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Effect of pressure on the magnetic properties of Kondo materials
ELSEVIER
Physica B 216 [1996) 319 322
Effect of pressure on the magnetic properties of Kondo materials Gendo Oomi ~'*, Yasuhiro Sakura?, Takeshi SakaP, Tomoko Kagayama ", Yoshiya Homma b, Kenji Sumiyama b, Kenji Suzuki b ~Department o[ Pt~vsics, FaculO' 01General Education, Kumamoto Universi~,, 40-1, Kurokami 2-ch6me, Kumamoto 860, Japan blnstitute [or Materials Research, Tohoku University, Sendal, M(vagi 980-77, Japan
Abstract The magnetoresistance or magnetostriction of ~t-Ce, CeA13 and amorphous CessRu,~z alloy (a-CeRu) has been measured at high pressure up to 2 GPa. The results show that the Kondo temperature T~ is increased by an application of pressure for ~t-Ce and CeAI~, while the behavior is opposite for a-CeRu.
1. Introduction Heavy fermions (H F) are characterized by a huge electronic specific heat coefficient ;' of the order of 1J/molK 2. The magnetostriction (MS) and magnetoresistance (MR) of HF are also anomalously large at low temperatures [1, 2]. These facts indicate that the electronic properties of HE are strongly dependent on the external forces such as temperature, pressure and magnetic field. The Kondo temperature TK of HF has been reported to be changed largely by the external forces [3]. Thus, the investigation of HF at high pressure and magnetic field is expected to give us useful information to clarify the anomalous electronic structure of HF. In the present work we report the measurement of MR or MS at high pressure for three Kondo materials having different TK, at-Ce, CeAI 3 and amorphous CessRu42 (a-CeRu) alloy. The characteristics of these specimens are (1) at-Ce is in an intermediate valence state having TK of several hundreds Kelvin [4], (2) CeAI3 is HF compound
* Corresponding author.
and its TK is about 5 K [5] and (3) a-CeRu may be a HF compound with TK ~-- 37 K [6]. The amorphous HF is expected to show different behavior against pressure from the usual crystalline HF [7]. The results will be discussed in connection with the pressure (or volume) dependence of TK.
2. Experimental The polycrystalline CeAI3 sample was prepared by arc melting weighed amounts of the constituent elements in an argon atmosphere and annealing at 900°C for 10 days, The a-CeRu alloy was prepared by a sputtering method and its thickness was about 200 I~m [6]. Electrical resistivity was measured by using DC four probe method. Thermal expansion and MS were measured by means of strain gauge. Hydrostatic pressure was generated with piston-cylinder device up to 2.0 GPa using Fluorinert as a pressure transmitting medium [8]. The pressure was changed only at room temperature to minimize a strain in the specimen and the load was
0921-4526'96S15.(X) ~ 1996 F'lsexicr Science B.V. All rights rcservcd
320
G. Oomi et al. Phvsica B 216 (1996) 319 322
controlled within + 1% throughout the measurement. The magnetic field up to 5 T was obtained by using a superconducting magnet.
3.2. The thermal expansion and the magnetostriction of CeA 1
3. R e s u l t s a n d d i s c u s s i o n
3.1. The magnetore~'istance ol zt-Ce at high pressure Fig. 1 shows the MR, A p t ) = [p(H) p(O)]/p(O), of~-Ce at 4.2 K as a function of magnetic field under high pressure. The Ap/p increases quadratically against magnetic field H (T) reflecting the coherent state at low temperature. The value of Ap~p increases with increasing pressure, suggesting that the coherence is stabilized at high pressure. This result is consistent with the previous one for CelnCu2 [9]. The coefficient A in Ap< t) = AH 2 is plotted as a function of pressure in Fig. 2. The A increases rapidly at low pressures and tends to saturate at higher pressure above 1 GPa. According to the theory of Kawakami and Okiji [10], A becomes positive and increases with decreasing T~ TK below TK. We reported previously [11] that the coefficient of the TZ-term in the low-temperature p(T/ curve decreases with increasing pressure but saturates above ca. 1 GPa. The result indicates the decrease of the electronic density of states N0:v) at Fermi level or the effective mass m* of conduction electron. Considering the relation N(;:v) ~ TK ~ [12], Ti~ is enhanced by applying
F.
