Magnetocaloric effect of Co(S1-xSex)2 under high pressure

Article abstract of DOI:10.1143/JPSJ.79.024701

We examined the magnetocaloric effect of Co(S_1-xSe _x)₂, which shows typical itinerant electron metamagnetism, under high pressures up to 1.2 GPa. It was found that the magnetic entropy change, δS_M, of x = 0 incr

Full text of DOI:10.1143/JPSJ.79.024701

Journal of the Physical Society of Japan
Vol. 79, No. 2, February, 2010, 024701
#2010 The Physical Society of Japan
Magnetocaloric Effect of Co(S1 Se ) under High Pressure
Àx x 2
Osamu SADAKUNI, Akihiro MITUDA, and Hirofumi WADA
Department of Physics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
(
Received September 3, 2009; accepted November 16, 2009; published January 25, 2010)
We examined the magnetocaloric effect of Co(S1ꢀxSex)2, which shows typical itinerant electron
metamagnetism, under high pressures up to 1.2 GPa. It was found that the magnetic entropy change,
ꢀ
SM, of x ¼ 0 increases with increasing pressure, while that for x ¼ 0:05 is not sensitive to pressure. For
x ¼ 0:08, ꢀSM is decreased with pressure. The temperature dependence of ꢀSM was calculated on the
basis of the spin fluctuation theory of itinerant electron metamagnetism. The calculated results reproduce
the experimental ꢀSM–T curves well. The pressure dependence of TC of Co(S1ꢀxSex)2 is also discussed.
KEYWORDS: magnetocaloric effect, metamagnetism, pyrite, magnetic refrigeration, itinerant electron
DOI: 10.1143/JPSJ.79.024701
pressure dependence of the magnetic entropy change of
Co(S1 Se ) . The observed results are compared with the
1
.
Introduction
When a magnetic solid is exposed to a magnetic field at a calculated ones from the theory of IEM, in which the effect
ꢀx
x 2
constant temperature, its entropy is decreased. By removing of spin fluctuations is taken into account.
the magnetic field in an adiabatic condition, the temperature
2
.
Experiments
of the magnetic solid is decreased. These properties
are called the magnetocaloric effect (MCE). In the last
The samples with x ¼ 0, 0.05, and 0.08 were prepared by
decade, materials with large MCEs have been attracting direct reaction of the constituent elements in vacuum at high
considerable interest for their potential application as temperatures. Details on the sample preparation and char-
6
)
working materials in magnetic refrigeration. Several materi- acterization were described elsewhere. X-ray diffraction
als, such as Gd5Si2Ge2, MnAs1ꢀxSbx, MnFeP0:45As0:55 and measurements indicated that all the samples have a single
La(Fe1ꢀxSix)13 and its derivations were found to exhibit phase with the Pyrite structure. The lattice parameters of the
6)
1–4)
giant MCEs near room temperature.
It has been estab- present samples are in agreement with the previous results.
lished that giant MCEs are observed in materials which The magnetization under pressure was measured by using
undergo a first-order magnetic transition from a ferromag- either a Quantum Design superconducting quantum inter-
netic state to a paramagnetic one. According to the Maxwell ference device magnetometer or our extraction-type magne-
relation, the isothermal entropy change, ꢀS , is given by
tometer combined with a clamp cell made of a Cu–Ti alloy
up to 1.2 GPa. A mixture of Fluorinert FC-77 and FC-70
ð1Þ with a volume ratio of 1 : 1 was used as the pressure
transmitting medium and the pressure was calibrated by the
M
Z
ꢀ
ꢁ
H
@
M
ꢀ
SM
¼
dH:
@
T
0
H
In the case of a first-order magnetic transition, the superconducting transition temperature of lead. After the
magnetization changes discontinuously at the Curie tem- samples were cooled down far below T in zero field, the
C
perature, T , which gives a large ꢀS . Above T , a temperature dependence of magnetization was measured at
C
M
C
ferromagnetic state is induced by a magnetic field. When various magnetic fields in the heating process. The iso-
this behavior is observed in itinerant electron systems, it is thermal magnetic entropy change was calculated from the
called the itinerant electron metamagnetism (IEM). The following equation:
Co(S1ꢀxSex)2 system with a Pyrite structure is a typical
example showing IEM. The parent compound CoS2 is a
ferromagnet with T of 122 K. By substituting Se for S, T
X
MðT þ ꢀT; H Þ ꢀ MðT; H Þ
i
i
ꢀSMðT; HÞ ¼
ꢀH; ð2Þ
ꢀ
T
i
C
C
is rapidly decreased and the ferromagnetism disappears where MðT; HiÞ represents the magnetization in a magnetic
at around x ¼ 0:12. The compounds with 0:01 ꢁ x ꢁ 0:11 field Hi at the temperature T.
