric quantities,∆S and ∆Tad, are possible. They however require specific devices for which

there is still no standardization. As a consequence, indirect determination of the MCE on commercially available magnetometers or calorimeters remains the most common way to characterize MCE materials. The basis of these indirect methods for the MCE evaluation, both∆S and ∆Tad, in first-order and second-order magnetic phase transition materials

will be discussed. In the second part, some important concepts of X-ray absorption and X-ray magnetic circular dichroism will be introduced, as well as the sum rules to analyze the experimental data.

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8 2.THEORETICAL ASPECTS

2.1.

THEROMODYNAMICS OF THE MAGNETOCALORIC EFFECT

2.1.1.

T

HERMODYNAMIC POTENTIALS AT PLAY

I

MPLEMENTINGthe potential for a magnetic substance in an external magnetic field (B =µ0H ) into the First law of thermodynamics, the total differential of internal energy U

= U (S,V, M ) of the system will obey the following relation for a reversible transformation:

dU = δQ + δW = T dS − PdV + Bd M (2.1)

where T represents the absolute temperature, S the total entropy, P the pressure, V the volume and M the magnetization.

The thermodynamic properties of a magnetic system are described by the Gibbs free energy G [38–40]:

G = U − T S + PV − MB (2.2)

Correspondingly, by implementing equation (2.1) in equation (2.2), the variation in

G is given by:

dG = V dP − SdT − MdB (2.3)

On the other hand, at constant pressure the total differential of the Gibbs free energy can also be written:

dG(T, B ) = µ∂G ∂TB d T + µ∂G ∂BT d B (2.4)

The crossed second derivatives of dG are equal:

µ ∂B µ∂G ∂TBT = µ ∂T µ∂G ∂BTB (2.5)

If these partial derivatives exist and are continuous, then from equation (2.3), the in-ternal parameters, such as system’s entropy, volume and magnetization can be obtained in terms of partial derivatives of G [38–40]:

S(T, B, P ) = − µ∂G ∂TB,P (2.6) V (T, B, P ) = µ ∂G ∂PT,B (2.7) M (T, B, P ) = − µ∂G ∂BT,P (2.8)

Combining of equation (2.5), (2.6), (2.7) and (2.8) leads to one of the so-called “Maxwell” relations: µ ∂S ∂BT= µ ∂M ∂TB (2.9)

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2.1.THEROMODYNAMICS OF THE MAGNETOCALORIC EFFECT 9

2.1.2.

M

AXWELL RELATION AND

C

LAUSIUS

-C

LAPEYRON EQUATION

I

NTEGRATIONof equation (2.9) is the most common way to derive the entropy change on the basis of the magnetization data. The isothermal entropy change induced by an applied magnetic field change from B0to B1corresponds to:

∆S(T,∆B) = ZB1 B0 µ ∂M(T,B) ∂TB d B (2.10)

Considering the controversies in the literature [41–48] about the application of equa-tion (2.10) for the determinaequa-tion of∆S, a few remarks should be made. In principle, the Maxwell relation of equation (2.9) can only be used for magnetocaloric materials under following conditions [49–51]:

- the system is homogeneous (can be problematic in case of a phase separation) - the system is in thermodynamic equilibrium (can be problematic in case of thermal or magnetic hysteresis)

- the first derivative of the Gibbs free energy is continuous (problematic for the applica-tion to first-order transiapplica-tions, c.f. the first controversies about Gd5Si2Ge2[44])

In practice, this Maxwell relation however remains the most used method for first-order phase transitions as a first-first-order transition always has a finite transition width. Practical illustrations of these points will be developed in chapter 4. It should also be noted that equations (2.9) and (2.10) have been established on the basis of the total en-tropy of the system. We will thus consider in this thesis that the Maxwell relation reflects the total entropy change of the MCE material.

At constant pressure, the total entropy change of a magnetic solid material can in general be described as the sum of the magnetic (Sm), lattice (Sl) and electronic (Se) entropy terms:

S(T, B ) = Sm(T, B ) + Sl(T, B ) + Se(T, B ) (2.11) For systems with localized magnetic moments, like rare earth magnetic material (EuO, Gd, CrO2etc.), the entropy change∆S might be presented as a purely magnetic entropy

change∆Sm. But, for magnetic materials where the magnetic moments are carried by itinerant electrons, the above equation is not so useful. In these systems, the separation of the three contributions cannot be made, so that the Maxwell relation will represent the total isothermal entropy change of the MCE material.

As pointed out above, for a material undergoing a second-order phase transition, the application of Maxwell relations is straightforward due to the continuity of the first derivative of the Gibbs free energy, such as entropy, volume and magnetization (see equation (2.6), (2.7) and (2.8)). Whereas when a material undergoes a first-order phase transition, the first derivative of the Gibbs free energy changes discontinuously and the heat capacity presents a sharp peak at the transition temperature due to the accompa-nied latent heat. To analyze the entropy change for such a material undergoing a first-order phase transition, several studies [44–46] proposed that one should in principle use the Clausius-Clapeyron equation rather than the Maxwell relations (2.10).

The Clausius-Clapeyron equation describes a phase transformation (phase A → phase B), for which there is a phase coexistence at the transition line separating the two phases.

