- Email: [email protected]
High-temperature resistivity of URh2Ge2
ARTICLE IN PRESS
Physica B 378–380 (2006) 371–372 www.elsevier.com/locate/physb
High-temperature resistivity of URh2Ge2 A. Otopa, I. Maksimova, E.-W. Scheidtb, J.A. Mydoshc,d, S. Su¨llowa, a
Institut fu¨r Physik der Kondensierten Materie, TU Braunschweig, 38106 Braunschweig, Germany CPM, Institut fu¨r Physik, Universita¨t Augsburg, Universita¨tsstraX e 1, 86159 Augsburg, Germany c Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands d Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
b
Abstract We present a study of the anomalous resistivity, with a large r and negative temperature coefficient dr=dT, of the moderately disordered uranium heavy fermion compound URh2Ge2. We establish that the anomalous behavior persist up to high temperatures, i.e., 620 K 2YD , with YD as the Debye temperature. Our finding reinforces the clear comparison of the transport behavior of URh2Ge2 to that of metallic glasses. r 2006 Elsevier B.V. All rights reserved. PACS: 72.15.Eb; 72.15.Qm; 72.15.Rn Keywords: URh2Ge2; UCu4Pd; High-temperature resistivity
In recent years, it has been realized that in the field of quantum criticality close to magnetic instabilities crystallographic disorder represents a relevant perturbation [1]. Regarding this topic, studies have been carried out mostly on heavy fermion-related materials. For these systems, aside from the magnetic ground-state properties, in particular the electronic transport properties are strongly affected by the disorder, giving rise to anomalously large (a few hundred mO cm) resistivities r, with a non-metallic temperature dependence dr=dTo0 (for a review of the experimental situation see Ref. [2]). In most cases, such a behavior is attributed to incoherent Kondo scattering with a disorder-induced wide distribution of Kondo temperatures T K (for a review of theoretical approaches see Ref. [3]). Recently, on experimental grounds, we have challenged the notion of the resistivity being predominantely controlled by magnetic scattering processes in moderately disordered (uranium) heavy fermion compounds. We have presented evidence that the anomalous electronic transport in URh2Ge2 and UCu4Pd more likely is the result of Corresponding author. Tel.: +49 531 391 5116; fax: +49 531 391 5129.
E-mail address: [email protected] (S. Su¨llow). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.130
disorder-induced localization processes rather than as arising from Kondo-like scattering processes [4]. Quantitatively, we have described our experimental data in terms derived from the theory of metallic glasses. The functional dependence used to fit our data represents a model taking into account Anderson localization in the presence of electron–electron and electron–phonon interaction as well as spin–orbit coupling [5]. However, even today and even for metallic glasses, the range of applicability of this model is under dispute. Most importantly, the approach seems to predict that for metallic glasses, as the temperature is increased, a transition in r should occur around the Debye temperature YD from a non-metallic T dependence (dr=dTo0) to a metallic one (dr=dT40). This, however, is not typically observed for metallic glasses (for a discussion of this issue see Ref. [6]). In contrast, for some disordered uranium compounds such a transition has been observed, albeit at temperatures much smaller than YD [7]. In this situation, an apparent question arises if such transitions are more common for moderately disordered uranium compounds. Hence, we have carried out a 4-probe ac resistive study on a poly- and single-crystalline piece of the moderately disordered uranium heavy fermion URh2Ge2 at temperatures up to
ARTICLE IN PRESS A. Otop et al. / Physica B 378–380 (2006) 371–372
372 520
500
ρ (µΩcm)
400 260
260
single crystal
255 0
0
20
40 60 T (K)
ρ (µΩcm)
poly crystal
500
240
80 0 100 200 300 400 500 600 T (K)
Fig. 1. The resistivity of single- and polycrystalline URh2Ge2.