undergo a first-order magnetic transition and exhibit IEM
just above TC.5) Previously, we have reported the MCE
3. Results
of Co(S1ꢀxSex)2. The peak value of ꢀSM increases with
Figures 1(a) and 1(b) show the M–T curves of CoS2 and
increasing x from 0, showing a maximum value at around Co(S0:95Se0:05)2 at ꢀ0H ¼ 0:4 T under various pressures,
6
)
x ¼ 0:06, followed by a decrease with further increasing x.
respectively. The magnetization of Co(S1ꢀxSex)2 is saturated
The peak width of ꢀS becomes narrower as the peak value at about 0.2 T below TC. The CoS2 compound undergoes a
M
is increased. These results are in qualitative agreement with second-order magnetic transition at ambient pressure but its
the theoretically calculated results based on the theory of magnetization decreases more steeply around TC compared
IEM.7
,8)
with ordinary ferromagnets. With increasing pressure,
It has been reported that the magnetic properties of the magnetic transition becomes sharper, suggesting the
5)
Co(S1ꢀxSex)2 are strongly sensitive to pressure. The occurrence of a first-order magnetic transition under
magnetic transition of CoS2 becomes first-order at P > 0:4 high pressures. These observations are consistent with the
5
)
GPa. These results suggest the enhancement of the MCE previous report by Goto et al. On the other hand, the
of CoS under high pressures. In this paper, we present Co(S0:95Se0:05)2 compound undergoes a first-order magnetic
2
024701-1

J. Phys. Soc. Jpn., Vol. 79, No. 2
O. SADAKUNI et al.
40
35
30
25
20
15
10
5
0
3.5
3
(
a)
(a)
0-0.4T
0-0.8T
0GPa
.4GPa
0.8GPa
.2GPa
0
0
0
0
-1.2T
-1.6T
-2.0T
2
1
0
.5
2
1
CoS2
μ0H=0.4T
P=0GPa
.5
1
CoS2
.5
0
9
0
100
110
120
130
140
110
115
120
125
130
135
140
T(K)
T(K)
5
4
3
2
1
0
4
0
(b)
0-0.4T
0-0.8T
0-1.2T
0
0
0
0
1
GPa
3
3
2
2
1
1
5
0
5
0
5
0
5
0
.3GPa
.6GPa
.9GPa
.2GPa
(
b)
0-1.6T
0-2.0T
CoS2
P=0.8GPa
μ0H=0.4T
Co(S0.95Se
)
0.05 2
6
0
70
80
90
100
110
100
105
110
115
T(K)
120
125
130
T(K)
Fig. 1. Temperature dependence of magnetization of (a) CoS2 and (b)
Co(S0:95Se0:05)2 under various pressures at a magnetic field of 0.4 T.
Fig. 2. Temperature dependence of the magnetic entropy change, ꢀSM, of
x ¼ 0 up to 2 T at (a) 0 GPa and (b) 0.8 GPa.
transition under any pressures we studied. For both com- obtain the area of a ꢀSM–T curve. The value of the area in a
pounds, the Curie temperature strongly depends on the maximum field of 2 T is about ꢀ65 J/kg, irrespective of
applied pressure. The value of @TC=@P is approximately 8 applied pressure. This is called the sum rule, pointed out by
9
)
and 13 K/GPa for x ¼ 0 and 0.05, respectively. We also McMichael et al. From eq. (2), it is easy to show that the
R
T2
measured the M–T curves of Co(S Se ) up to 0.9 GPa. value of
0:08 2
ꢀS dT is given by the area between two
M
0
:92
T1
A first-order magnetic transition was observed in this magnetization curves at T and T up to the maximum field.
