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Tunneling measurements of the energy gap in CeRhSb and CeNiSn
ELSEVIER
Physica B 206 & 207 (1995) 837-839
Tunneling measurements of the energy gap in CeRhSb and CeNiSn T. Ekino*, T. Takabatake, H. Tanaka, H. Fujii Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 724, Japan
Abstract
We report on the first tunneling measurements of the Kondo semiconductors CeRhSb and CeNiSn. The observed gap values at 4.2 K for CeRhSb and CeNiSn are 24-27 and 10 meV, respectively, which are much larger than the transport gaps. The broadened gap structure strongly suggests an anisotropic gap. The temperature dependence of the tunneling data shows the structures at 8-11 and 23-25 K for CeRhSb and 6 K for CeNiSn. These values are in agreement with the resistivity and susceptibility data for these compounds.
1. Introduction
Since the discovery of the Kondo semiconductors CeNiSn and CeRhSb, a number of experimental and theoretical efforts have been made to clarify their unique ground state properties. In these semiconductors, it is believed that an anisotropic energy gap opens at the Fermi energy due to the hybridization between the 4f-electrons and a conduction band. From transport measurements, the energy gaps in these compounds were estimated to be 0.2-0.5 meV [1,2]. Furthermore, inelastic neutron measurements on CeNiSn revealed the spin gap of 2-4 meV at a particular wave vector space [3,4]. However, there has been no direct evidence for the energy gap in the quasiparticle excitation spectrum. In this paper, tunneling measurements of CeRhSb and CeNiSn are reported. This technique provides the most direct probe to elucidate the energy gap through the measurement of the differential conductance (dI/ dV) which is proportional to the quasiparticle density
* Corresponding author.
of states, where I and V are the tunneling current and the bias voltage, respectively. For the measurements, break junctions were used, which were obtained by cleaving the polycrystalline samples in liquid helium.
2. Results and discussion
Figs. l(a)-(c) show typical dl/dV for CeRhSb taken from the different junctions. The decreased conductance at zero bias with the well defined peaks at both sides is characteristic of the energy gap due to tunneling, and the gap structures resemble the broadened density of states for the superconductors [5]. The low junction resistance in Fig. 1 is due to the face contact of the break junction with the relatively large area of ~1 mm 2. The broadened gap structure can be attributed to the gap anisotropy or lifetime effect of quasiparticles. The peak-to-peak separations Vp_~, in d l / d V of Fig. 1 were 55, 27, and 24 mV for (a), (b), and (c), respectively. In the break-junction method, an SIS (S = semiconductor, I = insulator) junction is usually formed because both sides of the barrier consist of identical materials. The Vp p = 5 5 mV in Fig. l(a),
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0921-4526(94)00601-6
838
T. Ekino et al. / Physica B 206 & 207 (1995) 837-839 •
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CeRhSb
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VOLTAGE (mY) Fig. 2. Temperature variations of d l / d V for GeRhSb. I
I
o
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VOLTAGE (mY)
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'
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Fig. 1. Tunneling conductances from CeRhSb ((a)-(c)) and CeNiSn (d) break junctions. which is the largest value in our measurements, can be due to 4zlp_p of the SIS junction, where zap_p is defined by a half value of the peak-to-peak separation in the dI/dV of SIN (N = normal metal) junction. On the other hand, the eVp_p = 24-27 meV in Figs. l(b) and (c), which are half that of Fig. l(a), can be attributed to 2zlp_p of the accidentally formed SIN junction. The 2Ap_o = 24-27 meV is extremely large compared to the activation energy of 0.4-0.5 meV determined from the transport measurements [1,2]. This may be due to the residual density of states inside the gap. The d / / d V of CeNiSn at 2.1 K is shown in Fig. l(d), where the broadened feature is similar to that of CeRhSb. The eVp_p = 9 . 5 m e V can be attributed to 2np_p because the 20meV gap (=4zao_p) of a SIS junction was also obtained. The large gap value compared to the spin gap of 2.5 and 4 meV from the neutron scattering data [3,4] demonstrates that CeNiSn is really in the Kondo insulator regime [6]. Fig. 2 displays the temperature variations in dl/dV for CeRhSb as shown in Fig. l(b). In this measurement, temperature was slowly increased from 4.2 K at the rate of 0 . 3 - 1 K / h so that the junction was mechanically stable during temperature changes. Therefore the temperature dependence of the gap structure under the same junction condition was easily ob-