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10 2.THEORETICAL ASPECTS

The transition line can be described as the transition temperature as a function of the applied magnetic field Ttr(B ). For an isobaric transformation (constant pressure), the

derivative of the Gibbs free energy can be written from equation (2.3):

dG = −SdT − MdB (2.12)

Considering that the two phases are in equilibrium with each other at all points on the transition line, dGA= dGBcan be re-written as

− MAd B − SAd T = −MBd B − SBd T ; SB− SA= −(MB− MA) d B d T (2.13) Thus, ∆St r= − ∆M d Tt r/d B (2.14)

where∆M is the difference in magnetization between the low- and high-field phases and d Ttr/d B describes the shift in transition temperature as a function of the change in

magnetic field. It should be noted that this method to quantify the difference in total en-tropy between the two phases at the transition point, is annotated as∆Strhere. To relate

∆Strto the magnetocaloric∆S from the Maxwell relation is not straightforward. When

∆Stris estimated on the Ttr(B ) line near B ≈ 0, it bears a resemblance to the latent heat

(L) derived from differential scanning calorimetry at B = 0. Hereafter, we will consider that∆Str≈ L/Ttr.

2.1.3.

C

ALORIMETRIC METHOD

T

HEMCE can also be determined by a calorimetric measurements. The indirect calori-metric method consists in determining the S(T, B ) lines. Using the second law of thermodynamics at constant pressure and magnetic field:

d S =δQ

T (2.15)

whereδQ is the heat flow into the sample. On the other hand, the specific heat is defined as:

CB,P= (δQ

T )B,P (2.16)

Combining equations (2.15) and (2.16) and writing the integral form, one can obtain:

S(T, B ) =

ZT

0

C (T, B )

T d T (2.17)

Once the entropy versus the temperature lines are established after integrating C (T, B ) measured from the calorimetric method, the calculation of isothermal entropy change and adiabatic temperature change is straightforward. For the field variation from B0to

B1(∆B = B1- B0), the∆S(T ,∆B) and ∆Tad(T ,∆B) will simply correspond to vertical and

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2.1.THEROMODYNAMICS OF THE MAGNETOCALORIC EFFECT 11

∆S(T,∆B) = S(T,B1) − S(T,B0) (2.18)

∆Tad(∆B) = T (S,B1) − T (S,B0) (2.19)

At first glance, the calorimetric method might seem less indirect than the magnetic methods as the experimental S(T, B ) lines are measured. In practice, this method can be complex. Percharsky et al. reported a detailed analysis of the errors and the main issues involved in the characterization of this method [52,53].

In equation (2.17), the lower limit of the integration equals to T ≈ 0 K, which is not applicable in practice. In fact, the temperature of interest for the calorimetry measure-ments are usually relatively far above 0 K, in particular to study materials presenting a MCE near room temperature. Nevertheless, this issue can be overcome using a simplifi-cation described below.

Equation (2.17) can be rewritten as:

S(T, B ) = S(Ti) + Z Tf

Ti

C (T, B )

T d T (2.20)

where S(Ti) is the entropy at initial temperature Ti. Thus, combining equations (2.18) and (2.20) yields: ∆S(T,∆B) = S(T,B1) − S(T,B0) = [ Z Ti 0 C (T, B1) T d T + ZTf Ti C (T, B1) T d T ] − [ Z Ti 0 C (T, B0) T d T + Z Tf Ti C (T, B0) T d T ] = ZTf Ti C (T, B1) T d T − Z Tf Ti C (T, B0) T d T + ∆S(Ti,∆B) (2.21)

This equation indicates that rather than the absolute entropy of the material at low temperature for different magnetic fields, the estimated entropy difference below the transition range (this can be determined from a magnetization measurement) can be used as a reference to rescale the difference between the S(T, B ) lines at Ti. In such a way, a reliable estimation of the entropy curves can be made.

On the other hand, it has been reported that it is possible to combine the heat ca-pacity measurement and the magnetization data to calculate the adiabatic temperature change using the simplified equation [54–56]:

∆Tad= −

T

C (T, B )∆S (2.22)

However, in this approach it has been assumed that the heat capacity is independent of both temperature and magnetic field. This assumption is only valid at high tempera-ture, high magnetic field or for continuous phase transitions, but it is inapplicable close to the transition temperature of a first-order phase transition of MCE materials studied here as the heat capacity peak is particularly sharp at TC[53]. Therefore, this method

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12 2.THEORETICAL ASPECTS

2.2.

X-RAY ABSORPTION SPECTROSCOPY AND

X-RAY MAGNETIC

CIRCULAR DICHROISM

2.2.1.

X-

RAY ABSORPTION SPECTROSCOPY

X

-RAYAbsorption Spectroscopy (XAS) measures the absorption of photons as a func-tion of the energy near the edge of a chosen element. When the energy of the absorp-tion edge (sharp increase in absorpabsorp-tion) is equal to the binding energy of a core state in the absorber, electrons are excited from an initial core state to the lowest empty state just above the Fermi level. These edges are at different energies because of the differ-ent nuclear charges of the absorbing elemdiffer-ent and the orbitals involved, which makes XAS an element-specific and orbital-specific technique. The X-ray absorption spectrum of a certain edge is generally divided into two regions: Near-edge X-ray absorption fine structure (XANES) and Extended X-ray absorption fine structure (EXAFS). XANES is sev-eral tens of eV above and below an absorption edge and mainly contains information about the density of empty states of the absorbing atom. It changes, for example, with the oxidation state. EXAFS is an extended region well above the edge (till approximately 1 keV above the edge for transition-metal K -edges), and mainly contains information about the local crystalline structure of the absorbing atom.

