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Anomalous electronic transport in CuIr2S4 and CuIr2Se4
Physb1=17275=Durai=Venkatachala=BG
Physica B 281&282 (2000) 629}630
Anomalous electronic transport in CuIr S and CuIr Se 2 4 2 4 A.T. Burkov!,#, T. Nakama!,*, K. Shintani!, K. Yagasaki!, N. Matsumoto", S. Nagata" !Department of Physics, College of Science, University of the Ryukyus, Okinawa 903-01, Japan "Department of Materials Science and Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan #A.F. Iowe Physical-Technical Institute, Russian Academy of Sciencies, Sankt-Petersburg 194021, Russia
Abstract The resistivity (o) and the thermopower (S) of spinel-type compounds CuIr S and CuIr Se have been measured at 2 4 2 4 temperatures from 2 to 900 K under magnetic "eld from 0 to 15 T. The thermopower of both compounds is positive in the metallic phase except for the low-temperature region in CuIr Se . It is also positive in the insulating state of CuIr S , 2 4 2 4 implying p-type charge carriers, in agreement with the recent photoemission results. The low-temperature resistivity of CuIr S is well described by Efros}Shklovskii variable-range hopping conductivity mechanism: o"o exp[(¹H/¹)1@2]. 2 4 0 The most unusual feature of the transport is that the resistivity of both compounds in the metallic state reveals an activation type of the temperature dependence. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Metal}insulator transition; Electrical resistivity; Thermopower; CuIr S 2 4
Spinel-type compound CuIr S is known for the 2 4 metal}insulator transition (MIT) at ¹+230 K [1,2]. Despite rather extensive studies the precise driving force of the transition remains unknown. Moreover, recent photoemission results [3] suggest that the metallic phase of CuIr S and the isostructural compound CuIr Se 2 4 2 4 have unusual features in their electronic structure which may have an important impact on the electronic transport. The transport property measurements were made with polycrystalline sintered samples of CuIr S and 2 4 CuIr Se . The sample preparation procedures were de2 4 scribed elsewhere [1,2]. The resistivity and the thermopower of CuIr Se at 2 4 temperatures from 2 up to 900 K are shown in Fig. 1. To reveal the type of the resistivity dependency on temperature, we plot in Fig. 2 the logarithmic temperature derivative of the resistivity: 1/(o!o )(do/d¹), as a func0 tion of temperature in double logarithmic scale. For
* Corresponding author. Tel.: #81-98-895-8514; fax: #8198-895-8509. E-mail address: [email protected] (T. Nakama)
a power dependence on temperature, which is expected for resistivity of a conventional metal: o(¹)"a¹m#o , 0 the logarithm of the derivative is expressed as: ln [1/(o!o ) (do/d¹)]"lnm!ln¹, i.e., is a linear func0 tion of ln ¹ with the gradient of !1. The experimental dependence, shown in Fig. 2, reveals two regions of a linear variation with ln ¹: below ¹ "190 K it has the 5 gradient of about ! 3/2; whereas at higher temperatures than ¹ the gradient is close to !2. These values of the 5 gradient of ln[1/(o!o ) do/d¹] versus ln ¹ dependence 0 correspond to an exponential temperature dependence of the resistivity: o!o "exp [!(¹H/¹)n] with n+1/2 0 for temperatures below ¹ and n+1 for above ¹ , re5 5 spectively. The experimental data give unambiguous evidence of the activation-type temperature dependence of the resistivity well beyond the experimental uncertainty in the range of 2}900 K. It is also interesting that the value of ¹ is very close to the temperature of 5 MIT"230 K in CuIr S . 2 4 The resistivity and the thermopower of CuIr S are 2 4 depicted in Fig. 3. Below MIT the resistivity of CuIr S 2 4 does not follow a simple activation law. At temperatures below 50 K and at temperatures much above MIT, the temperature dependence is well described by o" a exp[G(¹H/¹)1@2], with `!a for the high-temperature
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 9 8 7 - 4
Physb1=17275=Durai=VVC=BG 630
A.T. Burkov et al. / Physica B 281&282 (2000) 629}630
Fig. 1. Temperature dependence of the thermopower (#) and the resistivity (L) of CuIr Se in zero magnetic "eld. The lines 2 4 are guides for the eye.