tained. As shown in Fig. 2, the gap area in d l / d V is rapidly filled with increased temperature up to the characteristic temperature of Tch = 8 K, and the temperature dependence of the filling becomes weak above 10-11 K. The Tch of 8 K corresponds to the onset temperature of the upturn of resistivity in this compound [1,2]. More interestingly, the gap structure can be seen at least up to 16 K. For CeNiSn, a rapid filling of the gap area occurs with increasing temperature up to Tch = 6 K. The gap structure survives up to 8-9 K in this case. Fig. 3 shows the temperature dependence of the normalized zero-bias conductance d l / d V ( O m V ) / d l / dV(75 mV) for CeRhSb (Fig. l(c)). After showing a rapid decrease between 25 and 22 K, it levels off down to 11 K and then steeply decreases again. A kink was observed at T~h = 8 K. These structures may be the result of the behavior of the thermal smeared density of states at the Fermi energy (V= 0 mV) because the junction of Fig. l(c) was stable and no abrupt changes in the junction occurred during the measurements. Similar structures were also observed in the temperature dependence of the normalized dI/dV(O mV) for Fig. l(b), indicating that these data are reproducible. The relatively sharp onsets of decrease at 25 and 11 K resemble what occurs in the superconducting tunnel junction at the critical temperature [7]. Because the temperature of 25-22 K is nearly consistent with the peak at 21 K in the susceptibility [8] and the shoulder at 25 K in the resistivity [2], we speculate that a coherent state occurs below an apparent critical tem-
T. Ekino et al. / Physica B 206 & 207 (1995) 837-839 1 . 3
.
.
.
.
,
.
.
.
.
,
.
.
.
.
,
.
.
.
Fig. 4 shows the temperature dependence of 2Ap_p taken from Fig. 2. The gap value decreases almost linearly with increasing temperature up to 9 K, above which the decrease is weakened. The gap structure is smeared out above 16 K. The decrease of the gap is much more rapid than the BCS prediction [7]. The temperature of 9 K corresponds to that in Fig. 3 where the normalized zero-bias conductance steeply decreases with decreasing temperature below 11 K due to the rapid development of the gap structure.
.
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Acknowledgement
CeRhSb 0°8
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.
.
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20
.
.
.
.
30
T(K)
Fig. 3. Temperature dependence dV(75 mV) for CeRhSb.
40
of dl/dV(OmV)/dl/
perature T c = 25 K due to a significant change in hybridization between conduction and 4f-electron states near the Fermi energy. In this viewpoint, the ratio 2 A p _ p / k B T c = 11-14 is defined as a measure of the coupling strength. This value is much larger than the BCS value of 3.5, but in agreement with that for the charge-density wave compounds [9]. 30 25
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CeRhSb 0
.
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T(K)
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.
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.
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839
.
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Fig. 4. Temperature dependence of 2Ap_p for CeRhSb.
This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan.
References
[1] T. Takabatake, G. Nakamoto, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, H. Goshima, T. Suzuki, T. Fujita, I. Oguro, T. Hiraoka and S.K. Malik, Physica B 199 & 200 (1994) 457. [2] T. Takabatake, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, T. Suzuki and T. Fujita, Phys. Rev. B 50 (1994) 623. [3] T.E. Mason, G. Aeppli, A.P. Rairez, K.N. Clausen, C. Broholm, N. Stucheli, E. Bucher and T.T.M. Palstra, Phys. Rev. Lett. 69 (1992) 490. [4] H. Kadowaki, T. Sato, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault and Y. Ishikawa, J. Phys. Soc. Japan 63 (1994) 2074. [5] T. Ekino and J. Akimitsu, in: Frontiers in Solid State Sciences, Vol. 1, Superconductivity, eds. L.C. Gupta and M.S. Multani (World Scientific, Singapore, 1993) p. 477. [6] H. Tsunetsugu, Y. Hatsugai, K. Ueda and M. Sigrist, Phys. Rev. (B) 46 (1992) 3175. [7] T. Ekino and J. Akimitsu, in: Studies of High Temperature Superconductors, Vol. 9, ed. A.V. Narlikar (Nova Science, New York, 1992) p. 259. [8] T. Takabatake, T. Yoshino, H. Tanaka and H. Fujii, Physica B 206 & 207 (1995) 804. [9] T. Ekino and J. Akimitsu, Jpn. J. Appl. Phys. 26-3 (1987) 625.