Each absorption edge occurs at the photon energies that correspond to the energy difference of the occupied level to the Fermi level. These edges are identified by the core-state designation: K , L, M -edges for core states with principal quantum number n = 1, 2, 3, respectively. The allowed transitions between different quantum states due to absorption and emission are governed by the dipole selection rules. For linearly polar-ized light, they are given by:

∆j = 0,±1 ∆s = 0 ∆l = ±1 ∆m = 0 (2.23)

and for circularly polarized light they correspond to:

∆j = 0,±1 ∆s = 0 ∆l = ±1 ∆m = +1(left circular),−1(right circular) (2.24) Spectroscopically, the most interesting XAS edges are in general the K , L2,3and M4,5.

In this thesis, the XAS L2,3for the 3d transition metals Fe and Mn will be mainly

dis-cussed. They correspond to the soft X-ray range with an energy between 500 to 1000 eV. A typical Fe L-edge absorption spectrum is shown in Fig2.1.

The spin of the hole left in the core-state can be either parallel or antiparallel to the hole’s orbital angular momentum l , leading to two possible final core states with j±=

l ± 1/2, which differ in energy by the spin-orbit interaction of the core state. Spin-orbit

interaction of the core states results in a peak splitting in the absorption spectrum. In the case of Fe L-edges, L2and L3are split as shown in the inset of Fig.2.1. In Chapter 7, the

spin-orbit interaction of the core states will be discussed in relation to the quantitative derivation of spin and orbital moments.

2.2.2.

X-

RAY MAGNETIC CIRCULAR DICHROISM

X

-RAY magnetic circular dichroism (XMCD) is the difference in absorption of left-and right-circularly polarized (positive left-and negative helicity) X-rays by a magnetized

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2.2.X-RAY ABSORPTION SPECTROSCOPY ANDX-RAY MAGNETIC CIRCULAR DICHROISM 13

690 700 710 720 730 740

Espin-orbit L2

XAS (arb.units)

Photon energy (eV) Fe

L3

Figure 2.1: The XAS at the Fe L-edge. The inset shows a schematic of the transition from the spin-orbit split 2p state.

sample. Analyzing the XMCD enables one to obtain information about the magnitude and orientation of both orbital and spin magnetic moments for one specific element in the sample. The XMCD was first theoretically predicted by Erskine and Stern on the

M2,3edges of ferromagnetic nickel [57]. Schütz et al. [58] reported the first experimental

evidence of a small, but non-negligible XMCD at the Fe K edge.

The physical principle of XMCD can be explained by the single particle two-step model proposed by G. Schütz et al. [58]. This model describes the transitions of the 2p core state to the 3d valence state (see Figure2.2for a schematic representation). Here, the spin-orbit interaction is only taken into account in the initial 2p core state. The first step involves the absorption of a circularly polarized photon that carries an angular mo-mentum (-ħ for the left and +ħ for the right circularly polarized photon) and subsequent excitation of core electron (2P3/2: L3edge and 2P1/2: L2edge). The absorption of the

left (right) circularly polarized photon mostly results in spin-up (spin-down) polariza-tion from 2P3/2level via spin-orbit coupling (l + s). Due to the opposite spin-orbit

cou-pling for the 2P1/2(l − s), the spin polarization of the excited electron is reversed at L2

edges. In the second step, the d -valence band is like a spin-resolving detector of the spin-polarized photoelectron. Due to the unbalance in the spin-up and spin-down va-lence band for materials presenting a net magnetization (like a ferromagnetic material or a paramagnetic material in an applied magnetic field), the absorption of the two po-larization directions will be different. This difference gives rise to the XMCD signal.

The XMCD is measured by taking the difference in absorption spectra for an alter-nating left- and right-circularly polarized beam of X-rays in an applied magnetic field parallel or antiparallel to the beam. The XMCD spectrum∆µ is defined as:

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14 2.THEORETICAL ASPECTS

spin-up spin-down

690 700 710 720 730 740

Photon energy (eV)

  L2 XA S ( ar b .u ni ts ) Fe L3 X M C D (a rb .u n its )

Figure 2.2: Schematic representation illustrating the principle of XMCD (left panel). The two sub-bands of the 3d valence band of the transition metal are split by the exchange interaction. In the right panel, L2,3-edge XAS and XMCD spectra of Fe are shown.

whereµ+(µ) is the absorption coefficients for the right (left) circularly polarized X-rays. Changing the helicity of the incoming photons at a fixed magnetic field direction is equivalent to a fixed helicity and reversing the magnetic field direction. In practice, the two approaches, reversing helicities and reversing the magnetic field, are both used to get rid of artifacts. The resulting spectra are illustrated in Figure2.2.

