Novel Materials for Magnetic

Refrigeration

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Universiteit van Amsterdam

op gezag van de Rector Magnificus

prof. mr. P.F. van der Heijden

ten overstaan van een door het college voor promoties

ingestelde commissie, in het openbaar te verdedigen

in de Aula der Universiteit

op donderdag 23 oktober 2003 te 11.00 uur

door

Tegusi

geboren te Chifeng (P.R. China)

AMSTERDAM 2003

Promotiecommissie Promotores Prof. dr. F.R. de Boer Prof. dr. K.H.J. Buschow Co-promotor Dr. E. Brück Overige leden Prof. dr. W.C. Sinke Dr. A.M. Tishin Dr. M. ter Brake

Prof. dr. J.J.M. Franse Prof. dr. M.S. Golden Dr. A. de Visser

Faculteit der Natuurwetenschappen, Wiskunde en Informatica

The work described in this thesis was supported by the Dutch Technology Foundation (STW), the applied science division of Netherlands Organization for Scientific Research (NWO) and the technology program of the ministry of Economic Affairs, carried out in the Materials Physics group

at the

Van der Waals-Zeeman Instituut, Universiteit van Amsterdam

Valckenierstraat 65-67, 1018 XE Amsterdam, the Netherlands

Where a limited number of copies of this thesis is available ISBN: 90 5776 107 6

Printed in the Netherlands by PrinterPartners Ipskamp B.V.,

P.O. Box 333, 7500 AH Enschede

Cover illustration: Ton Riemersma

To my parents, my wife Dagula and my son Yiliqi

Contents 1 Introduction……………………………………………………….. 1

1.1 General introduction ………………………………………… 1

1.2 The magnetocaloric effect …………………………………… 2

1.3 Magnetic refrigeration..………………………………………. 3

1.4 Outline of this thesis …………………………………………. 5

References …………………………………………………….……. 5

2 Theoretical aspects ………………………………..……………….. 7

2.1 Gibbs free energy ………………………..…………………….. 8

2.2 Magnetic entropy …………………………..………………….. 9

2.3 The Bean-Rodbell model ……………………………………... 11

References ………………………………………………………….. 14

3 Experimental …………………………………..…………………. 15

3.1 Sample preparation ………………………………………….. 15

3.1.1 Arc melting and ball milling ………………………… 15

3.1.2 Crystal growth ……………………………………….. 17

3.2 Sample characterization ……………………………………… 18

3.3 Magnetic measurements ……………………………………… 19

3.4 Specific-heat measurements …………………………………. 19

3.5 Electrical-resistivity measurements ……………………………... 20

3.6 Determination of the magnetocaloric effect ……….………….. 21

3.6.1 Determination of the magnetocaloric effect from

magnetization measurements ………………………… 21

3.6.2 Determination of the magnetocaloric effect from

ii

specific-heat measurements …………………………….. 22

References ………………………………………………………………. 24

4 Magnetic phase transitions and magnetocaloric effect in

Gd-based compounds……………………………………………… 25

4.1 Introduction …………………………………………………… 25

4.2 GdRu2Ge2 …………………………………………………….. 26

4.2.1 Introduction …………………………………………… 26

4.2.2 Experimental …………………………………………. 27

4.2.3 Results and discussion ………………………………... 27

4.2.4 Conclusions …………………………………………... 33

4.3 Single-crystalline Gd5Si1.7Ge2.3 ……………………………… 33

4.3.1 Introduction ………………………………………….. 33

4.3.2 Cyrstal growth and characterization …………………. 34

4.3.3 Magnetic properties ………………………………….. 36

4.3.4 Specific heat …………………………………………. 41

4.3.5 Magnetocaloric effect ……………………………….. 43

4.3.6 Discussion and conclusions ………………………….. 45

References ……………………………………………………….…. 48

5 Magnetocaloric effect in hexagonal MnFeP1-xAsx

compounds ………………………………………………………… 51

5.1 Introduction ………………………………………………….. 51

5.2 Sample preparation and characterization ……………………. 53

5.3 Structural properties …………………………………………. 54

5.4 Magnetic properties ………………………………………….. 56

5.5 Specific heat and dc susceptibility …………………………… 60

iii

5.6 Magnetocaloric effect ..………………………………………. 62

5.7 Electrical resistivity and magnetoresistivity …………………. 68

5.8 A model description of the first-order magnetic

phase transition ……………………………………………….. 71

5.9 Discussion and conclusions …………………………………… 77

References……...…………………….……………………………… 82

6 Effects of Mn/Fe ratio on the magnetocaloric properties of

hexagonal MnFe(P,As) compounds ……………………………… 85

6.1 Introduction …………………………………………………… 85

6.2 Experimental …………………………………………………. 87

6.3 Results and discussion ……………………………………….. 87

6.3.1 Structural and magnetic properties …………………… 87

6.3.2 Magnetocaloric properties …………………………… 94

6.3.3 Electrical resistivity …………………….……..…….. 102

6.4 Conclusions ……………………………..…………………… 104

References …….…………………………….……….…………….. 105

Summary ….…..……………………………..……………….……… 107

Samenvatting ……………………………………….………………. 110

Publications ..…………….…………………….……………….…….. 113

Acknowledgments ...……..……….………..…………………….…… 117

1

Chapter 1 Introduction 1.1 General introduction Modern society relies very much on readily available cooling. Next to the food

storage and transport, air-conditioning in buildings and cars gains more

importance, and in the near future it is envisaged that superconducting electronics

may be operated at liquid-nitrogen temperatures. These developments call for

energy-efficient and versatile refrigeration technology.

The vapor-compression refrigerators have become ubiquitous in a large

number of cooling applications. However, the use of chlorofluorocarbons (CFCs)

and hydrochlorofluorocarbons (HCFCs) as working fluids has raised serious

environmental concerns, primarily for the role in the destruction of the ozone layer

[1, 2] and the global warming. Replacement by fluid hydrofluorocarbons (HFCs),

which contain no chlorine and therefore have no ozone depletion potential, is not

without problems because the HFCs are greenhouse gases [3] with higher global

warming potential than CO2. In addition, the efficiency of the vapor-compression

refrigeration systems is not expected to be significantly improved in the future.

Thus, due to slow improvement of the efficiency and serious concern for the

environment, alternative technologies that use either inert gases or no fluid at all

become attractive solutions to the environment problems.

2 Chapter 1

Magnetic refrigeration has been in use in scientific applications for a long

time for cooling below 1 K. But there are no commercial applications at

temperatures around room temperature due to the fact that the magnetocaloric

effect (MCE) is relatively weak in most ferromagnetic materials at these

temperatures. Only gadolinium exhibits a considerable MCE, about 2 K/T, at room

temperature. Recently, this technique has been demonstrated [4] as a promising

alternative for the conventional gas-compression/expansion technique generally in

use today. But the major problem in magnetic refrigeration is still to find working

materials with a large MCE in different temperature regions.

In 1997, Pecharsky and Gschneidner [5] have reported the discovery of the

so-called giant MCE in the Gd5(SixGe1-x)4 system. Subsequently, a large number of

materials were reported as candidate materials for magnetic cooling [6-9].

Although considerable success has been achieved in developing magnetic

refrigerants, the search for novel working materials is still an important task, in

particular, in order to develop suitable materials for room-temperature applications

in lower fields, which can be generated by permanent magnets [10, 11].

The motivation of our research project, namely to explore new materials for

magnetic cooling, was two-fold. From the application point of view, we have

focused on finding potential refrigerants, specifically among Mn- or Fe-based

compounds, in order to establish the appropriateness for room-temperature

magnetic-cooling application. From the fundamental point of view, our motivation

was to gain a deeper insight into the fundamental relations between the MCE and

magnetic phase transitions, compositions, and the thermomagnetic properties of

solid magnetic materials. This insight may serve as a guide in the search for new

materials suitable for application.

1.2 The magnetocaloric effect The MCE is defined as the thermal response of a magnetic material to an applied

magnetic field and is apparent as a change in its temperature. It was discovered by

Introduction 3

Warburg [12] in 1881 and is intrinsic to all magnetic materials. In the case of a

ferromagnetic material as depicted in Fig. 1.1, the material heats up when it is

magnetized and cools down when it is removed out of the magnetic field.

The magnitude of the MCE of a magnetic material is characterized by the

adiabatic temperature change adT∆ , or by the isothermal magnetic -entropy change

mS∆ due to a varying magnetic field. The nature of the MCE in a solid is the result

of the entropy variation due to the coupling of the magnetic spin system with the

magnetic field [13]. For the various aspects of the MCE and magnetic refrigeration

we refer to Kuz′man and Tishin [14], Gschneidner and Pecharsky [15], and Tishin

[16].

1.3 Magnetic refrigeration Magnetic refrigeration is a method of cooling based on the MCE. The heating and

cooling caused by a changing magnetic field are similar to the heating and cooling

of a gaseous medium in response to compression and expansion. A schematic

representation of a magnetic -refrigeration cycle is depicted in Fig. 1.1.

When a ferromagnetic material containing atoms that carry magnetic

moments is placed in an external magnetic field, the field forces the magnetic

moments to align, reducing the magnetic entropy. Since the total entropy is

constant under adiabatic conditions, the reduced part of the magnetic entropy is

transferred from spin subsystem to lattice subsystem via spin and lattice coupling.

This causes an increase of the lattice entropy, which makes the atoms vibrate more

rapidly, and results in an increase of temperature of the material. Conversely, when

the material is taken out of the magnetic field, the moments randomize again and

remove entropy from the lattice, creating a cooling effect.

In 1926, Debye [17] and Giauque [18] have independently proposed the

principle of adiabatic magnetic cooling, which utilizes the MCE of paramagnetic

salts, as a means of reaching temperatures below the boiling point of liquid helium.

4 Chapter 1

Figure 1.1: Schematic representation of a magnetic -refrigeration cycle in which heat is transported from the heat load to its surroundings. Initially randomly oriented magnetic moments are aligned by a magnetic field, resulting in heating of the material. This heat is removed from the material to its surroundings by a heat-transfer medium. On removing the field, the magnetic moments randomize, which leads to cooling of the magnetic material to below the ambient temperature. Depending on the operating temperature, the heat-transfer medium may be water (with antifreeze) or air, and, for very low temperatures, helium.

In 1933, Giauque and MacDougall [19] have put this idea into practice and have

experimentally demonstrated the use of the MCE to achieve temperatures below 1

K. From then on, the MCE has been successfully utilized to achieve ultra-low

temperatures by employing a process known as adiabatic demagnetization. In 1976,

Brown [20] has reported a prototype of a room-temperature magnetic refrigerator

and demonstrated that magnetic refrigeration can be realized in the room-

temperature region. In 2001, Astronautics Corporation of America [4] has realized

the world’s first successful room-temperature magnetic refrigerator, in which

Introduction 5

permanent magnets were used to generate the magnetic field. This achievement

moves the magnetic refrigerator a step closer to commercial applications.

1.4 Outline of this thesis The work presented in this thesis is a study of the MCE and related physical

properties of several systems of intermetallic compounds.

The theoretical aspects of the MCE and the Bean-Rodbell model that

describes magnetic phase transitions observed in MnFeP1-xAsx compounds are

presented in Chapter 2. In Chapter 3, a short review is given of the experimental

techniques and set-ups that have been employed for the sample preparation, the

characterization and the investigation of the physical properties of the materials

studied in this thesis.

Chapter 4 is designated to the MCE and related physical properties of the

Gd-based compounds GdRu2Ge2 and Gd5Si1.7 Ge2.3. The isothermal magnetic -

entropy change of GdRu2Ge2 was determined by means of both magnetization and

specific-heat measurements, which are in good agreement. We have also grown a

single crystal of Gd5Si1.7Ge2.3 and have studied the thermomagnetic properties and

the MCE of this single crystal.

The highlight of the work is the discovery of the giant MCE in transition-

metal-based compounds of the type MnFeP1-xAsx. A systematic study of the MCE

and related physical properties of the MnFeP1-xAsx compounds is presented in

Chapter 5. The magnetocaloric properties of MnFe(P,As)-based compounds can be

improved by varying the Mn/Fe ratio. This is reported in Chapter 6. The last part is

the summary of the present thesis work.

6 Chapter 1

References [1] F. Drake, M. Purvis and J. Hunt, Public Understand. Sci. 10 (2001) 187. [2] Montreal Protocol on Substances that Deplete the Ozone Layer, United

Nations (UN), New York, NY, USA, 1987. [3] Kyoto Protocol to the United Nations Framework Convention on Climate

Change, United Nations (UN), New York, NY, USA, 1997. [4] http://www.external.ameslab.gov/News/release/01magneticrefrig.htm. [5] V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. Lett. 78 (1997) 4494. [6] F.X. Hu, B.G. Shen and J.R. Sun, Appl. Phys. Lett. 76 (2000) 3460. [7] H. Wada and Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3302. [8] O. Tegus, E. Brück, K.H.J. Buschow and F.R. de Boer, Nature 415 (2002)

150. [9] A. Fujita, S. Fujieda, Y. Hasegawa and K. Fukamichi, Phys. Rev. B 67

(2003) 104416. [10] J.M.D. Coey, J. Magn. Magn. Mater. 248 (2002) 441. [11] S.J. Lee, J.M. Kenkel, V.K. Pecharsky and D.C. Jiles, J. Appl. Phys. 91

(2002) 8543. [12] E. Warburg, Ann. Phys. Chem. 13 (1881) 141. [13] V.K. Pecharsky, K.A. Gschneidner, Jr., A.O. Pecharsky and A.M. Tishin,

Phys. Rev. B 64 (2001) 144406. [14] M.D. Kuz′min and A.M. Tishin, Cryogenics 32 (1992) 545.

M.D. Kuz′min and A.M. Tishin, Cryogenics 33 (1993) 868. [15] K.A. Gschneidner, Jr., and V.K. Pecharsky, Ann. Rev. Mater. Sci. 30 (2000)

387. [16] A.M. Tishin, Magnetocaloric effect in the vicinity of phase transitions, in

Handbook of Magnetic Materials, Vol. 12, Edited by K.H.J. Buschow (North Holland, Amsterdam, 1999) pp. 395-524.

[17] P. Debye, Ann. Physik 81 (1926) 1154. [18] W.F. Giauque, J. Amer. Chem. Soc. 49 (1927) 1864. [19] W.F. Giauque and D.P. MacDougall, Phys. Rev. 43 (1933) 768. [20] G.V. Brown, J. Appl. Phys. 47 (1976) 3673.

7

Chapter 2 Theoretical aspects The magnetocaloric effect (MCE) of a magnetic material is associated with the

magnetic-entropy change of the material. The theoretical aspects of the MCE have

been discussed in Refs. 1 and 2. According to thermodynamics, the MCE is

proportional to ∂M/∂T at constant field and inversely proportional to the field

dependence of the specific heat cp(T,B). In the temperature region of a magnetic

phase transition, the magnetization changes rapidly and, therefore, a large MCE is

expected in this region [3,4]. However, the critical behavior of the physical

quantities in the phase-transition region is so complicated that there is no unified

theory. The theoretical description of MCE is still far from complete. Therefore,

the adiabatic temperature change ∆Tad of a given material can only be determined

by using experimental methods.

The understanding of magnetic phase transitions and the evaluation of the

entropy change associated with the magnetic phase transitions, therefore, form an

important part of this thesis. In this chapter, we will first introduce the theoretical

background of the MCE. Then, we will give outlines of the Bean-Rodbell model

[5] that we will use to describe the first-order magnetic phase transition in the

hexagonal MnFe(P,As)-type compounds.

8 Chapter 2

2.1 Gibbs free energy The thermodynamic properties of a system are fully determined by the Gibbs free

energy or free enthalpy of the system. The system we consider here consists of a

magnetic material in a magnetic field B at a temperature T under a pressure p. The

Gibbs free energy G of the system is given by

MBpVTSUG −+−= , (2.1)

where U is the internal energy of the system, S the entropy of the system, and M

the magnetization of the magnetic material. The volume V, magnetization M, and

entropy S of the material are given by the first derivatives of the Gibbs free energy

as follows

.),,(

),,(

),,(

,

,

,

pB

pT

BT

TG

pBTS

BG

pBTM

pG

pBTV

∂∂

−=

∂∂

−=

∂∂

−=

(2.2)

The specific heat of the material is given by the second derivative of the

Gibbs free energy with respect to temperature

.),(2

2

p

p TG

TBTc

∂∂

−= (2.3)

Theoretical aspects of the MCE 9

By definition, if the first derivative of the Gibbs free energy is discontinuous

at the phase transition, then the phase transition is of first order. Therefore, the

volume, magnetization, and entropy of the magnetic material are discontinuous at a

first-order phase transition. If the first derivative of the Gibbs free energy is

continuous at the phase transition but the second derivative is discontinuous, then

the phase transition is of second order.

2.2 Magnetic entropy The total entropy of a magnetic material in which the magnetism is due to localized

magnetic moments, as for instance in lanthanide-based materials, is presented by

),,,(),,(),,(),,( pBTSpBTSpBTSpBTS mel ++= (2.4)

where S l represents the entropy of the lattice subsystem, S e the entropy of

conduction-electron subsystem and Sm the magnetic entropy, i.e. the entropy of the

subsystem of the magnetic moments. In magnetic solids exhibiting itinerant-

electron magnetism, separation of these three contributions to the total entropy is,

in general, not straightforward because the 3d electrons give rise to the itinerant-

electron magnetism but also participate in the conduction. Separation of the lattice

entropy is possible only if electron-phonon interaction is not taken into account.

Since the entropy is a state function, the full differential of the total entropy

of a closed system is given by

.,,,

dBBS

dppS

dTTS

dSpTBTBp

∂∂

+

∂∂

+

∂∂

= (2.5)

Among these three contributions, the magnetic entropy is strongly field

dependent, and the electronic and lattice entropies are much less field dependent.

Therefore, for an isobaric-isothermal (dp = 0; dT = 0) process, the differential of

the total entropy can be represented by

10 Chapter 2

.,

dBB

SdS

pT

m

∂∂

= (2.6)

For a field change from the initial field B i to the final field B f , integration of

Eq. (2.6) yields for the total entropy change

),(),(),(),( BTSBTSBTSBTS mif ∆∆=−=∆∆ , (2.7)

where B∆ = B f - B i. This means that the isothermal-isobaric total entropy change

of a magnetic material in response to a field change B∆ is also presented by the

isothermal-isobaric magnetic -entropy change.

The magnetic-entropy change is related to the bulk magnetization, the

magnetic field and the temperature through the Maxwell relation

.),(),(

,, pBpT

m

TBTM

BBTS

∂∂

=

∂

∂ (2.8)

Integration yields

dBT

BTMBTSpB

B

Bm

f

i ,

),(),( ∫

∂∂=∆∆ . (2.9)

On the other hand, according to the second law of thermodynamics

.),(

, T

BTc

dTdS p

pB

=

(2.10)

Integration yields

Theoretical aspects of the MCE 11

.),(

),( '

0'

'

0 dTT

BTcSBTS

Tp

∫+= (2.11)

In the absence of configurational entropy, the entropy will be zero at T = 0 K, so

that the value of S0 is usually chosen to be zero. Therefore, the entropy change in

response to a field change B∆ is given by

'

0'

'' ),(),(),( dT

T

BTcBTcBTS

Tipfp

∫−

=∆∆ , (2.12)

where ),( 'fp BTc and ),( '

ip BTc represent the specific heat at constant pressure p

in the magnetic field Bf and Bi, respectively.

2.3 The Bean-Rodbell model Bean and Rodbell [5] have proposed a phenomenological model that describes the

first-order phase transition in MnAs. Blois and Rodbell have used this model to

explain the first-order magnetic phase transition observed for MnAs [6]. Zach et al.

[7] have used this model in a semiquantitative analysis of the magnetic phase

transition in the MnFeP1-xAsx series of compounds. In this section, we will

introduce the Bean-Rodbell model.

This model correlates strong magnetoelastic effects with the occurrence of a

first-order phase transition. The central assumption in the model of Bean and

Rodbell is that the exchange interaction (or Curie temperature) is strongly

dependent on the interatomic spacing. In this model, the dependence of Curie

temperature on the volume is represented by

],/)(1[ 000 VVVTTC −+= β (2.13)

12 Chapter 2

where TC is the Curie temperature, whereas T0 would be the Curie temperature if

the lattice were not compressible, and V0 would be the volume in the absence of

exchange interaction. The coefficient ß may be positive or negative.

