- Email: [email protected]
Thermoelectric power of Ce-based Kondo alloys
PHYSICA Physica B 199&200 11994) 556--557
ELSEVIER
Thermoelectric power of Ce-based Kondo alloys B.D Rainford*, D.T. Adroja, J.M.E. Geers Department q]"Physics, University of Southampton, S09 5NH, UK
Abstract The Kondo lattice compounds CePdSn, CePdGa and CePtGa display pronounced anomalies in thermopower as a function of temperature, with a characteristic inverted tilda ( ,-- ) shape. We have attempted to correlate these anomalies with the dynamical susceptibility derived from inelastic neutron scattering. The TEP of CePdSb has a large positive slope, while that of CeRhSb shows a large peak at 20 K, signalling the onset of the Kondo insulator state.
The thermoelectric power (TEP) in Kondo systems often shows the presence of giant anomalies, due to the strong correlations between the conduction electrons and the local f electrons. Where the eigenstates of the f electrons are split by the crystalline electric field, there is the possibility of both spin-flip and non-spin-flip inelastic scattering processes of the conduction electrons. Typical crystal field splittings A lie in the range 10-50 meV, so that TEP ~momalies can appear on a temperature scale of order A/kB, which might be much larger than the Kondo temperature in a particular alloy. A theoretical treatment of the TEP in the presence of crystal fields was given by Bhattacharjee and Coqblin [1], but they could not explain the sign change observed in the TEP of many Kondo systems. More recently Fischer [2] has presented a formalism in which the sign change appears naturally, as a consequence of the different temperature dependence 2. of two terms Sa,1 Sd, these terms are of orders J3V and J: I/ ia the coupling constants, and are therefore of opposite sign when J, the 4f-conduction electron exchange interaction, is negative. In Fischer's theory S~ and S~ are given in terms of the dynamical susceptibility Im Z(~o) of the 4f electrons, which may be derived from inelastic * Corresponding author.
neutron scattering data. We have attempted to correlate the TEP anomalies with Imx(~o) in the Kondo lattice compouads CePdSn, CePdGa and CePtGa. We also present TEP data for the ferromagnetic Kondo compound CePdSb and the "Kondo insulator" CeRhSb. Ther,~noelectric power measurements were carried out using the differential method in the temperature range 5 K-30~ K. Temperature gradients (AT) were measured with a Au-Fe-chromel thermocouple and the induced voltage IAV) was measured with a Solartron voltmeter (model 7071) using a pure (5N~ Pb reference wire. The total thermopower was calculated from the slope of A V versus AT, and the sample thermopower was obtained by subtracting that of the reference wire. For CePdSn we have used the results in Ref. [3]. The inelastic neutron scattering spectra for CePdGa [.4j, CePtGa and CePdSb were measured at the ISIS Facility, using the HET spectrometer. For CePdSn we have used the neutron data of Khogi et al. 15]. CePdGa, CePtGa and CePdSn share the same TiNISi crystal structure, and all three order antiferromagnetically at low temperatures ( < 8 KI. Their inelastic neutron spectra are also similar, with two crystal field excitations at 18.9, 33.8 meV ~CePdGa), 18.0, 34.5 meV ICePtGa) and ]7.1, 24.8 meV (CePdSnL A simultaneous
0921-4526 94 $07.00 {i~ 1994 Elsevier Science B.V. All rights reserved SSDf 0921-4526193)E0347.3
B.D. Rainjord et al./ Physica B 199&200 (1994) 556-557
-12 -18a 0
0
20
. , " I-6 100 200 300 TEMPERATURE ( K )
557
CeRhSt) 100 200 ---:300 TEMPERATURE ( K )
Fig. 1. Thermopower versus temperature for CePdGa, CePtGa and CePdSn. Solid lines are fits to the theory of Fischer [2].
Fig. 2 Thermopower versus temperature for CePdSb (closed squares) and CeRhSb (open squares).