2.2.3.

S

UM RULES FOR THE TRANSITION METAL

L

EDGE

T

HEXMCD sum rules can be used to separately determine the orbital [59] and spin [60] components of the magnetic moment on the absorbing atom. It turns out that the ground state expectation values of the orbital and spin moments are related to the in-tegrated area of the XAS and XMCD spectra. For a transition from the 2p core state to the 3d valence states in a transition metal system, Chen et al. have developed a prac-tical method to extract the spin and orbital moments by applying the sum rules to the experimental XMCD and XAS spectra [61]:

µspin= − 6R L3(µ+− µ)dω − 4RL3+L2(µ+− µ)dω R L3+L2(µ++ µ)dω × (10 − n3d) µ 1 +7〈TZ2〈Sz〉 ¶−1 (2.26) µorb= − 4R L3+L2(µ+− µ)dω 3R L3+L2(µ++ µ)dω× (10 − n 3d) (2.27)

whereµspinandµorbare the spin and orbital magnetic moments in units ofµBper

atom, n3dis the occupancy of the 3d states, 〈TZ〉 the magnetic dipole operator and 〈SZ〉 the spin operator. For clarity the integrals can be renamed as [61]:

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2.2.X-RAY ABSORPTION SPECTROSCOPY ANDX-RAY MAGNETIC CIRCULAR DICHROISM 15

690 700 710 720 730 740

Photon energy (eV)

L2 A b sorption (arb.units)

Fe

L3 (a) (b) XMCD (arb.units) (c) XA S (arb.units) p q r µ+ µ - -

    

  

Figure 2.3: Illustration of the application of the sum rules to the L2,3edge of Fe. (a) shows the XAS for the two opposite circular polarizations. (b) and (c) are the XMCD and summed XAS spectra. The dotted line shown in (c) is the removal of a two-step function(adapted from [61]).

p = Z L3 (µ+− µ)dω (2.28) q = Z L3+L2 (µ+− µ)dω (2.29) r = Z L3+L2 (µ++ µ)dω (2.30)

where the parameters p, q and r are the three integrals needed in the sum rules anal-ysis. Figure2.3illustrates the application of the sum rules to the L2,3edge of Fe.

The applicability and validity of the XMCD sum rules have been reviewed in a num-ber of studies [62–65]. The validity of the sum rules was confirmed for the heavy 3d transition elements Co, Ni and Fe. For the L edge of light 3d transition elements like Mn, application of the sum rules is problematic. Due to the relatively strong core–valence Coulomb interaction compared to the spin-orbit interaction of the core state, the 2P3/2

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16 2.THEORETICAL ASPECTS

In this case, further correction steps will be needed to derive the final spin and orbital moments. This will be discussed in detail in Chapter 7.

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3

E

XPERIMENTS AND

T

ECHNIQUES

This chapter provides an overview of most of the experimental techniques that were used in this thesis. It covers the synthesis and characterization of magnetocaloric materials as well as a general presentation of each technique. Attention will be paid to some specific aspects that reappear regularly in the next chapters.

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18 3.EXPERIMENTS ANDTECHNIQUES

3.1.

SAMPLE

PREPARATION

3.1.1.

S

YNTHESIS BY

H

IGH

E

NERGY

B

ALL

M

ILLING

I

Ngeneral, high energy planetary ball milling is used to grind and blend materials by high-energy collisions between the materials, the grinding balls and the grinding jars. The grinding jars rotate around their own axis on a main disk while the direction of ro-tation of the main disk, is opposite to that of the grinding jars. This technique is partic-ularly attractive for Mn-Fe-P-Si, as it involves the preparation of a highly-reactive (sub-micrometric particle size), homogeneous and partially amorphized mixture of starting materials prior the solid-state reaction. It decreases the reaction temperature, which in turn limits the loss of volatile starting materials such as Mn or P. In addition, Fe2P phase

can be formed by this mechanical alloying process. The polycrystalline samples stud-ied in this thesis were prepared by the ball-milling method using a Fritsch Pulverisette 5. Typically, an amount of 10 g of raw starting materials were placed in the grinding jars with 15 grinding balls (10 mm diameter and 4 g each) in an argon gas atmosphere. The usual effective ball-milling time was 10 h at a rotation speed of 380 rpm. The obtained fine powder was then uniaxially pressed into pellets with a diameter of 10 mm and a length of about 20 mm. The pellets were then sealed in quartz ampoules with 200 mbar Ar atmosphere. The most often used annealing procedure was the previously optimized double-step process [37].

3.1.2.

M

ETALLIC

F

LUX

C

RYSTAL

G

ROWTH

(Mn,Fe)2(P,Si) single crystals were successfully grown for the first time by the molten

metal flux method. The grown crystals were investigated as part of this thesis and the results are presented in Chapter 7.

The Metallic flux crystal growth is a solution method. The appropriate materials (re-actants) are dissolved in a solvent, the so-called flux, leading to a homogeneous solution, which is then slowly cooled to promote spontaneous nucleation. The advantages of this method are that it requires simple equipment, produces high-purity crystals and that it can grow a wide variety of congruently and incongruently melting materials. The chal-lenges to use this method are the selection the right flux, its concentration and the ap-propriate reaction temperature and time in order to get close to the targeted final chem-ical composition.