0.2
.
.
.
pressure. Thus, the result in Fig. 2 is explained qualitatively by the above theoretical model.
.
~
T = 4.2K
The thermal expansion AI/I was measured at various pressures and its coefficient c~- d l n l / d T was obtained by differentiating A1/l with respect to temperature for H F compound CeAI3. Similar experiment was carried out for isostructural c o m p o u n d LaAI3 at ambient pressure as a reference since La has no 4f-electron. Fig. 3 shows a plot of ~/T as a function of T 2 below 40 K. ct/T of LaA13 indicates an approximately linear dependence against T 2, which is c o m m o n in non-magnetic normal metal. At low temperature, ~/T of CeA13 increases largely with decreasing temperature, analogous to an enhancement of C / T (C is a heat capacity) which corresponds to the huge value of ?. Taking a Griineisen relation into account, large value of ~/T at low temperature suggests a large enhancement in the N(ev) or the m*. The value of ~/T is decreased by applying pressure. The extrapolated value of ~t/T to 0 K, a, which is related to Ni);Fk is plotted as a function of pressure in the inset of Fig. 3. The a decreases with increasing pressure at a rate of Olna/~P = 0 . 4 G P a ~. The compressibility of CeAI3 is about 0 . 0 2 G P a a [13]. Thus, a 1% compression of volume results in a 20% decrease in the magnitude of a. It means that the N(ev) or m* decreases strongly with the decrease of volume. This indicates that the application of pressure enhances strongly the K o n d o temperature TK.
~
H~-,I 2.O(iPa
1 ()(]Pa
~
xl() -~ 15
o~>°°
...
T = 4.2K HZJ
10
0. I
,.y-\'\ ~
?e
J
o2L..,< /
5
/
/
~/
J
/0
"0 0
L
1
2
3
4
-
H(Tt
Fig. 1. The transverscmagncloresistanceof~-Ce at4.2 K under various pressures
0
. . . .
I
i
1
i
i
i
I
2
P(GPa) Fig. 2. The coeffcient A (T 2) in Ap/p = AH 2 for a-Ce as a function of pressure.
G. Oomi et al. Phvsica B 216 (1996) 319 322 xl[] -3
T(K)
o 1()
20
321
3
40
3[I
[a-CessRu42 I
/j" d~ d'
1.0 ?
H-J iN %..(.2Ge~
o.o
Se/
:D_
..~Grtrg:XT(rrR-f ~W,~-Cf-~-gi U,6-¢-,g ~ - , ~ ~ K~7)C0 0 0 0 Q0 0 Q 0 0 Q o o ~
0
~
50(1
.~
., 1000
.y
ul-' :
150t)
~(K ~)
~
Fig. 3. ~,,'T of CeAI~ plotted as a function of T2 al various pressures, where :~ is the thermal expansion coefficient. The inset shows pressure dependence of the extrapolated value of :~ 7" toOK.
r
2
~ ' e
0
"2.0 GPa
t
1
2
3
4
5
H(T) Fig 5. Transverse magnetoresistance Ap/p at 4.2K for amorphous CessRu42 alloy at various pressures. The solid lines are a guide to the eye.
x l 0 -4 i
0
,
y
i
0.5 G P
T = 4.2K
10
/ zx--
i
i
c~)°p O/ 5Tz~ g]- 1.0 GPa
v.s,~v"
.P" Qq-l~-z'a~-c'P£~/
0
EV
©--,
T = 4.2K HZJ
.'7/";7/1.5. G P a
I
i
,
I
1
2
3
4
H(T) Fig. 4. The magnetostriction of CeAI3 perpendicular to H. as a function of H at 4.2 K under high pressure.