Fig. 2. Derivative of resistivity 1/(o(¹)!o )(do/d¹) of 0 CuIr Se against temperature in double logarithmic scale. Solid 2 4 and broken lines show the derivative for function o"a exp[!(¹H/¹)n] with n"0.4, and 0.9. The line marked by n"0 displays the derivative for a power dependence of resistivity on temperature: o!o "b¹m. There is a change in the 0 gradient of the experimental temperature dependence at ¹"¹ . 5
region and with `#a for the low-temperature range. In low-temperature range, in the insulator phase, o" a exp(¹H/¹)1@2, it is similar to the dependence which follows from Efros}Shklovskii hopping mechanism with long-range Coulomb correlations [4]. This indicates that the Coulomb correlations may play an important role in the formation of the insulating phase of CuIr S . 2 4 In the high-temperature range above MIT, the resistivity of CuIr S has the same temperature dependence 2 4 as the low-temperature phase of CuIr Se : 2 4 o"a exp[!(¹H/¹)1@2]. Note that o+a exp(!¹H /¹) H at high-temperatures of CuIr Se . 2 4 A few mechanisms, which can lead to an exponential dependence of resistivity on temperature have been discussed. The most familiar is Mott's s}d scattering model
Fig. 3. Temperature dependence of the thermopower (#) and the resistivity (L) of CuIr S in zero magnetic "eld. The lines 2 4 are guides for the eye.
[5]. The others include scattering on localized states split by crystal "eld [6], or low-dimensional models of conductivity [7]. It seems that a modi"ed Mott's model is appropriate in the present case. It is assumed in the model that s-band is the main current carrying band. The d-band in the actual energy region near to Fermi energy is composed of low lying, almost completely "lled sub-band d , and higher 1 lying, empty sub-band d , separated by an energy gap. 2 The partially "lled s-band slightly overlaps the d sub1 band. We further assume, as in usual s}d model, that resistivity arises mainly due to s}d scattering, with the scattering probability being proportional to the d state density at the Fermi energy. As temperature increases, the chemical potential shifts to higher energy to satisfy the charge conservation condition. This shift opens a gap between the chemical potential and the top of d 1 sub-band, thus resulting in the exponential variation of the s}d scattering rate, and, consequently, of the resistivity. The temperature variation of the energy gap alters exponential temperature dependency of the resistivity, reducing n value from n"1 to n"1/2.
References [1] S. Nagata, T. Hagino, Y. Seki, T. Bitoh, Physica B 194}196 (1994) 1077. [2] S. Nagata, N. Matsumoto, Y. Kato, T. Furubayashi, T. Matsumoto, J.P. Sanchez, P. Vullet, Phys. Rev. B 58 (1998) 6844. [3] J. Matsuno, T. Mizokawa, A. Fujimori, D.A. Zatsepin, V.R. Galakhov, E.Z. Kurmaev, Y. Kato, S. Nagata, Phys. Rev. B 55 (1997) R15 979. [4] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49. [5] A.H. Wilson, Proc. Roy. Soc. London 167 (1938) 580. [6] R.J. Elliott, Phys. Rev. 94 (1954) 564. [7] D.W. Woodard, G.D. Cody, Phys. Rev. 136 (1964) A166.
Physica B 281&282 (2000) 629}630
Anomalous electronic transport in CuIr S and CuIr Se 2 4 2 4 A.T. Burkov!,#, T. Nakama!,*, K. Shintani!, K. Yagasaki!, N. Matsumoto", S. Nagata" !Department of Physics, College of Science, University of the Ryukyus, Okinawa 903-01, Japan "Department of Materials Science and Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan #A.F. Iowe Physical-Technical Institute, Russian Academy of Sciencies, Sankt-Petersburg 194021, Russia
Abstract The resistivity (o) and the thermopower (S) of spinel-type compounds CuIr S and CuIr Se have been measured at 2 4 2 4 temperatures from 2 to 900 K under magnetic "eld from 0 to 15 T. The thermopower of both compounds is positive in the metallic phase except for the low-temperature region in CuIr Se . It is also positive in the insulating state of CuIr S , 2 4 2 4 implying p-type charge carriers, in agreement with the recent photoemission results. The low-temperature resistivity of CuIr S is well described by Efros}Shklovskii variable-range hopping conductivity mechanism: o"o exp[(¹H/¹)1@2]. 2 4 0 The most unusual feature of the transport is that the resistivity of both compounds in the metallic state reveals an activation type of the temperature dependence. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Metal}insulator transition; Electrical resistivity; Thermopower; CuIr S 2 4
Spinel-type compound CuIr S is known for the 2 4 metal}insulator transition (MIT) at ¹+230 K [1,2]. Despite rather extensive studies the precise driving force of the transition remains unknown. Moreover, recent photoemission results [3] suggest that the metallic phase of CuIr S and the isostructural compound CuIr Se 2 4 2 4 have unusual features in their electronic structure which may have an important impact on the electronic transport. The transport property measurements were made with polycrystalline sintered samples of CuIr S and 2 4 CuIr Se . The sample preparation procedures were de2 4 scribed elsewhere [1,2]. The resistivity and the thermopower of CuIr Se at 2 4 temperatures from 2 up to 900 K are shown in Fig. 1. To reveal the type of the resistivity dependency on temperature, we plot in Fig. 2 the logarithmic temperature derivative of the resistivity: 1/(o!o )(do/d¹), as a func0 tion of temperature in double logarithmic scale. For
