- Email: [email protected]
NQR study of Kondo semiconductors CeNiSn and CeRhSb
Physica B 206 & 207 (1995) 829-831
ELSEVIER
N M R / N Q R study of Kondo semiconductors CeNiSn and CeRhSb K. Nakamura a, Y. Kitaoka a'*, K. Asayama a, T. Takabatake b, G. Nakamoto b, H. Tanaka b, H. Fujii b "Department of Material Physics, Osaka University, Toyonaka 560, Japan bFaculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 724, Japan
Abstract
The gapped state in Kondo semiconductors CeNiSn and CeRhSb has been investigated by measurements of nuclear-spin laftice relaxation rate, 1/T~ of ll9Sn and 1235b and Knight shift of 1195n and 12~Sb. The T-dependences of T 1 and the shift in both compounds have revealed a novel feature for the gap state at low-T. Especially, the former has established that the energy gap is of a pseudo type with a V-shaped structure, where the band width, D and the pseudogap, A were estimated to be D = 140 and 210 K and A = 14 and 28 K for CeNiSn and CeRhSb, respectively. At very low-T, the TIT= constant behavior has, however, been found in both compounds. The fact that the T~T=constant behavior appears from much higher-T in CeNil.0~Sn and CeNio.97Co0.03Snsuggest that impurities and/or imperfections yield a finite density of states at the Fermi level. Together with the Knight shift result, we highlight that the gapped state in Ce-based compounds belongs to a different class from the activated-type gap state in such as SmB6 and YbB~2.
I. Introduction
The energy-gap formation in the mixed valence systems such as StuB 6 and YbB12, etc. has attracted much interest as one of the unique ground states resulting from the hybridization effect between 4f- and conduction electrons [1]. The activated gap with magnitude of about 100 K was well established from the transport and thermal measurements in these compounds. Remarkably, the recent neutron scattering experiment on SmB 6 has revealed that the gap is due to the local formation of the excitonic bound state between f-electrons and d-holes with excitation energy of 14 meV [2]. On the other hand, the gapped state found in Cebased Kondo semiconductors, CeNiSn [3] and CeRhSb [4] is not fully established as yet in a consistent way by the thermal and transport experiments. By contrast, the T-dependence of nuclear-spin lattice * Corresponding author.
relaxation rate, 1/T1, led to a conclusion that the gapped state possess a V-shaped structure in the spin excitation spectrum [5], although a finite density of states emerges at the Fermi level at low energy or low temperature, inevitably affected by impurities and imperfections [6]. The overall T-dependences of 1/TI of 1195n in CeNiSn and 123Sb in CeRhSb presented in Figs. 1 and 2, respectively, were consistently interpreted by the model density of states for the spin excitation spectrum of quasi-particles shown in the inset of Fig. 1, which possesses the V-shaped structure with a finite density of states at the Fermi level. From the best fit to the data, the band width, D = 210 K and pseudogap, A = 28 K for CeRhSb were estimated, which are almost two times larger than those of CeNiSn (D = 140 K and A = 14 K). Furthermore, the fractions of the residual density of states at the Fermi level, N(EF) .... against the value without gap for the Lorentzian band, No(EF), i.e. N(EF)/No(EF) were estimated to be 0.077 and 0.085 for CeNiSn and CeRhSb, respectively [6].
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD1 0921-4526(94)00598-2
830
K. Nakamura et al. / Physica B 206 & 207 (1995) 829-831
......
i
........
I
........
CeNil -
i
x
........
G
i
'
'
~
1000
1013 1(3
~ /
o x=O
_/ /
.x:o.o
,I/• 0;1
~
'
'
0.01
E' , ,,,,,I
,
, ......
0.1
I
........
i
1
. . . . . . . .
10
i
,
100
T (K)
Fig. 1. T-dependence of IlT~ of ll9Sn in CeNil_,Co,Sn (x = 0, 0.03) and CeNil.01Sn. The solid line for each compound is a best fit based on the model density of states with modified V-shaped structure indicated in the inset where a constant density of states, Nro,(EF) is introduced at the Fermi level to interpret the T 1 T = constant law at low-T.
1000
........
I
........
i
........