analysis of the neutron spectra and the susceptibility allowed the crystal field parameters to be determined, and hence lm X(o:) could be calculated. The T E P data for the three compounds (Fig. I) show similar inverted tilda ( ,,- )-shaped anomalies, with maxima between 100 and 200 K, a sign change between 50 and 100 K, followed by minima at lower temperatures. The solid lines in Fig. 1 represent fits of the form -a~ -- bS] - aT, where a T is a small normal metallic contribution and S~, S2d were calculated from lm X(co)using the expressions in Fischer's paper, except that for the S~ term we have omitted the elastic components of Im Z((o). In addition we have used the Suhl-Nagaoka correction for Sdt (Eq. (68) in Ref. i-2] ) which introduces the Kondo temperature TK as an extra parameter. The fitted values of TK were 19.9 K (CePdGa), 26.7 K (CePtGa) and 28.3 K (CePdSn). The effect of neglecting the elastic components of Im X(o~) in the Sdt term is to decrease its magnitude at low temperatures. It is likely that elastic scattering of conduction electrons is suppressed at low temperatures by magnetic shortrange order and by the onset of coherence due to the translational symmetry of the lattice. In contrast, the thermopower of CePdSb increases monotonically with temperature (Fig. 2). CePdSb has the hexagonal Cain2 structure, and is a ferromagnet with an
in CePdSb; while its resistivity shows a weak maximum near 150K, there is no obvious - I n ( T ) behaviour at any temperature. The T E F for CeRhSb is also shown in Fig. 2; its overall form is similar to that of CeNiSn [7]. Both CeRhSb and CeNiSn are " K o n d o insulators" which develop energy gaps in the density of states at Er below 10 K. The T E P is positive over the whole temperature range, but has a negative slope at high temperatures, a flat plateau between 8(? and 150 K and a pronounced peak near 20 K, The plateau occurs in the same temperature range as the broad peaks in z ( T ) and p(T) for CeRhSb [8]. The peak near 20 K is associated with the development of temperature-dependent structure in the density of states, at the onset of the K o n d o insulator state
dlll.k'llldlOldl31~/
I[1~11
I C I l f It'~] k,-~1111].7¢I.11K:tkl L'O [ , J i g q, P l lg3~.Yk.rllk.ll"
ing Gd compound [6]. The absence of a sign change in the T E P might indicate that the SF exchange J is positive
References [1] A.K. Battacharjee and B. Coqblia, Phys. Rev. B 13 (1976) 3441. [2] K.H. Fischer, Z. Phys. B 76 (1989) 315. [3] D.T. Adroja, B.D. Padalia, S.N. Bhatia and S.K. Malik, Phys. Re¢. B 45 (1992) 477. [4] D.T. Adroja, B.D. Rainford and S.K. Malik, Physica B 194-196 (1994) 169. [5] M. Khogi et al.. J. Magn. Magn. Mater. 108 (1992) 187. [6] P.C. Riedi et al., Physica B i99&2f~3 (i994i 558. [7] T. Takabalake et al., Phys. Rev. B 41 [1990) 960"/. [8] SK. Malik and D.T. Adroja, Phys. Rex. B 43 {199116277
ELSEVIER
Thermoelectric power of Ce-based Kondo alloys B.D Rainford*, D.T. Adroja, J.M.E. Geers Department q]"Physics, University of Southampton, S09 5NH, UK
Abstract The Kondo lattice compounds CePdSn, CePdGa and CePtGa display pronounced anomalies in thermopower as a function of temperature, with a characteristic inverted tilda ( ,-- ) shape. We have attempted to correlate these anomalies with the dynamical susceptibility derived from inelastic neutron scattering. The TEP of CePdSb has a large positive slope, while that of CeRhSb shows a large peak at 20 K, signalling the onset of the Kondo insulator state.
The thermoelectric power (TEP) in Kondo systems often shows the presence of giant anomalies, due to the strong correlations between the conduction electrons and the local f electrons. Where the eigenstates of the f electrons are split by the crystalline electric field, there is the possibility of both spin-flip and non-spin-flip inelastic scattering processes of the conduction electrons. Typical crystal field splittings A lie in the range 10-50 meV, so that TEP ~momalies can appear on a temperature scale of order A/kB, which might be much larger than the Kondo temperature in a particular alloy. A theoretical treatment of the TEP in the presence of crystal fields was given by Bhattacharjee and Coqblin [1], but they could not explain the sign change observed in the TEP of many Kondo systems. More recently Fischer [2] has presented a formalism in which the sign change appears naturally, as a consequence of the different temperature dependence 2. of two terms Sa,1 Sd, these terms are of orders J3V and J: I/ ia the coupling constants, and are therefore of opposite sign when J, the 4f-conduction electron exchange interaction, is negative. In Fischer's theory S~ and S~ are given in terms of the dynamical susceptibility Im Z(~o) of the 4f electrons, which may be derived from inelastic * Corresponding author.
