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Pressure dependence of the Hall effect in single crystals of CeNiSn
PHYSICAi Physica B 199&200 (1994) 440-442
ELSEVIER
Pressure dependence of the Hall effect in single crystals of CeNiSn T. Hiraoka "'*, E. Kinoshita a, T. Takabatake b, H. Tanaka b, H. Fujii b aFaculty q]"Science and Engineering, Saga University. Saga 840. Japan ~Faculty q["b~tegrated Arts and Sciences. Hiroshima University. Hiroshima 730, Japan
Abstract The pressure dependence of the Hall effect in single crystals of CeNiSn (JIIb, nlla; Jlla, HIIb; JIIb, HIIc) has been r,'easured. The Hall coefficient Rn decreases with pressure in the low-temperature range, indicating a decrease of gap energy under pressure due to the decrease of slope in the log p versus 1/T dependence. A crossover temperature is observed in the slope of this dependence.
1. Introduction
A study of these effects under pressure would yield useful knowledge and shed some light on these problems.
Recently Kondo semiconductors with gap states at low temperature, such as CeNiSn [1], CeRhSb [2] and Ce3Bi4Pt3 [3] have been found. These systems show marked changes in their transport properties, such as electrical resistivity and Hall effect, as the temperature is lowered. This behavior comes from gap opening at low temperatures. However, the gap energy varies markedly from 70 K in Ce3Bi4Pt,~ [3] to as low as about 4 K in CeNiSn [1] and CeRhSb [2]. These gap states are usually believed to be a result of hybridization of the 4f band and the conduction band. In the latter systems the origin of such a small gap state has been of interest. These systems are unstable under external environments such as hi~h~ magnetle . . . . .field~ . . . . t..aral and high pressure change the gap state into a heavy-fermion state at low temperature as concluded from electrical resistivity measurements [5]. The Hall effect in single crystals of CeNiSn displays a large anisotropy [6] which might be thought of being due to anisotropic hybridization effects. .......
* Corresponding author.
2. Results and discussion The samples used are the same as those used in the measurements in Ref. 16]. Figure 1 shows the change of Hall coefficient under pressure in a J Ila, HIIb sample. All the measuremeo*.s are done in a magnetic field of 1.08 T. The Hall coefficient RH decreases steeply as the temperature decreases at ambient pressure, but decreases slowly as the pressure increases in the lowest temperature region. It should be noted that a crossover point appears near 2.7 K at which R H is unchanged with change of pressure, n,.i .... ,r,;o ~^~, ,~,~ , ~ _ '~'~'e .~. . of . .ex H ~.,llatt~w~ i. . . . . . ~,~,,-- - o r,,,.,-.,- ~at,~,~r, into a slow one, and RH decreases with an increase of pressure. However, above this point R u increases slightly with pressure a small but a little more rapidly at lower pressures. The behavior of the Jtlb, Htlc sample is very similar. The decrease of R , is due to the decrease of the gap energy with pressure which can be seen from the resistivity measurements simultaneously performed with the measurement of the Hall effect.
0921-452694/$07.00 ~ 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0258-I
T. Hiraoka et al. / Plo'sica B 199&200 (1994) 440-442
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i
i
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T(K) Fig. I. Hall coefficient Ru in the JIM, HIIb sample under several pressures in the low-temperature range. The inset shows the behavior of RH near its maximum.