I
'
''
CoRhSb 100
The unique pseudo gapped state in Ce-based compounds should be distinguished from that in SmB 6 and YbB12 of an activated type. The sensitivity of the gap structure to impurities and imperfections in the former case made the identification of the gapped state difficult. This unstable gapped state itself may be associated with the fact that the size of energy gap is by one order of magnitude smaller for the former than for the latter. In order to shed further light on the novel sensitivity of the gapped state to imperfections and impurities, we have investigated to what extent the V-shaped structure is modified by a slight off-stoichiometry for Ni sites and by substitution of Co impurities into Ni sites in CeNiSn. Furthermore, we have measured the Knight shift of ~2~Sb to confirm whether the evidence of gap, which has unambiguously been provided from the T l measurement in CeNiSn and CeRhSb, is reflected in the T-dependence of the susceptibility i.e. the Knight shift for both compounds.
2. Experimental procedures
Polycrystalline samples of CeNi~ olSn, CeNio.97Coo.03Sn were prepared by arc melting in purified argon atmosphere [7]. The sample of CeRhSb was the same as that used in T~ measurement reported previously [6]. For NMR and N Q R measurements, samples crushed into fine powder of diameter less 70 ixm to avoid the skin-depth effect of R F field. T1 of lt9Sn was measured in a T-range of 0.04-300 K and the Knight shift of 12tSb was obtained at 7 T and in a T-range of 2-200 K, using a home-made phase-coherent pulsed-NMR spectrometer.
10
3. Results and discussion 0
1
0.1
0.01 . . . . . . . .
0.1
I
1
. . . . . . . .
i
10
. . . . . . . .
i
. . . .
100
T(K)
Fig. 2. T-dependence of 1 / T 1 of 1235h in CeRhSb. Solid line is a best fit based on the same model for CeNiSn, i.e. the inset in Fig. 1.
Fig. 1 shows the T-dependence of 1 / T 1 of 1195n in CeNio.97Co0.03Sn (open squares) and CeNil 01Sn (solid circles) together with the results of CeNiSn (open circles) reported previously [6]. 1/T~ in CeNiSn starts to decrease appreciably below 30 K and is proportional to T 3 in a T-range of 0.4-1 K. A t very low temperature, it deviates from such a prominent relaxation behavior into a T 1T = constant, which gives direct evidence of a finite density of states at the Fermi level. The inset in Fig. 1 is the model density of states characterized by the V-shaped structure which well reproduces the T-dependence of 1 / T 1 for both compounds.
K. Nakamura et al. / Physica B 206 & 207 (1995) 829-831
As clearly seen in the figure, 1/T 1 of CeNio.97Coo.oaSn is strongly enhanced compared with that of CeNiSn below 1 K and obeys a T~ T = constant law in a wide T-range of 0.04-1 K. 1 / T 1 in CeNi~ 0lSn starts to deviate moderately from that in CeNiSn below 2 K followed by a T1 T = constant behavior only below 0.15 K. Thus, the relaxation behavior markedly depends on impurities and inhomogeneities in the sample, which, as a result, mask the intrinsic V-shaped structure of the energy gap by yielding a finite density of states at the Fermi level. Similar to the case of CeNiSn, the T-dependences of 1 / T 1 for CeNi~.0lSn and CeNi0.97Co0.oaSn are consistently interpreted by the modified V-shaped density of states as demonstrated by solid lines in Fig. 1. Here we estimate the fraction, N ( E F ) , e s / N o ( E F ) , to be 0.53 and 0.096 for CeNio.97Co0.03Sn and CeNiL01Sn, respectively. Only a few at.% impurities and inhomogeneities in the sample easily induce the residual density of states at the Fermi level. In other words, the intrinsic pseudogap structure in CeNiSn and CeRhSb might be of V-shaped type, if the sample were impurity free. Next, we present in Fig. 3 the T-dependence of the Knight shift of 1215b in CeRhSb together with the data of ~19Sn in CeNiSn [5]. The magnetic susceptibility along the magnetically easy a-axis, Xa, of single crystals CeNiSn and CeRhSb were reported to have a pronounced peak at around 12 K and 20 K, respectively [3,7]. The T-dependence of the shift shown in Fig. 3 shows clearly the decreases in the local susceptibility below 12 and 17 K for CeNiSn and CeRhSb,
831
respectively, associated with the opening of the pseudogap. The result is consistent with that of 1 / T 1 in CeRhSb and CeNiSn. Since the Knight shift is confirmed to be dominated by the spin part of Ce 4felectrons through the isotropic transferred hyperfine interaction, the T-independent orbital contribution is safely neglected [5]. In such a case, the T-dependence of the shift should be analyzed based on the same density of states as in the inset of the Fig. 1, if the energy gap were independent of wave number (Q). This is, however, not the case, suggesting the novel feature of the gapped state in these compounds [8]. The recent neutron scattering experiments have revealed the significant Q-dependence of magnetic scattering profile and simultaneously the pseudogap behavior for the magnetic excitation spectrum along the specific Q vector [9,10].