In the Bean-Rodbell model, the critical behavior of the magnetic system is

analyzed on the basis of the Gibbs free energy consisting of the following

contributions

,pressentropyelasticZeemanexch GGGGGG ++++= (2.14)

where Gexch, GZeeman, Gelastic, Gentropy, and Gpress represent the exchange interaction,

the Zeeman energy, the elastic energy, the entropy term, and the pressure term,

respectively. Within the molecular-field approximation, for arbitrary spin j, Eq.

(2.14) is given by [6]

pVSSTV

VVK

BTNkj

jG ljCB ++−

−+−

+

−= )()(

21

123 2

0

00

2 σσσ , (2.15)

where N is the number of magnetic atoms per kilogram, kB the Boltzmann constant,

σ0 the saturation magnetization per kilogram at 0 K, σ the relative magnetization

(M/σ0), K the compressibility, Sj the entropy of the spin subsystem, and S l the

entropy of the lattice subsystem. Inserting Eq. (2.13) into Eq. (2.15) and

minimizing the expression for G with respect to volume, we obtain the equilibrium

volume for arbitrary j

.)1(2

3 20

00

0 pKTKTNkj

jVV

VVB −+

+=

−αβσ (2.16)

This result shows that the magnetization depends on the volume change. The

term αT, in which α is the lattice thermal expansion coefficient, is from the thermal

expansion.

Inserting Eqs. (2.13) and (2.16) into Eq. (2.15), we obtain

Theoretical aspects of the MCE 13

,)0()(

))(1)(1

(23

189)0()(

00

02

420

2

00

−−−−−

+−

+

−=−

B

jj

B

BB

Nk

SS

TT

TNkB

TpKj

j

KTNkj

jVTNk

GG

σσσσαβ

σβσ

(2.17)

The implicit dependence of the magnetization on temperature is obtained by

minimizing Eq. (2.17) with respect to σ. In the case of absence of external pressure

(p = 0), we obtain

,)(1

2

/

0

003

0

σ

σσαβ

σσησ

∂

∂−−

++=

j

B

Bjjj

S

NkT

TNkBba

TT

(2.18)

where

.]1)12[(2

)]1(4[5

,)]1(2[

1)12(59

,1

3

20

04

2

4

4

βη KTNkVj

jj

jj

b

jj

a

Bj

j

j

−++

=

+−+

=

+=

(2.19)

Here, η j is an important parameter, involving the parameters K and ß that are

related to the volume change. In the molecular-field approximation, the spin

entropy, Sj, is a function of the relative magnetization σ and can be expressed as a

series in even powers of σ [5]. For the compounds MnFeP1-xAsx (0.25 < x < 0.65),

magnetization measurements at 5 K show that the saturation magnetization is about

4 µB/f.u., from which we conclude that the angular momentum j equals 2 (assuming

that g = 2). In this case, Eq. (2.18) becomes

14 Chapter 2

.2606.0867.02

/867.02

053

003

2

0 σαβσσσσσησ

T

TNkBTT B

−++++

= (2.20)

This equation may express the temperature and field dependence of the

magnetization of MnFeP1-xAsx in the vicinity of the phase transition. In Chapter 5,

we will fit our experimental results based on Eqs. (2.17) and (2.20), and will give a

model description of the first-order magnetic phase transition in MnFeP1-xAsx

compounds.

References [1] M.D. Kuz′min and A.M. Tishin, Cryogenics 32 (1992) 545. [2] M.D. Kuz′min and A.M. Tishin, Cryogenics 33 (1993) 868. [3] K.A. Gschneidner, Jr., and V.K. Pecharsky, Mater. Sci. Eng. A287 (2000)

301. [4] O. Tegus, E. Brück, L. Zhang, Dagula, K.H.J. Buschow and F.R. de Boer,

Physica B 319 (2002) 174. [5] C.P. Bean and D.S. Rodbell, Phys. Rev. 126 (1962) 104. [6] R.W. de Blois and D.S. Rodbel, Phys. Rev. 130 (1963) 1347. [7] R. Zach, M. Guilot and J. Tobola, J. Appl. Phys. 83 (1998) 7237.

15

Chapter 3

Experimental 3.1 Sample preparation 3.1.1 Arc melting and ball milling Generally, intermetallic compounds are prepared by melting. In this way, also the

intermetallic compounds investigated in this present thesis were prepared by arc

melting appropriate amounts of the constituent elements, typically about 5 g, of at

least 99.9 % purity in a water-cooled copper crucible pre-evacuated to better than

2×10-6 mbar and refilled with high-purity Ar gas. In order to obtain homogeneous

samples, arc melting was repeated several times. In order to eliminate the stress

and to obtain a homogeneous single -phase sample with large grains, the ingots

were annealed at appropriate temperatures for several days, depending on the series

of alloys.

The vapor pressures of P and As are too high to prepare the intermetallic

compounds containing P and/or As by means of arc melting. Therefore, instead of

arc melting, the ball-milling technique was used to prepare fine metallic powders

of these compounds. This technique is also suitable to accomplish a wide range of

chemical reactions. Milling devices include vibratory and planetary mills; products

include amorphous and nanocrystalline materials, and solid solutions. During

milling, solid-state reactions are initiated through repeated deformation and

fracture of the powder particles. In this thesis work, a solid-state reaction method

16 Chapter 3

was used for the preparation of the samples discussed in Chapters 5 and 6. First,

the mixture of starting materials with appropriate amounts was ball milled, then the

powder was sealed in a molybdenum crucible under argon atmosphere and placed

in a quartz ampoule for a couple of hours at a temperature at which the reaction

could take place. Subsequent annealing was performed at a temperature below the

reaction temperature.

Figure 3.1: Schematic representation of the high-energy vibratory mill

used in the present work.

The vibratory ball mill used in the present study is presented in Fig. 3.1. The

device consists of a stainless-steel vial with a hardened-steel bottom, the central

part of which consists of a tungsten-carbide disk. Inside the vial, a single hardened-

steel ball with a diameter of 6 cm is kept in motion by a water-cooled vibrating

frame. The amount of milled sample varied from about 5 to 10 g in this thesis

work. The device is evacuated during the milling down to a pressure of 10-6 mbar

in order to prevent reactions with the gas atmosphere.

Experimental 17

3.1.2 Crystal growth A single crystal of Gd5Si1.7 Ge2.3 was grown with the traveling-floating-zone

method in an adapted NEC double-ellipsoidal-type image furnace. A schematic

picture of the image furnace is shown in Fig. 3.2.

Figure 3.2: A schematic picture of the NEC SC-N35HD image furnace (taken from [1]).

The furnace consists of two mirrors, which are plated with gold for enhanced

reflectivity and corrosion resistance. The heat sources are two halogen lamps. The

filaments of the two halogen lamps are positioned in the focus of each of the

mirrors, and are projected on the common focal point of the two mirrors. In this

way, the input power is concentrated on the molten zone between the feed and the

18 Chapter 3

seed. The temperature of the molten zone is controlled by controlling the dc-

voltage of the two lamps.

Feeds were prepared by arc-melting the pure starting materials into a button,

which was then cast into a cylindrical rod of 4 to 5 mm diameter. A quartz tube

served as growth chamber. Before the growth, the chamber was evacuated to a

pressure of 10-6 mbar, and then filled with about 900 mbar Ar gas. During the

growth, the Ar atmosphere was continuously purified with Ti - Zr getter. The feed

and seed were counter-rotated with speeds of 20 rpm. The pulling speed of the

shafts was 3 mm/h for the Gd5Si1.7Ge2.3 crystal. After the growth, the sample was

slowly cooled down to room temperature. In this way, a single crystal of

Gd5Si1.7Ge2.3 was obtained with a diameter of 4 mm.

3.2 Sample characterization Powder x-ray diffraction (XRD) patterns were taken at room temperature by means

of a Philips diffractometer with Cu K α radiation. In this way, the main phase as

well as the impurity phases can be detected, when the latter are present in amounts

of at least 5 vol. %. The crystal structure and the lattice parameters (with an

accuracy of 0.5 %) of the crystalline materials were analyzed by means of a

refinement procedure using Philips X’pert software. Laue x-ray back-scattering

diffraction was used to examine the single -crystallinity and to determine the

crystallographic directions of the single crystal. A Laue photo gives information on

the crystal quality of the surface over an area of about 1 mm2. By taking several

pictures at different positions information on single -crystallinity is obtained. The

crystallographic directions of the samples were determined by using the software

Orient Express [2].

Electron-probe microanalysis (EPMA) was used to check the homogeneity

and the stoichiometry, and also the single -crystallinity of the samples. The

measurements were performed in the JEOL JXA-8621 equipment [3] at the FOM-

ALMOS facility at the Kamerlingh Onnes Laboratory, University of Leiden.

Experimental 19

3.3 Magnetic measurements A Quantum Design MPMS2-type SQUID magnetometer [4] was employed to

investigate the temperature and magnetic -field dependence of the magnetization.

This SQUID magnetometer is capable of measuring magnetization values in the

range of 10-12 to 103 Am2 with an accuracy of 0.1 % in the temperature range from

1.7 to 400 K and in the field range from – 5 T to 5 T. The samples used for

magnetization measurements in the SQUID magnetometer are single crystals,

polycrystalline bulk pieces and powders.

Measurements of the magnetization loop in fields higher than 5 T and of the

magnetoresistance were performed in an Oxford Instruments MagLab system [5] in

the temperature range from 1.7 to 400 K and in the field range from – 9 to 9 T. The

sensitivity of the system for magnetization measurements is 10-6 Am2.

3.4 Specific-heat measurements Specific -heat measurements on GdRu2Ge2 at low-temperatures and in high-

magnetic field were performed in the Amsterdam 17 T specific -heat measurement

set-up [6]. In this set-up, the magnetic -field dependence of the specific heat can be

measured at temperatures between 300 mK and 90 K, by using the well known, and

reliable, semi-adiabatic method. Electrical heat pulses with a duration of 15 to 30 s

are applied to a sample holder, which is made of gold-plated cold-rolled silver. The

temperature before and after the heat pulse is monitored by a so-called combination

thermometer [7], which exhibits a very limited field dependence. The 3He cryostat

is a closed system, working with a room-temperature gas-storage vessel, and a

cryopump for cooling the system down to 300 mK.

Specific -heat measurements on Gd5Si1.7 Ge2.3 were performed in the

temperature range from 4.2 to 300 K in a home-built set-up [8]. The accuracy of

the measurement is better than 1 % in the whole temperature range. The sample,

with a flat surface and a mass of about 100 mg, was fixed on a sapphire plate by N-

20 Chapter 3

type apiezon for good thermal contact. The temperature of the sample is monitored

by a Cernox resistance-temperature sensor over the whole range of temperatures. A

carbon-glass thermometer and a PID temperature controller are used to control the

environment temperature. In this way, semi-adiabatic measurements can be

performed. The magnetic -field dependence of the specific heat can be obtained by

positioning the system into a superconducting magnet system.

Because of its high ordering temperature, the specific -heat measurements of

MnFeP0.45As0.55(I) were performed in a PPMS system [9] at the Kamerlingh Onnes

Laboratory, University of Leiden. In this system, the specific heat can be measured

in the temperature range from 1.7 to 400 K.

3.5 Electrical-resistivity measurements The electrical resistance was measured by means of the four-point method using an

Oxford Instruments MagLab system [5]. The system at the Van der Waals-Zeeman

Institute is equipped with a 9 T magnet and is capable of measurements between

1.7 K and 400 K. The ac-frequency range is from 1 Hz to 10 kHz. The maximum

input current (both ac and dc) is 250 mA. The sensitivity of the voltage

measurements is about 2 nV.

The electrical resistivity ρ is obtained from the electrical resistance by

lA

R=ρ , (3.1)

where R is the electrical resistance, A the cross section of the sample

perpendicular to the current direction, and l the distance between the voltage

contacts. The magnetoresistance is obtained from the electrical-resistance

measurements in an applied magnetic field by

Experimental 21

),0(),0(),(

),(TB

TBTBTB

==−

=∆ρ

ρρρ , (3.2)

where B is the magnetic field and T is the absolute temperature.

3.6 Determination of the magnetocaloric effect There are several ways to determine the MCE in a magnetic material

experimentally. Clark and Callen [10], Kuhrt et al. [11], and Ponomarev [12] have

directly measured the temperature of the sample with a thermocouple during the

application or removal of a magnetic field. For the principal scheme of these direct-

measurement methods and set-ups we refer to Dan’kov et al. [13]. The accuracy of

the direct measurements depends on the errors in thermometry, the errors in field

setting rates, the quality of thermal isolation of the samples, and the quality of the

compensation circuitry to eliminate the effect of the changing magnetic field on the

temperature sensors. As Pecharsky and Gschneidner [14] have pointed out, the

accuracy is claimed to be in the 5 to 10 % range. Larger errors will occur if one of

the above mentioned issues affecting the accuracy are not resolved properly. Other

techniques for determining the MCE are indirect. Indirect methods that are often

used include the ones based on magnetization measurements and on specific -heat

measurements in a constant magnetic field.

3.6.1 Determination of the magnetocaloric effect from magnetization

measurements For magnetization measurements made at discrete temperatures, the integral in Eq.

(2.9) can be numerically evaluated by

,),(),(

),( '

'

ii ii

iiiiiim B

TTBTMBTM

BTS ∆−−

=∆∆ ∑ (3.3)

22 Chapter 3

where ),( '

ii BTM and ),( ii BTM represent the values of the magnetization at a

magnetic field Bi at the temperatures 'iT and Ti, respectively. T is the mean value of

'iT and Ti. iB∆ is the step of field increase, and B∆ = Bf - B0. In the experiments that

we have conducted, the field is varied from B0 = 0 to a field B = Bf. The

accumulation of experimental errors in the determination of ),( BTS m ∆∆ has been

analyzed by Pecharsky and Gschneidner [15], and the validity of using this method,

even for a first-order magnetic phase transition, is discussed in Refs. 16 and 17.

Although a magnetization measurement by means of a SQUID magnetometer is the

most accurate method to determine the bulk magnetization of a magnetic material,

the accumulated errors in the determination of magnetic -entropy change

),( BTSm ∆∆ can be as high as 20 to 30 %, mainly because of the poor thermal

contact between the sample and the thermocouple. Nevertheless, this method is

often used to quickly establish the potential magnetocaloric properties of a

magnetic material.

3.6.2 Determination of the magnetocaloric effect from specific-heat

measurements A specific -heat measurement is the most accurate method of determining heat

effects in a material. The total entropy change of a magnetic material can be

derived from the specific heat by using Eq. (2.12). According to Eq. (2.7), this

entropy change is equal to the magnetic -entropy change for an isobaric -isothermal

process. This means that we can also obtain the magnetic -entropy change from the

field dependence of the specific -heat measurements by using Eq. (2.12).

The determination of the absolute value of the adiabatic temperature change

in different magnetic materials is a rather complicated task. By combining Eqs.

(2.6), (2.8), and (2.10), the infinitesimal adiabatic temperature change for the

adiabatic-isobaric process is found to be

Experimental 23

.),(

),(,

dBTM

BTcT

BTdTpBp

∂∂

−= (3.4)

By integration of Eq. (3.4), the adiabatic temperature change for a field change

from Bi to Bf is given by

.),(

),(,

dBTM

BTcT

BTTf

i

B

B pBpad ∫

∂∂

−=∆∆ (3.5)

Analytical integration of Eq. (3.5) is actually impossible since both the

magnetization and the specific heat are material dependent and generally unknown

functions of temperature and magnetic field in the vicinity of the phase transition.

Above the Debye temperature, the lattice specific heat of solids approaches the

Dulong-Petit limit of 3R. Therefore, at higher temperatures, if the specific heat can

be considered to be only weakly dependent on temperature, and the variation of T/

cp(T,B) with temperature is slow compared with the variation of the magnetization

with temperature, then, Eq. (3.5) can be simplified to

).,(),(

),( BTSBTc

TBTT m

pad ∆∆−=∆∆ (3.6)

Obviously, MCE is large when ( ) pBTM ,/∂∂ is large and cp(T,B) is small at the same

temperature. Since ( ) pBTM ,/ ∂∂ peaks around the magnetic ordering temperature, a

large MCE is expected in the vicinity of the temperature of the magnetic phase

transition. The determination of the MCE from magnetization, specific heat, or the

combined magnetization and specific -heat data can be used to characterize the

magnetocaloric properties of magnetic refrigerant materials. Magnetization data

provides the magnetic -entropy change ),( BTSm ∆∆ . Specific heat at constant field

provides both magnetic -entropy change ),( BTSm ∆∆ and adiabatic temperature

24 Chapter 3

change ),( BTTad ∆∆ . However, an analysis of experimental errors in the MCE as

derived from magnetization measurements and specific -heat measurements has

been shown that the accumulation of experimental errors may be as high as 20 % to

30 % near room temperature [15].

References [1] N.P. Duong, Correlation between magnetic interactions and magnetic

structures in some antiferromagnetic rare-earth intermetallic compounds, Ph.D. Thesis, University of Amsterdam (2002).

[2] OrientExpress, Version 2.03, ILL, Cyberstar S.A. [3] http://www.cameca.fr/html/epma_technique.html. [4] http://www.qdusa.com. [5] http://www.science.uva.nl/research/mmm/eindex.html. [6] http://www.science.uva.nl/research/mmm/17Tindex.html. [7] J.C.P. Klaasse, Rev. Sci. Instrum. 68 (1997) 89. [8] N.H. Kim-Ngan, Magnetic phase-transitions in NdMn2 and related

compounds, Ph.D. Thesis, University of Amsterdam, 1993. [9] http://www.physics.leidenuniv.nl/sections/cm/msm/welcome.htm. [10] A.E. Clark and E. Callen, Phys. Rev. Lett. 23 (1969) 307. [11] C. Kuhrt, T. Schitty and K. Bärner, Phys. Stat. Sol. (a) 91 (1985) 105. [12] B.K. Ponomarev, J. Magn. Magn. Mater. 61 (1986) 129. [13] S.Yu. Dan’kov, A.M. Tishin, V.K. Pecharsky and K.A. Gschneidner, Jr.,

Rev. Sci. Instr. 68 (1997) 2432. S.Yu. Dan’kov, A.M. Tishin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 57 (1998) 3478.

[14] K.A. Gschneidner, Jr., and V.K. Pecharsky, Ann. Rev. Mater. Sci. 30 (2000) 387.

[15] V.K. Pecharsky and K.A. Gschneidner, Jr., J. Appl. Phys. 86 (1999) 565. [16] K.A. Gschneidner, Jr., V.K. Pecharsky, E. Brück, H.G.M. Duijn and E.M.

Levin, Phys. Rev. Lett. 85 (2000) 4190. [17] J.R. Sun, F.X. Hu and B.G. Shen, Phys. Rev. Lett. 86 (2000) 4191.

25

Chapter 4

Magnetic phase transitions and magnetocaloric effect in Gd-based compounds

4.1 Introduction Magnetic cooling takes advantage of the entropy difference between the

magnetized and the demagnetized state of the working material. The entropy

change depends on both the properties of the material and the strength of the

applied magnetic field. The magnetocaloric effect (MCE) in heavy rare-earth

metals and their compounds has been studied intensively for some decades because

of the fact that they possess the largest magnetic moments and, therefore, the

largest available magnetic entropy. Among them, Gd 3+ has a 8S7/2 ground state and

the highest effective exchange coupling around room temperature. Thus, for

magnetic-cooling purposes, Gd metal and its compounds appear to be superior to

others in the sub-room-temperature range.

The discovery of the giant MCE in the ferromagnetic (FM) material

Gd5Si2Ge2 [1] and the high magnetic fields that can be generated by high-energy-

product permanent magnets [2] have revived interest in magnetic cooling as a

technology competitive with vapor-cycle refrigeration. In the meantime, the basic

26 Chapter 4

understanding of the MCE and its relationship with the magnetic phase transitions,

and the methods of determination of MCE in the investigated materials have been

improved. In the second section of this chapter, we present a study of the magnetic

phase transition and the MCE in the compound GdRu2Ge2 by means of both

magnetization and specific -heat measurements. In the third section, we present the

magnetic phase transitions and the dependence of the MCE in single -crystalline

Gd5Si1.7Ge2.3 on the crystallographic directions.

