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Anisotropic thermal expansion coefficient of the Kondo compound CeCu2
485
Journal of Magnetism 'and Magnetic Materials 90 & 91 (1990) 485-486 North-Holland
Anisotropic thermal expansion coefficient of the Kondo compound CeCu 2 Y. Uwatoko, H. Okita, G. Oomi, I. Umehara
a
and Y. Onuki
a
Department of Physics, Faculty of General Education, Kumamoto University, Kumamoto 860, Japan Institute of Materials Science, The Unicersity of Tsukuba, Ibaraki 305, Japan
a
The thermal expansion of single crystalline CeCu 2 has been measured by using strain gauge method in the temperature range from 4.2 to 300 K. The influences of Kondo effect and crystal electric field splitting on the thermal expansion coefficient are discussed.
CeCu2 crystallizes in the orthorhombic structure with space group D;~(lmma) and exhibits antiferromagnetism below TN = 3.0 K[I]. Recently Onuki et al. [1] measured the electrical resistivity, specific heat, magnetoresistance, magnetic susceptibility and magnetization of the CeCu2 single crystal. They revealed that CeCu2 should be characterized as a dense Kondo compound having the Kondo temperature T K = 6 K and the specific heat coefficient C/T= 180 mJ mol- 1 K- 2 at 10 K. It is well known that the crystal electric field (CEF) splitting and the Kondo effect have a large effect on the thermal expansion coefficient of dense Kondo compounds [2]. In this work, we made an attempt to clarify these effects on the thermal expansion coefficients of single crystalline CeCu2' The details of the sample preparation of single crystals and their characterization have been described in ref. [1]. The thermal expansion, M/I was measured by means of the strain gauge method. The strain gauge (Kyowa Dengyo, KFL 02-C 1-Il, gauge factor 2.03) was glued to a clean surface of the specimen in the direction parallel to each crystal axis (a, b or c-axis). 5N copper was used as reference material. \Ve observed a difference in the length change between sample and copper, B(M/l) = (M/l)sample - (M/l)copper' In order to get the linear thermal expansion coefficient a(K- 1 ) , differentiated the values of B(M/I) by T and then obtained Ba, where Ba = asample - acopper' Thus the values of asample were obtained by knowing acoppep whose values published by White and Collins [3] were used in the present work. In fig. I, the temperature dependence of linear thermal expansion coefficients, aa' ab and a c above TN is shown. The a- T curves are found to be largely different among the three crystal axes. Above 20 K, ab shows a large increase with increasing temperature until it reaches a broad maximum centered near 120 K having a large value, about 70 X 10- 6 K- 1• On the other hand, 0304-8853/90/S03.50
«')
a c increases rapidly with increasing temperature up to about 70 K and then the increasing rate becomes small. However, aa( < 0) decreases with increasing temperature until it reaches a minimum centered near 120 K. Fig. 2 shows the values of av for CeCu2 as a function of temperature, where av is defined as av = ('aa + ab + a c )/3. For comparison, the av for polycrystalline YCU2 [4] is also shown. av of CeCu2 has a maximum around 120 K. At low temperature, av has a shoulder around 15 K. Electrical resistivity [1] also has a minimum around 15 K. Since the thermal expansion coefficient of YCU2 have no such minimum [4] in the av-T curve, this shoulder of av at low temperature may be attributed to the large enhancement of the effective mass of f electrons as wiII be shown later. The broad maximum at high temperature near 120 K is
80
CeCuz b-oxls
60
':.::
--
40
x
20
CD
a
e
a
c-axis
J
-20
o
100
200
300
T(K) Fig. 1. Temperature dependence of the linear thermal expansion coefficients, a, = (//li)(dIJdT), along a, band c-axis in CeCu2, where i= a, b or c.
1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation
486
Y. Uwatoko et al. / Thermal expansion coefficient of CeCu z
0.3 0 0
.
20
0
CeCuz
:.c
0
~
0
N
~
z: 0.2
"'-' to
~
0
0
0
0
~ >< >
10
1:1
j
X
/
I-
ceCuz
o
"3:~
0.1
VCuz
--- --YCuz
0
100
200
300
T( K) Fig. 2. Calculated thermal variations of expansion coefficient defined as etv = (eta + etb + et c )/ 3 of CeCu2 and YCU2 [4].