620 K. Previously, we have demonstrated that in this compound, as result of about 10% Rh/Ge site exchange, bond-length disorder is present even in single-crystalline specimens [8]. The samples have been studied via susceptibility measurements with respect to their magnetic properties and found to be antiferromagnetically ordered below T N ¼ 13 K (for a discussion of the sample dependencies in URh2Ge2 see Refs. [9,10]). From specific heat measurements on URh2Ge2 we have established Debye temperatures YD of the order of 250–300 K [9]. In Fig. 1 we plot the overall resistivity and the lowtemperature regime of poly- and single-crystalline (current Ika-axis) URh2Ge2. Altogether, for both samples we find the non-metallic resistive behavior reported previously [4,9,10]. Up to highest temperatures T42YD , the absolute resistivity values are much larger than the Mooij-rule value of 150 mO cm [11], consistent with the observation of a negative dr=dT at all T. Only at low temperatures small resistive anomalies can be seen. For the single crystal the anomaly is clearly associated to the antiferromagnetic transition, and thus reflects the reduction of spin disorder scattering at T N in a small and likely crystallographically better ordered part of the crystal. For the polycrystalline sample the anomaly sets in at a somewhat higher temperature (40 K). Here, we believe that this reflects the onset of coherent scattering in a small and better ordered part of the sample. Yet, these anomalies are neglible compared to the overall resistive signal and the dominant non-metallic T dependence. In addition, we have carried out similar experiments on polycrystalline as-cast material of the Non-Fermi-Liquid (NFL) compound UCu4Pd. Here, we have investigated a sample previously studied in Ref. [12]. For this material, we actually find a very shallow minimum in r at 350 K, with a metallic dr=dT40 at higher T (not shown). Interestingly,
the absolute value of r at 350 K is about 150 mO cm, viz., the Mooij-rule value [11]. Possibly, this might reflect a transition from low temperatures, where r is controlled by static disorder, to high temperatures, with thermally induced vibrational (phononic) disorder. Unfortunately, since for our sample the absolute value of r in our recent measurement is slightly lower than the one reported in Ref. [12], we cannot exclude an aging effect on the resistivity in this compound. In conclusion, we report high-temperature resistivity measurements on poly- and single-crystalline specimens of the moderately disordered heavy fermion compound URh2Ge2 and as-cast polycrystalline material of the NFL systems UCu4Pd. For URh2Ge2 we have established that the anomalous resistive behavior persist up to high temperatures T42YD . With respect to the experimental situation, this finding reinforces the notion of a similarity of the transport behavior to that of metallic glasses. In contrast, a detailed theoretical understanding of our observations is lacking. We believe that developing such an understanding will be an important future task. This work has partially been supported by the DFG under Contract no. SU229/1-3 and within the SFB 484. Samples URh2Ge2 have been produced within FOMALMOS. References [1] [2] [3] [4]
[5]
[6] [7] [8] [9]
[10]
[11] [12]
A. Rosch, Phys. Rev. B 62 (2000) 4945. G. Stewart, Rev. Mod. Phys. 73 (2001) 797. E. Miranda, V. Dobrosavljevic´, Rep. Prog. Phys. 68 (2005) 2337. S. Su¨llow, I. Maksimov, A. Otop, F.J. Litterst, A. Perucchi, L. Degiorgi, J.A. Mydosh, Phys. Rev. Lett. 93 (2004) 266602; A. Otop, S. Su¨llow, M.B. Maple, A. Weber, E.-W. Scheidt, T.J. Gortenmulder, J.A. Mydosh, Phys. Rev. B 72 (2005) 024457. B.L. Altshuler, A.G. Aronov, in: A.L. Efros, M. Pollak (Eds.), Electron–Electron Interaction in Disordered Systems, Elsevier, New York, 1985, p. 1; B.J. Hickey, D. Greig, M.A. Howson, J. Phys. F 16 (1986) L13. P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287. D. Li, Y. Shiokawa, Y. Haga, E. Yamamoto, Y. Onuki, J. Phys. Soc. Japan 71 (2002) 418. C.H. Booth, S.W. Han, S. Su¨llow, J.A. Mydosh, J. Magn. Magn. Mater. 272–276 (2004) 941. S. Su¨llow, S.A.M. Mentink, T.E. Mason, R. Feyerherm, G.J. Nieuwenhuys, A.A. Menovsky, J.A. Mydosh, Phys. Rev. B 61 (2000) 8878. S. Su¨llow, M.B. Maple, R. Chau, D. Tomuta, G.J. Nieuwenhuys, A.A. Menovsky, J.A. Mydosh, J. Magn. Magn. Mater. 226–230 (2001) 35. J.H. Mooij, Phys. Status Solidi A 17 (1973) 521. A. Weber, S. Ko¨rner, E.W. Scheidt, S. Kehrein, G.R. Stewart, Phys. Rev. B 63 (2001) 205116.