4. Conclusion
We have found that the Kondo semiconductors CeNiSn and CeRhSb possess a pseudo energy gap with V-shaped structure which is quite different from the gapped state in SmB 6 and YbBI2 of an activated type. It is also notable that the presence of the pseudo spin gap is clear, whereas any clear gap of the charge excitation is not well defined. The energy gap in CeNiSn and CeRhSb is filled up in such a manner that the presence of impurities and inhomogeneities induces the residual density of states at the Fermi level.
References
4.0
r... •
3.C
CeNiSn •
¢~Ooo° o
¢-
•E 2.C
1.0~
5=0
•
CeRhSb o
~'o"°o I
100
g
o
o
I
150
200
T (K)
Fig. 3. T-dependence of the 121SbKnight shift of CeRhSb together with the data of CeNiSn [5].
[1] See e.g.T. Kasuya, Jpn. J. Appl. Phys. Ser. 8 (1993) 3. [2] P.A. Alekseev et al., Physica B 186-188 (1993) 384. [3] T. Takabatake, Y. Nakazawa and M. Ishikawa, Jpn. J. Appl. Phys. Suppl. 26 (1987) 547; T. Takabatake et al., Phys. Rev. B 45 (1992),5740. [4] S.K. Malik and D.T. Adroja, Phys. Rev. B 43 (1991) 6277. [5] M. Kyogaku et al., J. Phys. Soc. Japan 59 (1990) 1728. [6] K. Nakamura et al., J. Phys. Soc. Japan 63 (1994) 433. [7] T. Takabatake, T. Yoshino, H. Tanaka, T. Tadaoka, Y. Bando, H. Fujii, T. Fujita, H. Shida and T. Suzuki, Physica B 206 & 207 (1995) 804. [8] K. Nakamura et ai., unpublished. [9] T.E. Mason et al., Phys. Rev. Lett. 69 (1992) 490. [10] H. Kadowaki et al., J. Phys. Soc. Japan 63 (1994) 6.
ELSEVIER
N M R / N Q R study of Kondo semiconductors CeNiSn and CeRhSb K. Nakamura a, Y. Kitaoka a'*, K. Asayama a, T. Takabatake b, G. Nakamoto b, H. Tanaka b, H. Fujii b "Department of Material Physics, Osaka University, Toyonaka 560, Japan bFaculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 724, Japan
Abstract
The gapped state in Kondo semiconductors CeNiSn and CeRhSb has been investigated by measurements of nuclear-spin laftice relaxation rate, 1/T~ of ll9Sn and 1235b and Knight shift of 1195n and 12~Sb. The T-dependences of T 1 and the shift in both compounds have revealed a novel feature for the gap state at low-T. Especially, the former has established that the energy gap is of a pseudo type with a V-shaped structure, where the band width, D and the pseudogap, A were estimated to be D = 140 and 210 K and A = 14 and 28 K for CeNiSn and CeRhSb, respectively. At very low-T, the TIT= constant behavior has, however, been found in both compounds. The fact that the T~T=constant behavior appears from much higher-T in CeNil.0~Sn and CeNio.97Co0.03Snsuggest that impurities and/or imperfections yield a finite density of states at the Fermi level. Together with the Knight shift result, we highlight that the gapped state in Ce-based compounds belongs to a different class from the activated-type gap state in such as SmB6 and YbB~2.
I. Introduction
The energy-gap formation in the mixed valence systems such as StuB 6 and YbB12, etc. has attracted much interest as one of the unique ground states resulting from the hybridization effect between 4f- and conduction electrons [1]. The activated gap with magnitude of about 100 K was well established from the transport and thermal measurements in these compounds. Remarkably, the recent neutron scattering experiment on SmB 6 has revealed that the gap is due to the local formation of the excitonic bound state between f-electrons and d-holes with excitation energy of 14 meV [2]. On the other hand, the gapped state found in Cebased Kondo semiconductors, CeNiSn [3] and CeRhSb [4] is not fully established as yet in a consistent way by the thermal and transport experiments. By contrast, the T-dependence of nuclear-spin lattice * Corresponding author.