In the present work, tin was chosen as flux for its excellent viscosity and previous successful growth of transition-metal phosphides crystals [66,67]. The equipment used for the growth consist of: a quartz ampoule, vertical furnaces, silica wool, tin and pre-alloying materials. The use of an alumina crucible (usually necessary for flux growth) was eliminated in this work as neither the Mn-Fe-P-Si alloy nor Sn are reactive with the quartz ampoule below 1423 K. As depicted in Fig.3.1, an appropriate amount of the Mn-Fe-P-Si materials is mixed with tin. This mixture was then sealed in a quartz ampoule and heated to a temperature well above the melting point of the tin (T = 504.9 K). At this high temperature, the materials are dissolved in molten tin and crystallization occurs when the solution becomes critically supersaturated. This can be achieved by slowly cooling the mixture, generally the slower the cooling rate, the better the crystal. A trial and error approach allowed defining the typical growth parameters. More details on the

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3.2.STRUCTURALANALYSIS 19

tin

Mn-Fe-P-Si materials

crystallize with time and temperature dissolved in tin

at high temperature

Figure 3.1: Schematics of the flux method.

optimized growth parameters will be discussed in Section 7.2.

3.2.

STRUCTURAL

ANALYSIS

3.2.1.

P

OWDER

X-

RAY

D

IFFRACTION

X

-RAYdiffraction (XRD) patterns of the polycrystalline samples were measured with a PANalytical X-pert Pro diffractometer using Cu Kα radiation. An Anton Paar TTK450 Low-Temperature Chamber was used for measurements at non-ambient condition (150 K <T <720 K). In order to resolve the crystal structure, the XRD patterns were analyzed by Rietveld refinement using the FullProf software [68].

3.2.2.

S

INGLE

C

RYSTALS

X-

RAY

D

IFFRACTION

S

INGLE-crystal XRD data were collected at different temperatures in zero field using a Bruker D8 Venture diffractometer operating with graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) and equipped with a Photon 100 area detector. The sample was mounted in a nylon loop using cryo-oil and cooled using a nitrogen flow from an Oxford Cryosystems Cryostream Plus. The data were processed using the Bruker Apex II software. The structures were solved using direct methods and refined using the full-matrix least-squares method against F2with the SHELXTL software [69].

3.2.3.

S

CANNING

E

LECTRON

M

ICROSCOPY

M

ICROANALYSISof the (Mn,Fe)2(P,Si) single crystals was performed using a JEOL

JSM-7500F scanning electron microscope (SEM) equipped with an energy-dispersive spectrometer (EDS). The sample morphology of the crystals was studied by SEM and the chemical composition was determined with EDS by probing several locations for each crystal.

3.3.

MAGNETIZATION

MEASUREMENTS

T

HEmagnetization measurements were conducted in a superconducting quantum interference devices (SQUID) MPMS-XL magnetometer equipped with a

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reciprocat-20 3.EXPERIMENTS ANDTECHNIQUES

ing sample option (RSO). The SQUID MPMS provides an exceptional sensitivity, as high as 10−5Am2, so that the DC magnetic moment and the AC magnetic susceptibility of a

few milligram of sample can be measured. As the maximal moment that can be probed by the RSO option bis 0.5×10−3Am2, the typical sample mass used in this thesis is about

2 mg. The temperature range is between 1.7 and 400 K and the applied magnetic field is up to 5 T.

The isofield magnetization curves MB(T ) were recorded in a two steps process: first, a

MB(T ) curve is measured in magnetic field (B ) upon cooling, and then a warming branch

is successively measured. When the MB(T ) curves are recorded to construct∆S, a

mag-netic field increment of 0.25 T and temperature step of 0.5 K are used. Some tests have demonstrated that working with a slow temperature sweep (0.5 to 1 K/min) is prefer-able to measurements in stprefer-able temperature mode. In contrast to the stprefer-able temperature mode, which hinders the evaluation of thermal hysteresis due to the thermal overshoot at each stabilization, measurements with slow thermal sweep allows one to control the thermomagnetic history of the samples. Isothermal magnetization curves MT(B) were

registered at various temperatures (T ). Around TCtemperature increments of 2 K were

used. For each temperature, the sample was first zero-field cooled to the measurement temperature from T >TCand then three MT(B) curves were consecutively measured: i)

B is increased from 0 to Bmax; then ii) B is decreased back to 0 ; iii) B is increased again

to Bmax. The magnetic field-induced entropy change(∆S) was derived from the

magneti-zation data MB(T ) and MT(B) for different magneto-thermal histories using the Maxwell

relation (2.10).

3.4.

DIFFERENTIAL

SCANNING

CALORIMETRY

3.4.1.