pressure range but the transition becomes less sharper with When T ! 1, this integral is approximately given by
1
2
2
increasing pressure. This is probably due to concentration ꢀMSðT1ÞH, where MSðT1Þ is the saturation magnetization at
fluctuations, which broaden a magnetic transition in the T ¼ T1. Using MSðT1 ¼ 60 KÞ ¼ 35 emu/g at ambient pres-
vicinity of ferromagnetic instability. Moreover, @TC=@P for sure and ꢀ0H ¼ 2 T, we have ꢀMSðT1ÞH ¼ 70 J/kg. The
x ¼ 0:08 is about 30 K/GPa, which is more than twice as integrated values of ꢀSM are close to this value. A constant
large as those for x ꢁ 0:05. The latter point will be discussed value of the area irrespective to pressure is consistent with
later.
the observed results that the magnetization at T ¼ 60 K is
1
Figures 2(a) and 2(b) show the temperature dependence of independent of pressure, as shown in Fig. 1(a).
SM of x ¼ 0 up to 2 T at 0 and 0.8 GPa, respectively. The Figures 3(a), 3(b), and 3(c) illustrate the ꢀS –T curves in
ꢀ
ꢀ
M
SM has peaks at around TC and the peak values increase a field change of 2 T under various pressures for x ¼ 0, 0.05,
with increasing a maximum field. Compared with ꢀSM at and 0.08, respectively. The peak value of jꢀSMj of x ¼ 0
ambient pressure, the ꢀSM–T curves at 0.8 GPa are fairly increases with increasing pressure, while that of x ¼ 0:05
asymmetric, characterized by a rapid rise at TC in zero does not depend on pressure strongly. On the other hand,
field, followed by a gradual decrease at TC in a maximum pressure decreases the peak value of jꢀSMj for x ¼ 0:08.
field. These are typical behavior of a first-order magnetic The overall features of the ꢀS –T curves under pressures
M
transition. The peak height of jꢀS j in a maximum field of are similar to the concentration dependence of ꢀSM in
M
2
T is about 4.9 J/(K kg) at P ¼ 0:8 GPa, which is larger than Co(S1 Se ) , in which the peak value of jꢀS j shows a
ꢀx
x 2
M
that at P ¼ 0 GPa, 3.5 J/(K kg). This means that the pressure maximum at around x ¼ 0:06 with TC ¼ 85 K. The values
enhances the magnetocaloric effect for CoS2. By integrating of the area of ꢀSM–T curves is about ꢀ70 to ꢀ73 J/kg for
ꢀ
SM with respect to T over the whole temperature range, we x ¼ 0:05, which are a slightly larger that those for x ¼ 0.
024701-2

J. Phys. Soc. Jpn., Vol. 79, No. 2
O. SADAKUNI et al.
6
4
.
Discussion
Yamada and Goto developed the theory of IEM, in
which the effect of spin fluctuations is taken into consid-
(
a)
0
0
0
1
GPa
5
4
3
2
1
0
.4GPa
.8GPa
.2GPa
7,8)
eration and discussed the MCE. In this section, we will
CoS2
μ0H=0-2T
calculate the ꢀSM–T curves in the framework of the
phenomenological theory of IEM and compare them with
the experimental results. First, we summarize the theory
briefly.
In the Landau theory, expanded up to the M term, the
equation of state is given by
8
)
6
3
5
H ¼ aðTÞM þ bðTÞM þ cðTÞM :
ð3Þ
The condition for the occurrence of itinerant electron
9
0
100
110
120
T(K)
130
140
150
metamagnetic transition is given by aðTÞ > 0, bðTÞ < 0,
2
cðTÞ > 0, and 3=16 < aðTÞcðTÞ=bðTÞ < 9=20. The Landau
7
(
b)
coefficients aðTÞ, bðTÞ, and cðTÞ are expressed as
0
0
0
0
1
GPa
6
5
4
3
2
1
0
.3GPa
.6GPa
.9GPa
.2GPa
5
35
2
4
aðTÞ ¼ a0 þ b0ꢁðTÞ þ
14
c0ꢁðTÞ ;
3
9
2
bðTÞ ¼ b þ 3 c ꢁðTÞ ;
ð4Þ
0
0
μ0H = 0-2T
cðTÞ ¼ c ;
0
Co(S0.95Se
)
0.05 2
2
where ꢁ ðTÞ is the mean-square amplitude of spin fluc-
T
tuations and a0, b0 and c0 is the coefficient determined
from the electronic structure. We define the following
parameters:
sffiffiffiffiffiffiffiffiffiffi
3
jb0j
4
3
M ¼
0
;
H ¼ 5 jb jM :
ð5Þ
0
0
0
6
0
70
80
90
T(K)
100
110
120
1
0c0
Assuming the T2 dependence of ꢁT ðTÞ and using
eqs. (4) and (5), eq. (3) is rewritten as a dimensionless
equation:
2
7
6
5
4
3
2
1
0
(
c)
0
0
0
0
GPa
.3GPa
.6GPa
.9GPa
25
6
5
3
3
5
H~ ¼
a~ ðTÞM ꢀ 4 bðTÞM þ c~ ðTÞM ;
~
~
~
~
ð6Þ
8
μ0H=0-2T
where
and
Co(S0.92Se
)
H
M
T
0.08 2
H~ ¼
;
M~ ¼
;
T~ ¼
;
ð7Þ
H0
M0
TM
a0c0
a~ ðTÞ ¼ b02
5
8
2
4
~
~
ꢀ
T þ
T ;
14
25
2
^
~
bðTÞ ¼ 1 ꢀ T ; c~ ðTÞ ¼ 1:
ð8Þ
1
0
20
30
40
50
T(K)
60
70
80
and TM was determined from bðT Þ ¼ 0.