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pressure and it coincides with the crossover temperature of R . as mentioned above. Two gap energies E~, and Eat are obtained from above and below this temperature as 1.96 and 0.65 K at P = 0. Both energies decrease linearly with increase of pressure at rates of - 0 . 1 and - 0 . 0 8 5 K k b a r - t respectively. However, on the other hand, the log RH versus I / T shows less clear linear relations in the same temperature range, but a similar behavior can be seen at the lowest temperature region as shown in the inset of Fig. 2. This means that not only the electron density n but also the ratio of the relaxation time to the electron mass, t/m, are temperature dependent in the free-electron (single-band} model. The above-mentioned crossover points in Figs. 1 and 2 are also observed in another sample. This fact suggests the existence of some structure in the density of states which might be different from the proposed model of a valley-type density of states derived from N M R measurement [7]. The inset of Fig. ! shows the behavior near the m a x i m u m of RH. Pressure causes the maximum of RH tO decrease and the temperature of the RH maximum to increase. This behavior is reminiscent of that of RH in the heavy-fermion system CeRuzSiz under pressure [8]. These results indicate that this sample behaves as a K o n d o metallic system above this temperature. Figure 3 shows the behavior of Rtt in a Jlfb, Hlla sample under pressure. Similar pressure effects are shown at low temperature, but, as shown in the inset, Rn shows a kink at
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i 10-3
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/.7
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Fig 2. log/) versus I T in the JIB+, HIIb sample under several pressures. The inset shows log RH versus 1 T under pressure• Figure 2 shows the log p versus I / T dependence in which the linear relation between them can be seen and the slope decreases as the pressure increases. In Fig. 2, two linear regions centering at about 2.7 K can be clearly seen. This temperature is unchanged with change of
6
i 1
P=5.2kb
4
i
0
I
I
~K)~ I
|
5
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J J
10
T(K) Fig. 3. Hall coefficient RH in the J]]b. tt i!a sample under pressure in the low-temperature range. The inset shows the behavior of RH under pressure below 100 K.
442
T. Hiraoka et al./ Physica B 199&200 (1994) 440-442
12 K for the P = 0 curve which corresponds to the peak of Z for the HI[o direction [1]. Furthermore, pressure increases R~ at the maximum, contrary to the other samples, and Ru continues to increase up to 200 K, contrary to tll¢ other samples as shown in the inset of Fig, !. This behavior shows the unstable state in the H Ila direction compared to other samples, The Hall mobility t~u, RH/P, changes its sign from positive to negative followed by a steep decrease in the low-temperature region. This behavior is anisotropic for all three samples, This behavior reflects the anisotropy and strong temperature dependence of Tim in the freeelectron model as mentioned above. Recent theory Eg] explains the anisotropy of transport properties taking into account the anisotropy of z in the Kondo compounds. The effect of pressure causes the size of/~a to increase in the Jlla, Hllb sample but the effect becomes smaller down to 1.8 K where it almost disappears.
References [1] T. Takabatake, F. Teshima, H. Fujii, S. Nishigori, T. Suzuki, T. Fujita, Y. Yamaguchi and J. Sakurai, Phys. Rev. B 41 (1990) 9607.
[2] S.M. Malik and D.T. Adroja, Phys. Rev. B 43 (1991) 6277. [3] M.F. Hundley, P.C. Canfield, J.D. Thompson, Z. Fisk and J. M. Lawrence, Phys. Rev. B 42 (1990) 6842. [4] T. Takabatake, G. Nakamoto, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, H. Goshima, T. Suzuki, T. Fujita, !. Oguro, T. Hiraoka and S.K, Malik, Physica B 199&200 (1994) 457. [5] M. Kurisu, T. Takabatake and H. Fujii, in: Proc. Hiroshima Workshop on Transport and Thermal Properties of f-Electron Systems, H. Fujii, T. Fujita and G. Oomi, eds. (Plenum Press, New York, 1993). ['6] T. Takabatake, M. Nagasawa, H. Fujii, M. Nohara, T. Suzuki, T. Fujita, G. Kido and T. Hiraoka, J. Magn. Magn. Mater. 108 (1992) 155. E7] M. Kyot,aku, Y. Kitaoka, H. Nakamura, K. Asayama, T. Takabatake, F. Teshima and H. Fujii, J. Phys. Soc. Japan 59 (1990) 1728. ['8] R. Djerbi, P. Haen and J.-M. Mignot, Physica B 171 (1991) 258. [9] B. Coqblin, A.K. Bhattacharjee and S.M.M. Evans, J. Magn. Magn. Mater. 90&91 (1990) 393.
ELSEVIER
Pressure dependence of the Hall effect in single crystals of CeNiSn T. Hiraoka "'*, E. Kinoshita a, T. Takabatake b, H. Tanaka b, H. Fujii b aFaculty q]"Science and Engineering, Saga University. Saga 840. Japan ~Faculty q["b~tegrated Arts and Sciences. Hiroshima University. Hiroshima 730, Japan
Abstract The pressure dependence of the Hall effect in single crystals of CeNiSn (JIIb, nlla; Jlla, HIIb; JIIb, HIIc) has been r,'easured. The Hall coefficient Rn decreases with pressure in the low-temperature range, indicating a decrease of gap energy under pressure due to the decrease of slope in the log p versus 1/T dependence. A crossover temperature is observed in the slope of this dependence.
