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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
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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.
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