Physica B 206 & 207 (1995) 837-839
Tunneling measurements of the energy gap in CeRhSb and CeNiSn T. Ekino*, T. Takabatake, H. Tanaka, H. Fujii Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 724, Japan
Abstract
We report on the first tunneling measurements of the Kondo semiconductors CeRhSb and CeNiSn. The observed gap values at 4.2 K for CeRhSb and CeNiSn are 24-27 and 10 meV, respectively, which are much larger than the transport gaps. The broadened gap structure strongly suggests an anisotropic gap. The temperature dependence of the tunneling data shows the structures at 8-11 and 23-25 K for CeRhSb and 6 K for CeNiSn. These values are in agreement with the resistivity and susceptibility data for these compounds.
1. Introduction
Since the discovery of the Kondo semiconductors CeNiSn and CeRhSb, a number of experimental and theoretical efforts have been made to clarify their unique ground state properties. In these semiconductors, it is believed that an anisotropic energy gap opens at the Fermi energy due to the hybridization between the 4f-electrons and a conduction band. From transport measurements, the energy gaps in these compounds were estimated to be 0.2-0.5 meV [1,2]. Furthermore, inelastic neutron measurements on CeNiSn revealed the spin gap of 2-4 meV at a particular wave vector space [3,4]. However, there has been no direct evidence for the energy gap in the quasiparticle excitation spectrum. In this paper, tunneling measurements of CeRhSb and CeNiSn are reported. This technique provides the most direct probe to elucidate the energy gap through the measurement of the differential conductance (dI/ dV) which is proportional to the quasiparticle density
* Corresponding author.
of states, where I and V are the tunneling current and the bias voltage, respectively. For the measurements, break junctions were used, which were obtained by cleaving the polycrystalline samples in liquid helium.
2. Results and discussion
Figs. l(a)-(c) show typical dl/dV for CeRhSb taken from the different junctions. The decreased conductance at zero bias with the well defined peaks at both sides is characteristic of the energy gap due to tunneling, and the gap structures resemble the broadened density of states for the superconductors [5]. The low junction resistance in Fig. 1 is due to the face contact of the break junction with the relatively large area of ~1 mm 2. The broadened gap structure can be attributed to the gap anisotropy or lifetime effect of quasiparticles. The peak-to-peak separations Vp_~, in d l / d V of Fig. 1 were 55, 27, and 24 mV for (a), (b), and (c), respectively. In the break-junction method, an SIS (S = semiconductor, I = insulator) junction is usually formed because both sides of the barrier consist of identical materials. The Vp p = 5 5 mV in Fig. l(a),
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0921-4526(94)00601-6
838
T. Ekino et al. / Physica B 206 & 207 (1995) 837-839 •
w
CeRhSb
•
I
i
i
i
C;Rh p-Sb
'
I
..Z 25.3K 15.7K
2£
15.1 K
13.9K
1.e
0.4O 4.2K .70
.1K
15 I
I
I
I
I
I
I
o. o (d)
-Xo
0.08 006
T = 2.1K
-ioo
I
-go
;
20
8'0
VOLTAGE (mY) Fig. 2. Temperature variations of d l / d V for GeRhSb. I
I
o
I
VOLTAGE (mY)
s'o
'
ioo
Fig. 1. Tunneling conductances from CeRhSb ((a)-(c)) and CeNiSn (d) break junctions. which is the largest value in our measurements, can be due to 4zlp_p of the SIS junction, where zap_p is defined by a half value of the peak-to-peak separation in the dI/dV of SIN (N = normal metal) junction. On the other hand, the eVp_p = 24-27 meV in Figs. l(b) and (c), which are half that of Fig. l(a), can be attributed to 2zlp_p of the accidentally formed SIN junction. The 2Ap_o = 24-27 meV is extremely large compared to the activation energy of 0.4-0.5 meV determined from the transport measurements [1,2]. This may be due to the residual density of states inside the gap. The d / / d V of CeNiSn at 2.1 K is shown in Fig. l(d), where the broadened feature is similar to that of CeRhSb. The eVp_p = 9 . 5 m e V can be attributed to 2np_p because the 20meV gap (=4zao_p) of a SIS junction was also obtained. The large gap value compared to the spin gap of 2.5 and 4 meV from the neutron scattering data [3,4] demonstrates that CeNiSn is really in the Kondo insulator regime [6]. Fig. 2 displays the temperature variations in dl/dV for CeRhSb as shown in Fig. l(b). In this measurement, temperature was slowly increased from 4.2 K at the rate of 0 . 3 - 1 K / h so that the junction was mechanically stable during temperature changes. Therefore the temperature dependence of the gap structure under the same junction condition was easily ob-