4.2 GdRu2Ge2 4.2.1 Introduction Recently, large MCEs have been observed in materials that exhibit a magnetic

field-induced first-order phase transition. Pecharsky and Gschneidner [1] have

discovered the so-called giant MCE in Gd5Ge2Si2, originating from a first-order

structural and magnetic transition at TC = 276 K. Wada et al. [3] have observed a

large MCE in DyMn2Ge2, originating from two successive first-order phase

transitions at 36 and 40 K. The ternary rare-earth compounds of the type GdT2X2

(T = transition metal; X = Si, Ge) have been studied intensively because of the

large variety of structural and physical properties shown by these phases [4, 5].

Duong [6] has studied the magnetic properties of GdT2Ge2 (T = 3d, 4d) and found

that there are several types of magnetic phase transitions in these compounds. For

instance, GdRu2Ge2 displays a field-induced magnetic phase transition at low field

strengths. In this section, we report on the magnetic phase transitions and the

determination of the MCE in this compound by means of specific -heat

measurements and magnetization measurements.

4.2.2 Experimental A polycrystalline sample of GdRu2Ge2 was prepared by repeatedly arc-melting

appropriate amounts of the starting materials with a purity of 99.9 wt.% and

Magnetic phase transitions and MCE in Gd-based compounds 27

subsequent annealing at 1073 K for two weeks in a 200 mbar Ar atmosphere. The

annealed sample was examined by x-ray diffraction (XRD) and found to be mainly

single phase with the tetragonal ThCr2Si2-type structure. The composition of the

sample was examined by electron-probe micro-analysis (EPMA) and found to be

mainly the stoichiometric composition GdRu2Ge2 with a small amounts of second

phase of Gd oxide [6].

The temperature and the field dependence of the magnetization of the sample

was measured in a SQUID magnetometer and an Oxford Instruments MagLab

system in the temperature range from 5 to 300 K.

Specific -heat measurements were performed by means of a semi-adiabatic

heat-pulse method in the temperature interval from 300 mK to 70 K in fields of 0,

2, 4, 6, and 15 T. The magnetic -entropy changes in GdRu2Ge2 were determined

from magnetization data by using Eq. (3.3) and from the specific -heat data by

using Eq. (2.12). Finally, the adiabatic temperature change ∆Tad was obtained by

using Eq. (3.6).

4.2.3 Results and discussion The temperature dependence of the specific heat of GdRu2Ge2, measured on a

polycrystalline sample, is shown in Fig. 4.1 in the representation cp/T vs T. Two

distinct peaks at T1 = 29 K and T2 = 33 K are observed in the zero-field specific -

heat curve, indicating two separate phase transitions exist in this compound. The

temperature dependence of the magnetization measured in a field of 0.1 T is shown

in Fig. 4.2. This result agrees with the result of the specific -heat measurements,

28 Chapter 4

0 10 20 30 40 50 60 700.0

0.2

0.4

0.6

0.8

1.0

1.2

0 T 2 T 4 T 6 T 15 T

GdRu2Ge

2c p

/T (

J/m

olK

2)

T (K)

T1T2

Figure 4.1: Temperature dependence of the specific heat, plotted as cp/T vs

T, of GdRu2Ge2 in zero field and in fields of 2, 4, 6, and 15 T. These results have been taken from Ref. [6].

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

T2 = 33 KT

1 = 29 K GdRu

2Ge

2

M (

Am

2/k

g)

T (K)

Figure 4.2: Temperature dependence of the magnetization of GdRu2Ge2

determined on a sample cooled to 5 K in zero field. The measurement was made on heating in a field of 0.1 T.

Magnetic phase transitions and MCE in Gd-based compounds 29

although the two separate transitions are less clear in the M(T) curve. The peak in

the cp/T curve at lower temperature T1 still persists in a field of 2 T, but has become

markedly broadened and has disappeared in the curves measured in higher fields.

The peak at higher temperature has become invisible in the 2 T field curve due to

broadening. At about 34 K, the specific heat in a field of 2 T exceeds the value in

zero field. These results indicate that the observation of T1 and T2 strongly depends

on the strength of the applied field.

0

10

20

30

40

B = 0 T

GdRu2Ge2

0 10 20 30 40 50 600

10

20

30

40 B = 2 T 4 T 6 T 15 T

S (J

/kgK

)

T (K)

Figure 4.3: Total entropy of GdRu2Ge2 as a function of temperature and

magnetic field, derived from specific -heat measurements.

The temperature dependence of the total entropy S in different fields was

obtained by integrating cp/T with respect to T by using Eq. (2.11). The results are

depicted in Fig. 4.3. The zero-field S(T) curve shows a small change at the

transitions. In the non-zero-field S(T) curves, no clear changes are found at the

transitions. The field dependence of the magnetization of GdRu2Ge2 at 5 K, 15 K

and 31 K, measured with increasing field and subsequent decreasing field, is shown

30 Chapter 4

in Fig. 4.4. The M(B) curves measured at 5 K and 15 K show a rapid increase in

magnetization at 1 T and 0.8 T, respectively. The saturation moment at 9 T is about

7.4 µB/Gd-atom, which is close to the value for the free Gd3+ ion. These results

show that the field-induced magnetic transition is of the antiferromagnetic to FM

type and that the transition is magnetically reversible. This transition is closely

0 2 4 6 8 100

1

2

3

4

5

6

7

8

increasing field decreasing field

31 K

15 K5 K

M (

µ Β/f.

u.)

µ0H (T)

GdRu2Ge2

Figure 4.4: Field dependence of the magnetization of GdRu2Ge2 at 5, 15

and 31 K, measured with increasing fie ld and subsequently with decreasing field.

associated with the fact that the PM Curie temperature is positive ( pθ = 37.2 K)

[6]. It means that the overall interaction between the Gd moments in this compound

is FM and that the antiferromagnetic ground state is rather instable. The broadening

of the transition in the cp/T(T) curves measured at H ≠ 0 can be ascribed to this

field-induced magnetic transition.

Figure 4.5 shows a set of magnetic isotherms of GdRu2Ge2, measured in the

Magnetic phase transitions and MCE in Gd-based compounds 31

0 1 2 3 4 50

10

20

30

40

50

60

70

80

∆T = 5 K

75 K

5 KGdRu2Ge2

M (

Am

2 /kg)

µ0H (T)

Figure 4.5: Magnetic isotherms of GdRu2Ge2 between 5 and 75 K, measured with increasing magnetic field.

0 20 40 60 80 100-1

0

1

2

3

4

5

6

GdRu2Ge

2

0-2 T from magnetization 0-4 T from magnetization 0-2 T from specific heat 0-4 T from specific heat

T (K)

- ∆S

(J/k

gK)

Figure 4.6: Comparison of the magnetic -entropy changes of GdRu2Ge2 derived from the magnetization and from the specific heat.

32 Chapter 4

temperature range from 5 to 75 K and fields up to 5 T, with increasing temperature

steps of 5 K. From these magnetization data, the isothermal magnetic -entropy

change mS∆ has been derived by using Eq. (3.3). The results are shown in Fig. 4.6

together with the results obtained from the specific -heat measurements by using

Eq. (2.12). mS∆ is seen to peak around 33 K, which is close to the magnetic -

ordering temperature. The negative values of - mS∆ obtained below 20 K for a field

change from 0 to 2 T are due to the fact that the material is in the antiferromagnetic

state, in which the external field reduces the magnetic order rather than enhances

it. The maximal values of - mS∆ are 1.7 J/kgK and 5.0 J/kgK in 2 T and 4 T,

respectively. The entropy changes associated with the two successive transitions

are only a small fraction of the maximum available magnetic entropy of Gd,

Rln(2J+1) = 110 J/kgK (J = 7/2 for Gd3+). The magnetic -entropy changes

determined by means of the two types of measurements agree quite well. This

confirms that magnetic measurements form a reliable method to determine the

isothermal magnetic -entropy change of magnetic materials.

0 10 20 30 40 50-2

0

2

4

6

∆Β 0 - 2 T 0 - 4 T 0 - 6 T

GdRu2Ge2

∆T ad

(K)

T (K)

Figure 4.7: Adiabatic temperature change adT∆ in GdRu2Ge2 between 5

and 50 K for magnetic field changes from 0 to 2, 0 to 4, and 0 to 6 T.

Magnetic phase transitions and MCE in Gd-based compounds 33

The temperature dependence of the adiabatic temperature change adT∆ in

the temperature range from 5 to 50 K upon field changes ranging from 0 to 2, 0 to

4 and 0 to 6 T has been derived from the specific -heat measurements by using Eq.

(3.6). The results are shown in Fig. 4.7. The maximum values of adT∆ are

approximately 1.5, 3.5 and 4.5 K for field change from 0 to 2, 0 to 4 and 0 to 6 T,

respectively. The profiles of adT∆ are similar to those of mS∆ , although there is

some broadening of the peaks.

4.2.4 Conclusions GdRu2Ge2 orders antiferromagnetically below T2 = 33 K. The antiferromagnetic

ground state is rather unstable. At 5 K, a field-induced transition occurs at a field of

1 T. This transition is closely associated with the overall interaction between the

Gd moments as indicated by the positive paramagnetic Curie temperature. We

found that the maximum value of the adiabatic temperature change adT∆ is about

4.5 K in 6 T, which is a moderate MCE for a rare-earth compound in the

temperature range below 40 K. The results confirm that specific -heat and

magnetization measurements can both be employed to assess the MCE of a

magnetic material.

4.3 Single-crystalline Gd5Si1.7Ge2.3 4.3.1 Introduction The discovery of the giant MCE in Gd5Si2Ge2 [1] has led to a revival of the

research dealing with magnetic refrigeration. This compound belongs to the

pseudo-binary system Gd5(SixGe1-x)4, in which the magnetic properties change

from antiferromagnetic to ferromagnetic (FM) upon increasing the Si content x.

The composition range 0.24 ≤ x ≤ 0.5 is of special interest since a giant MCE, giant

magnetoresistance [7], and colossal magnetostriction [8] are observed in this

34 Chapter 4

composition range. All these unusual features are related to a first-order magnetic

phase transition accompanied by a structural transition from the low-temperature

orthorhombic FM state to the high-temperature monoclinic paramagnetic (PM)

state. This magneto-structural transition can be induced by temperature and/or by

magnetic field.

A better understanding of the nature of the first-order phase transition in the

Gd5(SixGe1-x)4 system is of fundamental and practical importance. Especially the

relation between the structural and magnetic phase transitions from the low-

temperature orthorhombic FM state to the high-temperature monoclinic PM state

and the giant MCE in the Gd5(SixGe1-x)4 alloys is intriguing. Choe et al. [9] have

studied the formation and breaking of the covalent bonds between Si(Ge) and

Ge(Si) atoms in Gd5Si2Ge2, and have pointed out that the structural transition

occurs by a shear mechanism in which the (Si,Ge)-(Si,Ge) dimers increase their

distance by 0.859(3) Å which leads to twinning. The structural transition changes

the electronic structure and provides on micro-structural level an explanation of the

change in magnetic behavior with temperature in this system. Both the magnetic

and the crystal structure are easily affected by temperature and/or magnetic field,

indicating a strong coupling between the magnetism and the lattice. The changes in

the magnetic and crystallographic parameters of such a system may lead to unusual

phenomena, such as unusual magnetic behavior and the spontaneous generation of

an electrical voltage in Gd5(SixGe1-x)4 during the transition [10].

In order to obtain more insight into the mechanism of this unusual physical

behavior and the MCE in the Gd5(SixGe1-x)4 system, we have grown a single crystal

of Gd5Si1.7Ge2.3 and studied the magnetic and magnetocaloric properties and their

relationship with the structural and magnetic phase transitions.

4.3.2 Crystal growth and characterization A single crystal of Gd5Si1.7Ge2.3 was grown by means of the traveling-floating-zone

method in an adapted NEC double-ellipsoid image furnace. The starting materials

Magnetic phase transitions and MCE in Gd-based compounds 35

were 4N Gd (from Ames Lab., USA), 6N Si and 6N Ge. The crystal was grown

under an Ar atmosphere of 900 mbar with a speed of 3 mm/h. The feed and seed

were counter-rotated at 22 and 31 rpm, respectively. The characteristic region

between 2θ = 20 and 40 ° of a powder XRD pattern of Gd5Si1.7 Ge2.3 is shown in

Fig. 4.8. Si powder was added as internal standard. The diagram was indexed

within the monoclinic structure (space group P1121/a) with the unit-cell parameters

a = 7.585 Å, b = 14.800 Å, c = 7.777 Å, ß = 93.29 °. The unit cell contains four

formula units and has a volume Ω = 871.6 Å3. The molar volume Vm equals 1.312

x 10-4 m3/mol. These crystallographic data are in good agreement with literature

values [11,12].

26 28 30 32 34 36 38 40

Si

Cu Kα

Gd5Si1.7Ge2.3

Inte

nsity

(arb

. uni

t)

2θ (deg.)

Figure 4.8: XRD pattern of the Gd5Si1.7Ge2.3 collected at room temperature. The open circles represent the observed data and the lines represent the

calculated XRD pattern. The vertical bars indicate the calculated positions

of the Bragg reflections for Cu Ka 1 radiation. The difference between the experimental and calculated intensities is shown at the bottom as a solid

line.

36 Chapter 4

Figure 4.9: EPMA micrograph of a Gd5Si1.7 Ge2.3 single crystal.

The as-grown single crystal was checked as regards composition,

homogeneity and single -crystallinity by means of EPMA and x-ray Laue

backscattering. The EPMA micrograph as presented in Fig. 4.9 shows that the

crystal is homogeneous. A slight gradient of the Si content has been detected along

the growth direction of the crystal. The average composition of the crystal is 56.3

at. % Gd, 18.4 at. % Si and 25.3 at. % Ge, which corresponds to the actual formula

Gd5.06Si1.66Ge2.28.

4.3.3 Magnetic properties Figure 4.10 shows the temperature dependence of the magnetization of single-

crystalline Gd5Si1.7Ge2.3, measured in a magnetic field of 50 mT and 5 T,

respectively, applied along the three principal crystallographic axes. The magnetic

ordering is observed as a pronounced change in magnetization, which is clearly

different from a second-order FM phase transition, indicating that the transition is

of first order. The Curie temperature TC, determined as the temperature

Magnetic phase transitions and MCE in Gd-based compounds 37

0 50 100 150 200 250 300 350 4000

10

20

30

400

1

2

3

4

5

5 T

B //a-axis //b-axis //c-axis

M (µ

B/ f

.u.)

T (K)

M (µ

B/ f

.u.)

50 mT

B // a-axis // b-axis // c-axis

Gd5Si

1.7Ge

2.3

Figure 4.10: Temperature dependence of the magnetization of Gd5Si1.7Ge2.3

in a field of 50 mT (top panel) and 5 T (bottom panel), respectively, measured with the field direction along the three principal axes a ([100]), b

([010]), and c ([001]).

corresponding to the extreme of dM/dT, is 240.2 K. In the FM state, the M(T)

curves measured for Gd5Si1.7Ge2.3 in a field of 50 mT display anisotropic behavior.

This anisotropy in the M(T) curves of Gd5Si1.7Ge2.3 disappears in a field of 5 T as

indicated in the bottom panel of Fig. 4.10. This is, therefore, possibly due to

domain-wall displacement and/or rotation of the magnetization of the domains,

while one cannot exclude that it is related to a spin reorientation. In the

paramagnetic state, the temperature dependence of the inverse dc magnetic

susceptibility of Gd5Si1.7Ge2.3 obeys the Curie-Weiss law in the higher-temperature

region with an effective moment µeff of 8.2, 8.4, and 8.6 µB/Gd-atom for the a, b,

and c direction, respectively. These values are slightly larger than the theoretical

38 Chapter 4

value of 7.94 µB for a free Gd3+ ion and the experimental value of 7.98 µB for Gd

metal. The PM Curie temperature pθ equals 204 K.

In order to determine the change of the Curie temperature with applied

magnetic field and the thermal hysteresis, we have performed measurements of the

temperature dependence of the magnetization with increasing and decreasing

temperature in fields of 1, 2, 3, 4 and 5 T. The results are shown in Fig. 4.11. It is

clear that the Curie temperature increases with increasing field and that there is a

large thermal hysteresis.

0102030

0102030

0102030

180 200 220 240 260 280 3000

1020300

102030

B //a-axisGd

5Si

1.7Ge

2.3

1 T

M (

µ B/f

.u.)

2 T

3 T

T (K)

5 T

4 T

Figure 4.11: Temperature dependence of the magnetization of

Gd5Si1.5Ge2.3, measured with increasing and decreasing temperature in a

field of 1, 2, 3, 4, and 5 T, respectively. Figure 4.12 shows the magnetic isotherms of single -crystalline Gd5Si1.7Ge2.3

measured at 5 K and at several temperatures around TC, measured with the

magnetic-field direction along the three principal crystallographic axes [100], [010]

Magnetic phase transitions and MCE in Gd-based compounds 39

0 1 2 3 4 5 60

15

30

0

15

30

0

15

30

260 K

257.5 K250 K240 K

5 KB // c - axis

µ0H (T)

240 K

5 K

230 K

252.5K257.5 K

260 K

B // a - axisM

(µ B

/f.u.

)

Bc1Bc2

Bc3

Bc4

250 K257.5 K

240 K

260 K265 K

230 K

5 KB // b - axis

Figure 4.12: Magnetic isotherms of Gd5Si1.7Ge2.3 along the three principal

axes at 5 K and at several temperatures, which are in the vicinity of the

Curie temperature, measured with increasing (Ú) and decreasing (∇) field. and [001] with increasing and decreasing magnetic fields. The spontaneous

magnetization at 5 K is 7.08, 7.18, and 7.28 µB/Gd-atom along the a, b, and c axis,

respectively. These values are slightly larger than the value of 7.0 µB/Gd-atom for

the free Gd3+ ion. Below TC, the magnetization curves show FM behavior. Above

TC, the magnetization increases linearly in low field strengths, which is

characteristic for simple PM behavior. Above a lower field Bc1, the magnetization

40 Chapter 4

increases sharply and saturates at a higher field Bc2, indicating that the applied

magnetic field gives rise to a field-induced PM to FM phase transition. With

decreasing field, a reverse magnetic phase transition FM to PM starts at the field

Bc3 and ends at the field Bc4. The field hysteresis observed in the field dependence

of the magnetization, which is about 1 T, also indicates that the transition is of first

order.

236 240 244 248 252 256 260 2640

1

2

3

4

5 data from

M-T, B//[100] M-T, [100] M-B, [001] M-B, [001] M-B, [010] M-B, [010] M-B, [100] M-B, [100]

Gd5Ge

2.3Si

1.7

FM

PM

B (

T)

T (K)

Figure 4.13: Magnetic phase diagram of Gd5Si1.7Ge2.3.(à) and („) indicate

the data from the temperature dependence of the magnetization. (Ú, Û), (Ù, ı) and (Ë, È) indicate the data from the field dependence of the

magnetization, measured along the [001], [010] and [100] direction,

respectively. The solid lines are guides to the eye.

The magnetic phase diagram of Gd5Si1.7Ge2.3 constructed from the

temperature dependence of the magnetization and the field dependence of the

magnetization, measured with the field direction along three principal

crystallographic axes. The results are shown in Fig. 4.13. The critical-field values

were taken as the mean value of Bc1 and Bc2 for increasing field and, Bc3 and Bc4 for

decreasing field, respectively. Both sets of experimental data are in good

Magnetic phase transitions and MCE in Gd-based compounds 41

agreement with each other and there are no clear differences along the three

directions. TC almost linearly increases with increasing field at a rate of 4.4 K/T.

Extrapolation of the temperature dependence of the critical-field lines to zero field

shows that the zero-field Curie temperature TC of Gd5Si1.7Ge2.3 is 240.1 K for a

measurement with increasing temperature and 235.3 K for decreasing temperature,

respectively. It indicates that a thermal hysteresis of about 5 K exists between the

increasing- and decreasing-temperature measurements. This is in good agreement

with the result observed in thermal-expansion measurements [13].