associated with the combined effect of the CEF splitting of Ce 3 +-ion. The thermal expansion coefficient av can be expressed approximately by the following equation [3], av=AT +BT3 ,
(1)
where the first term is an electronic and magnetic contribution, and the second term is a lattice contribution. We neglected higher order term. Now we can rewrite eq. (1) in the following form, av(T) _ A
T
-
+ BT 2
(2)
The usual approach to obtain the values of A and B is to plot av/T against T 2 , which is shown in fig. 3. A is obtained from the intercept at T= 0 and B from the linear slope of the plot near T = O. From fig. 3 we find the value of A = 6 X 10- 8 K -2, which is smaller than that of the non-magnetic heavy fermion compound CeCu6' 1.6 X 10- 7 K- 2 [2]. This result suggests that the enhancement in the magnitude of av/T is closely related to the physical properties of heavy fermion as is mentioned in the following. The thermal expansion coefficient and the specific heat are related each other by the so called Gruneisen relation, which is described as ay(T)
=
3Vr(T)kC(T),
(3)
where reT) is the Grimeisen parameter, k the compressibility [5]. Assuming that k is weakly temperature
o
-----
--... -----5
10
15
20
----25
T(K) Fig. 3. Values of etv/T as a function of T 2 for single crystalline CeCu 2 and YCu 2' The broken line indicates an extrapolation of etv/T from the high temperature part (T> 18 K) toOK.
dependent and reT) is nearly constant [5], av(T) is approximately propotional to C(T). Thus a large enhancement in the magnitude of av/T at low temperature (T < 19 K) in fig. 3 is found to corre spond to the enh ancement of heat capacity C(T)/T[I]. In conclusion, we obtained two typical characteristics in the present thermal expansion measurements: (1) a broad maximum at 120 K due to the crystal field effect and . Kondo effect and (2) the enhancement of av/T at low temperature due to the large mass enhancement of the 4f electrons of CeCu2 ' In order to clarify the detailed behaviour of low temperature range in this system, the thermal expansion measurements on single crystalline YCU2 are now in progress . References [1] Y. Onuki , Y. Machii, Y. Shimizu, T. Komatsubara and T. Fujita, J. Phys. Soc. Jpn. 54 (1985) 3562. E. Gratz, E. Bauer, B. Barbara, S. Zemirli, F. Steglich, C.D. Bredl and W. Lieke, J. Phys. F 15 (1985) 1975. [Z] G. Oomi, Y. Onuki and T. Komatsubara, J. Phys. Soc. Jpn. 59 (1990) 803. [3] G.K. While and J.G. Collins, J. Low Temp . Phys. 7 (1972) 43. (4) N.H. Luon g, JJ.M. Franse and T.D . Hien, J. Phys. F 15 (1985) 1751. [5] M. Yoshizawa , B. LUthi and K.D. Schotte, Z. Phys. B 64 (1986) 169.
Journal of Magnetism 'and Magnetic Materials 90 & 91 (1990) 485-486 North-Holland
Anisotropic thermal expansion coefficient of the Kondo compound CeCu 2 Y. Uwatoko, H. Okita, G. Oomi, I. Umehara
a
and Y. Onuki
a
Department of Physics, Faculty of General Education, Kumamoto University, Kumamoto 860, Japan Institute of Materials Science, The Unicersity of Tsukuba, Ibaraki 305, Japan
a
The thermal expansion of single crystalline CeCu 2 has been measured by using strain gauge method in the temperature range from 4.2 to 300 K. The influences of Kondo effect and crystal electric field splitting on the thermal expansion coefficient are discussed.
CeCu2 crystallizes in the orthorhombic structure with space group D;~(lmma) and exhibits antiferromagnetism below TN = 3.0 K[I]. Recently Onuki et al. [1] measured the electrical resistivity, specific heat, magnetoresistance, magnetic susceptibility and magnetization of the CeCu2 single crystal. They revealed that CeCu2 should be characterized as a dense Kondo compound having the Kondo temperature T K = 6 K and the specific heat coefficient C/T= 180 mJ mol- 1 K- 2 at 10 K. It is well known that the crystal electric field (CEF) splitting and the Kondo effect have a large effect on the thermal expansion coefficient of dense Kondo compounds [2]. In this work, we made an attempt to clarify these effects on the thermal expansion coefficients of single crystalline CeCu2' The details of the sample preparation of single crystals and their characterization have been described in ref. [1]. The thermal expansion, M/I was measured by means of the strain gauge method. The strain gauge (Kyowa Dengyo, KFL 02-C 1-Il, gauge factor 2.03) was glued to a clean surface of the specimen in the direction parallel to each crystal axis (a, b or c-axis). 5N copper was used as reference material. \Ve observed a difference in the length change between sample and copper, B(M/l) = (M/l)sample - (M/l)copper' In order to get the linear thermal expansion coefficient a(K- 1 ) , differentiated the values of B(M/I) by T and then obtained Ba, where Ba = asample - acopper' Thus the values of asample were obtained by knowing acoppep whose values published by White and Collins [3] were used in the present work. In fig. I, the temperature dependence of linear thermal expansion coefficients, aa' ab and a c above TN is shown. The a- T curves are found to be largely different among the three crystal axes. Above 20 K, ab shows a large increase with increasing temperature until it reaches a broad maximum centered near 120 K having a large value, about 70 X 10- 6 K- 1• On the other hand, 0304-8853/90/S03.50
«')
a c increases rapidly with increasing temperature up to about 70 K and then the increasing rate becomes small. However, aa( < 0) decreases with increasing temperature until it reaches a minimum centered near 120 K. Fig. 2 shows the values of av for CeCu2 as a function of temperature, where av is defined as av = ('aa + ab + a c )/3. For comparison, the av for polycrystalline YCU2 [4] is also shown. av of CeCu2 has a maximum around 120 K. At low temperature, av has a shoulder around 15 K. Electrical resistivity [1] also has a minimum around 15 K. Since the thermal expansion coefficient of YCU2 have no such minimum [4] in the av-T curve, this shoulder of av at low temperature may be attributed to the large enhancement of the effective mass of f electrons as wiII be shown later. The broad maximum at high temperature near 120 K is
80
CeCuz b-oxls
60
':.::
--
40
x
20
CD
a
e
a
c-axis
J
-20
o
100
200
300
T(K) Fig. 1. Temperature dependence of the linear thermal expansion coefficients, a, = (//li)(dIJdT), along a, band c-axis in CeCu2, where i= a, b or c.