1. Introduction
A study of these effects under pressure would yield useful knowledge and shed some light on these problems.
Recently Kondo semiconductors with gap states at low temperature, such as CeNiSn [1], CeRhSb [2] and Ce3Bi4Pt3 [3] have been found. These systems show marked changes in their transport properties, such as electrical resistivity and Hall effect, as the temperature is lowered. This behavior comes from gap opening at low temperatures. However, the gap energy varies markedly from 70 K in Ce3Bi4Pt,~ [3] to as low as about 4 K in CeNiSn [1] and CeRhSb [2]. These gap states are usually believed to be a result of hybridization of the 4f band and the conduction band. In the latter systems the origin of such a small gap state has been of interest. These systems are unstable under external environments such as hi~h~ magnetle . . . . .field~ . . . . t..aral and high pressure change the gap state into a heavy-fermion state at low temperature as concluded from electrical resistivity measurements [5]. The Hall effect in single crystals of CeNiSn displays a large anisotropy [6] which might be thought of being due to anisotropic hybridization effects. .......
* Corresponding author.
2. Results and discussion The samples used are the same as those used in the measurements in Ref. 16]. Figure 1 shows the change of Hall coefficient under pressure in a J Ila, HIIb sample. All the measuremeo*.s are done in a magnetic field of 1.08 T. The Hall coefficient RH decreases steeply as the temperature decreases at ambient pressure, but decreases slowly as the pressure increases in the lowest temperature region. It should be noted that a crossover point appears near 2.7 K at which R H is unchanged with change of pressure, n,.i .... ,r,;o ~^~, ,~,~ , ~ _ '~'~'e .~. . of . .ex H ~.,llatt~w~ i. . . . . . ~,~,,-- - o r,,,.,-.,- ~at,~,~r, into a slow one, and RH decreases with an increase of pressure. However, above this point R u increases slightly with pressure a small but a little more rapidly at lower pressures. The behavior of the Jtlb, Htlc sample is very similar. The decrease of R , is due to the decrease of the gap energy with pressure which can be seen from the resistivity measurements simultaneously performed with the measurement of the Hall effect.
0921-452694/$07.00 ~ 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0258-I
T. Hiraoka et al. / Plo'sica B 199&200 (1994) 440-442
x 10 -2 1 +l : 0
i
i
l
i
i
i
~
Pf5.7kb
0
o~,**~"-
I
CeNiSn
,
~
•
=
i
P=O
*-a
-5
: ~)+
~-2
,
•
o~
"7>pa43kb
-~ •"" ~!,
-
",
-9
.
• :/
~
o%,. e**
J//a, H//b
..
t
o,..,.,,,,
,
t
. . . .
!
"°
5
10
T(K) Fig. I. Hall coefficient Ru in the JIM, HIIb sample under several pressures in the low-temperature range. The inset shows the behavior of RH near its maximum.
f
I
I
I
,,:,:"
CeNiSn
-8
I • IE"41+4l, ' .
I
J//a, H//b
:~."--
.
P=O ~ P=4.3kb
441
pressure and it coincides with the crossover temperature of R . as mentioned above. Two gap energies E~, and Eat are obtained from above and below this temperature as 1.96 and 0.65 K at P = 0. Both energies decrease linearly with increase of pressure at rates of - 0 . 1 and - 0 . 0 8 5 K k b a r - t respectively. However, on the other hand, the log RH versus I / T shows less clear linear relations in the same temperature range, but a similar behavior can be seen at the lowest temperature region as shown in the inset of Fig. 2. This means that not only the electron density n but also the ratio of the relaxation time to the electron mass, t/m, are temperature dependent in the free-electron (single-band} model. The above-mentioned crossover points in Figs. 1 and 2 are also observed in another sample. This fact suggests the existence of some structure in the density of states which might be different from the proposed model of a valley-type density of states derived from N M R measurement [7]. The inset of Fig. ! shows the behavior near the m a x i m u m of RH. Pressure causes the maximum of RH tO decrease and the temperature of the RH maximum to increase. This behavior is reminiscent of that of RH in the heavy-fermion system CeRuzSiz under pressure [8]. These results indicate that this sample behaves as a K o n d o metallic system above this temperature. Figure 3 shows the behavior of Rtt in a Jlfb, Hlla sample under pressure. Similar pressure effects are shown at low temperature, but, as shown in the inset, Rn shows a kink at
4'"
0 P=5.7kb
0*'
.