2
,
Next we will show the result of the MS m e a s u r e m e n t at high pressures. Fig. 4 indicates the transverse MS subtracted by that at 2 GPa:
).±(P, H) =
A/
T
(P, H)
Al = - ( P = 2 G P a . HI. l
(1)
2± increases smoothly with increasing H up to 5 T. The positive MS implies that the m a g n e t i z a t i o n M decreases with pressure from the Maxwell relation, ~ M / ~ P = OV/SH. ).± decreases with increasing pressure. T a k i n g account of the fact that the MS is approximately proportional to M 2, the decrease of the M S c o r r e s p o n d s to the decrease of M. Since the magnetic susceptibility Z is -
1
0
1 P(GPa)
2
Fig. 6. The value of A,o/p at 4 T as a function of pressure for
amorphous Ces~Ru42 alloy'. roughly p r o p o r t i o n a l to the NO:v), the decrease of M indicates the decrease of N(~:v), i.e., the e n h a n c e m e n t of the T~:. 3.3. The magnetoresistance o f the amorphous ('e~,Ru~: alloy (a-CeRu) Fig. 5 shows the MR of a - C e R u at various pressures. The A p / p increases a p p r o x i m a t e l y linearly against magnetic field. This indicates that a-CeRu is in the coherent state as was reported previously [6]. The m a g n i t u d e of
322
G. Oorni et aL Physica B 216 (1996) 319 322
the MR decreases with increasing pressure. To examine this behavior more clearly, the value of A p / p at 4 T is plotted as a function of pressure in Fig. 6. This negative pressure dependence of MR is opposite to those for other crystalline H F compounds, in which Tk increases with pressure. It is reported [14] that the coefficient of log T term in the p ( T ) curve of a-CeRu is decreased by applying pressure, which implies that TK decreases at high pressure. The behavior of a-CeRu at high pressure is different from that of crystalline HF. The origins for such a difference are an open question at present. More systematic investigations are needed to settle this point.
4. Conclusion
The thermal expansion coefficient and MS of CeAI~ decreases with increasing pressure, which indicates the large enhancement of the TK at high pressure. The increase of the positive MR of ~-Ce at high pressure is interpreted by considering the increase of the TK. On the other hand, the MR of a-CeRu behaves as if the TK is decreased by pressure. It is suggested that the disorder in the atomic site or particularly in the localized 4f electrons plays an important role to determine the electronic structure of H F compounds at low temperature [7].
References
[1] J. Zieglowski, H.U. HMner and D. Wohlleben, Phys. Rev. Len. 56 (1986) 193. [2] A. Sumiyama, Y. Oda, H. Nagano, Y. Onuki, K. Shibutani and T. Komatsubara, J. Phys. Soc. Japan 55 (1986) 1294. [3] T. Kagayama, G. Oomi, H. Takahashi, N. M6ri, Y. Onuki and T. Komatsubara, Phys. Rev. B 44 (1991) 7690. [4] J.W. Allen and R.M. Martin, Phys. Rev. Lett. 49 (1982) 1106. [5] K. Andres, J.E. Graebner and H.R. Ott, Phys. Rev. Lett. 35 (1975) 1779. [6] Y. Homma, K. Sumiyama, H. Yamauchi and K. Suzuki, J. Phys. Soc. Japan 62 (1993) 1442. [7] T. Kagayama, G. Oomi, H. Amano, K. Sumiyama and K. Suzuki, J. Alloys Compounds 207 & 208 (1994) 267. [8] G. Oomi, T. Kagayama and Y. Uwatoko, Japan J. Appl. Phys. 32 (1993) 349. [9] T. Kagayama, G. Oomi, R. Yagi, Y. lye, Y. Onuki and T. Komatsubara, J. Phys. Soc. Japan 61 (1992) 2632. [10] N. Kawakami and A. Okiji, J. Phys. Soc. Japan 55 (1986) 2114. [11] G. Oomi, J. Phys. Soc. Japan 49 (1980) 256. [12] F.J. Ohkawa, J. Phys. Soc. Japan 53 (1984) 3577. [13] T. Kagayama and G. Oomi, J. Magn. Magn. Mater. 140 144 (1995) 1227. [14] T. Sakai, T. Kagayama, G. Oomi, K. Sumiyama, Y. Homma and K. Suzuki, to be submitted.