C

OMMERCIAL

D

IFFERENTIAL

S

CANNING

C

ALORIMETRY

D

IFFERENTIAL Scanning Calorimeter (DSC) is a common thermo-analytical device to obtain the heat flux. The DSC measurements were conducted using a TA-Q2000 DSC instrument equipped with a liquid nitrogen cooling system. The temperature range can vary from 100 to 820 K with variable temperature sweep rates. One pan that contains the sample and another empty pan that serves as a reference, sit on two separated plat-forms. The surrounding temperature is controlled by a liquid N2cooler or a furnace

depending on the temperature range. A controlled He gas flow is used to assist thermal-ization. The temperature of each platform, as well as the temperature of the base (the so-called Tzero), are measured for a thermal ramp. By comparing the difference between

the sample temperature, the reference temperatures and Tzero, the heat flow can be

de-termined [70]. Even though the outcome of a DSC measurement can be given in terms of the heat capacity, it should be recalled that this technique has a large uncertainty (of the order of 5%) when measuring the heat capacity in the absence of enthalpic events. The DSC method is most suited to derive the latent heat at phase transitions. For samples of 30 to 50 mg, the ideal sweeping rate ensuring a large heat flow contrast compatible with the sensitivity of the instrument is of the order of 10 K/min (cooling and warming).

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3.5.DIRECTADIABATICTEMPERATURECHANGE 21

Figure 3.2: Schematic set-up of the Peltier calorimeter [74]. (b) Top view of the DSC in between the coils of the electromagnet.

3.4.2.

I

N

-

FIELD

D

IFFERENTIAL

S

CANNING

C

ALORIMETRY

A

Nin-field DSC was built in home by G. Porcari. It has a similar working principle as the aforementioned DSC. It however aims at a better measurement of the heat capacity, as required for the determination of the magnetocaloric effect. It enables the measurement of specific heat as a function of both temperature and magnetic field. In contrast to the TA Q2000 DSC, the maximum thermal ramp is much slower (between 1 to 2 Kmin-1). This setup aims to be a compromise between a standard DSC and a heat-capacity setup working under quasi-isothermal conditions (like the relaxation method on a Quantum-Design PPMS). The slow sweep rate ensures a limited parasitic heat ex-change between the samples/reference and the surrounding (heat losses should be mi-nor compared to the heat flow going through the sensors). This setup works under high-vacuum (∼ 10−6mbar) and it was designed to limit the radiative heat transfer. The heat flow sensors of this DSC are thin Peltier elements [71–74]. The Peltier cells measure the heat flow using the thermoelectric effect, which translates the temperature difference between the sample and reference into a voltage drop. Calibration with sapphire and Cu standards allows one to convert this signal into heat capacity. A schematic setup and a top view of the calorimeter are shown in Fig.3.2.

The base temperature of this set-up is controlled by a thermoelectric element. The temperature ramp is driven by an Lake Shore temperature controller. The output voltage was then converted into a current by a KEPCO bipolar amplifier. The external magnetic field is generated by an electromagnet (all the measurements of this thesis were made for a magnetic field of 0.95 T). In order to enhance the thermal contact between the sample and sensors, Apiezon grease is used. Its contribution can be subtracted with a background measurement.

3.5.

DIRECT

ADIABATIC

TEMPERATURE

CHANGE

T

HEexperimental setup used for the direct∆Tcyclicmeasurements is designed to track

the temperature of the MCE materials during the magnetization/demagnetization processes, while the surrounding temperature is continuously swept over the range of interest. This probe is very similar to other cyclic∆Tcyclicsetups recently developed in

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22 3.EXPERIMENTS ANDTECHNIQUES

other laboratories (see for instance review [33]).

The temperature is measured by a Chromel-Constantan thermocouple glued directly between two sample disks with a diameter of 10 mm and a thickness of 1-2 mm. Then this sandwich is wrapped in thermally insulating materials to reduce the heat losses. Af-terwards, the sample is fixed inside a holder to ensure mechanical and thermal stability and to maintain the orientation of the sample plates (with the long axis along the mag-netic field). The∆Tcyclicresults are presented in terms of the external magnetic field

change (∆B = 1.1 T). The obtained ∆Tcyclicvalues are necessarily underestimated as the

internal field is reduced by the demagnetizing field of the samples. The sample holder moves in and out of a magnetic field generated by the permanent magnet at a frequency of 0.1 Hz. The surrounding temperature is regulated by a climate chamber. The ther-mal exchange between the samples and the measurement chamber is kept limited by the isolation material. The sweeping rate (0.5-1.5 K/min) is relatively low with respect to the thermal relaxation rate of the sample (defined by the ∆T jump resulting from the MCE, the intrinsic d T /d t related to the MCE is of about 150 K/min). This setup is working under quasi-adiabatic conditions. The thermocouple and glue masses are negligible compared to sample mass (1 to 2 g), and therefore no thermal mass correc-tion was required. The measurements were performed upon warming and cooling for several cycles to ensure the reproducibility of the measurements. It should be noted that same∆Tcyclicmaxima were systematically observed upon warming and cooling. For

each sample three complete temperature cycles were consecutively registered without showing any significant evolution.

3.6.

HIGH-FIELD

MCE MEASUREMENT

H

IGHfield MCE measurements have been carried out in a Bitter magnet, at the Inter-national Laboratory of High Fields and Low Temperatures in Wroclaw, Poland. The field ramp is 12 T/min and the field homogeneity is of the order of 10−3T. The probe is similar to the one reported in ref. [75]. The bulk sample (a pellet with a diameter of 13 mm and a mass of 2.34 g) was placed with the long axis oriented along the magnetic field. A relaxation curve has been measured, the time constant (≈ 800 s) is significantly larger than the duration of the field ramp, so that quasi-adiabatic conditions are ensured.