1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation
486
Y. Uwatoko et al. / Thermal expansion coefficient of CeCu z
0.3 0 0
.
20
0
CeCuz
:.c
0
~
0
N
~
z: 0.2
"'-' to
~
0
0
0
0
~ >< >
10
1:1
j
X
/
I-
ceCuz
o
"3:~
0.1
VCuz
--- --YCuz
0
100
200
300
T( K) Fig. 2. Calculated thermal variations of expansion coefficient defined as etv = (eta + etb + et c )/ 3 of CeCu2 and YCU2 [4].
associated with the combined effect of the CEF splitting of Ce 3 +-ion. The thermal expansion coefficient av can be expressed approximately by the following equation [3], av=AT +BT3 ,
(1)
where the first term is an electronic and magnetic contribution, and the second term is a lattice contribution. We neglected higher order term. Now we can rewrite eq. (1) in the following form, av(T) _ A
T
-
+ BT 2
(2)
The usual approach to obtain the values of A and B is to plot av/T against T 2 , which is shown in fig. 3. A is obtained from the intercept at T= 0 and B from the linear slope of the plot near T = O. From fig. 3 we find the value of A = 6 X 10- 8 K -2, which is smaller than that of the non-magnetic heavy fermion compound CeCu6' 1.6 X 10- 7 K- 2 [2]. This result suggests that the enhancement in the magnitude of av/T is closely related to the physical properties of heavy fermion as is mentioned in the following. The thermal expansion coefficient and the specific heat are related each other by the so called Gruneisen relation, which is described as ay(T)
=
3Vr(T)kC(T),
(3)
where reT) is the Grimeisen parameter, k the compressibility [5]. Assuming that k is weakly temperature
o
-----
--... -----5
10
15
20
----25
T(K) Fig. 3. Values of etv/T as a function of T 2 for single crystalline CeCu 2 and YCu 2' The broken line indicates an extrapolation of etv/T from the high temperature part (T> 18 K) toOK.
dependent and reT) is nearly constant [5], av(T) is approximately propotional to C(T). Thus a large enhancement in the magnitude of av/T at low temperature (T < 19 K) in fig. 3 is found to corre spond to the enh ancement of heat capacity C(T)/T[I]. In conclusion, we obtained two typical characteristics in the present thermal expansion measurements: (1) a broad maximum at 120 K due to the crystal field effect and . Kondo effect and (2) the enhancement of av/T at low temperature due to the large mass enhancement of the 4f electrons of CeCu2 ' In order to clarify the detailed behaviour of low temperature range in this system, the thermal expansion measurements on single crystalline YCU2 are now in progress . References [1] Y. Onuki , Y. Machii, Y. Shimizu, T. Komatsubara and T. Fujita, J. Phys. Soc. Jpn. 54 (1985) 3562. E. Gratz, E. Bauer, B. Barbara, S. Zemirli, F. Steglich, C.D. Bredl and W. Lieke, J. Phys. F 15 (1985) 1975. [Z] G. Oomi, Y. Onuki and T. Komatsubara, J. Phys. Soc. Jpn. 59 (1990) 803. [3] G.K. While and J.G. Collins, J. Low Temp . Phys. 7 (1972) 43. (4) N.H. Luon g, JJ.M. Franse and T.D . Hien, J. Phys. F 15 (1985) 1751. [5] M. Yoshizawa , B. LUthi and K.D. Schotte, Z. Phys. B 64 (1986) 169.