* Corresponding author. Tel.: #81-98-895-8514; fax: #8198-895-8509. E-mail address: [email protected] (T. Nakama)
a power dependence on temperature, which is expected for resistivity of a conventional metal: o(¹)"a¹m#o , 0 the logarithm of the derivative is expressed as: ln [1/(o!o ) (do/d¹)]"lnm!ln¹, i.e., is a linear func0 tion of ln ¹ with the gradient of !1. The experimental dependence, shown in Fig. 2, reveals two regions of a linear variation with ln ¹: below ¹ "190 K it has the 5 gradient of about ! 3/2; whereas at higher temperatures than ¹ the gradient is close to !2. These values of the 5 gradient of ln[1/(o!o ) do/d¹] versus ln ¹ dependence 0 correspond to an exponential temperature dependence of the resistivity: o!o "exp [!(¹H/¹)n] with n+1/2 0 for temperatures below ¹ and n+1 for above ¹ , re5 5 spectively. The experimental data give unambiguous evidence of the activation-type temperature dependence of the resistivity well beyond the experimental uncertainty in the range of 2}900 K. It is also interesting that the value of ¹ is very close to the temperature of 5 MIT"230 K in CuIr S . 2 4 The resistivity and the thermopower of CuIr S are 2 4 depicted in Fig. 3. Below MIT the resistivity of CuIr S 2 4 does not follow a simple activation law. At temperatures below 50 K and at temperatures much above MIT, the temperature dependence is well described by o" a exp[G(¹H/¹)1@2], with `!a for the high-temperature
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 9 8 7 - 4
Physb1=17275=Durai=VVC=BG 630
A.T. Burkov et al. / Physica B 281&282 (2000) 629}630
Fig. 1. Temperature dependence of the thermopower (#) and the resistivity (L) of CuIr Se in zero magnetic "eld. The lines 2 4 are guides for the eye.
Fig. 2. Derivative of resistivity 1/(o(¹)!o )(do/d¹) of 0 CuIr Se against temperature in double logarithmic scale. Solid 2 4 and broken lines show the derivative for function o"a exp[!(¹H/¹)n] with n"0.4, and 0.9. The line marked by n"0 displays the derivative for a power dependence of resistivity on temperature: o!o "b¹m. There is a change in the 0 gradient of the experimental temperature dependence at ¹"¹ . 5
region and with `#a for the low-temperature range. In low-temperature range, in the insulator phase, o" a exp(¹H/¹)1@2, it is similar to the dependence which follows from Efros}Shklovskii hopping mechanism with long-range Coulomb correlations [4]. This indicates that the Coulomb correlations may play an important role in the formation of the insulating phase of CuIr S . 2 4 In the high-temperature range above MIT, the resistivity of CuIr S has the same temperature dependence 2 4 as the low-temperature phase of CuIr Se : 2 4 o"a exp[!(¹H/¹)1@2]. Note that o+a exp(!¹H /¹) H at high-temperatures of CuIr Se . 2 4 A few mechanisms, which can lead to an exponential dependence of resistivity on temperature have been discussed. The most familiar is Mott's s}d scattering model
Fig. 3. Temperature dependence of the thermopower (#) and the resistivity (L) of CuIr S in zero magnetic "eld. The lines 2 4 are guides for the eye.
[5]. The others include scattering on localized states split by crystal "eld [6], or low-dimensional models of conductivity [7]. It seems that a modi"ed Mott's model is appropriate in the present case. It is assumed in the model that s-band is the main current carrying band. The d-band in the actual energy region near to Fermi energy is composed of low lying, almost completely "lled sub-band d , and higher 1 lying, empty sub-band d , separated by an energy gap. 2 The partially "lled s-band slightly overlaps the d sub1 band. We further assume, as in usual s}d model, that resistivity arises mainly due to s}d scattering, with the scattering probability being proportional to the d state density at the Fermi energy. As temperature increases, the chemical potential shifts to higher energy to satisfy the charge conservation condition. This shift opens a gap between the chemical potential and the top of d 1 sub-band, thus resulting in the exponential variation of the s}d scattering rate, and, consequently, of the resistivity. The temperature variation of the energy gap alters exponential temperature dependency of the resistivity, reducing n value from n"1 to n"1/2.
References [1] S. Nagata, T. Hagino, Y. Seki, T. Bitoh, Physica B 194}196 (1994) 1077. [2] S. Nagata, N. Matsumoto, Y. Kato, T. Furubayashi, T. Matsumoto, J.P. Sanchez, P. Vullet, Phys. Rev. B 58 (1998) 6844. [3] J. Matsuno, T. Mizokawa, A. Fujimori, D.A. Zatsepin, V.R. Galakhov, E.Z. Kurmaev, Y. Kato, S. Nagata, Phys. Rev. B 55 (1997) R15 979. [4] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49. [5] A.H. Wilson, Proc. Roy. Soc. London 167 (1938) 580. [6] R.J. Elliott, Phys. Rev. 94 (1954) 564. [7] D.W. Woodard, G.D. Cody, Phys. Rev. 136 (1964) A166.