neutron scattering data. We have attempted to correlate the TEP anomalies with Imx(~o) in the Kondo lattice compouads CePdSn, CePdGa and CePtGa. We also present TEP data for the ferromagnetic Kondo compound CePdSb and the "Kondo insulator" CeRhSb. Ther,~noelectric power measurements were carried out using the differential method in the temperature range 5 K-30~ K. Temperature gradients (AT) were measured with a Au-Fe-chromel thermocouple and the induced voltage IAV) was measured with a Solartron voltmeter (model 7071) using a pure (5N~ Pb reference wire. The total thermopower was calculated from the slope of A V versus AT, and the sample thermopower was obtained by subtracting that of the reference wire. For CePdSn we have used the results in Ref. [3]. The inelastic neutron scattering spectra for CePdGa [.4j, CePtGa and CePdSb were measured at the ISIS Facility, using the HET spectrometer. For CePdSn we have used the neutron data of Khogi et al. 15]. CePdGa, CePtGa and CePdSn share the same TiNISi crystal structure, and all three order antiferromagnetically at low temperatures ( < 8 KI. Their inelastic neutron spectra are also similar, with two crystal field excitations at 18.9, 33.8 meV ~CePdGa), 18.0, 34.5 meV ICePtGa) and ]7.1, 24.8 meV (CePdSnL A simultaneous
0921-4526 94 $07.00 {i~ 1994 Elsevier Science B.V. All rights reserved SSDf 0921-4526193)E0347.3
B.D. Rainjord et al./ Physica B 199&200 (1994) 556-557
-12 -18a 0
0
20
. , " I-6 100 200 300 TEMPERATURE ( K )
557
CeRhSt) 100 200 ---:300 TEMPERATURE ( K )
Fig. 1. Thermopower versus temperature for CePdGa, CePtGa and CePdSn. Solid lines are fits to the theory of Fischer [2].
Fig. 2 Thermopower versus temperature for CePdSb (closed squares) and CeRhSb (open squares).
analysis of the neutron spectra and the susceptibility allowed the crystal field parameters to be determined, and hence lm X(o:) could be calculated. The T E P data for the three compounds (Fig. I) show similar inverted tilda ( ,,- )-shaped anomalies, with maxima between 100 and 200 K, a sign change between 50 and 100 K, followed by minima at lower temperatures. The solid lines in Fig. 1 represent fits of the form -a~ -- bS] - aT, where a T is a small normal metallic contribution and S~, S2d were calculated from lm X(co)using the expressions in Fischer's paper, except that for the S~ term we have omitted the elastic components of Im Z((o). In addition we have used the Suhl-Nagaoka correction for Sdt (Eq. (68) in Ref. i-2] ) which introduces the Kondo temperature TK as an extra parameter. The fitted values of TK were 19.9 K (CePdGa), 26.7 K (CePtGa) and 28.3 K (CePdSn). The effect of neglecting the elastic components of Im X(o~) in the Sdt term is to decrease its magnitude at low temperatures. It is likely that elastic scattering of conduction electrons is suppressed at low temperatures by magnetic shortrange order and by the onset of coherence due to the translational symmetry of the lattice. In contrast, the thermopower of CePdSb increases monotonically with temperature (Fig. 2). CePdSb has the hexagonal Cain2 structure, and is a ferromagnet with an
in CePdSb; while its resistivity shows a weak maximum near 150K, there is no obvious - I n ( T ) behaviour at any temperature. The T E F for CeRhSb is also shown in Fig. 2; its overall form is similar to that of CeNiSn [7]. Both CeRhSb and CeNiSn are " K o n d o insulators" which develop energy gaps in the density of states at Er below 10 K. The T E P is positive over the whole temperature range, but has a negative slope at high temperatures, a flat plateau between 8(? and 150 K and a pronounced peak near 20 K, The plateau occurs in the same temperature range as the broad peaks in z ( T ) and p(T) for CeRhSb [8]. The peak near 20 K is associated with the development of temperature-dependent structure in the density of states, at the onset of the K o n d o insulator state
dlll.k'llldlOldl31~/
I[1~11
I C I l f It'~] k,-~1111].7¢I.11K:tkl L'O [ , J i g q, P l lg3~.Yk.rllk.ll"
ing Gd compound [6]. The absence of a sign change in the T E P might indicate that the SF exchange J is positive
References [1] A.K. Battacharjee and B. Coqblia, Phys. Rev. B 13 (1976) 3441. [2] K.H. Fischer, Z. Phys. B 76 (1989) 315. [3] D.T. Adroja, B.D. Padalia, S.N. Bhatia and S.K. Malik, Phys. Re¢. B 45 (1992) 477. [4] D.T. Adroja, B.D. Rainford and S.K. Malik, Physica B 194-196 (1994) 169. [5] M. Khogi et al.. J. Magn. Magn. Mater. 108 (1992) 187. [6] P.C. Riedi et al., Physica B i99&2f~3 (i994i 558. [7] T. Takabalake et al., Phys. Rev. B 41 [1990) 960"/. [8] SK. Malik and D.T. Adroja, Phys. Rex. B 43 {199116277