4.3.4 Specific heat Usually, the specific heat of a material at constant pressure behaves anomalously

near the magnetic phase transition and hence measurements of the specific heat can

be a useful tool for studying the nature of a given magnetic phase transition. Figure

4.14 shows the temperature dependence of the specific heat of Gd5Si1.7Ge2.3,

measured with increasing temperature in zero field.

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

8

zero fieldincreasing T

Gd 5Si1.7Ge 2.3

θD = 237 K

γ = 32.3 mJ/molK 2

TC = 239 K

c p/T (

J/m

olK

2 )

T (K)

Figure 4.14: Temperature dependence of the specific heat of Gd5Si1.7 Ge2.3,

in the representation cp/T vs T, measured with increasing temperature in

zero field. The solid line is a Debye fit with Dθ = 237 K.

42 Chapter 4

190 200 210 220 230 240 250 260 2700

1

2

3

4

5

6

7

8

T 'C = 246 K

TC = 239 K

0 T 2 T

Gd5Si

1.7Ge

2.3

cp/

T (

J/m

olK

2 )

T (K)

Figure 4.15: Temperature dependence of the specific heat of Gd5Si1.7 Ge2.3, in the representation cp/T vs T, measured with increasing temperature in

zero field and in 2 T.

The peak position corresponds to a TC of about 239 K, which is slightly smaller

than the value of TC obtained from magnetic measurement. The sharpness and the

large amplitude of the peak suggest that the phase transition in Gd5Si1.7 Ge2.3 is of

first order. A fit of the low-temperature data to the formula cp/T = γ + ßT 2 yields

an electronic contribution to the specific heat γ = 32.3 mJ/molK2 and a Debye

temperature Dθ = 237 K.

Figure 4.15 shows the specific heat of Gd5Si1.7Ge2.3 measured across the

phase-transition region in zero field and in 2 T with increasing temperature. The

magnetic field suppresses the magnetic part of the specific heat and shifts the peak

position to a higher temperature 'CT , which is about 246 K at 2 T. This value is

slightly smaller than the value of TC (in 2 T) obtained from the magnetic

measurement.

Magnetic phase transitions and MCE in Gd-based compounds 43

4.3.5 Magnetocaloric effect The magnetic-entropy changes of Gd5Si1.7Ge2.3, which have been derived from the

magnetic isotherms measured with increasing temperature and increasing field

along the three principal axes by using Eq. (3.3), are displayed in Fig. 4.16.

200 220 240 260 280 300 320

0

10

20

30

40

50

// c-axis 0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 5 T

T (K)

0

10

20

30

40

50

// a-axis

0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 5 T

- ∆S

m (J

/kgK

)

0

10

20

30

40

50

// b-axis

∆B 0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 5 T

Figure 4.16. Temperature dependence of the magnetic-entropy changes of

Gd5Si1.7Ge2.3 along the three principal crystallographic axes, for field changes from 0 to 1, 0 to 2, 0 to 3, 0 to 4 and 0 to 5, derived from the

magnetization data.

44 Chapter 4

0 50 100 150 200 2500

50

100

150

200

250

300

350

400

Gd5Si

1.7Ge

2.3

S

(J/

kgK

)

T (K)

Figure 4.17: Temperature dependence of the total entropy of Gd5Si1.7Ge2.3

determined from the zero-field specific heat. The inset shows an enlarged view of the entropy at the transition.

The shape of - mS∆ consists of a spike and a plateau part. The spike is probably

related to an irreversible magnetization process and most likely associated with the

fact that the magnetic transition occurs simultaneously with the crystal-structure

change, and it boosts the value of - mS∆ to higher values. With increasing field, the

plateau part saturates and extends to higher temperatures.

The entropy evolution as a function of temperature, ∫= TdTTcTS p /)()( ,

of the system can directly be obtained from the specific -heat data. The S(T) curve

in zero field is depicted in Fig. 4.17. The entropy change associated with the

transition is about ∆S = 11 J/kgK and the latent heat L = TC ∆S = 2.63 kJ/kg.

230 235 240 245 250 255330

335

340

345

350

355

360

365

370

S (

J/kg

K)

T (K)

Magnetic phase transitions and MCE in Gd-based compounds 45

4.3.6 Discussion and conclusions First, we discuss the magnetic phase transition and the magnetic interactions in

Gd5Si1.7Ge2.3. On the basis of the observed discontinuous behavior of the

magnetization and the entropy at the transition, and the constructed magnetic phase

diagram of Gd5Si1.7 Ge2.3, we conclude that the phase transition observed in this

material is a first-order phase transition. From the specific -heat measurements, we

have determined the latent heat involved in this phase transition is about 2.63

kJ/kgK. According to the study reported in Ref. 8, the origin of the transition is a

simultaneous structural and magnetic phase transition. The crystal structure adopts

the orthorhombic structure in the FM state and changes into the monoclinic

structure in the PM state. The major crystallographic structure change occurs due

to the breaking of covalent-like Si-Si, Si-Ge and Ge-Ge bonds at the transition

from the FM state to the PM state [9,14].

The large effective magnetic moment, the abrupt change in the magnetization

at the transition, and the anisotropy observed in Gd5Si1.7Ge2.3 cannot well be

explained in the framework of the indirect RKKY 4f-4f exchange interaction.

Therefore, there may exist other exchange interactions that play an important role

in this compound. One possible exchange interaction in this compound may be the

indirect exchange between the 4f-electron spins via polarization of the 5d-electron

spins [15]. The experimental observation of saturation magnetic moments at 5 K

that are slightly larger than the Gd free-ion moment and the somewhat enhanced

effective magnetic moment support the occurrence of polarized 5d-electron spins in

this compound. Another possible interaction is a Gd-Si(Ge)-Gd superexchange

interaction in the low-temperature FM phase propagating through the interlayer

covalent-like bonds [15]. The fact that the long-range FM order is abruptly

destroyed at the transition where the material becomes PM is because of the

breaking Si(Ge)-Ge(Si) bond between the slabs occurs at the structural

transformation which leads to the disappearance of the superexchange interaction.

46 Chapter 4

However, the determination of these interactions is complicated because they are

strongly dependent on composition and temperature [9].

Secondly, we discuss the MCE observed in this compound. The MCE in this

phase-transition region is extremely large. Not only the magnitude of the MCE is

large, but also the full width at the half maximum of the MCE with respect to the

field change is large. The maximum value of - mS∆ for a field change from 0 to 5

T is 44.6 J/kgK at the spike and around 30 J/kgK at the plateau part. These values

are consistent with the results reported earlier on polycrystalline material [16]. If

we take 30 J/kgK as maximum value of the magnetic -entropy change - mS∆ (max)

then the full width at the half maximum ( FWHMTδ = T2 – T1 ) [16] is about 19 K for

a field change from 0 to 5 T. A recent study [17] has shown that the plateau part

perfectly matches the S∆ values given by the Clausius-Clapeyron equation

∆S=∆MdBc /dT (where M∆ is the jump of the magnetization at the magneto-

structural transition, and dBc /dT is the rate of critical-field change with

temperature). From the linear relation between Bc and T, we have obtained dBc /dT

= 0.23 T/K. If we take the value of M at the TC as M∆ , then we obtain S∆ as 32

J/kgK for a field change from 0 to 1 T and 35 J/kgK for a field change from 0 to 5

T. These values roughly match with the values of S∆ on the plateau part shown in

Fig. 4.16. However, we should mention that the value of dBc /dT can be easily

determined from the phase diagram (see Fig. 4.13), but the determination of the

jump of the magnetization at the transition is complicated because the first-order

transition does not occur infinitely fast. One may determine M∆ in different ways

from the M(T) curve or from the M(B) curve and may obtain different values.

Finally, we discuss the magnetic anisotropy in this compound. The magnetic

anisotropy of the Gd-based compounds is usually negligible due to the spherical

symmetry of the 4f orbitals of Gd3+ ions and the isotropic nature of the RKKY

interaction. There are, however, some indications for anisotropic behavior in this

material. First, the temperature dependence of the magnetization in low field

Magnetic phase transitions and MCE in Gd-based compounds 47

exhibits an anisotropic behavior. As we discussed this anisotropic behavior may

belong to the domain-wall displacement and/or rotation of the magnetization of the

domains. However, the anisotropy may arise from anisotropic exchange

interactions. Duijn [18] has proposed a possible mechanism for the occurrence of

anisotropy in the Gd5(Si1-xGex)4 compounds. Our magnetic measurements show

that the magnetic anisotropy is negligibly small and/or has only a minor effect on

the magnetization along three principal crystallographic axes as well as the MCE in

the compound Gd5Si1.7Ge2.3, as indicated by the similar magnetic behavior and

magnitude of - mS∆ obtained along the three principal axes. It should be noted that

these magnetic parameters are determined for the monoclinic structure, while the

FM phase adopts the orthorhombic structure. The other anisotropic behavior in this

compound that should be mentioned is found in the thermal-expansion

measurements along the principal crystallographic axes that have been performed

on the same single crystal [13]. They show that the magnetic and structural phase

transition occur at one and the same temperature. The thermal expansion shows a

pronounced anisotropy between the bc-plane and the a-axis. The resulting steps in

LL /∆ for the b- and c-axis attain negative values of – 2.0 x 10-3 and – 2.1 x 10-3 ,

upon heating, respectively, while for the a-axis the step is positive and much larger,

6.8 x 10-3. The volume change VV /∆ at TC is positive and amounts to 2.7 x 10-3.

By combining the specific -heat and the thermal-expansion data and by making use

of the Clausius-Clapeyron relation, we extract a hydrostatic pressure dependence of

TC equal to dTC /dp = 3.2 ± 0.2 K/kbar. This value is in good agreement with the

value dTC /dp = 3.46 K/kbar extracted from thermal-expansion measurements under

hydrostatic pressure for a Gd5Si1.8Ge2.2 sample [8]. The result points out that the

pressure effect is strongly anisotropic. Uniaxial pressure along the a-axis enhances

TC, while uniaxial pressure in the bc-plane suppresses TC. This provides important

information how to chemically substitute the system in order to further enhance TC.

In conclusion, we have studied the magnetic and magnetocaloric properties

of a single crystal of Gd5Si1.7 Ge2.3. The bulk-property measurements show that the

48 Chapter 4

unusual magnetic properties and the giant MCE in this compound is associated

with a simultaneous magnetic and structural transition. This phase transition is of

first order. The magnetic properties observed in this compound suggest that not

only the indirect RKKY exchange interaction, but also the indirect 4f-electron

spins coupling via polarization of 5d-electron spins and the Gd-Si(Ge)-Gd

superexchange interaction may play important roles in governing the magnetic

properties of Gd5Si1.7Ge2.3. The MCE in this compound system is large. There are

some indications of the magnetic anisotropy in this compound. But the magnetic

anisotropy has a negligible effect on the MCE in this compound. However, an

accurate determination of the magnetic structure, the magnetic interactions and the

microstructure of the Gd5Si1.7 Ge2.3 compound are still required for a full

understanding of the unusual magnetic behavior observed in this interesting alloy

system.

References [1] V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. Lett. 78 (1997) 4494. [2] J.M.D. Coey, J. Magn. Magn. Mater. 248 (2002) 441. [3] H. Wada, Y. Tanabe, K. Hagiwara and M. Shiga, J. Magn. Magn. Mater. 218

(2000) 203. [4] A. Szytula and J. Leciejewicz, Magnetic properties of ternary intermetallic

compounds of the RT2X2 type, Ch. 83 of Handbook on the physics and chemistry of rare earths, Vol. 12, K.A. Gschneidner, Jr., and Eyring Eds. (North-Holland, Amsterdam, 1998).

[5] A. Szytula, Magnetic properties of ternary intermetallic compounds, Ch. 2 of Handbook of Magnetic Materials, Vol. 6, K.H.J. Buschow Ed. (North-Holland, Amsterdam, 1991).

[6] N.P. Duong, Correlation between magnetic interactions and magnetic structures in some antiferromagnetic rare earth intermetallic compounds, Ph.D. Thesis, University of Amsterdam (2002).

[7] L. Morollon, J. Stankiewicz, B. Garcia -Landa, P.A. Algarabel and M.R. Ibarra, Appl. Phys. Lett. 73 (1998) 3462.

Magnetic phase transitions and MCE in Gd-based compounds 49

[8] L. Morollon, P.A. Algarabel, M.R. Ibarra, J. Blasco, B. Garcia -Landa, Z. Arnold and F. Albertini, Phys. Rev. B 58 (1998) R14721.

[9] W. Choe, V.K. Pecharsky, A.O. Pecharsky, K.A. Gschneidner, Jr., V.G. Young, Jr., and G.J. Miller, Phys. Rev. Lett. 84 (2000) 4617.

[10] E.M. Levin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 63 (2001) 174110.

[11] V.K. Pecharsky and K.A. Gschneidner, Jr., J. Alloys Compds. 260 (1997) 98. [12] V.K. Pecharsky, A.O. Pecharsky and K.A. Gschneidner, Jr., J. Alloys

Compds. 344 (2002) 362. [13] M. Nazih, A. de Visser, L. Zhang, O. Tegus and E. Brück, Solid State

Commun. 126 (2003) 255. [14] E.M. Levin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 60

(1999) 7993. [15] E.M. Levin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 62

(2000) R14625. [16] K.A. Gschneidner, Jr., and V.K. Pecharsky, Ann. Rev. Mater. Sci. 30 (2000)

387. [17] F. Casanova, X. Batle, A. Labarta, J. Marcos, L. Manosa and A. Planes,

Phys. Rev. B 66 (2002) 10040 (R). [18] H.G.M. Duijn, Magnetotransport and magnetocaloric effects in intermetallic

compounds, Ph.D. Thesis, University of Amsterdam (2000).

50 Chapter 4

51

Chapter 5

Magnetocaloric effect in hexagonal MnFeP1-xAsx compounds 5.1 Introduction Since the discovery of the giant magnetocaloric effect (MCE) in Gd5Ge2Si2 at

Ames Laboratory [1], the research on magnetic refrigerant materials has been

strongly intens ified worldwide. Currently, most research groups study the MCE in

rare-earth-based materials because the large moments of the rare-earth atoms imply

the possibility of large MCE. However, especially for the important applications

around room temperature only a very limited number of rare-earth compounds

(usually the ordering temperature of the rare earth compounds is below room

temperature) are suitable because the MCE is optimal around the magnetic -

ordering temperature. The largest MCE known so far in rare-earth materials near

room temperature is observed in Gd metal. The maximum MCE in Gd occurs at the

temperature where it orders ferromagnetically (294 K). When the magnetic field

changes from 0 to 1.5 T, the MCE is about 4 K, and it is 11 K when the magnetic

field changes from 0 to 5 T [2]. It is unclear whether the giant-MCE material

Gd5Ge2Si2, which was reported to exceed the reversible MCE in any known

magnetic material by at least a factor of two, will be suitable for practical

application. Because of the low Curie temperature (about 276 K) and the relatively

large thermal hysteresis, this may not be the case.

52 Chapter 5

On the other hand, a number of transition-metal-based materials, such as

FeRh [3, 4], MnP1-xAsx [5], Mn2Sb [6], MnAs1-xSbx [7], and La1-xCaxMnO3 [8, 9]

have been investigated with respect to their MCE. In general, the MCE in

transition-metal-based materials is lower than in rare-earth alloys in the same

temperature range. Interestingly, FeRh exhibits an unusual and irreversible, but

giant, MCE as la rge as –13 K at 307 K for a field change from 0 to 1.95 T. This

effect is related to a first-order metamagnetic phase transition. The lanthanum-

manganese perovskite oxides La1-xCaxMnO3, known as colossal-magnetoresistance

(CMR) material, also show considerable magnetic -entropy changes. In these CMR

materials, only the Mn ions have magnetic moments. However, Pecharsky et al.

[10] and Sun et al. [11] have pointed out that the CMR materials do not seem

promising candidates for magnetic refrigeration as previously claimed in many

reports, because of their relatively small adiabatic temperature change.

The results on the above-mentioned Mn-based materials have in common

that their MCE can be rather large. This motivated us to study the MCE in the

vicinity of the first-order metamagnetic phase transition in other Mn-based

materials. These materials have various phase transitions and frequently order

around room temperature, and Mn ions can have relatively large magnetic

moments compared to other transition metals. However, the magnetic moments of

Mn are generally about two times smaller than those of the heavy rare-earth

elements. Enhancement of the MCE associated with magnetic -moment alignment

may be achieved through the induction of a first-order phase transition.

Among Mn-based compounds, the hexagonal MnFeP1-xAsx compounds that

are stable for 0.15 < x < 0.66 exhibit peculiar magnetic properties [12-14]

associated with a first-order metamagnetic transition. Our recent studies [15,16]

have shown that MnFeP1-xAsx compounds possess a large magnetic -entropy change

with the same magnitude as Gd5Ge2Si2. This result is of significant importance,

because it not only makes these compounds attractive candidates for working

materials in magnetic refrigeration but also indicates significant progress in the

MCE in MnFeP1-xAsx compounds 53

search for new magnetic refrigerant materials. In this chapter, we report on a

detailed study of the magnetic and magnetocaloric properties of the hexagonal

MnFeP1-xAsx compounds.

5.2 Sample preparation and characterization Polycrystalline samples of MnFeP1-xAsx compounds with nominal compositions x

= 0.25, 0.35, 0.45, 0.50, 0.53, 0.55 and 0.65 were synthesized by a solid-state

reaction. The starting materials used in our sample preparation are the binary

compounds Fe2P (purity 99.5 %, Alfa Aesar) and FeAs2 (purity 99.5 %, Alfa

Aesar), pure Mn chips (purity 99.99 %) and red-P powder (purity 99.99 %). In

order to obtain homogeneous samples, appropriate proportions of the starting

materials were ball milled in a high-energy vibratory ball-mill before the solid-state

reaction.

Figure 5.1 presents the x-ray diffraction (XRD) patterns of MnFeP0.5As0.5

after various periods of milling. With increasing milling time, the characteristic

30 35 40 45 50 55 60

Mn

Mn

Mn

Mn

Fe2A

s

Fe2A

sFe2A

sFe

2As

Fe2A

s

Fe2A

s

MnFeP0.5As0.5

1 h

10 h

20 h

40 h

90 h

Inte

nsity

(a.u

.)

2 θ

Figure 5.1: XRD patterns of MnFeP0.5As0.5 after various periods of milling.

54 Chapter 5

peaks of the starting materials become broadened. After 90 hours milling, only the

broad profile of Mn is visible. For complete homogenization, all the samples are

milled up to 200 hours.

The solid-state reaction was performed in a molybdenum crucible. First, the

obtained mixture was sealed in the crucible in a 100 - 200 mbar Ar atmosphere.

Then, this crucible was heated at 1273 K for 100 hours, followed by a

homogenization process at 923 K for 120 hours. Finally, the crucible was slowly

cooled down to ambient conditions.

The powder XRD patterns of the samples show that the MnFeP1-xAsx

compounds with x = 0.25, 0.35, 0.45, 0.50, 0.53, 0.55 and 0.65 crystallize in the

hexagonal Fe2P-type of structure (space group mP 26 ) with a small amount of

MnO as a second phase. From the broadening of the XRD patterns, the mean grain

size is estimated to be about 100 nm. The homogeneity and stoichiometry of the

samples with x = 0.45, 0.53, and 0.55 were checked by means of electron-probe

microanalysis (EPMA). Also the MnFeP0.45As0.55 sample contains an extra phase

with Mn, which is probably MnO as detected by XRD. The MnFeP0.47As0.53 sample

also contains an extra phase with Mn. The actual composition of the main phase of

MnFeP0.47As0.53 is 30.1 at. % Mn, 34.5 at. % Fe, 16.0 at. % P and 18.8 at. % As,

which corresponds to the formula Mn0.93Fe1.04P0.48As0.56. The composition of the

sample is very sensitive to the starting materials and the preparation process. For

the composition x = 0.55, we used two samples for the measurements presented in

this chapter. Because their properties are slightly different, one is indicated as

MnFeP0.45As0.55(I), and the other as MnFeP0.45As0.55(II).