Physica B 216 [1996) 319 322
Effect of pressure on the magnetic properties of Kondo materials Gendo Oomi ~'*, Yasuhiro Sakura?, Takeshi SakaP, Tomoko Kagayama ", Yoshiya Homma b, Kenji Sumiyama b, Kenji Suzuki b ~Department o[ Pt~vsics, FaculO' 01General Education, Kumamoto Universi~,, 40-1, Kurokami 2-ch6me, Kumamoto 860, Japan blnstitute [or Materials Research, Tohoku University, Sendal, M(vagi 980-77, Japan
Abstract The magnetoresistance or magnetostriction of ~t-Ce, CeA13 and amorphous CessRu,~z alloy (a-CeRu) has been measured at high pressure up to 2 GPa. The results show that the Kondo temperature T~ is increased by an application of pressure for ~t-Ce and CeAI~, while the behavior is opposite for a-CeRu.
1. Introduction Heavy fermions (H F) are characterized by a huge electronic specific heat coefficient ;' of the order of 1J/molK 2. The magnetostriction (MS) and magnetoresistance (MR) of HF are also anomalously large at low temperatures [1, 2]. These facts indicate that the electronic properties of HE are strongly dependent on the external forces such as temperature, pressure and magnetic field. The Kondo temperature TK of HF has been reported to be changed largely by the external forces [3]. Thus, the investigation of HF at high pressure and magnetic field is expected to give us useful information to clarify the anomalous electronic structure of HF. In the present work we report the measurement of MR or MS at high pressure for three Kondo materials having different TK, at-Ce, CeAI 3 and amorphous CessRu42 (a-CeRu) alloy. The characteristics of these specimens are (1) at-Ce is in an intermediate valence state having TK of several hundreds Kelvin [4], (2) CeAI3 is HF compound
* Corresponding author.
and its TK is about 5 K [5] and (3) a-CeRu may be a HF compound with TK ~-- 37 K [6]. The amorphous HF is expected to show different behavior against pressure from the usual crystalline HF [7]. The results will be discussed in connection with the pressure (or volume) dependence of TK.
2. Experimental The polycrystalline CeAI3 sample was prepared by arc melting weighed amounts of the constituent elements in an argon atmosphere and annealing at 900°C for 10 days, The a-CeRu alloy was prepared by a sputtering method and its thickness was about 200 I~m [6]. Electrical resistivity was measured by using DC four probe method. Thermal expansion and MS were measured by means of strain gauge. Hydrostatic pressure was generated with piston-cylinder device up to 2.0 GPa using Fluorinert as a pressure transmitting medium [8]. The pressure was changed only at room temperature to minimize a strain in the specimen and the load was
0921-4526'96S15.(X) ~ 1996 F'lsexicr Science B.V. All rights rcservcd
320
G. Oomi et al. Phvsica B 216 (1996) 319 322
controlled within + 1% throughout the measurement. The magnetic field up to 5 T was obtained by using a superconducting magnet.
3.2. The thermal expansion and the magnetostriction of CeA 1
3. R e s u l t s a n d d i s c u s s i o n
3.1. The magnetore~'istance ol zt-Ce at high pressure Fig. 1 shows the MR, A p t ) = [p(H) p(O)]/p(O), of~-Ce at 4.2 K as a function of magnetic field under high pressure. The Ap/p increases quadratically against magnetic field H (T) reflecting the coherent state at low temperature. The value of Ap~p increases with increasing pressure, suggesting that the coherence is stabilized at high pressure. This result is consistent with the previous one for CelnCu2 [9]. The coefficient A in Ap< t) = AH 2 is plotted as a function of pressure in Fig. 2. The A increases rapidly at low pressures and tends to saturate at higher pressure above 1 GPa. According to the theory of Kawakami and Okiji [10], A becomes positive and increases with decreasing T~ TK below TK. We reported previously [11] that the coefficient of the TZ-term in the low-temperature p(T/ curve decreases with increasing pressure but saturates above ca. 1 GPa. The result indicates the decrease of the electronic density of states N0:v) at Fermi level or the effective mass m* of conduction electron. Considering the relation N(;:v) ~ TK ~ [12], Ti~ is enhanced by applying
F.