3.7.

X-RAY

MAGNETIC

CIRCULAR

DICHROISM

T

HEX-ray Magnetic Circular Dichroism (XMCD) measurements were performed at the ID08 beamline of the European Synchrotron Radiation Facility in Grenoble, France. The data were collected by scanning the energy around the L2,3edges (2p → 3d

transi-tion) Mn and Fe.

The X-ray absorption spectra were recorded using the total electron yield (TEY) mode, and normalized to the intensity of the incident beam (see Fig. 3.3for schematic repre-sentation of XMCD setup). The sample temperature was regulated in the temperature range from 230 to 330 K. The X-ray absorption (XAS) spectra correspond to the sum of positive (µ+) and negative (µ−) absorption signals for the cicularly polarised X-rays, while the XMCD spectrum is calculated from the difference betweenµ+andµ−. The bulk polycrystalline samples (circular disks with a diameter of 10 mm and a thickness of

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3.7.X-RAYMAGNETICCIRCULARDICHROISM 23 X-ray monochromator Synchrotron Left/right circularly polarized x-rays B IS Photoemitted electrons

Figure 3.3: A schematic representation of the XMCD measurements.

2 mm) were placed in an ultrahigh vacuum (UHV) system equipped with a 5 T split coil superconducting magnet. The incident X-ray beam and magnetic field are parallel to each other and oriented perpendicular to the sample surface. The pellets were scrapped

in situ with a diamond file in the preparation chamber before the measurements. In

or-der to reduce the occurrence of systematic errors, all measurements were performed for two directions of the applied magnetic field, along and opposite to the incident X-ray beam.

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4

D

ETERMINATION OF THE

MAGNETOCALORIC EFFECT IN

(M

N

,F

E

)

2

(P,S

I

,B)

MATERIALS

In this Chapter, the MCE of one prototypical sample MnFe0.95P0.582B0.078Si0.34displaying

a first-order magnetic phase transition (FOMT) near room temperature has been investi-gated using various direct and indirect methods. The aim is to identify the challenges for MCE quantification at FOMT by each technique, as well as establishing the influence of the cyclic field and temperature change on the character of the MCE. The isothermal en-tropy change∆S is indirectly determined from magnetization and heat capacity measure-ments and directly determined by isothermal calorimetric measuremeasure-ments. The adiabatic temperature change is directly measured by applying cyclic magnetic field changes to the sample (∆Tcyclic) and is indirectly determined from heat capacity measurements (∆Tad).

The resulting MCE properties are compared and discussed.

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264.DETERMINATION OF THE MAGNETOCALORIC EFFECT IN(MN,FE)2(P,SI,B)MATERIALS 250 260 270 280 290 300 310 320 0.0 0.5 1.0 1.5 T cyclic ( B = 1.1 T) T ad (B = 1.0 T) [ref.] Pr 0.65 Sr 0.35 M nO 3 T ( K ) T (K)

Figure 4.1: Comparison between cyclic∆Tcyclicprobe in B = 1.1 T (red solid line) and calorimetric measure-ment in∆B = 1.0 T (open circle) taken from ref. [76] for (Pr0.65Sr0.35)MnO3.

4.1.

THE CASE OF SECOND-ORDER PHASE TRANSITIONS

B

EFOREdiscussing the determination of the magnetocaloric effect for materials ex-hibiting a FOMT, it is useful to first present a few characteristics of the magnetic phase transitions of second-order (SOMT). For a SOMT, the transition is continuous and reversible. The thermo-magnetic path used for the measurements does not influence the determination of the MCE. It is now well recognized that the different MCE mea-surements should in principle lead to the same∆S and ∆Tadvalues in case of a SOMT.

Only a few exceptions can be found. Indirect methods based on magnetization measure-ments and the calorimetric heat capacity in magnetic field, have been found to match the direct techniques for the SOMT. Discussion on the accuracy of the various methods can be found in several reviews [33,52,53]. As the methods used in this thesis (1) the direct cyclic∆Tcyclicprobe and (2) the in-field DSC setup, can be considered as

uncon-ventional MCE measurement methods, they were first tested on a material presenting a ferro-paramagnetic SOMT to assure their reliability and accuracy.

For a SOMT, the MCE is reversible, and therefore the direct∆Tcyclicresults are

ex-pected to be identical to indirect∆Tadmeasurements. Given the fact that the MCE of

metallic Gd is influenced by impurities and oxidation, these preliminary measurements were carried out on an oxide (Pr0.65Sr0.35)MnO3previously studied in [76]. The∆Tcyclic

as a function of temperature for (Pr0.65Sr0.35)MnO3has been measured on the setup

de-scribed in section 3.5. The results are presented in Fig. 4.1and compared to the∆Tad

calculated from heat capacity measurement by means of the semi-adiabatic heat capac-ity option of a Physical Properties Measurement System (Quantum Design) [76]. There is a very good agreement between the two methods in terms of both shape of the tempera-ture dependence of∆T and maximal ∆T values. The slightly higher ∆Tcyclicmaximum of