Physica B 378–380 (2006) 371–372 www.elsevier.com/locate/physb
High-temperature resistivity of URh2Ge2 A. Otopa, I. Maksimova, E.-W. Scheidtb, J.A. Mydoshc,d, S. Su¨llowa, a
Institut fu¨r Physik der Kondensierten Materie, TU Braunschweig, 38106 Braunschweig, Germany CPM, Institut fu¨r Physik, Universita¨t Augsburg, Universita¨tsstraX e 1, 86159 Augsburg, Germany c Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands d Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
b
Abstract We present a study of the anomalous resistivity, with a large r and negative temperature coefficient dr=dT, of the moderately disordered uranium heavy fermion compound URh2Ge2. We establish that the anomalous behavior persist up to high temperatures, i.e., 620 K 2YD , with YD as the Debye temperature. Our finding reinforces the clear comparison of the transport behavior of URh2Ge2 to that of metallic glasses. r 2006 Elsevier B.V. All rights reserved. PACS: 72.15.Eb; 72.15.Qm; 72.15.Rn Keywords: URh2Ge2; UCu4Pd; High-temperature resistivity
In recent years, it has been realized that in the field of quantum criticality close to magnetic instabilities crystallographic disorder represents a relevant perturbation [1]. Regarding this topic, studies have been carried out mostly on heavy fermion-related materials. For these systems, aside from the magnetic ground-state properties, in particular the electronic transport properties are strongly affected by the disorder, giving rise to anomalously large (a few hundred mO cm) resistivities r, with a non-metallic temperature dependence dr=dTo0 (for a review of the experimental situation see Ref. [2]). In most cases, such a behavior is attributed to incoherent Kondo scattering with a disorder-induced wide distribution of Kondo temperatures T K (for a review of theoretical approaches see Ref. [3]). Recently, on experimental grounds, we have challenged the notion of the resistivity being predominantely controlled by magnetic scattering processes in moderately disordered (uranium) heavy fermion compounds. We have presented evidence that the anomalous electronic transport in URh2Ge2 and UCu4Pd more likely is the result of Corresponding author. Tel.: +49 531 391 5116; fax: +49 531 391 5129.
E-mail address: [email protected] (S. Su¨llow). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.130
disorder-induced localization processes rather than as arising from Kondo-like scattering processes [4]. Quantitatively, we have described our experimental data in terms derived from the theory of metallic glasses. The functional dependence used to fit our data represents a model taking into account Anderson localization in the presence of electron–electron and electron–phonon interaction as well as spin–orbit coupling [5]. However, even today and even for metallic glasses, the range of applicability of this model is under dispute. Most importantly, the approach seems to predict that for metallic glasses, as the temperature is increased, a transition in r should occur around the Debye temperature YD from a non-metallic T dependence (dr=dTo0) to a metallic one (dr=dT40). This, however, is not typically observed for metallic glasses (for a discussion of this issue see Ref. [6]). In contrast, for some disordered uranium compounds such a transition has been observed, albeit at temperatures much smaller than YD [7]. In this situation, an apparent question arises if such transitions are more common for moderately disordered uranium compounds. Hence, we have carried out a 4-probe ac resistive study on a poly- and single-crystalline piece of the moderately disordered uranium heavy fermion URh2Ge2 at temperatures up to
ARTICLE IN PRESS A. Otop et al. / Physica B 378–380 (2006) 371–372
372 520
500
ρ (µΩcm)
400 260
260
single crystal
255 0
0
20
40 60 T (K)
ρ (µΩcm)
poly crystal
500
240
80 0 100 200 300 400 500 600 T (K)
Fig. 1. The resistivity of single- and polycrystalline URh2Ge2.