tained. As shown in Fig. 2, the gap area in d l / d V is rapidly filled with increased temperature up to the characteristic temperature of Tch = 8 K, and the temperature dependence of the filling becomes weak above 10-11 K. The Tch of 8 K corresponds to the onset temperature of the upturn of resistivity in this compound [1,2]. More interestingly, the gap structure can be seen at least up to 16 K. For CeNiSn, a rapid filling of the gap area occurs with increasing temperature up to Tch = 6 K. The gap structure survives up to 8-9 K in this case. Fig. 3 shows the temperature dependence of the normalized zero-bias conductance d l / d V ( O m V ) / d l / dV(75 mV) for CeRhSb (Fig. l(c)). After showing a rapid decrease between 25 and 22 K, it levels off down to 11 K and then steeply decreases again. A kink was observed at T~h = 8 K. These structures may be the result of the behavior of the thermal smeared density of states at the Fermi energy (V= 0 mV) because the junction of Fig. l(c) was stable and no abrupt changes in the junction occurred during the measurements. Similar structures were also observed in the temperature dependence of the normalized dI/dV(O mV) for Fig. l(b), indicating that these data are reproducible. The relatively sharp onsets of decrease at 25 and 11 K resemble what occurs in the superconducting tunnel junction at the critical temperature [7]. Because the temperature of 25-22 K is nearly consistent with the peak at 21 K in the susceptibility [8] and the shoulder at 25 K in the resistivity [2], we speculate that a coherent state occurs below an apparent critical tem-
T. Ekino et al. / Physica B 206 & 207 (1995) 837-839 1 . 3
.
.
.
.
,
.
.
.
.
,
.
.
.
.
,
.
.
.
Fig. 4 shows the temperature dependence of 2Ap_p taken from Fig. 2. The gap value decreases almost linearly with increasing temperature up to 9 K, above which the decrease is weakened. The gap structure is smeared out above 16 K. The decrease of the gap is much more rapid than the BCS prediction [7]. The temperature of 9 K corresponds to that in Fig. 3 where the normalized zero-bias conductance steeply decreases with decreasing temperature below 11 K due to the rapid development of the gap structure.
.
A 000
I:= 1.2 In I',. v >
00
00
~ 1.1 "0
,t
~ 1.0
E
"o
Acknowledgement
CeRhSb 0°8
.
.
.
.
0
'
"
"
"
10
i
i
,
,
,
,
i
20
.
.
.
.
30
T(K)
Fig. 3. Temperature dependence dV(75 mV) for CeRhSb.
40
of dl/dV(OmV)/dl/
perature T c = 25 K due to a significant change in hybridization between conduction and 4f-electron states near the Fermi energy. In this viewpoint, the ratio 2 A p _ p / k B T c = 11-14 is defined as a measure of the coupling strength. This value is much larger than the BCS value of 3.5, but in agreement with that for the charge-density wave compounds [9]. 30 25
et m e
A
4)
/t O
20
E 15
CeRhSb 0
.
0
.
.
.
'
5
.
.
.
.
|
10
T(K)
.
.
.
.
'
15
.
.
.
839
.
20
Fig. 4. Temperature dependence of 2Ap_p for CeRhSb.
This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan.
References
[1] T. Takabatake, G. Nakamoto, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, H. Goshima, T. Suzuki, T. Fujita, I. Oguro, T. Hiraoka and S.K. Malik, Physica B 199 & 200 (1994) 457. [2] T. Takabatake, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, T. Suzuki and T. Fujita, Phys. Rev. B 50 (1994) 623. [3] T.E. Mason, G. Aeppli, A.P. Rairez, K.N. Clausen, C. Broholm, N. Stucheli, E. Bucher and T.T.M. Palstra, Phys. Rev. Lett. 69 (1992) 490. [4] H. Kadowaki, T. Sato, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault and Y. Ishikawa, J. Phys. Soc. Japan 63 (1994) 2074. [5] T. Ekino and J. Akimitsu, in: Frontiers in Solid State Sciences, Vol. 1, Superconductivity, eds. L.C. Gupta and M.S. Multani (World Scientific, Singapore, 1993) p. 477. [6] H. Tsunetsugu, Y. Hatsugai, K. Ueda and M. Sigrist, Phys. Rev. (B) 46 (1992) 3175. [7] T. Ekino and J. Akimitsu, in: Studies of High Temperature Superconductors, Vol. 9, ed. A.V. Narlikar (Nova Science, New York, 1992) p. 259. [8] T. Takabatake, T. Yoshino, H. Tanaka and H. Fujii, Physica B 206 & 207 (1995) 804. [9] T. Ekino and J. Akimitsu, Jpn. J. Appl. Phys. 26-3 (1987) 625.