5.3 Structural properties The MnFeP1-xAsx compounds crystallize in three different types of structures: the

orthorhombic Co2P type (Pnma, No. 62) for low As contents (0 ≤ x ≤ 0.15), the

hexagonal Fe2P type ( mP 26 , No. 189) for intermediate As contents (0.15 < x ≤

MCE in MnFeP1-xAsx compounds 55

0.66), and the tetragonal Fe2As type (P4/nmm, No. 129) for the highest As contents

(0.66 < x ≤ 1) [14]. In the present thesis, only the isostructural hexagonal series of

compounds is considered in which the large MCEs are observed.

A schematic drawing of the structure of the hexagonal MnFeP1-xAsx

compounds is shown in Fig. 5.2. There are two different metal sites: Fe(3f) at the

tetragonal position (x1, 0, 0) with local symmetry m2m and Fe(3g) at the pyramidal

position (x2 , 0, 1/2) with the same local symmetry. There are also two different

non-metal sites: one two-fold position P(2c) at (1/3, 2/3, 0) and one single position

P(1b) at (0, 0, 1/2) [14]. Substitution of Mn for Fe in this structure leads to

preferential Mn occupation of the 3g sites and substitution of As for P leads to a

random distribution of As over the 1b and 2c sites. Therefore, the MnFeP1-xAsx

compounds magnetically consist of two basal planes alternating along the

hexagonal c-axis, one containing the Mn atoms and the other one containing the Fe

atoms. The shortest Mn-Mn distance within the Mn-layer is dMn-Mn =

a 222 331 xx +− [17], in which a represents the lattice parameter. It should be

Figure 5.2: Schematic representation of the Fe2P-type of structure. The

volume shown contains three unit cells.

56 Chapter 5

Table 5.1: Lattice parameters determined by means of XRD at room temperature, and Curie temperatures of MnFeP1-xAsx compounds.

Nominal, x 0.25 0.35 0.45 0.50 0.53 0.55(I) 0.65

a (Å) 6.0392 6.0677 6.1080 6.1290 6.1628 6.1739 6.2120 c (Å) 3.4870 3.4874 3.4900 3.4805 3.4946 3.4511 3.4633 c/a 0.5774 0.5748 0.5714 0.5679 0.5670 0.5590 0.5575

TC(K) 168 213 240 282 290 300(I) 307(II)

332

noted that, because 1/2 < x2 < 2/3, only the a axis and not the b axis is a two-fold

axis. The structural parameters x1 and x2 depend on the constituents of the

compound under consideration, and can be obtained from intensity fits to XRD or

neutron-diffraction patterns [14].

The lattice parameters of MnFeP1-xAsx determined by means of XRD at room

temperature, and the Curie temperature TC are listed in Table 5.1. The lattice

parameter c remains constant in the paramagnetic (PM) state and displays a

pronounced decrease in the ferromagnetic (FM) state, while the parameter a

increases markedly with increasing x both in the PM and the FM state. The c/a

ratio decreases with increasing x.

5.4 Magnetic properties The temperature dependence of the magnetization of the MnFeP1-xAsx compounds,

measured in a field of 50 mT, is shown in Fig. 5.3. The compounds with x > 0.25

are FM and exhibit a sharp magnetic phase transition. Only the compound with x =

0.25 behaves differently, the magnetization having a much smaller value and an

anomaly in the M(T) curve around 40 K.

Figure 5.4 shows the composition dependence of the Curie temperature (left

axis) and the spontaneous magnetization (right axis) of MnFeP1-xAsx at 5 K. The

MCE in MnFeP1-xAsx compounds 57

0 50 100 150 200 250 300 350 4000

5

10

15

20

25 x

0.250.350.450.50.55(I)0.65

MnFeP1-x

Asx

50 mT

M (A

m2 /k

g)

T (K)

Figure 5.3: Temperature dependence of the magnetization of

MnFeP1-xAsx compounds in a field of 50 mT.

0.2 0.3 0.4 0.5 0.6 0.7

160

200

240

280

320

0

1

2

3

4

TC (K

)

X

Ms (

µ B/f.

u.)

Figure 5.4: Composition dependence of the Curie temperature (left axis)

and the spontaneous magnetization (right axis) of MnFeP1-xAsx compounds at 5 K.

58 Chapter 5

Curie temperature, which is listed in Table 5.2, was determined as the temperature

where the first derivative of the magnetization with respect to temperature has an

extreme value. Upon substitution of As for P, the Curie temperature increases

linearly from 168 K for x = 0.25 to 332 K for x = 0.65, indicating that the Curie

temperature is very sensitive to the variation of the P/As ratio. The spontaneous

magnetization at 5 K is about 4 µB per formula unit, but it slightly decreases with

increasing x.

270 280 290 300 310 320 330 340 350 3600

20

40

60

80

100

120MnFeP

0.45As

0.55(II)

1 T 2 T 3 T 4 T 5 T

M (

Am

2 /kg

)

T (K)

Figure 5.5: Temperature dependence of the magnetization of MnFeP0.45As0.55(II), measured in constant fields of 1, 2, 3, 4, and 5 T with

temperature increasing and decreasing in steps of 1 K.

For MnFeP0.45As0.55(II), we have measured the M(T) curves in fields of 1, 2,

3, 4, and 5 T with increasing and decreasing temperature. The results are shown in

Fig. 5.5. Based on these measurements, we have constructed a magnetic phase

diagram, which is shown in Fig. 5.6. The result shows that the Curie temperature of

the sample increases linearly with applied field at a rate of dBdTC / = 3.3 K/T.

MCE in MnFeP1-xAsx compounds 59

304 308 312 316 320 324 3280

1

2

3

4

5

Decreasing B

Increasing T

Decreasing T

Increasing B

MnFeP0.45

As0.55

(II)

PM phase

FM phase

B (

T)

T (K)

Figure 5.6: Magnetic phase diagram of MnFeP0.45As0.55(II). The arrows

indicate the phases in the history-dependent region.

0 1 2 3 4 50

20

40

60

80

100

Increasing B Decreasing B

314 K

312

K

308

K

304

K

300

K

MnFeP0.45

As0.55

(I)

M (

Am

2 /kg)

µ0H (T)

Figure 5.7: Magnetic-field dependence of the magnetization of

MnFeP0.45As0.55(I), measured with increasing and decreasing field in the vicinity of the phase transition.

60 Chapter 5

Extrapolation of the temperature dependence of the critical fields to zero field

shows that the PM to FM transition occurs at 302.8 K on cooling, and that the

inverse transition occurs at 306.6 K on heating. This indicates a thermal hysteresis

of 3.8 K. As we have seen, the transition becomes smoother in higher fields, and

the thermal hystersis decreases slightly with increasing field.

Figure 5.7 shows the magnetic isotherms of MnFeP0.45As0.55(I) in the vicinity

of its Curie temperature measured with increasing and decreasing field. The

magnetization processes show that there exists a field-induced magnetic phase

transition from the PM to the FM state. At low fields, the phase transition exhibits

a stepwise discontinuity in the magnetization, but at higher fields the transition

becomes smoother. The hysteresis is limited to a small field range of about 0.5 T

and does not extend to zero field.

5.5 Specific heat and dc susceptibility The specific heat of MnFeP0.45As0.55(I) was measured in zero field with temperature

decreasing from 390 to 250 K, utilizing the adiabatic heat-pulse relaxation method

in the PPMS described in Chapter 3. The result is given in Fig. 5.8. The

temperature corresponding to the peak is 294 K. This is slightly smaller than the

value of 296 K, which is the Curie temperature determined from the magnetic

measurement with decreasing temperature in a field of 50 mT. The dotted line in

Fig. 5.8 represents the high-temperature limit of the molar lattice specific heat 9 R

(R is the universal gas constant).

The evolution of the entropy of MnFeP0.45As0.55(I) in the temperature range

from 250 to 390 K is depicted in the inset of Fig. 5.8. The entropy exhibits a

discontinuous change at the transition and this entropy change S∆ associated with

the transition is about 5.2 J/molK (31.4 J/kgK) The latent heat involved in the

transition is determined as L = TC ∆ S = 1.53 kJ/mol (9.2 kJ/kg).

MCE in MnFeP1-xAsx compounds 61

260 280 300 320 340 360 380 4000

50

100

150

200

250

MnFeP0.45

As0.55

(I)

c p (J/

mo

lK)

T (K)

Figure 5.8: Temperature dependence of the specific heat of MnFeP0.45As0.55(I) measured in zero field with decreasing temperature.

The dotted line indicates the value of 9R, which is the high-temperature

limit of the lattice specific heat. The inset shows the temperature dependence of the total entropy difference S(T) - S(250) of

MnFeP0.45As0.55(I), derived from the specific -heat data.

For the MnFeP1-xAsx compounds, anomalous behavior is found in the

magnetic susceptibility just above the Curie temperature. As representative

examples, the temperature dependence of the reciprocal susceptibility of the

MnFeP1-xAsx compounds with x = 0.35, 0.45 and 0.55(II), measured in a field of

1T, is shown in Fig. 5.9. It is seen that, at higher temperatures, the compounds

exhibit Curie-Weiss behavior. Near the Curie temperature, the reciprocal

susceptibility abruptly drops to zero. A further analysis of the temperature

dependence of the PM susceptibility in terms of the Bean-Rodbell model, that we

250 275 300 325 350 3750

10

20

30

40zero field

MnFeP0.45As0.55(I)

S (

T) -

S (

250)

(J/m

olK

)

T (K)

62 Chapter 5

0 50 100 150 200 250 300 350 4000.0

0.1

0.2

0.3

0.4

0.5

0.6

x = 0.35

x = 0.55(II)

x = 0.45MnFeP1-xAsx

1/χ

(Tkg

/Am

2 )

T (K) Figure 5.9: Temperature dependence of the reciprocal susceptibility of

MnFeP0.55As0.45.

have introduced in Chapter 2, will be presented in Section 5.8 in conjunction with

the analysis of the temperature dependence of the magnetization of MnFeP1-xAsx

compounds.

5.6 Magnetocaloric effect In order to determine the magnetic -entropy changes in the MnFeP1-xAsx system, we

have carried out measurements of the field dependence of the magnetization at

different temperatures across the Curie temperature of each sample. A

representative measurement result is presented in Fig. 5.10.

The magnetic-entropy changes mS∆ have been derived from the

magnetization data on the basis of Eq. (3.3). The results for field changes from 0 to

2 and 0 to 5 T are shown in Fig. 5.11. It is found that the MnFeP1-xAsx compounds

exhibit large magnetic -entropy changes, for instance, the maximum values of the

MCE in MnFeP1-xAsx compounds 63

0 1 2 3 4 50

20

40

60

80

100

120 274--342 K ∆T = 4 KMnFeP0.45

As0.55

(I)M

(Am

2/k

g)

µ0H (T)

Figure 5.10: Magnetic isotherms of MnFeP0.45As0.55(I) in the vicinity of the

Curie temperature, measured with increasing temperature and field.

150 175 200 225 250 275 300 325 350 375

0

5

10

15

20

25

30

35

∆Β0- 2 T0- 5 T

x=0.35

x=0.5

x=0.25

x=0.65x=0.55(I)

x=0.45

MnFeP1-x

Asx

- ∆S

m (

J/kg

K)

T (K)

Figure 5.11: Magnetic-entropy changes of MnFeP1-xAsx for field changes

from 0 to 2 and 0 to 5 T.

64 Chapter 5

magnetic-entropy changes are 20 J/kg K for x = 0.45 for a field change from 0 to 2

T and 33 J/kg K for x = 0.35 for a field change of 0 to 5 T. The large magnetic -

entropy changes of the MnFeP1-xAsx compounds are concentrated in a certain

temperature interval. This interval increases with increasing field change. For

comparison, the magnetic -entropy changes of the metal Gd and the giant MCE

compound Gd5Ge2Si2 are shown in Fig. 5.12 together with those of

MnFeP0.45As0.55(I). It is evident that the magnetic -entropy changes of

MnFeP0.45As0.55(I) are larger than of Gd and comparable with the ones of

Gd5Ge2Si2.

250 260 270 280 290 300 310 320 330 340 350

02

4

68

10

1214

1618

20

Gd5Ge

2Si

2

5T

2T5T

2T

5T

2T

MnFeP0.45

As0.55

(I)

Gd

- ∆S

m (J

/kg

K)

T (K)

Figure 5.12: Magnetic-entropy changes of MnFeP0.45As0.55(I) for field changes from 0 to 2 and 0 to 5 T, derived from the magnetization data,

compared with those for Gd and Gd5Ge2Si2 (after [1]).

In order to further examine the MCE in the MnFeP1-xAsx compounds, also a direct

measurement was made by Tishin’s group at Moscow State University. The

temperature change of MnFeP0.45As0.55(II) was measured under adiabatic conditions

MCE in MnFeP1-xAsx compounds 65

with a continuous registration of the temperature change upon fast increase of the

applied magnetic field from 0 to 1.45 T. The rate of the field change was 0.4 T/s.

The accuracy of these measurements was about 5-20 % depending on the

temperature interval. More details of these direct measurements of the MCE are

given in Ref. 18. The results are shown in Fig. 5.13. The largest value of the MCE

is about 4 K for a field change from 0 to 1.45 T. This value is about same as that

for Gd.

300 305 310 3150

1

2

3

4 MnFeP0.45As0.55(II)

∆ Β 0 - 1.45 T

∆T

ad (

K)

T (K)

Figure 5.13: Temperature dependence of the adiabatic temperature change

adT∆ of MnFeP0.45As0.55(II) for a field change from 0 to 1.45 T. This measurement was performed by Tishin’s group at Moscow State

University.

The field dependence of adT∆ measured at different temperatures in the

vicinity of the Curie temperature is shown in Fig. 5.14. It can be seen that

adT∆ increases with increasing field. The MCE is as high as 3 K for a field change

from 0 to 1 T, and it is 2.2 K when field changes from 0 to 0.8 T at 306 K.

66 Chapter 5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

MnFeP0.45

As0.55

(II)

T = 304.7 K T = 305.5 K T = 306.0 K T = 307.4 K

∆Tad

(K

)

∆ Β (Τ)

Figure 5.14: Adiabatic temperature change adT∆ of MnFeP0.45As0.55(II) as a function of applied-magnetic -field change, obtained by direct

measurements in the vicinity of TC. The measurement was performed by

Tishin’s group at Moscow State University.

The refrigerant capacity or cooling power is one of the most important

parameters for magnetic refrigeration. It is defined as [19]

,),(2

1

∫ ∆∆−=T

Tm dTBTSq (5.4)

where T1 and T2 are the temperatures of the cold reservoir and the hot sink,

respectively. It indicates how much heat can be transferred between the cold and

hot parts in a single ideal refrigeration cycle. Figure 5.15 shows the dependence of

the refrigerant capacity (left axis) of MnFeP0.45As0.55(I) on the field change in the

corresponding full-width-at-half-maximum temperature interval, FWHMTδ (right

axis).

MCE in MnFeP1-xAsx compounds 67

0 1 2 3 4 50

50

100

150

200

250

300

350

0

5

10

15

20

25

30

35

MnFeP0.45

As0.55

(I)

q (J

/kg

)

∆B (T)

δ T

FWH

M (K

)

Figure 5.15: Field-change dependence of the refrigerant capacity and the

full-width-at-half-maximum temperature interval of MnFeP0.45As0.55(I).

150 175 200 225 250 275 300 325 3500

400

500

600

700

Temperature span from Tc-25 to Tc+25 K

MnFeP1-x

Asx

x = 0.35

x = 0.65

x = 0.45

x = 0.55(I)x = 0.5

Gd

Gd5Ge

2Si

2

Field Change 0 - 5 T

q (J

/kg)

Temperature (K)

∆

O

Figure 5.16: Refrigerant capacities of MnFeP1-xAsx compounds and the materials Gd and Gd5Ge2Si2, for a field change of 5 T and a temperature

span from TC – 25 to TC + 25 K.

68 Chapter 5

The refrigerant capacity almost linearly increases with the field change up to

5 T. In order to compare the refrigerant capacities of our samples with those of Gd

and Gd5Ge2Si2, we used a field change of 5 T and a temperature range from TC - 25

to TC + 25 K for the calculations. The results are shown in Fig. 5.16. It is clear that

the refrigerant capacity of the MnFeP1-xAsx compounds is larger than that of Gd

metal, which is used as magnetic refrigerant in the prototypes of magnetic

refrigerators

5.7 Electrical resistivity and magnetoresistivity Bearing in mind the use of MnFe(P,As) materials in magnetic refrigerators, next to

the magnetocaloric properties also the electrical and heat conductivity are of

utmost importance. There is hardly any information on the electrical-transport

properties of these materials. The electrical resistance can also be useful for a more

detailed investigation of the magnetic phase transition because it is very sensitive

to changes in the interactions between magnetic ions. The availability of electrical-

resistance data would make it possible to compare the critical magnetic fields

derived from magnetic and electrical measurements and to understand the role of

the electron-phonon and electron-magnon interactions. In order to study this, we

have selected one of the samples, MnFeP0.55As0.45, for measurements of the

electrical resistance and magnetoresistance. Figure 5.17 shows the temperature

dependence of the electrical resistivity of MnFeP0.55As0.45, normalized to its room

temperature value measured during cooling of the sample. It can be seen that there

is an anomaly at Tcr = 231 K. Below Tcr, the resistance increases with increasing

temperature and has metallic character, but above Tcr it decreases dramatically in a

narrow temperature range and then recovers the metal-like temperature

dependence. The total contribution from both electron-phonon scattering and

electron-magnon scattering in the PM phase is smaller than in the FM phase which

is in contrast with normal FM metallic materials.

MCE in MnFeP1-xAsx compounds 69

0 50 100 150 200 250 3000.00

0.25

0.50

0.75

1.00

1.25

1.50

zero field

MnFeP0.55As0.45

ρ(T)

/ρ(T

= 2

95 K

)

T (K)

Figure 5.17: Temperature dependence of the electrical resistivity of MnFeP0.55As0.45, normalized to the room temperature value, measured with

decreasing temperature.

The isothermal magnetic -field dependence of the hysteresis loops of the

magnetoresistance, ∆ρ/ρ0 = (R(B,T) – R(0,T))/R(0,T), of MnFeP0.55As0.45 in the

temperature interval from 243 to 265 K is shown in Fig. 5.18. An increase of the

magnetic field leads to an increase of the electrical resistance, beginning at a

critical field Bcr1 and ending at Bcr2. Hence, between 243 and 265 K the sample is in

the PM phase in zero-field, but the application of a magnetic field exceeding Bcr1

brings it into the FM regime. The field-induced PM-FM transition ends at Bcr2.

During the decrease of the magnetic field, the reversible FM-PM transition begins

at Bcr3 and ends at Bcr4.

70 Chapter 5

-10 -8 -6 -4 -2 0 2 4 6 8 100

20406080

020406080

020406080

020406080

020406080

243.4 K

µ0H (T)

248.1 K

254.2 K

Bcr4

Bcr3 B

cr2

Bcr1

258.8 K

264.5 K

∆ρ/

ρ 0(%

)

Figure 5.18: Isothermal magnetic -field dependence of the magnetoresistance of MnFeP0.55As0.45 in the temperature range from 243 K

to 265 K, measured with increasing and decreasing magnetic field.

MCE in MnFeP1-xAsx compounds 71

240 245 250 255 260 2650

1

2

3

4

5

6

7

8

Decreasing T

Increasing T

Decreasing BIncreasing B

MnFeP0.55

As0.45

FM phase

PM phase

B (T

)

T (K)

Figure 5.19: Magnetic phase diagram of MnFeP0.55As0.45.

The solid lines are guides to the eye.

The magnetic phase diagram of MnFeP0.55As0.45 is given in Fig. 5.19. The

critical fields displayed in this figure were determined as midpoints of the

transition curves in increasing and decreasing magnetic field in Fig. 5.18. The

behavior of the electrical resistance in a magnetic field reflects the presence of

magnetic field hysteresis for the complete PM-FM transitions and indicates that

also the field-induced transition is of first order.