620 K. Previously, we have demonstrated that in this compound, as result of about 10% Rh/Ge site exchange, bond-length disorder is present even in single-crystalline specimens [8]. The samples have been studied via susceptibility measurements with respect to their magnetic properties and found to be antiferromagnetically ordered below T N ¼ 13 K (for a discussion of the sample dependencies in URh2Ge2 see Refs. [9,10]). From specific heat measurements on URh2Ge2 we have established Debye temperatures YD of the order of 250–300 K [9]. In Fig. 1 we plot the overall resistivity and the lowtemperature regime of poly- and single-crystalline (current Ika-axis) URh2Ge2. Altogether, for both samples we find the non-metallic resistive behavior reported previously [4,9,10]. Up to highest temperatures T42YD , the absolute resistivity values are much larger than the Mooij-rule value of 150 mO cm [11], consistent with the observation of a negative dr=dT at all T. Only at low temperatures small resistive anomalies can be seen. For the single crystal the anomaly is clearly associated to the antiferromagnetic transition, and thus reflects the reduction of spin disorder scattering at T N in a small and likely crystallographically better ordered part of the crystal. For the polycrystalline sample the anomaly sets in at a somewhat higher temperature (40 K). Here, we believe that this reflects the onset of coherent scattering in a small and better ordered part of the sample. Yet, these anomalies are neglible compared to the overall resistive signal and the dominant non-metallic T dependence. In addition, we have carried out similar experiments on polycrystalline as-cast material of the Non-Fermi-Liquid (NFL) compound UCu4Pd. Here, we have investigated a sample previously studied in Ref. [12]. For this material, we actually find a very shallow minimum in r at 350 K, with a metallic dr=dT40 at higher T (not shown). Interestingly,
the absolute value of r at 350 K is about 150 mO cm, viz., the Mooij-rule value [11]. Possibly, this might reflect a transition from low temperatures, where r is controlled by static disorder, to high temperatures, with thermally induced vibrational (phononic) disorder. Unfortunately, since for our sample the absolute value of r in our recent measurement is slightly lower than the one reported in Ref. [12], we cannot exclude an aging effect on the resistivity in this compound. In conclusion, we report high-temperature resistivity measurements on poly- and single-crystalline specimens of the moderately disordered heavy fermion compound URh2Ge2 and as-cast polycrystalline material of the NFL systems UCu4Pd. For URh2Ge2 we have established that the anomalous resistive behavior persist up to high temperatures T42YD . With respect to the experimental situation, this finding reinforces the notion of a similarity of the transport behavior to that of metallic glasses. In contrast, a detailed theoretical understanding of our observations is lacking. We believe that developing such an understanding will be an important future task. This work has partially been supported by the DFG under Contract no. SU229/1-3 and within the SFB 484. Samples URh2Ge2 have been produced within FOMALMOS. References [1] [2] [3] [4]
[5]
[6] [7] [8] [9]
[10]
[11] [12]
A. Rosch, Phys. Rev. B 62 (2000) 4945. G. Stewart, Rev. Mod. Phys. 73 (2001) 797. E. Miranda, V. Dobrosavljevic´, Rep. Prog. Phys. 68 (2005) 2337. S. Su¨llow, I. Maksimov, A. Otop, F.J. Litterst, A. Perucchi, L. Degiorgi, J.A. Mydosh, Phys. Rev. Lett. 93 (2004) 266602; A. Otop, S. Su¨llow, M.B. Maple, A. Weber, E.-W. Scheidt, T.J. Gortenmulder, J.A. Mydosh, Phys. Rev. B 72 (2005) 024457. B.L. Altshuler, A.G. Aronov, in: A.L. Efros, M. Pollak (Eds.), Electron–Electron Interaction in Disordered Systems, Elsevier, New York, 1985, p. 1; B.J. Hickey, D. Greig, M.A. Howson, J. Phys. F 16 (1986) L13. P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287. D. Li, Y. Shiokawa, Y. Haga, E. Yamamoto, Y. Onuki, J. Phys. Soc. Japan 71 (2002) 418. C.H. Booth, S.W. Han, S. Su¨llow, J.A. Mydosh, J. Magn. Magn. Mater. 272–276 (2004) 941. S. Su¨llow, S.A.M. Mentink, T.E. Mason, R. Feyerherm, G.J. Nieuwenhuys, A.A. Menovsky, J.A. Mydosh, Phys. Rev. B 61 (2000) 8878. S. Su¨llow, M.B. Maple, R. Chau, D. Tomuta, G.J. Nieuwenhuys, A.A. Menovsky, J.A. Mydosh, J. Magn. Magn. Mater. 226–230 (2001) 35. J.H. Mooij, Phys. Status Solidi A 17 (1973) 521. A. Weber, S. Ko¨rner, E.W. Scheidt, S. Kehrein, G.R. Stewart, Phys. Rev. B 63 (2001) 205116.