0.2
.
.
.
pressure. Thus, the result in Fig. 2 is explained qualitatively by the above theoretical model.
.
~
T = 4.2K
The thermal expansion AI/I was measured at various pressures and its coefficient c~- d l n l / d T was obtained by differentiating A1/l with respect to temperature for H F compound CeAI3. Similar experiment was carried out for isostructural c o m p o u n d LaAI3 at ambient pressure as a reference since La has no 4f-electron. Fig. 3 shows a plot of ~/T as a function of T 2 below 40 K. ct/T of LaA13 indicates an approximately linear dependence against T 2, which is c o m m o n in non-magnetic normal metal. At low temperature, ~/T of CeA13 increases largely with decreasing temperature, analogous to an enhancement of C / T (C is a heat capacity) which corresponds to the huge value of ?. Taking a Griineisen relation into account, large value of ~/T at low temperature suggests a large enhancement in the N(ev) or the m*. The value of ~/T is decreased by applying pressure. The extrapolated value of ~t/T to 0 K, a, which is related to Ni);Fk is plotted as a function of pressure in the inset of Fig. 3. The a decreases with increasing pressure at a rate of Olna/~P = 0 . 4 G P a ~. The compressibility of CeAI3 is about 0 . 0 2 G P a a [13]. Thus, a 1% compression of volume results in a 20% decrease in the magnitude of a. It means that the N(ev) or m* decreases strongly with the decrease of volume. This indicates that the application of pressure enhances strongly the K o n d o temperature TK.
~
H~-,I 2.O(iPa
1 ()(]Pa
~
xl() -~ 15
o~>°°
...
T = 4.2K HZJ
10
0. I
,.y-\'\ ~
?e
J
o2L..,< /
5
/
/
~/
J
/0
"0 0
L
1
2
3
4
-
H(Tt
Fig. 1. The transverscmagncloresistanceof~-Ce at4.2 K under various pressures
0
. . . .
I
i
1
i
i
i
I
2
P(GPa) Fig. 2. The coeffcient A (T 2) in Ap/p = AH 2 for a-Ce as a function of pressure.
G. Oomi et al. Phvsica B 216 (1996) 319 322 xl[] -3
T(K)
o 1()
20
321
3
40
3[I
[a-CessRu42 I
/j" d~ d'
1.0 ?
H-J iN %..(.2Ge~
o.o
Se/
:D_
..~Grtrg:XT(rrR-f ~W,~-Cf-~-gi U,6-¢-,g ~ - , ~ ~ K~7)C0 0 0 0 Q0 0 Q 0 0 Q o o ~
0
~
50(1
.~
., 1000
.y
ul-' :
150t)
~(K ~)
~
Fig. 3. ~,,'T of CeAI~ plotted as a function of T2 al various pressures, where :~ is the thermal expansion coefficient. The inset shows pressure dependence of the extrapolated value of :~ 7" toOK.
r
2
~ ' e
0
"2.0 GPa
t
1
2
3
4
5
H(T) Fig 5. Transverse magnetoresistance Ap/p at 4.2K for amorphous CessRu42 alloy at various pressures. The solid lines are a guide to the eye.
x l 0 -4 i
0
,
y
i
0.5 G P
T = 4.2K
10
/ zx--
i
i
c~)°p O/ 5Tz~ g]- 1.0 GPa
v.s,~v"
.P" Qq-l~-z'a~-c'P£~/
0
EV
©--,
T = 4.2K HZJ
.'7/";7/1.5. G P a
I
i
,
I
1
2
3
4
H(T) Fig. 4. The magnetostriction of CeAI3 perpendicular to H. as a function of H at 4.2 K under high pressure.