5.8 A model description of the first-order magnetic phase

transition The occurrence of a first-order magnetic phase transition in MnFeP1-xAsx

compounds is a very striking and intriguing feature. In this section, we will present

a description of the magnetic properties of the MnFeP1-xAsx compounds in terms of

the Bean-Rodbell model [20] that we have introduced in Chapter 2. First, we will

analyze the temperature dependence of the PM susceptibility of MnFeP1-xAsx

72 Chapter 5

compounds presented in Section 5.5. After this, we will present the results of an

analysis of the temperature dependence of the magnetization of the MnFeP1-xAsx

compounds.

Taking into account that the Curie temperature strongly depends on the

interatomic spacing, Blois and Rodbell have proposed the following expressions

for the PM susceptibility [21].

,)1( *

0

*

0 TTC

TTTC

TTC

C −=

+−=

−=

αβχ (5.1)

where C is the Curie constant, a is the coefficient of linear thermal expansion, and

β is the slope of the dependence of TC on the volume

0

*

1 TC

Cαβ−

= and 0

0*0 1 T

TT

αβ−= . (5.2)

The Curie constant is given by

,3/)1(22BB kjjgNC += µ (5.3)

where N is the number of magnetic ions per formula unit, µB is the Bohr magneton

and, g is the gyromagnetic ratio (about 2). The average total angular momentum

number j for a formula unit is estimated to be two from the saturation moment.

Figure 5.20 shows the Curie -Weiss fit of the temperature dependence of the

reciprocal PM susceptibility of MnFeP1-xAsx compounds with x = 0.35, 0.45 and

0.55 by using Eq. 5.1.

MCE in MnFeP1-xAsx compounds 73

0 50 100 150 200 250 300 350 4000.0

0.1

0.2

0.3

0.4

0.5

0.6

x = 0.35

x = 0.55(II)

x = 0.45

MnFeP1-x

Asx

1/χ

(Tkg

/Am

2 )

T (K)

Figure 5.20: The Curie-Weiss fit of the temperature dependence of the

reciprocal PM susceptibility of MnFeP1-xAsx compounds with x = 0.35,

0.45 and 0.55.

Table 5.2: The parameters C*, *0T , αβ T0 and T0 for MnFeP1-xAsx

compounds with x = 0.35, 0.45 and 0.55.

x C*(KµB/Tf.u.) *0T (K) T0(K)

0Tαβ

0.35 10.43 101 53 0.48

0.45 8.56 181 114 0.37

0.55(II) 6.15 299 263 0.12

From the fitting, we have determined the apparent Curie constant C*, the

apparent Curie temperature *0T . The parameters αβ T0 and T0 are calculated by

using Eq. 5.2 and 5.3. The results are listed in Table 5.2. We will use these

parameters in the following analysis of the temperature dependence of the

magnetization of MnFeP1-xAsx compounds.

74 Chapter 5

As a representative example of the analysis of the temperature dependence of

the magnetization, we have selected MnFeP0.45As0.55(II) for a detailed analysis.

Figure 5.21 shows the relative magnetization σ (which is M/ 0σ ) of

MnFeP0.45As0.55(II) as a function of temperature for different values of the

parameter 2η (for simplification, the subscript of η is neglected in the following

discussion) obtained by evaluating Eq. (2.20). The parameters that yield the best

match with the experimentally observed temperature dependence of the

magnetization of MnFeP0.45As0.55(II), measured in a field of 1 T, are η = 1.75, T0 =

263 K, and αβ T0 = 0.12. In order to understand the role of the parameter η , we

have calculated the σ (T) curves in zero field, on the basis of the obtained

parameters and for different η values. This is shown in Fig. 5.22. It can be seen

200 225 250 275 300 325 3500.0

0.2

0.4

0.6

0.8

1.0

j = 2B = 1 TT

0 = 263 K

αβT0 = 0.12

(a) η = 0(b) η = 1(c) η = 1.75(d) η = 2

(d)(c)(b)(a)

Experimental data

MnFeP0.45

As0.55

(II)

σ

T(K)

Figure 5.21: Relative magnetization σ in 1 T vs temperature for j = 2, T0

= 263 K and different values of η also shown is the experimentally determined relative magnetization for MnFeP0.45As0.55(II).

MCE in MnFeP1-xAsx compounds 75

160 180 200 220 240 260 280 300 3200.0

0.2

0.4

0.6

0.8

1.0

T2T1αβΤ0 = 0.12T0 = 263 K

MnFeP0.45

As0.55

(II)j = 2

B = 0 T

1.751.510.5η = 0

σ

T (K)

Figure 5.22: Relative magnetization vs temperature in zero field for

different η values calculated for the case of MnFeP0.45As0.55(II).

that η = 1 separates the first-order and the second-order transition. The curves

with η < 1 correspond to a continuous change in the magnetization. In this case,

the temperature T1 is the Curie temperature being also the paramagnetic Curie

temperature. The transition is of second order. If η > 1, then a discontinuous

change (indicated by dashed vertical lines) occurs in the magnetization, showing

the transition is of first order. The temperature T2 is the limiting temperature of the

FM state. Up to this temperature, with increasing temperature the system is found

in the FM phase.

We may illustrate some of the features of the first-order transition from the

evolution of the Gibbs-free-energy isotherms. Figure 5.23 shows the evolution of

the Gibbs free energy of MnFeP0.45As0.55(II) in the vicinity of the Curie

temperature, which is about 307 K (see Fig. 5.6), in zero field. Just above the Curie

76 Chapter 5

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

-6

-4

-2

0

2

4

6

315 K

312

310308

306

304

302

300

(G

-G0)

/Nk B

MnFeP0.45As0.55

B = 0 Tj = 2η = 1.75αβT0 = 0.12T0 = 263 k

σ

Figure 5.23: Reduced Gibbs-free-energy (G(σ)-G(0))/NkB isotherms vs σ in the vicinity of the transition as calculated on the basis of Eq. (2.17) for j

= 2; η = 1.75; T0 = 263 K; αβT0 = 0.12 and B = 0 T.

temperature, the Gibbs free energy has two shallow local minima besides the

absolute minimum at σ = 0, indicating the existence of a metamagnetic state.

These free-energy minima that are separated by an energy barrier determine the

metastable state of the magnetization, and are strongly dependent on temperature.

The minima disappear when the temperature increases. When the temperature

decreases from high temperature where the system is in the stable PM phase down

to T1, the PM phase becomes metastable. So T1 is the limiting temperature of the

PM state when temperature decreases and, therefore, corresponds to the PM Curie

temperature. The FM state and the PM state coexist in the temperature interval T1 <

T < T2. Therefore, there exists a temperature TC, which is the Curie temperature of

the first-order phase transition, at which the stability of the two phases is equal, in

MCE in MnFeP1-xAsx compounds 77

this interval. From Fig. 5.23, we may estimate this TC to be around 308 K, which is

in good agreement with the experimental value of 307 K (see Fig. 5.6).

Table 5.3: Composition dependence of the parameter η for

MnFeP1-xAsx compounds.

x 0.35 0.45 0.55 0.65

η 2.43 1.90 1.75 1.47

We carried out the same fitting procedure for the MnFeP1-xAsx compounds

and obtained the composition dependence of the parameter η that is listed in Table

5.3. All values of η are larger than one, indicating that these compounds exhibit a

first-order phase transition. This is consistent with the experimental observations.

Zach et al. [22] have carried out a similar analysis and obtained similar parameters

η = 1.62 and T0 = 250 K for MnFeP0.5As0.5. We conclude that the first-order phase

transition behavior, such as the discontinuous change of the magnetization, the

thermal hyteresis and the magnetic field-induced transition can be quite well

understood on the basis of the Bean-Rodbell model.

5.9 Discussion and conclusions We will now present a more general discussion of the magnetic properties of the

MnFeP1-xAsx compounds based on the results described above. At low

temperatures, the investigated MnFeP1-xAsx compounds have a FM ground state.

With increasing temperature, the compounds undergo a phase transition from the

FM state to the PM state. In the FM state, the moment of the MnFeP1-xAsx

compounds is about 4 µB/f.u. at 5 K, which is in good agreement with the results of

neutron-diffraction measurements on the MnFeP1-xAsx compounds with x = 0.3 and

0.5 [23]. These magnetic moments originate from the spin moments of the 3d

78 Chapter 5

electrons of the Mn and Fe atoms. Because of the itinerant character of the 3d

electrons, the magnetic moments are governed by the Fe 3d-band and Mn 3d-band,

and the main magnetic interactions in this system are direct exchange interactions.

As we see in Fig. 5.4, the Curie temperature of the MnFeP1-xAsx compounds,

which is a measure of the magnetic interactions, increases linearly with increasing

As contents, indicating that the FM interactions become stronger. The reason is that

the substitution of As with larger covalent radius (1.18 Å) for P (1.10 Å) leads to

an expansion of the lattice in the a-b plane. This expansion probably results in a

weakening of the magnetic interactions between the Mn- moments and between the

Fe-moments, which are claimed to be antiferromagnetic [23]. Thus, variation of the

composition as well as the presence of impurities and vacancies have a strong

effect on the magnetic interactions. Different manners of sample preparation

probably result in small differences in the stoichiometry, which may be the reason

that the magnetic ordering temperatures observed for our samples are different

from the values reported by Bacmann et al. [14]. The sharp transition and the big

difference between the paramagnetic Curie temperature and the Curie temperature

indicate that the exchange interaction in this system is strongly temperature

dependent.

Based on the occurrence of a discontinuous change in the magnetization at

the transition temperature, on the thermal hysteresis in the temperature dependence

of the magnetization, and on the very sharp peak of the specific heat at the

transition temperature, we have established that the magnetic phase transition is of

first order. Moreover, as illustrated in Fig. 5.7, the transition can be induced by the

application of an external magnetic field. The stepwise change of the magnetization

at the transition and the field hysteresis observed in the field dependence of the

magnetization present evidence that also the field-induced transition is of first

order.

The first-order transition observed in the MnFeP1-xAsx system has some

similarities with the transition observed in the Gd5(GexSi1-x)4 system. In both

MCE in MnFeP1-xAsx compounds 79

systems, the observed PM-FM transitions are rather sharp and occur with a certain

thermal hysteresis. The PM-FM transition can be induced by an applied field. In

the Gd5(GexSi1-x)4 system, the transition is accompanied by a simultaneous

structural transition as discussed in Section 3 of Chapter 4, but in the MnFeP1-xAsx

system there is no crystal-symmetry change at the magnetic phase transition.

However, the mechanism of the first-order transition in these compounds is not

clear, yet. Bean and Rodbell [20] have proposed that a first-order phase transition

could be driven by a strong dependence of the exchange interactions on the

interatomic distances, in which the lattice distortion due to the magnetoelastic

effect plays an important role. An applied magnetic field leads to a magnetoelastic

effect that results in an enhanced exchange interaction and thus in an effectively

enhanced applied field. Band-structure calculations have shown that the

magnetoelastic phase transitions observed in this system can be associated with the

distances between the magnetic atoms as well as with changes in the density of

states (DOS) near the Fermi level, mainly due to the DOS of the Fe 3d electrons

[14,24]. According to these calculations, the strong magnetic interactions between

the Fe-layer and the Mn-layer and between the Mn-moments lead to a contraction

of the lattice parameter c and result in a first-order type magnetic phase transition.

On the basis of the Bean-Rodbell model, we have proposed a model

description of the first-order transition observed in the MnFeP1-xAsx system. The

transition observed in this system is associated with a double minimum in the

Gibbs free energy as a function of magnetization. At a certain temperature, the

applied field shifts the energy minimum of the FM state to lower values than that

of the PM state above TC, resulting in the metamagnetic transition. The reasonably

good degree of agreement between the Bean-Rodbell model and the experimental

observations, and the equally reasonable values of the parameters obtained from

the fittings lend credence to the applicability of the model in its cardinal features to

the hexagonal MnFeP1-xAsx compounds.

80 Chapter 5

Now, we discuss the MCE observed in the hexagonal MnFeP1-xAsx

compounds. The entropy changes associated with the first-order magnetic phase

transition have been derived from the magnetization data by using Eq. (3.3). As we

have seen in Fig. 5.11, the maximum values of the isothermal entropy change are

quite large, for instance, as high as 20 J/kgK for x = 0.45 for a field change from 0

to 2 T. As we have mentioned in Chapter 3, the magnetic -entropy change derived

from the magnetization data does not guarantee a high accuracy for determining the

MCE. But the results obtained from the magnetization data provide a reasonable

estimate of the MCE in a material and of the possible origin of the MCE. The large

magnetic-entropy changes in the MnFeP1-xAsx system should be attributed to the

comparatively high 3d moments and, principally, to the rapid change of the

magnetization at the transition.

240 260 280 300 320 340 3600

20

40

60

80

100

120

140 Gd MnFeP

0.45As

0.55(I)

M (

Am

2 /kg

)

T (K)

Figure 5.24: Temperature dependence of the magnetization of MnFeP0.45As0.55(I) and Gd, measured with increasing temperature in a

field of 1 T.

MCE in MnFeP1-xAsx compounds 81

To illustrate the reason why this system has a large MCE, we have made a

comparison of the temperature dependence of the magnetization of Gd metal and

MnFeP0.45As0.55(I). As we see in Fig. 5.24, in Gd metal the moment fully develops

only at low temperatures and strongly decreases with increasing temperature due to

RKKY interaction. The transition observed in Gd metal, which is a second-order

phase transition, gives rise to a relatively small value of BTM )/( ∂∂ . The strong

and direct exchange interactions between the 3d moments in transition-metal

compounds lead to perfect long-range magnetic order below the ordering

temperature and a sharper transition at TC. As we have mentioned, the sharp

transition in the MnFeP1-xAsx compounds originates from the strong magnetoelastic

coupling, which leads to a modification of the distances between the magnetic ions,

and involves competing intra- and inter-atomic interactions.

The direct measurements of the MCE in MnFeP0.45As0.55 have confirmed the

large MCE in this system. The results obtained from the direct measurements show

that the MnFeP1-xAsx compounds exhibit a large MCE in low magnetic field, such

as 0.8 T. This result is very important for practical applications because lower

fields like 0.8 T are much easier to generate by permanent magnets than higher

fields like 2 T.

Finally, we discuss the temperature and field dependence of the electrical

resistance of MnFeP0.55As0.45. The results presented in Section 5.7 indicate that the

PM-FM phase transition can be induced both by temperature and magnetic field.

The former type of transition takes place from a high-resistance FM state at low

temperature to a low-resistance PM state at high temperature. The latter type of

transition leads to a positive magnetoresistance peak above TC. The magnetic phase

diagram based on the electrical resistance data shows that the FM-PM transition

has a field hysteresis of about 1 T. It is interesting to note that the transition at Tcr is

accompanied by a change of the c/a ratio [23], which may lead to a change in the

Fermi surface topology and affect the electron-phonon scattering.

82 Chapter 5

In conclusion, we have prepared the hexagonal MnFeP1-xAsx compounds by

means of ball milling and a solid-state reaction method. In the MnFeP1-xAsx system,

the magnetic and structural properties are strongly related to a first-order magnetic

phase transition. The first-order phase transition in this compound system can

reasonably well be described by the Bean-Rodbell model. The MCE associated

with this first-order transition is large. Besides the large MCE, two additional

features make these materials excellent candidates for magnetic refrigerants in

room-temperature applications. The first is the fact that their Curie temperature can

be tuned between 168 K and 332 K by varying the P/As ratio between 1.5 and

about 0.5. This in turn allows one to tune the maximum MCE in this temperature

range, without losing the large MCE. The second is the fact that, unlike FeRh, the

giant MCE in the MnFeP1-xAsx compounds is reversible.

References [1] V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. Lett. 78 (1997) 4494. [2] C.B. Zimm, A. Jastrab, A. Sternberg, V.K. Pecharsky, K.A. Gschneidner, Jr.,

M. Osborne and I. Anderson, Adv. Cryog. Eng. 43 (1998) 1759. [3] S.A. Nikitin, G. Myalikgulev, A.M. Tishin, M.P. Annaorazov, K.A. Asatryan

and A.L. Tyurin, Phys. Lett. A 148 (1990) 363. [4] M.P. Annaorazov, S.A. Nikitin, A.L Tyurin, K.A. Asatryan and A.K.

Dovletov, J. Appl. Phys. 79 (1996) 1689. [5] C.H. Kuhrt, T.H. Schittny and K. Bärner, Phys. Stat. Sol. A 91 (1985) 105. [6] R.B. Flippen and F.J. Darnell, J. Appl. Phys. 34 (1963) 1094. [7] H. Wada and Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3302. [8] X.X. Zhang, J. Tejada, Y. Xin, G.F. Sun, K.W. Wong and X. Bohigas, Appl.

Phys. Lett. 69 (1996) 3596. [9] Z.B. Guo, Y.W. Du, J.S. Zhu, H. Huang, W.P. Ding and D. Feng, Phys. Rev.

Lett. 78 (1997) 1142. [10] V.K. Pecharsky, and K.A. Gschneidner, Jr., J. Appl. Phys. 90 (2001) 4614. [11] Young Sun, M.B. Salamon and S.H. Chun, J. Appl. Phys. 92 (2002) 3235. [12] L. Pytlik and A. Zieba, J. Magn. Magn. Mater. 51 (1985) 199.

MCE in MnFeP1-xAsx compounds 83

[13] R. Zach, M. Guillot and R. Fruchart, J. Magn. Magn. Mater. 89 (1990) 221. [14] M. Bacmann, J.L. Soubeyrousx, R. Barrett, O. Fruchart, R. Zach, S. Niziol,

and R. Fruchart, J. Magn. Magn. Mater. 134 (1994) 59. [15] O. Tegus, E. Brück, K.H.J. Buschow and F.R. de Boer, Nature 415 (2002)

150. [16] O. Tegus, E. Brück, L. Zhang, Dagula, K.H.J. Buschow and F.R. de Boer,

Physica B 319 (2002) 174. [17] E. Brück, Hybridization in cerium and uranium intermetallic compounds,

Ph.D. Thesis, University of Amsterdam, 1991. [18] A.M. Tishin, Magnetocaloric effect in the vicinity of phase transitions, in

Handbook of Magnetic Materials, Vol. 12, pp. 398-518, Edited by K.H.J. Buschow, Elsevier Science Publ. Amsterdam 1999.

[19] K.A. Gschneidner, Jr., V.K. Pecharsky, A.O. Pecharsky and C.B. Zimm, Mater. Sci. Forum 315-317 (1999) 69.

[20] C.P. Bean and D.S. Rodbell, Phys. Rev. 126 (1962) 104. [21] R.W. Blois and D.S. Rodbell, Phys. Rev. 130 (1963) 1347. [22] R. Zach, M. Guillot and J. Tobota, J. Appl. Phys. 83 (1998) 7237. [23] O. Beckman and L. Lundgren, Compounds of transition elements with non-

metals, in Handbook of Magnetic Materials, Vol. 6, pp 186-276, Edited by K.H.J. Buschow, Elsevier Science Publ. Amsterdam 1991.

[24] R. Zach, M. Bacmann, D. Fruchart, P. Wolfers, R. Fruchart, M. Guillot, S. Kaprzyk, S. Niziol and J. Tobola, J. Alloys Compds. 262-263 (1997) 508.

84 Chapter 5

85

Chapter 6

Effects of Mn/Fe ratio on the magnetocaloric properties of hexagonal MnFe(P,As) compounds 6.1 Introduction The three most important factors for the realization of domestic magnetic

refrigeration are a low-cost magnetic -field source, an active magnetic refrigerant,

and a proper design of the thermodynamic refrigeration cycle. The best choice of

the field source for domestic applications would be a permanent magnet. However,

the field generated by permanent magnets is typically below 1 T, but it is also

possible to generate a field of 2 T with high-energy-product magnets [1,2].

Usually, the magnetocaloric effect (MCE) of a magnetic material is very small for

such a low-field change. This calls for new materials that possess a large MCE.

Recently developed new materials exhibit a very large MCE [3-5]. For example, as

we have reported in Chapter 5, the compound MnFeP0.45As0.55 exhibits an adiabatic

temperature change of about 3 K at a field change of 1 T around 30ºC. These

achievements are very promising for developing domestic magnetic refrigerators as

an alternative for the conventional gas compression/expansion refrigerators in use

today. The large MCE observed in the new materials reported in Refs. [3]-[5] is

related to a first-order phase transition and is strongly material dependent.