~" O' .~"
-
+ . ® 0,_ -e -®- =
-7"-,~ ~ ~
,~O 0 ~ , -<>-
X 10 -2
..
_
-
CeNiSn
2
J//b H//a . , ~ , , . . . . . . . . . , , . +pe.,.+¢~ ~,:* • . ]
-8.5
-.41-
,¢
.."
,
........
i-
+ ~.
OP--O
"
,
: 1~5.Tkb
I
0
I
.... 0,~ + +
•0:4 +
I
I'~I IIK)
I
0.2
•
E
-10t~ ,
0.4
' "0:6" I
o =
z
i 10-3
C~NiSn
"~
J/tblt/la @P--O o ~S.2~
,t, %o.
41 {
'
0.6
.
/.7
d#
G -2
,..
,~o---',~,-~_... . . . . . . . . . . . . . . . . . . . . . . . . . . .
!f
•. . : "- ,..,
Irrom)
Fig 2. log/) versus I T in the JIB+, HIIb sample under several pressures. The inset shows log RH versus 1 T under pressure• Figure 2 shows the log p versus I / T dependence in which the linear relation between them can be seen and the slope decreases as the pressure increases. In Fig. 2, two linear regions centering at about 2.7 K can be clearly seen. This temperature is unchanged with change of
6
i 1
P=5.2kb
4
i
0
I
I
~K)~ I
|
5
tO0
J J
10
T(K) Fig. 3. Hall coefficient RH in the J]]b. tt i!a sample under pressure in the low-temperature range. The inset shows the behavior of RH under pressure below 100 K.
442
T. Hiraoka et al./ Physica B 199&200 (1994) 440-442
12 K for the P = 0 curve which corresponds to the peak of Z for the HI[o direction [1]. Furthermore, pressure increases R~ at the maximum, contrary to the other samples, and Ru continues to increase up to 200 K, contrary to tll¢ other samples as shown in the inset of Fig, !. This behavior shows the unstable state in the H Ila direction compared to other samples, The Hall mobility t~u, RH/P, changes its sign from positive to negative followed by a steep decrease in the low-temperature region. This behavior is anisotropic for all three samples, This behavior reflects the anisotropy and strong temperature dependence of Tim in the freeelectron model as mentioned above. Recent theory Eg] explains the anisotropy of transport properties taking into account the anisotropy of z in the Kondo compounds. The effect of pressure causes the size of/~a to increase in the Jlla, Hllb sample but the effect becomes smaller down to 1.8 K where it almost disappears.
References [1] T. Takabatake, F. Teshima, H. Fujii, S. Nishigori, T. Suzuki, T. Fujita, Y. Yamaguchi and J. Sakurai, Phys. Rev. B 41 (1990) 9607.
[2] S.M. Malik and D.T. Adroja, Phys. Rev. B 43 (1991) 6277. [3] M.F. Hundley, P.C. Canfield, J.D. Thompson, Z. Fisk and J. M. Lawrence, Phys. Rev. B 42 (1990) 6842. [4] T. Takabatake, G. Nakamoto, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, H. Goshima, T. Suzuki, T. Fujita, !. Oguro, T. Hiraoka and S.K, Malik, Physica B 199&200 (1994) 457. [5] M. Kurisu, T. Takabatake and H. Fujii, in: Proc. Hiroshima Workshop on Transport and Thermal Properties of f-Electron Systems, H. Fujii, T. Fujita and G. Oomi, eds. (Plenum Press, New York, 1993). ['6] T. Takabatake, M. Nagasawa, H. Fujii, M. Nohara, T. Suzuki, T. Fujita, G. Kido and T. Hiraoka, J. Magn. Magn. Mater. 108 (1992) 155. E7] M. Kyot,aku, Y. Kitaoka, H. Nakamura, K. Asayama, T. Takabatake, F. Teshima and H. Fujii, J. Phys. Soc. Japan 59 (1990) 1728. ['8] R. Djerbi, P. Haen and J.-M. Mignot, Physica B 171 (1991) 258. [9] B. Coqblin, A.K. Bhattacharjee and S.M.M. Evans, J. Magn. Magn. Mater. 90&91 (1990) 393.