2
,
Next we will show the result of the MS m e a s u r e m e n t at high pressures. Fig. 4 indicates the transverse MS subtracted by that at 2 GPa:
).±(P, H) =
A/
T
(P, H)
Al = - ( P = 2 G P a . HI. l
(1)
2± increases smoothly with increasing H up to 5 T. The positive MS implies that the m a g n e t i z a t i o n M decreases with pressure from the Maxwell relation, ~ M / ~ P = OV/SH. ).± decreases with increasing pressure. T a k i n g account of the fact that the MS is approximately proportional to M 2, the decrease of the M S c o r r e s p o n d s to the decrease of M. Since the magnetic susceptibility Z is -
1
0
1 P(GPa)
2
Fig. 6. The value of A,o/p at 4 T as a function of pressure for
amorphous Ces~Ru42 alloy'. roughly p r o p o r t i o n a l to the NO:v), the decrease of M indicates the decrease of N(~:v), i.e., the e n h a n c e m e n t of the T~:. 3.3. The magnetoresistance o f the amorphous ('e~,Ru~: alloy (a-CeRu) Fig. 5 shows the MR of a - C e R u at various pressures. The A p / p increases a p p r o x i m a t e l y linearly against magnetic field. This indicates that a-CeRu is in the coherent state as was reported previously [6]. The m a g n i t u d e of
322
G. Oorni et aL Physica B 216 (1996) 319 322
the MR decreases with increasing pressure. To examine this behavior more clearly, the value of A p / p at 4 T is plotted as a function of pressure in Fig. 6. This negative pressure dependence of MR is opposite to those for other crystalline H F compounds, in which Tk increases with pressure. It is reported [14] that the coefficient of log T term in the p ( T ) curve of a-CeRu is decreased by applying pressure, which implies that TK decreases at high pressure. The behavior of a-CeRu at high pressure is different from that of crystalline HF. The origins for such a difference are an open question at present. More systematic investigations are needed to settle this point.
4. Conclusion
The thermal expansion coefficient and MS of CeAI~ decreases with increasing pressure, which indicates the large enhancement of the TK at high pressure. The increase of the positive MR of ~-Ce at high pressure is interpreted by considering the increase of the TK. On the other hand, the MR of a-CeRu behaves as if the TK is decreased by pressure. It is suggested that the disorder in the atomic site or particularly in the localized 4f electrons plays an important role to determine the electronic structure of H F compounds at low temperature [7].
References
[1] J. Zieglowski, H.U. HMner and D. Wohlleben, Phys. Rev. Len. 56 (1986) 193. [2] A. Sumiyama, Y. Oda, H. Nagano, Y. Onuki, K. Shibutani and T. Komatsubara, J. Phys. Soc. Japan 55 (1986) 1294. [3] T. Kagayama, G. Oomi, H. Takahashi, N. M6ri, Y. Onuki and T. Komatsubara, Phys. Rev. B 44 (1991) 7690. [4] J.W. Allen and R.M. Martin, Phys. Rev. Lett. 49 (1982) 1106. [5] K. Andres, J.E. Graebner and H.R. Ott, Phys. Rev. Lett. 35 (1975) 1779. [6] Y. Homma, K. Sumiyama, H. Yamauchi and K. Suzuki, J. Phys. Soc. Japan 62 (1993) 1442. [7] T. Kagayama, G. Oomi, H. Amano, K. Sumiyama and K. Suzuki, J. Alloys Compounds 207 & 208 (1994) 267. [8] G. Oomi, T. Kagayama and Y. Uwatoko, Japan J. Appl. Phys. 32 (1993) 349. [9] T. Kagayama, G. Oomi, R. Yagi, Y. lye, Y. Onuki and T. Komatsubara, J. Phys. Soc. Japan 61 (1992) 2632. [10] N. Kawakami and A. Okiji, J. Phys. Soc. Japan 55 (1986) 2114. [11] G. Oomi, J. Phys. Soc. Japan 49 (1980) 256. [12] F.J. Ohkawa, J. Phys. Soc. Japan 53 (1984) 3577. [13] T. Kagayama and G. Oomi, J. Magn. Magn. Mater. 140 144 (1995) 1227. [14] T. Sakai, T. Kagayama, G. Oomi, K. Sumiyama, Y. Homma and K. Suzuki, to be submitted.