relaxation rate, 1/T1, led to a conclusion that the gapped state possess a V-shaped structure in the spin excitation spectrum [5], although a finite density of states emerges at the Fermi level at low energy or low temperature, inevitably affected by impurities and imperfections [6]. The overall T-dependences of 1/TI of 1195n in CeNiSn and 123Sb in CeRhSb presented in Figs. 1 and 2, respectively, were consistently interpreted by the model density of states for the spin excitation spectrum of quasi-particles shown in the inset of Fig. 1, which possesses the V-shaped structure with a finite density of states at the Fermi level. From the best fit to the data, the band width, D = 210 K and pseudogap, A = 28 K for CeRhSb were estimated, which are almost two times larger than those of CeNiSn (D = 140 K and A = 14 K). Furthermore, the fractions of the residual density of states at the Fermi level, N(EF) .... against the value without gap for the Lorentzian band, No(EF), i.e. N(EF)/No(EF) were estimated to be 0.077 and 0.085 for CeNiSn and CeRhSb, respectively [6].
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD1 0921-4526(94)00598-2
830
K. Nakamura et al. / Physica B 206 & 207 (1995) 829-831
......
i
........
I
........
CeNil -
i
x
........
G
i
'
'
~
1000
1013 1(3
~ /
o x=O
_/ /
.x:o.o
,I/• 0;1
~
'
'
0.01
E' , ,,,,,I
,
, ......
0.1
I
........
i
1
. . . . . . . .
10
i
,
100
T (K)
Fig. 1. T-dependence of IlT~ of ll9Sn in CeNil_,Co,Sn (x = 0, 0.03) and CeNil.01Sn. The solid line for each compound is a best fit based on the model density of states with modified V-shaped structure indicated in the inset where a constant density of states, Nro,(EF) is introduced at the Fermi level to interpret the T 1 T = constant law at low-T.
1000
........
I
........
i
........
I
'
''
CoRhSb 100
The unique pseudo gapped state in Ce-based compounds should be distinguished from that in SmB 6 and YbB12 of an activated type. The sensitivity of the gap structure to impurities and imperfections in the former case made the identification of the gapped state difficult. This unstable gapped state itself may be associated with the fact that the size of energy gap is by one order of magnitude smaller for the former than for the latter. In order to shed further light on the novel sensitivity of the gapped state to imperfections and impurities, we have investigated to what extent the V-shaped structure is modified by a slight off-stoichiometry for Ni sites and by substitution of Co impurities into Ni sites in CeNiSn. Furthermore, we have measured the Knight shift of ~2~Sb to confirm whether the evidence of gap, which has unambiguously been provided from the T l measurement in CeNiSn and CeRhSb, is reflected in the T-dependence of the susceptibility i.e. the Knight shift for both compounds.
2. Experimental procedures
Polycrystalline samples of CeNi~ olSn, CeNio.97Coo.03Sn were prepared by arc melting in purified argon atmosphere [7]. The sample of CeRhSb was the same as that used in T~ measurement reported previously [6]. For NMR and N Q R measurements, samples crushed into fine powder of diameter less 70 ixm to avoid the skin-depth effect of R F field. T1 of lt9Sn was measured in a T-range of 0.04-300 K and the Knight shift of 12tSb was obtained at 7 T and in a T-range of 2-200 K, using a home-made phase-coherent pulsed-NMR spectrometer.
10
3. Results and discussion 0
1
0.1
0.01 . . . . . . . .
0.1
I
1
. . . . . . . .
i
10
. . . . . . . .
i
. . . .
100
T(K)
Fig. 2. T-dependence of 1 / T 1 of 1235h in CeRhSb. Solid line is a best fit based on the same model for CeNiSn, i.e. the inset in Fig. 1.
Fig. 1 shows the T-dependence of 1 / T 1 of 1195n in CeNio.97Co0.03Sn (open squares) and CeNil 01Sn (solid circles) together with the results of CeNiSn (open circles) reported previously [6]. 1/T~ in CeNiSn starts to decrease appreciably below 30 K and is proportional to T 3 in a T-range of 0.4-1 K. A t very low temperature, it deviates from such a prominent relaxation behavior into a T 1T = constant, which gives direct evidence of a finite density of states at the Fermi level. The inset in Fig. 1 is the model density of states characterized by the V-shaped structure which well reproduces the T-dependence of 1 / T 1 for both compounds.