Therefore, a better understanding of the magnetocaloric properties of these

86 Chapter 6

materials is essential for developing new materials. Recent developments in new

designs of prototypes of magnetic refrigerators [6,7] have brought the magnetic -

refrigeration technology a step closer toward room-temperature applications. Due

to an enhanced lattice entropy above 20 K in relevant materials, the Ericsson cycle

is most suited for the high-temperature applications.

As reported in Chapter 5, the new materials MnFeP1-xAsx that consist of Mn,

Fe, P, and As with a ratio of Mn:Fe:(P+As) = 1:1:1, have advantages over existing

magnetic coolants. It exhibits a large MCE, which is larger than that of Gd metal

and its operating temperature can be easily tuned from 168 to about 332 K by

adjusting the P/As ratio between 1.5 and 0.5 without losing the large MCE [8]. The

main effect of varying the composition of the non-magnetic P and As is a variation

of the lattice parameters and a change of the magnetic-ordering temperature. In this

case, as may be expected, the size of the magnetic moments is hardly affected.

Only beyond 65 at. % P, the moment is reduced. The MCE increases with

decreasing magnetic -ordering temperature. The large entropy change is associated

with a field-induced first-order phase transition. The magnetoelastic effect plays an

important role in the phase transition, and may lead to an enhancement of the

exchange interactions and thus a change of the molecular field. This may enhance

the effective magnetic field.

We have studied the effects of substitution of some elements on the MCE of

MnFe(P,As)-based compounds [9-12]. We have found that the variation of the

composition of the magnetic elements Mn and Fe directly changes the magnetic

moments and simultaneously induces a change in the magnetic interactions. We

may expect an enhanced MCE with increasing Mn content since Mn has a larger

magnetic moment than Fe. We have also been aware of the fact that thermal

hysteresis or field hysteresis is one of the main obstacles for applications. Although

this hysteresis is intrinsic to the first-order phase transition, it may be reduced by

precisely adjusting the magnetic interactions. In this chapter, we report on our

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 87

studies that were motivated to improve and to optimize the MCE observed in the

MnFe(P,As)-based compounds by varying the Mn/Fe ratio.

6.2 Experimental Polycrystalline samples of Mn2-xFexP0.5As0.5 with x = 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6,

0.5, 0.4, and Mn1.1Fe0.9P0.47As0.53 were prepared by ball milling, followed by a

solid-state reaction as reported in Chapter 5. The starting materials are the binary

compounds Fe2P (99.5 % pure, Alfa Aesar), FeAs2 (99.5 % pure, Alfa Aesar), Mn

chips (99.99 % pure, Alfa Aesar), and red-P powder (99.5 % pure). X-ray

diffraction (XRD) was used for the characterization of the phases and for the

determination of the unit-cell parameters.

The temperature and field dependence of the magnetization of the samples

were measured with a Quantum Design SQUID magnetometer in the temperature

range from 5 to 400 K and in magnetic fields from 0 to 5 T. The resistance

measurements were carried out in an Oxford Instruments MagLab system using a

four-point method. The sample used in the measurements had dimensions 2 x 2 x

10 mm3. The measurements were performed with 10 mA ac current with a

frequency of 63 Hz, and the direction of the ac current was perpendicular to the

field direction.

Direct measurements of the MCE were carried out at Moscow State

University. The rate of the field change was up to 0.4 T/s. The accuracy of the

measurements was about 5-20 %.

6.3 Results and discussion 6.3.1 Structural and magnetic properties Figure 6.1 shows the XRD patterns of the Mn2-xFe xP0.5As0.5 compounds. With

increasing Mn content, we observe a small shift of the peak positions to lower

88 Chapter 6

20 30 40 50 60 70 80

032

122

131

121

030

120

021

111

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

x = 1.2

Inte

nsity

(arb

. uni

t)

2θ (deg)

Figure 6.1: XRD patterns of Mn2-xFexP0.5As0.5 compounds with x = 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5 and 0.4, measured at room temperature.

The indices of the main reflections of the Fe2P type are also given.

angle. This indicates a small increase of the unit-cell volume as may be expected

from the slightly larger atomic volume of Mn compared to that of Fe. Refinement

of the structure results in the lattice parameters as summarized in Table 6.1, where,

we see that with increasing Mn content, mainly the lattice parameter a increases

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 89

while the parameter c remains unchanged. This effect is quite similar to that caused

by variation of the P (and As) content.

Table 6.1: Lattice parameters of Mn2-xFexP0.5As0.5 compounds with x =

1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, and 0.4 at room temperature obtained through refinement of XRD data.

Nominal, x a(Å) c(Å) c/a v(Å3)

1.2 6.1126 3.4770 0.569 112.5 1.1 6.1224 3.4743 0.567 112.8 1.0 6.1243 3.4765 0.568 112.9 0.9 6.1344 3.4744 0.566 113.2 0.8 6.1470 3.4980 0.569 114.5 0.7 6.1372 3.4820 0.567 113.6 0.6 6.1507 3.4810 0.566 114.0 0.5 6.1610 3.4970 0.568 115.0 0.4 6.1621 3.4982 0.568 115.0

Figure 6.2 shows the magnetic-field dependence of the magnetization of the

Mn2-xFexP0.5As0.5 compounds with x = 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5 and 0.4 at

5 K. The Mn2-xFexP0.5As0.5 compounds with x = 1.2, 1.1, 1.0, 0.9, 0.8 and 0.7 are

ferromagnetic (FM). The observed magnetic moment varies between 3.8 and 4.2

µB/f.u.. The largest moments observed are 4.2 µB/f.u. for Mn1.2Fe0.8P0.5As0.5 and 4.1

µB/f.u. for Mn1.1Fe0.9P0.5As0.5, probably due to the higher moment of Mn compared

to that of Fe. In the case of excess of Fe, we would expect a reduction of the

magnetic moment, but the moment remains almost unchanged. This indicates that

Fe has a higher moment at the 3g sites than at the 3f sites. These results are in

agreement with neutron-diffraction results [13] and band-structure calculations

[14]. Because both Mn2P and Mn2As are antiferromagnetically ordered [15], we

expect that for the Mn-rich compounds beyond some amount of Mn substitution

the FM ground state will be destroyed. This is seemingly the case for the

compounds in which 40 - 60 % of the Fe is replaced by Mn, which are clearly not

FM.

90 Chapter 6

0 1 2 3 4 5 0 1 2 3 4 5

0

2

4

0

2

4

0 1 2 3 4 50

2

4

x = 0.9

x = 0.8

x = 0.7

x = 1.1

µ0H (T)

x = 1.2

µ0H (T)

µ0H (T)

x = 1.0x = 0.4

M (

µB/f.

u.)

x = 0.5

M (

µ B/f

.u.)

x = 0.6

M (

µ B/f

.u.)

Figure 6.2: Field dependence of the magnetization of Mn2-xFe xP0.5As0.5

compounds with x = 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2, measured at 5 K.

In Fig. 6.3, we have plotted the temperature dependence of the magnetization

of Mn2-xFexP0.5As0.5 compounds with x = 0.4, 0.5, 0.6 and 0.7, 0.8, 0.9, 1.0, 1.1 and

1.2, measured in an applied field of 50 mT. In the Mn2-xFexP0.5As0.5 compounds

with x = 0.4, 0.5 and 0.6, obviously no FM order occurs. Instead, we observe

complex magnetic behavior below the magnetic -ordering temperature, and

additionally we observe some differences between the field-cooled and zero-field-

cooled measurements, which may indicate a complicated spin structure in these

compounds at low temperatures. As a magnetocaloric material, these materials are

of less interest. The Mn2-xFexP0.5As0.5 compounds with x = 0.7, 0.8, 0.9, 1.0, 1.1

and 1.2 are FM. The sample with x = 0.9 has exactly the same critical temperature

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 91

0 50 100 150 200 250 300 350 4000

10

20

30 x = 0.7 x = 0.8 x = 0.9 x = 1.0 x = 1.1 x = 1.2

Mn2-xFexP0.5As0.5

B = 50 m T

M (A

m2 /k

g)

T (K)

0.0

0.1

0.2

0.3 x = 0.4 x = 0.5 x = 0.6

Figure 6.3: Temperature dependence of the magnetization of the

Mn2-xFexP0.5As0.5 compounds with x = 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2, measured with increasing temperature in a field of 50 mT. For x =

0.4, 0.5 and 0.6, also the measurements with decreasing temperature are

included.

TC = 282 K as MnFeP0.5As0.5. Further increase of the Mn content leads to the

expected reduction of the Curie temperature as can be seen for the samples with x

= 0.8 and 0.7. In these samples, the Curie temperature is strongly reduced to 240

and 203 K, respectively. The samples with x = 1.1 and 1.2 exhibit an increase of

the Curie temperature to 319 and 322 K, respectively. No thermal hysteresis is

observed in the samples with x = 1.1 and 1.2. These results suggest that the

magnetic interactions and the magnetic phase transition do not only depend on the

92 Chapter 6

250 260 270 280 290 300 310 320 330 340 3500

20

40

60

80

100

120

Mn1.1

Fe0.9

P0.47

As0.53

1 T 2 T 3 T 4 T 5 T

M

(Am

2 /kg)

T (K)

Figure 6.4: Temperature dependence of the magnetization of

Mn1.1Fe0.9P0.47As0.53, measured with increasing temperature in fields of 5, 4, 3, 2, and 1 T. The inset shows the field dependence of the Curie

temperature.

distances between the magnetic atoms but that they are also related to the

electronic structure of the magnetic atoms, presumably to the density of the 3d-

electron states near the Fermi level.

In order to adjust the ordering temperature of the material around room

temperature (assuming 293 K), we have prepared an additional sample with

composition Mn1.1Fe0.9P0.47As0.53. Figure 6.4 displays the temperature dependence

of the magnetization of Mn1.1Fe0.9P0.47As0.53, measured in fields of 5, 4, 3, 2, and 1

T with increasing temperature from 250 K to 350 K and, after this, decreasing the

temperature to 250 K. The Curie temperature increases almost linearly with

increasing field at a rate of 4.2 K/T. This rate is much larger than for

0 1 2 3 4 5285

290

295

300

305

310dT/dB = 4.2 K

T (K

)

B (T)

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 93

0 1 2 3 4 50

20

40

60

80

100

120

304 K

300 K

296 K

292 K288

K284 k

280 K

Mn1.1Fe0.9P0.47As0.53

M

(Am

2 /kg

)

µBH (T)

Figure 6.5: Magnetic isotherms of Mn1.1Fe0.9P0.47As0.53 in the vicinity of

the Curie temperature.

MnFeP0.45As0.55 (3.3 K/T), and almost same as for Gd5Si1.7Ge2.3 (4.4 K/T). The

extrapolated zero-field Curie temperature is about 286 K. The Curie temperature

has been determined as the temperature corresponding to the minimum point of the

first derivative of the M(T) curve.

Figure 6.5 shows the magnetic isotherms of Mn1.1Fe0.9P0.47As0.53, measured

with increasing field and subsequent decreasing field with steps of 50 mT. The

results show that, at temperatures above TC, a first-order transition from the PM

state to the FM state can be induced by application of a magnetic field. The critical

field needed to induce the transition increases with increasing temperature, whereas

the field hysteresis decreases with increasing temperature. The transition is much

smoother than the one observed in MnFeP0.45As0.55. There is no remanence when

the field decreases to zero, indicating that the transition can be reproduced upon

cycling through zero field.

94 Chapter 6

6.3.2 Magnetocaloric properties The isothermal mS∆ of the samples has been derived from the magnetic isotherms

by using Eq. (3.3). As a representative example, Fig. 6.6 shows the magnetic

isotherms of Mn1.1Fe0.9P0.5As0.5 in the vicinity of the Curie temperature (TC = 282

K). The magnetic isotherms display three different types of behavior: below 282

K, they are FM, above 298 K, they are paramagnetic (PM), and between these two

temperatures, there exists a field-induced magnetic phase transition from the PM

state to the FM state. The critical field of the phase transition increases with

temperature at a rate about 0.23 T/K. From the magnetic isotherms of each of the

samples, we have derived the isothermal magnetic -entropy changes in the samples.

To avoid unnecessary errors, all magnetization measurements have been

performed in the same manner with an increasing temperature step of 4 K and

0 1 2 3 4 50

20

40

60

80

100

120

∆T = 4 K

310 K

270 KMn1.1Fe0.9P0.5As0.5

M (A

m2 /k

g)

µ0H (T)

Figure 6.6: Magnetic isotherms of Mn1.1Fe0.9P0.5As0.5, measured with

increasing field and increasing temperature between 270 and 310 K with

temperature steps of 4 K.

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 95

180 200 220 240 260 280 300 320 340

0

5

10

15

20

25

30Mn

2-xFe

xP

0.5As

0.5

x = 1.2x = 1.1

x = 1.0

x = 0.9

x = 0.8

x = 0.7

∆B 0 - 1 T 0 - 2 T

- ∆

Sm

(J/k

gK

)

T (K)

Figure 6.7: Isothermal magnetic -entropy change in Mn2-xFe xP0.5As0.5

compounds as a function of temperature for field changes from 0 to 1 and 0

to 2 T.

increasing field steps of 0.1 T up to 1 T and steps of 0.2 T between 1 and 5 T. The

results are shown in Fig. 6.7. The maximum magnetic -entropy changes are

observed in the compound Mn1.1Fe0.9P0.5As0.5, being about 17 and 25 J/kgK for

field changes from 0 to 1 and 2 T, respectively. The Fe-richer samples with x = 1.1

and x = 1.2 exhibit an increase of TC and a simultaneous reduction of the

magnetic-entropy change. Moreover, the peak of the magnetic -entropy change

becomes much broader than for other compositions. For the other compositions,

both the TC and the magnetic -entropy change decrease with increasing Mn

contents.

The magnetic isotherms of Mn1.1Fe0.9P0.47As0.53 were measured in the vicinity

of the ordering temperature with the magnetic field increasing from 0 to 3 T. The

result is shown in Fig. 6.8. The isothermal magnetic -entropy change of

96 Chapter 6

0.0 0.5 1.0 1.5 2.0 2.5 3.00

20

40

60

80

100

120272 -- 312 K; ∆T = 4 KMn1.1Fe0.9P0.47As0.53

M

(Am

2 /kg

)

µ0H (T)

Figure 6.8: Magnetic isotherms of Mn1.1Fe0.9P0.47As0.53, measured with increasing field in the temperature range from 272 to 312 K with

temperature steps of 4 K and field steps of 0.1 T.

270 280 290 300 310 320 330

0

5

10

15

20

25

0 - 1 T 0 - 2 T 0 - 3 T

Mn1.1

Fe0.9

P0.47

As0.53

-∆S

m (J

/kg

K)

T (K)

∆Β

Figure 6.9: Temperature dependence of the isothermal magnetic -entropy

change in Mn1.1Fe0.9P0.47As0.53 for field changes from 0 to 1, 0 to 2, and 0 to

3 T.

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 97

Mn1.1Fe0.9P0.47As0.53 was derived from the magnetization data by using Eq. (3.3). In

this case, we used temperature steps of 4 K and field steps of 0.1 T.

The magnetic-entropy changes of Mn1.1Fe0.9P0.47As0.53 resulting from field

changes from 0 to 1, 0 to 2, and 0 to 3 T are shown in Fig. 6.9. The maximum

values of the magnetic -entropy changes for field changes of 1, 2, and 3 T are found

to be about 12, 21, and 23 J/kgK, respectively. The corresponding values for

FWHMTδ are 5, 6, and 9 K, respectively. The refrigerant capacity, in the temperature

range from 291 to 297 K for a field change of 2 T, is about 94 J/kg. It should be

mentioned, however, that the refrigerant capacity, which is essentially the integral

under the curves in Fig. 6.9, is not much altered. For magnetic -refrigeration cycles

in low magnetic fields , it may be of importance to absorb a large amount of heat

over a narrow temperature interval.

286 288 290 292 294 296 2980

1

2

3

4

∆B0 - 1.45 T

Mn1.1

Fe0.9

P0.47

As0.53

∆Tad

(K)

T (K)

Figure 6.10: Adiabatic temperature change adT∆ of Mn1.1Fe0.9P0.47As0.53 as a function of temperature, determined by direct measurement for a field

change from 0 to 1.45 T. This measurement was performed by Tishin’s

group at Moscow State University.

98 Chapter 6

The isothermal magnetic -entropy change is a fundamental parameter but not the

only one for a magnetic refrigerant. The adiabatic temperature change appears to

be more important for cooling applications. In order to assess the suitability of the

suggested compounds, we have collaborated with Tishin’s group at Moscow State

University and have performed direct measurements of the adiabatic temperature

change of Mn1.1Fe0.9P0.47As0.53. Figure 6.10 shows the results for a field change

from 0 to 1.45 T. The largest achieved value of adT∆ due to this field change is 4.2

K.

0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

291.1 K 292.2 K 293.4 K 295.4 K

Mn1.1Fe0.9P0.47As0.53

∆Tad

(K

)

B (T)

Figure 6.11: Adiabatic temperature change adT∆ of Mn1.1Fe0.9P0.47As0.53 in the vicinity of TC as a function of applied magnetic field obtained by means

of direct measurements. This measurement was performed by Tishin’s

group at Moscow State University.

Figure 6.11 shows the field dependence of adT∆ of Mn1.1Fe0.9P0.47As0.53 at

four different temperatures in the transition region. As we see, the MCE increases

with increasing field, and is not saturated up to the maximal applied field of 1.45 T.

This means that the values of the adiabatic temperature change will further increase

with increasing magnetic field. Around 292 K, the adiabatic temperature change

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 99

reaches 3 K for a field change from 0 to 1 T. This is larger than the value of 2.07

K/T for Gd and the same as the value of 3 K/T reported for Gd5Si2Ge2 [16].

In order to compare the magnetocaloric properties of the present compounds

with those of other systems, we present relevant data for these materials in Table

6.2. It can be seen that the largest magnetic -entropy change is observed in MnAs,

which is about 30 J/kgK for a field change from 0 to 2 T. But the corresponding

adT∆ is only 4.7 K. The largest MCE, as high as about 13 K for a field change of 2

T, has been reported for the FeRh system. This is almost three times larger than

Table 6.2: Magnetic-ordering temperature TC, isothermal magnetic -entropy

change – ∆ Sm, and adiabatic temperature change adT∆ of MnFe(P,As)-based compounds, compared with other materials.

Material

TC (K) - ∆ Sm(J/kgK) 0-2 T

∆ Tad (K)

Ref.

MnFeP1-xAsx

x = 0.35 0.45 0.50 0.55

213 240 282

300(I)

13 20

16.5 15(I)

3.9 (0-1.45T)*

present work

Mn2-xFexP0.5As0.5

x = 0.90 0.80 0.70

282 236 205

25.5 16.1 10.8

present work

Mn1.1Fe0.9P0.47As0.53 290 21 4.2 (0-1.45T)* present work

Gd 294 5 5.7 (0-2 T) [17] Fe49Rh51 316 22 12.9 (0-2 T) [18] Fe49Rh51 313 12 8.4 (0-2 T) [19] MnAs 318 31 4.7 (0-2 T) [20] Gd5Si2Ge2 278 14 7.3 (0-2 T) [3] Gd5Si1.97Ge2.03 262 - 2-3 (0-1.4 T)* [21] La(Fe0.9Si0.1)13

La(Fe0.88Si0.12)13H0.5

La(Fe0.89Si0.11)13H1.3

188 233 291

25 20 24

4 (0-1.4 T)* 6 (0-2 T) 6.9 (0-2 T)

[22] [5] [5]

100 Chapter 6

that of Gd metal in the vicinity of the magnetic phase transition. Some direct

measurements (denoted by * in Table 6.2) performed at Moscow State University

show that the MnFe(P,As)-based compounds have larger a MCE than Gd metal in

the same temperature range.

As has been pointed out in Ref. 23, the adiabatic temperature change mainly

depends on the change of the magnetic -ordering temperature upon application of a

magnetic field. We have observed dTC/dB of 3.3 K/T for hexagonal MnFeP1-xAsx

and 4.2 K/T for Mn1.1Fe0.9P0.47As0.53.