1.20 K than the calorimetric∆Tadmaximum of 1.11 K can be ascribed to the higher∆B

(with the usual assumption that for a second-order magnetic transition the maximum of∆Tadshows a B2/3field dependence). The agreement between the two techniques

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4.1.THE CASE OF SECOND-ORDER PHASE TRANSITIONS 27 260 280 300 320 500 550 600 650 700 270 280 290 300 310 320 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 (b) S ( J k g -1 K -1 ) T (K) isofield (heating) isotherms (field decreasing)

C p ( J k g -1 K -1 ) T (K) PPMS 0 T from [ref.] PPMS 1 T from [ref.] DSC 0 T DSC 0.95 T (a)

Figure 4.2: (a) Heat capacity of (Pr0.65Sr0.35)MnO3measured with the in-field DSC (line) and with the PPMS (symbols) taken from ref. [76]. (b) MCE of (Pr0.65Sr0.35)MnO3at B = 0.95 T determined with the in-field DSC setup using the isofield (line) and isotherm (symbols) modes.

clearly supports the reliability of the∆Tcyclicprobe.

Figure4.2(a) shows the heat capacity as a function of temperature measured with the in-field DSC setup described in section 3.4.2 and with semi-adiabatic calorimeter reported in ref. [76]. Both measurements show an asymmetrical heat capacity anomaly at the Curie temperature, which is characteristic for the SOMT. The in-field DSC setup succeeds in reproducing the broadening of the heat capacity peak due to the application of a magnetic field. However, the relatively scatter in the DSC results compared to the semi-adiabatic method and the difference in the slope of the heat capacity background between the heating and cooling branches indicates the limitations of the DSC setup. An accurate determination of the heat capacity around weak anomalies is difficult for the DSC. The DSC technique is in fact most often used to derive the MCE at a FOMT where the heat capacity anomaly is considerably more pronounced. As the MCE corresponds to an integral form of these Cp(T ) curves, the∆S values from in-field DSC, shown in Fig.4.2(b) appear less noisy. The∆S values are well in line with the expected ∆Smax≈

-2.4 Jkg-1K-1[76]. This demonstrates the reliability of the in-field DSC setup.

The in-field DSC setup also offers the possibility to record the heat flow between the MCE materials and the surrounding during a change in magnetic field at a constant tem-perature. This thus corresponds to a direct measurement of∆S. At one given temper-ature, several magnetization/demagnetization curves can be recorded so that a∆Scyclic

can be measured in a similar way as done for the∆Tcyclic. Figure4.2(b) shows a

com-parison between indirect isofield∆S measurements and direct isothermal ∆Scyclicdata

recorded with the in-field DSC setup. As expected for a SOMT, the results of both meth-ods overlap and are similar to the literature data [76]. This again confirms the reliability of the in-field setup and the obtained experimental parameters for isothermal∆Scyclic

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284.DETERMINATION OF THE MAGNETOCALORIC EFFECT IN(MN,FE)2(P,SI,B)MATERIALS 260 270 280 290 300 0 1000 2000 3000 Heating Cooling C p ( J k g -1 K -1 ) T (K) B = 0 T

Figure 4.3: Temperature dependence of the specific heat of MnFe0.95P0.582B0.078Si0.34measured in the com-mercial DSC in zero-field for heating (solid line) and cooling (dashed line).

4.2.

ISOTHERMAL ENTROPY CHANGE FOR A FIRST-ORDER PHASE

TRANSITION

A

Sintroduced in Chapter 2, a material that undergoes a FOMT shows latent heat at the transition. In the Mn-Fe-P-Si system, a FOMT usually results in a narrow, intense and symmetric heat capacity peak, which corresponds to a large discontinuous change in the temperature dependence of the entropy. Another characteristic of materials with FOMT is the presence of hysteresis, which results in a finite regions of irreversibility in the TC-B phase diagram. Due to these two characteristics of the FOMT, the

experimen-tal determination of the magnetocaloric effect turns out to be rather challenging. These difficulties can already be noticed in the very first works on the Gd5(Si,Ge)4giant

mag-netocaloric materials [44,77]. The MCE determination led to controversies in various giant-MCE materials systems, as for instance Heusler alloys [78,79]. Since then, many works have addressed the MCE determination for a FOMT. This thesis focuses on defin-ing practical experimental methods givdefin-ing MCE quantities, which reflects the material performances in applications.

The consequence of the irreversibility of the FOMT has not been fully explored yet. The MCE at a FOMT might vanish after one magnetization cycle unless the sample is treated thermally. In this case, it is impossible to use this material in a refrigeration cycle. One of the goal has thus been to look for methods that reflect cyclic MCE quantities and to compare them with the usual∆S and ∆Taddetermination method.

In order to compare the MCE determination by different direct and indirect methods, one prototypical composition MnFe0.95P0.582B0.078Si0.34has been selected. This boron

substituted material is close to the composition recently reported in ref [20]. The heat capacity of this MnFe0.95P0.582B0.078Si0.34 sample measured with the commercial DSC

setup in zero field is shown in Fig.4.3. The results are in line with the typical properties for this range of compositions: a near room temperature TC≈ 284 K, a limited thermal

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