K. Nakamura et al. / Physica B 206 & 207 (1995) 829-831
As clearly seen in the figure, 1/T 1 of CeNio.97Coo.oaSn is strongly enhanced compared with that of CeNiSn below 1 K and obeys a T~ T = constant law in a wide T-range of 0.04-1 K. 1 / T 1 in CeNi~ 0lSn starts to deviate moderately from that in CeNiSn below 2 K followed by a T1 T = constant behavior only below 0.15 K. Thus, the relaxation behavior markedly depends on impurities and inhomogeneities in the sample, which, as a result, mask the intrinsic V-shaped structure of the energy gap by yielding a finite density of states at the Fermi level. Similar to the case of CeNiSn, the T-dependences of 1 / T 1 for CeNi~.0lSn and CeNi0.97Co0.oaSn are consistently interpreted by the modified V-shaped density of states as demonstrated by solid lines in Fig. 1. Here we estimate the fraction, N ( E F ) , e s / N o ( E F ) , to be 0.53 and 0.096 for CeNio.97Co0.03Sn and CeNiL01Sn, respectively. Only a few at.% impurities and inhomogeneities in the sample easily induce the residual density of states at the Fermi level. In other words, the intrinsic pseudogap structure in CeNiSn and CeRhSb might be of V-shaped type, if the sample were impurity free. Next, we present in Fig. 3 the T-dependence of the Knight shift of 1215b in CeRhSb together with the data of ~19Sn in CeNiSn [5]. The magnetic susceptibility along the magnetically easy a-axis, Xa, of single crystals CeNiSn and CeRhSb were reported to have a pronounced peak at around 12 K and 20 K, respectively [3,7]. The T-dependence of the shift shown in Fig. 3 shows clearly the decreases in the local susceptibility below 12 and 17 K for CeNiSn and CeRhSb,
831
respectively, associated with the opening of the pseudogap. The result is consistent with that of 1 / T 1 in CeRhSb and CeNiSn. Since the Knight shift is confirmed to be dominated by the spin part of Ce 4felectrons through the isotropic transferred hyperfine interaction, the T-independent orbital contribution is safely neglected [5]. In such a case, the T-dependence of the shift should be analyzed based on the same density of states as in the inset of the Fig. 1, if the energy gap were independent of wave number (Q). This is, however, not the case, suggesting the novel feature of the gapped state in these compounds [8]. The recent neutron scattering experiments have revealed the significant Q-dependence of magnetic scattering profile and simultaneously the pseudogap behavior for the magnetic excitation spectrum along the specific Q vector [9,10].
4. Conclusion
We have found that the Kondo semiconductors CeNiSn and CeRhSb possess a pseudo energy gap with V-shaped structure which is quite different from the gapped state in SmB 6 and YbBI2 of an activated type. It is also notable that the presence of the pseudo spin gap is clear, whereas any clear gap of the charge excitation is not well defined. The energy gap in CeNiSn and CeRhSb is filled up in such a manner that the presence of impurities and inhomogeneities induces the residual density of states at the Fermi level.
References
4.0
r... •
3.C
CeNiSn •
¢~Ooo° o
¢-
•E 2.C
1.0~
5=0
•
CeRhSb o
~'o"°o I
100
g
o
o
I
150
200
T (K)
Fig. 3. T-dependence of the 121SbKnight shift of CeRhSb together with the data of CeNiSn [5].
[1] See e.g.T. Kasuya, Jpn. J. Appl. Phys. Ser. 8 (1993) 3. [2] P.A. Alekseev et al., Physica B 186-188 (1993) 384. [3] T. Takabatake, Y. Nakazawa and M. Ishikawa, Jpn. J. Appl. Phys. Suppl. 26 (1987) 547; T. Takabatake et al., Phys. Rev. B 45 (1992),5740. [4] S.K. Malik and D.T. Adroja, Phys. Rev. B 43 (1991) 6277. [5] M. Kyogaku et al., J. Phys. Soc. Japan 59 (1990) 1728. [6] K. Nakamura et al., J. Phys. Soc. Japan 63 (1994) 433. [7] T. Takabatake, T. Yoshino, H. Tanaka, T. Tadaoka, Y. Bando, H. Fujii, T. Fujita, H. Shida and T. Suzuki, Physica B 206 & 207 (1995) 804. [8] K. Nakamura et ai., unpublished. [9] T.E. Mason et al., Phys. Rev. Lett. 69 (1992) 490. [10] H. Kadowaki et al., J. Phys. Soc. Japan 63 (1994) 6.