A first-order transition is always associated with thermal or field

hysteresis. In the hysteresis region, the magnetic state of the material is

uncertain, depending on the history. Hysteresis will result in a reduced

efficiency of the refrigeration cycle, which will be especially important if

one works in low magnetic fields. For the samples with equal amounts of Fe

280 285 290 295 300 305 3100

20

40

60

80

100

M n1.1

F e0.9

P0.47

As0.53

B = 1 T

M (A

m2 /k

g)

T (K)

Figure 6.12: Temperature dependence of the magnetization of

Mn1.1Fe0.9P0.47As0.53, measured in a field of 1 T with increasing and, after

this, decreasing temperature.

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 101

and Mn, the thermal hysteresis is between 3 and 4 K, and the field hysteresis

about 0.5 T. In Fig. 6.12, we show the temperature dependence of the

magnetization of a Mn1.1Fe0.9P0.47As0.53 sample, measured in a constant

magnetic field of 1 T with increasing and, after this, decreasing temperature.

The observed thermal hysteresis is less than 2 K and, as we see in Fig. 6.5, the field

hysteresis is only about 0.2 T. This reduction of the thermal hysteresis makes it

feasible to employ refrigeration cycles even in fields below 2 T. The lower the

field, however, the more stages of magnetocaloric cycles one may have to employ

to achieve the desired temperature change.

The possibility to reduce the thermal hysteresis of the first-order phase

transition is the most important result of this study. The driving force for the first-

order character of the magnetic transition is clearly a magnetoelastic interaction

between the Mn- and Fe-containing planes in the hexagonal MnFe(P,As)

compounds. In contrast to compounds like Gd5Si2Ge2, MnAs or FeRh, which also

show a first-order magnetoelastic transition, the transition in MnFe(P,As) is not

associated with a change in crystal symmetry but merely with a change in c/a ratio.

This difference forms the basis of the rather low hysteresis observed. If the crystal

symmetry is altered in the magnetic phase transition, the magnetic state is locked

in, resulting in the generally observed large hysteresis. In the case of a change in

c/a ratio, only the exchange interaction between the sublattices varies. Addition of

Mn on the Fe sublattice may introduce some competing interactions. On

approaching the critical distance between the sublattices, already small thermal

fluctuations lead to a release of the locking. This idea is also corroborated by the

fact that substitution of 10 % of the Fe by Mn, which does not alter the lattice

parameter c and thus the distance between the sublattices, does not affect TC.

102 Chapter 6

6.3.3 Electrical resistivity

Figure 6.13 shows the temperature dependence of the electrical resistivity of

Mn1.1Fe0.9P0.47As0.53 measured in zero field with decreasing temperature in the

temperature interval from 5 to 310 K. With decreasing temperature, an anomaly

occurs in the electrical resistivity around 290 K. This temperature corresponds to

the magnetic phase transition. Above this temperature, the electrical resistance of

the sample decreases rapidly in a narrow temperature range and then becomes less

temperature dependent. A similar behavior of the electrical resistivity has been

reported for the isostructural compound MnRhP [24]. At 300 K, the electrical

resistivity of Mn1.1Fe0.9P0.47As0.53 is about 1800 µΩcm. This value is between the

resistivity, which is about 400 µΩcm, of Fe2P [25,26] and the resistivity, which is

about 3000 µΩcm of Mn2P [27] at room temperature, and also of the same order as

that of Gd5Si2Ge2, which is about 1100-2800 µΩcm [28].

0 50 100 150 200 250 3000

500

1000

1500

2000

290 K

Zero Field

Mn1.1Fe0.9P0.47As0.53

ρ (µ

Ωcm

)

T(K)

Figure 6.13: Temperature dependence of the electrical resistivity of

Mn1.1Fe0.9P0.47As0.53, measured with decreasing temperature in zero field.

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 103

The magnetic-field dependence of the isothermal electrical resistance of

Mn1.1Fe0.9P0.47As0.53, measured at four different temperatures, is shown in Fig. 6.14.

At 275 K, which is in the FM region, the electrical resistance of the sample

decreases with increasing magnetic field, indicating that the magnetic contribution

to the resistance is suppressed by the applied field. At temperatures of 295, 303,

and 310 K, which are in the PM region, we observe a field-induced phase transition

0 1 2 3 4 50.044

0.046

0.048

0.050

0.052

310 K303 K

295 K

275 K

Mn1.1

Fe0.9

P0.47

As0.53

R (Ω

)

B(T)

Figure 6.14: Field dependence of the isothermal resistance of

Mn1.1Fe0.9P0.5As0.5, measured with increasing and, after this, decreasing field.

with a field hysteresis of less than 0.3 T in the electrical-resistance curves. The

resistance has a step of about 8 % at the transition. These features also indicate that

the transition is of first order. The critical field increases with a rate of about 0.22

T/K for increasing temperature.

104 Chapter 6

6.4 Conclusions Variation of the Mn/Fe ratio has the following effects on the magnetic and the

magnetocaloric properties of the hexagonal Mn2-xFexP0.5As0.5 compounds:

1. The magnetic moment increases by 2 % and 5 % when going from

MnFeP0.5As0.5 to Mn1.1Fe0.9P0.5As0.5 and Mn1.2Fe0.8P0.5As0.5, respectively.

The maximum magnetic moment found in Mn1.2Fe0.8P0.5As0.5 is about 4.2

µB/f.u..

2. The Curie temperature, which is also the working point of a magnetic

refrigerant, increases from 203 K to 330 K in the composition range 0.7 ≤

x ≤ 1.2.

3. The magnetic-entropy change is maximal in the compound

Mn1.1Fe0.9P0.47As0.53. The maximum values are 21 and 23 J/kgK for field

changes of 0 to 1 and 0 to 2 T, respectively. A direct measurement of the

MCE shows that the adiabatic temperature change is 4.2 K for a field

increase from 0 to 1.45 T, and as high as 3 K for a field increase from 0 to

1 T around 292 K.

4. The thermal hysteresis is smaller than 2 K and the field hysteresis is about

0.3 T in the Mn2-xFexP0.5As0.5 system, both values being smaller than those

observed in the MnFeP1-xAsx system.

5. The electrical resistivity of the compounds is about 1800 µΩcm around

room temperature. The steplike change and the field hysteresis in the

electrical resistance of the compound Mn1.1Fe0.9P0.47As0.53 also confirm that

the transition is of first order.

Summarising, we have observed an enhanced MCE and a reduced thermal

hysteresis in the compounds with 10 % excess of Mn: Mn1.1Fe0.9P0.47As0.53 and

Mn1.1Fe0.9P0.5As0.5. These excellent features emphasize the large potential of the

present compounds for room-temperature magnetic -refrigeration applications.

Effects of Mn/Fe ratio on the magnetocaloric properties of MnFe(P,As) 105

References [1] J.M.D. Coey, J. Magn. Magn. Mater. 248 (2002) 441. [2] S.J. Lee, J.M. Kenkel, V.K. Pecharsky and D.C. Jile s, J. Appl. Phys. 91

(2002) 8543. [3] V.K. Pecharsky and K.A. Gechneidner, Jr., Phys. Rev. Lett, 78 (1997) 4494. [4] O.Tegus, E. Brück, K.H.J. Buschow and F.R. de Boer, Nature 415 (2002)

150. [5] A. Fujita, S. Fujieda, Y. Hasegawa and K. Fukamichi, Phys. Rev. B 67

(2003) 104416. [6] http://www.external.ameslab.gov/news/relase/01magneticrefrig.htm. [7] http://www.jarn.co.jp/News/2003_Q2/30520_Chubu_Magnet_cool.htm. [8] O.Tegus, E. Brück, L. Zhang, W. Dagula, K.H.J. Buschow and F.R. de Boer,

Physica B 319 (2002) 174. [9] E. Brück, O. Tegus, X.W. Li, F.R. de Boer and K.H. J. Buschow, Physica B

327 (2003) 431. [10] O. Tegus, L. Zhang, W. Dagula, E. Brück, K.H.J. Buschow and F.R. de

Boer, J. Appl. Phys. 93 (2003) 7655. [11] X.W. Li, O. Tegus, L. Zhang, W. Dagula, E. Brück, K.H.J. Buschow and

F.R. de Boer, submitted to IEEE Trans. Magn.. [12] O. Tegus, E. Brück, X.W. Li, L. Zhang, W. Dagula, F. R. de Boer and K.H.J.

Buschow, submitted to J. Magn. Magn. Mater.. [13] M. Bacmann, J.L. Soubeyroux, R. Barrett, R. Zach, S. Niziol and R.

Fruchart, J. Magn. Magn. Mater. 134 (1994) 59. [14] J. Tobola, M. Bacmann, D. Fruchart, S. Kaprzyk, A.Koumina, S. Niziol, J.L.

Soubeyroux, P. Wolfers and R. Zach, J. Magn. Magn. Mater. 157-158 (1996) 708.

[15] O. Beckman and L. Lundgren, in Handbook of Magnetic Materials, Edited by K.H.J. Buschow (North Holland, Amsterdam, 1991), Vol. 6, pp. 181-287.

[16] K.A. Gschneidner, Jr. and V.K. Pecharsky, Ann. Rev. Mater. Sci. 30 (2000) 387.

[17] S.Yu. Dan’kov, A.M. Tishin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 57 (1998) 3478.

[18] M.P. Annaorazov, K.A. Asatryan, G. Myalikgulyev, S.A. Nikitin, A.M. Tishin and A.L. Tyurin, Cryogenics 32 (1992) 867.

106 Chapter 6

[19] M.P. Annaorazov, S.A. Nikitin, A.L. Tyurin, K.A. Asatryan and A.Kh. Dovletov, J. Appl. Phys. 79 (1996) 1689.

[20] H. Wada and Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3302. [21] A.S. Chernyshov, D.A. Filippov, M.I. Ilyn, R.Z. Levitin, A.O. Pecharsky,

V.K. Pecharsky, K.A. Gschneidner, Jr., V.V. Snegirev and A.M. Tishin, Phys. Met. Metall. 93 (2002) S19.

[22] F.X. Hu, Max Ilyn, A.M. Tishin, J.R. Sun, G.J. Wang, Y.F. Chen, F. Wang, Z.H. Cheng and B.G. Shen, J. Appl. Phys. 93 (2003) 5503.

[23] V.K. Pecharsky, K.A. Gschneidner, Jr., A.O. Pecharsky and A.M. Tishin, Phys. Rev. B 64 (2001) 144406.

[24] I. Kanomata, T. Narita, N. Suzuki, K. Sato, T. Harada, N. Ogawara, K. Koyama and M. Motokawa, J. Alloys Compds. 334 (2002) 68.

[25] S. Chiba, J. Phys. Soc. Japan, 15 (1960) 581. [26] D. Bellavance, J. Mikkelson and A. Wold, J. Solid State Chem. 2 (1970)

285. [27] I.G. Fakidov and V.P. Krasovskii, Phys. Met. Metall. 7 (1959) 159. [28] E.M. Levin, V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. B 60

(1999-I) 7993.

107

Summary This thesis presents a study of the magnetocaloric effect (MCE) and related

physical properties of several intermetallic compounds: GdRu2Ge2, Gd5Ge2.3Si1.7 ,

and MnFe(P,As). Of particularly interest is the discovery of a very large MCE in

MnFe(P,As) compounds around room temperature and low fields that can be

generated by permanent magnets. This is a promising step in the direction of

refrigeration technology by means of the magnetocaloric effect.

After a brief overview on the conventional refrigeration techniques, the

significance of developing magnetic refrigeration and the motivation for this study

are pointed out in Chapter 1. The adiabatic temperature change and the isothermal

magnetic-entropy change are the two characteristic parameters for evaluating the

magnetocaloric properties of a magnetic material. The theoretical aspects of the

MCE and of magnetic phase transition are presented in Chapter 2. Since a large

MCE may be expected in the vicinity of a magnetic phase transition, our study is

focused on the MCE associated with such transitions, in particular first-order phase

transitions

For the determination of the MCE, we have used both magnetic and

specific-heat measurements, that are described in Chapter 3. Additionally, we also

present direct measurements, which were performed by Tishin’s group at Moscow

State University, of the MCE in some of the MnFe(P,As) compounds. A reliable

characterization technique for the MCE and a better understanding of the MCE and

related physical properties of the newly found compounds Gd5(Ge,Si)4 are,

therefore, crucial in fundamental as well as technological investigations for new

magnetic refrigerants. Therefore, in Chapter 4, the characterization techniques and

methods to determine the MCE were tested by studying the MCE in GdRu2Ge2.

108 Summary

The results of this study show that the isothermal magnetic - entropy change

derived from magnetization measurements is in good agreement with the values

obtained by means of specific -heat measurements in magnetic field, thus

confirming that it is reliable to investigate the MCE in new materials by means of

simple magnetization measurements. In Chapter 4, we also present the results of a

study of the MCE and of related physical properties of a single crystal of

Gd5Ge2.3Si1.7. This compound exhibits a large magnetic -entropy change, at least

three times larger than that of Gd, in the vicinity of its first-order simultaneous

structural and magnetic phase transition.

We have found that MnFe(P,As) compounds are very promising novel

magnetic coolants with a large MCE in the room-temperature region. In Chapter 5,

we present a study of the MCE and related physical properties, such as

magnetization and electrical resistivity, of the hexagonal MnFe1-xAsx compounds.

These materials that conta in elements that easily evaporate, such as P and As, have

been prepared by ball milling and subsequent solid-state reaction. The hexagonal

MnFeP1-xAsx compounds exhibit a MCE that is as large as the one found in

Gd5(Ge,Si)4. This MCE is also associated with a first-order magnetic phase

transition from the low-temperature ferromagnetic (FM) phase to the high-

temperature paramagnetic (PM) phase. An applied magnetic field induces a

transition from PM state to FM state. The first-order phase transition in the

MnFe(P,As) compounds studied is adequately described by the Bean-Rodbell

model, indicating the magnetoelastic effect plays an important role in the phase

transition. Besides their large MCE, two additional features make the MnFe(P,As)

compounds promising candidate materials for magnetic refrigerants in room-

temperature applications. The first one is the fact that their Curie temperature can

be tuned between 168 K and 332 K by varying the P/As ratio between 1.5 and 0.5,

which allows one to tune the maximum MCE in this temperature range without

losing the large MCE. The second important feature is that, unlike for instance in

FeRh, the large MCE in the MnFe(P,As) compounds is reversible, and that the

Summary, Samenvatting 109

thermal hysteresis observed in the compounds is smaller than that observed in

Gd5(Ge,Si)4 system. It is also commercially attractive that the price of the

MnFe(P,As) is much cheaper than Gd.

In Chapter 6, we present further studies on the magnetocaloric properties of

the MnFe(P,As)-based compounds in which the Mn/Fe ratio is varied. The

experimental results show that a small addition of Mn enhances the MCE and

reduces the thermal hysteresis. The best magnetocaloric properties are achieved for

Mn1.1Fe0.9P0.47As0.53, which exhibits a maximum adiabatic temperature change of 3

K for a field change from 0 to 1 T at 292 K. The thermal hysteresis is less than 2 K.

110 Summary

Samenvatting Magnetisch koelen is een mogelijk alternatief voor het welbekende gascompressie -

en verdampingsproces. Een warmtepomp is namelijk ook te realiseren met een

magnetische vaste stof die een groot magnetocalorisch effect vertoont. In de

koelcyclus van zo’n pomp warmt de magnetische stof op als een magneetveld

wordt aangelegd en koelt af als het veld wordt uitgeschakeld. Doordat zulke

pompen zeer compact kunnen worden gebouwd, zijn ze ideaal voor allerlei huis-,

tuin- en keukentoepassingen, zoals de koelkast, een aircosysteem, de koeling van

een computer of ook een warmtepomp voor verwarming, waarvoor nu nog de

gascompressor de meest gebruikte vorm is. Andere voordelen van magnetisch

koelen zijn: zuiniger, geen gebruik van broeikasgassen en geluidsarm. Een

magnetische koeler is echter vrij duur, omdat het materiaal dat thans als actief

koelmedium wordt gebruikt (gadolinium) relatief zeldzaam is en op den duur

oplost in het water dat als warmtemedium wordt gebruikt

Onderzoek naar geavanceerde magnetische materialen die een groot

koeleffect in lage magneetvelden vertonen is daarom van groot belang. Dit

is het onderwerp van het in dit proefschrift beschreven onderzoek. Uit

theoretische overwegingen, die in hoofdstuk 2 zijn uiteengezet, volgt dat

een groot magnetocalorisch effect verwacht kan worden bij een scherpe

magnetische faseovergang. Daarom is vooral onderzoek gedaan aan

materialen die een bijzondere magnetische faseovergang vertonen. Om het

magnetocalorisch effect te bepalen, zijn magnetische en calorische metingen

verricht. Aan enkele preparaten is in samenwerking met de groep van

Professor Tishin van de Staatsuniversiteit van Moskou de

Summary, Samenvatting 111

temperatuurverandering gemeten tengevolge van een verandering van het

aangelegde magnetisch veld.

Omdat er in de literatuur discussie is ontstaan of magnetische metingen altijd

een goede beschrijving van het magnetocalorisch effect leveren, is in hoofdstuk 4

een nauwkeurige vergelijking gemaakt tussen de resultaten van calorische

metingen en van magnetische metingen. Deze metingen leveren binnen de

foutmarges eenzelfde magnetocalorisch effect voor GdRu2Ge2 een materiaal dat

een zeer scherpe veldgeïnduceerde overgang vertoont. Hiermee is aangetoond dat

voor de bepaling van het magnetocalorisch effect van een materiaal volstaan kan

worden met de veel eenvoudigere magnetisatiemetingen. Metingen aan een

éénkristal van Gd5Ge2.3Si1.7 tonen een magnetocalor isch effect dat drie keer groter

is dan in zuiver Gd.

Een eerste grote doorbraak in magnetische koeling is de ontwikkeling van

een nieuw materiaal namelijk een legering van mangaan, ijzer, fosfor en arseen

MnFe(P,As), beschreven in hoofdstuk 5. Na het bepalen van allerlei eigenschappen

van deze legering konden wij vaststellen dat er sprake is van een geschikt

materiaal. Wij hebben aangetoond, dat het mogelijk is met dit materiaal te koelen

met lage magneetvelden gegenereerd m.b.v. permanente magneten. Door het

gebruik van het magneetveld van permanente magneten kan een warmtepomp zeer

energie-efficiënt gemaakt worden omdat alleen voor het warmtetransport arbeid

moet worden verricht. Een bijzonder interessante eigenschap van de nieuwe

legering, naast de veel lagere materiaalkosten, is dat de temperatuur waarbij deze

legering het beste koelt, het zogeheten werkpunt, kan worden ingesteld door een

kleine verandering van de samenstelling. Hiermee kan het werkpunt tussen –80 en

+70°C worden gevarieerd. Een warmtepomp die over dit temperatuurinterval gaat

koelen zal zijn gebaseerd op een soort cascade die in meerdere stappen werkt.

Belangrijk voor de levensduur van een magnetocalorische koeler is ook het feit dat

dit materiaal niet oplost in water. Zelfs in zoutzuur lost het niet op, daarom ook is

arseen in deze legering volkomen ongevaarlijk.

112 Summary

Verdere verbetering van het magnetocalorisch effect in MnFe(P,As) is

gevonden bij verhoging van het aandeel van Mn in deze legering. Dit is beschreven

in hoofdstuk 6. De grootste adiabatische temperatuurverandering wordt gevonden

voor een legering waarin 10 % van het ijzer is vervangen door mangaan.

Ten slotte, de techniek van magnetisch koelen is bijzonder geschikt voor

kleinschalige systemen. Voor een gewone koelkast is niet meer dan 0.1 liter (een

kopje koffie) magnetisch materiaal nodig. Met magnetisch koelen kan de industrie

niet alleen koelsystemen ontwikkelen voor koelkasten, maar ook voor airco’s en

voor computers. Ook voor de levensmiddelenindustrie kan het interessant zijn

koelwagens van deze koeltechniek te voorzien. Het spaart immers ruimte in

vergelijking met de huidige koelsystemen. Grote installaties als koelhuizen of

kunstijsbanen zullen hoogstwaarschijnlijk voortborduren op de geijkte

koelmethoden, omdat daar ruimtebesparing en geluidsoverlast veel minder

belangrijk zijn.