M
The magnetic entropy change, ꢀS ðT; HÞ is obtained
M
Fig. 3. ꢀSM–T curves in a field change of 2 T under various pressures for
a) x ¼ 0, (b) x ¼ 0:05, and (c) x ¼ 0:08.
from the Maxwell’s relation:
(
Z
~ ꢀ
ꢁ
H
~
@
M
~
~
ꢀ
SMðT; HÞ ¼ S0ꢀSMðT; HÞ ¼ S0
dH; ð9Þ
~
H
~
T
@
0
This is because the magnetization of Co(S0:95Se0:05)2 below
~
TC is larger than that of CoS2 [see Fig. 1(b)]. No significant where ꢀSMðT; HÞ is a dimensionless entropy and S0 is a
difference in the area of ꢀSM–T curves between 0 and 0.05 scale factor given by
indicate that the peak width becomes narrower, as the peak
H M
0
0
value is larger. This is also consistent with the previous
observations of the MCE of Co(S1 Se ) . The ꢀS –T
S0 ¼
:
ð10Þ
TM
ꢀx
x 2
M
curve of x ¼ 0:08 at P ¼ 0:9 GPa is somewhat different From eqs. (5)–(10), we can calculate ꢀS
, b , c , and T
and the peak width is broadened. This is probably due to the magnetization of Co(S1ꢀxSe
ðT; HÞ, when the
M
from those at P ꢂ 0:6 GPa. The peak value is much reduced parameters a
are given. Goto et al. analyzed
M
0
0
0
x
)
2
and obtained b
0
¼ ꢀ7:1 ꢃ
5 5)
ꢀ3
3
ꢀ3
concentration fluctuations, which broaden a magnetic tran- 10 T/(ꢀ
sition in the vicinity of ferromagnetic instability.
B
/Co) and c0 ¼ 8:3 ꢃ 10 T/(ꢀB/Co) . We
determined TM ¼ 160 K to reproduce the observed TC in
024701-3

J. Phys. Soc. Jpn., Vol. 79, No. 2
O. SADAKUNI et al.
x=0 1.2GPa
1
1
20
00
80
60
x=0
x=0.05 0GPa
x=0.05 0.9G
x=0.08 0GPa
x=0.08 0.6GPa
x=0.08 0.9GPa
x=0.05
x=0.08
theory
7
μ0H=0-2T
6
5
4
3
2
1
0
0
0
0
0
0
0
.1815
.183
.184
.185
.186
.187
4
2
0
0
0
0
1
2
3
4
5
6
P(GPa)
0
50
100
150
Fig. 5. A universal plot of pressure dependence of TC of Co(S1ꢀxSex)2.
The experimental data (circles) are plotted by assuming that 1% Se
substitution corresponds to a pressure of 0.48 GPa. The calculated results
Temperature(K)
(
solid line) are shown by assuming a linear relation between P and
2
Fig. 4. The calculated ꢀSM–T curves (lines) from eqs. (3)–(10) on
the basis of the theory of itinerant electron metamagnetism with
a0c0=b0 (see text).
2
0:1815 ꢁ a0c0=b0 ꢁ 0:187. The selected experimental data are also
shown by symbols with lines.
2
as, P [GPa] = 594:5 ꢃ a0c0=b0 ꢀ 105:9. The Curie temper-
ature decreases sharply with pressure near the critical
Co(S1 Se ) . This value of T is twice as large as that pressure for disappearance of ferromagnetism. The calcu-
ꢀx
x 2
M
reported by Goto et al., who estimated TM from the lated results account for nonlinear pressure dependence of
temperature, where the susceptibility shows a maximum, TC in the vicinity of ferromagnetic instability. The large
5)
for the compounds with 0:10 ꢁ x ꢁ 0:30. The theory of @TC=@P values near the critical pressure can be understood
IEM predicts a susceptibility maximum at TM. However, from the Clausius–Clapeyron relation for a first-order
the susceptibility above TC decreases monotonically with transition system:
increasing temperature, following the Curie–Weiss law
for 0 ꢁ x < 0:10. The discrepancy may come from the
@
TC
ꢀV
¼ ꢀS
;
ð11Þ
2
2
@P
assumption that ꢁ ðTÞ is proportional to T in the theory.
T
2
This is a low temperature approximation and ꢁ ðTÞ is where ꢀV is the volume change and ꢀS is the entropy
T
expected to be a linear function of T, as temperature change at TC. The value of ꢀS is approximated by the peak
is increased. To explain the paramagnetic susceptibility, value of ꢀSM, which decreases as TC goes to zero. The
further development of the theory of itinerant electron origin of ꢀV is a magnetovolume effect. In Co(S1ꢀxSex)2,
magnetism is necessary.
the spontaneous magnetization at 0 K is almost independent
Using these parameters, the calculations have been done in the ferromagnetic region, while the magnetization jump
2
for 0:1815 ꢁ a0c0=b0 ꢁ 0:187. The results are illustrated in at TC is increased with decreasing TC. Since the sponta-
2
Fig. 4, together with the selected experimental data. It is neous volume magnetostriction is proportional to MðTÞ ,
found that the calculated results reproduce the experimental ꢀV is expected to increase, as TC is lowered. Early
data quite well. The calculated peak values of jꢀS j are measurements of the temperature dependence of the lattice
M
11)
in agreement with the observed values and they have a parameter support this discussion. As a result, @TC=@P
maximum at around TC ¼ 80 K. The area of a ꢀSM–T curve becomes large near the critical pressure for magnetic
2
is 67 J/kg, which is independent of a0c0=b0 . This means instability.
that the peak width is narrower, as the peak height is
In conclusion, we have measured the pressure depend-
increased. These results are consistent with the observations. ence of MCE of Co(S1ꢀxSex)2. It was found that the
Finally, we discuss the pressure dependence of T . It Co(S1ꢀxSex)2 shows a variety of pressure effects of ꢀSM
C
has been reported that the T–P magnetic phase diagram of depending upon x. The peak value of jꢀSMj of x ¼ 0
CoS is quite similar to the T–x diagram of Co(S Se ) , increases with pressure, while that for x ¼ 0:05 is not
2
1ꢀx
x 2
although the substitution of Se for S increases the lattice sensitive to pressure. For x ¼ 0:08, the peak value is
parameter. According to electronic structure calculations, decreased by pressure. The ꢀSM–T curves are calculated
10)
the 3d eg band of CoSe2 is wider than that of CoS2. This on the basis of the spin fluctuation theory of IEM.
fact suggests that the Se substitution makes the bandwidth Satisfactory agreement between the calculated results and
wider, similarly to applying pressure. Assuming that 1% Se the experimental ones was obtained. We obtained a
substitution corresponds to a pressure of 0.48 GPa, which universal plot of pressure dependence of TC of Co(S1ꢀxSex)2
5
)
is close to the value estimated by Goto et al., 0.51 GPa,
by assuming a linear relation between P and x. Strong
we have a universal plot of pressure dependence of TC pressure dependence of TC was observed in the vicinity of
of Co(S1ꢀxSex)2, as depicted in Fig. 5. In the figure, the magnetic instability from both experiments and theoretical
calculated values of TC from the theory of IEM are also calculations, which is understandable from the thermody-
2
plotted by assuming a linear relation between P and a0c0=b0
namical point of view.
024701-4

J. Phys. Soc. Jpn., Vol. 79, No. 2
O. SADAKUNI et al.
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Acknowledgment
This work was partially supported by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Culture,
Sports, Science and Technology of Japan, New Energy and
Industrial Technology Development Organization (NEDO),
and The Asahi Glass Foundation.
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