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Transport properties in PrOs4Sb12 single crystals probed by radiation-induced disordering
ARTICLE IN PRESS
Physica B 359–361 (2005) 913–916 www.elsevier.com/locate/physb
Transport properties in PrOs4Sb12 single crystals probed by radiation-induced disordering A. Karkin, A. Krivoshchekov, S. Naumov, N. Kostromitina, B. Goshchitskii Institute of Metal Physics, S. Kovalevskoi Str. 18, Ekaterinburg 620219, Russian Federation
Abstract Resistivity rðTÞ and Hall coefficient RH ðTÞ in magnetic fields H up to 13.6 T were studied in superconducting (T C ¼ 1:8 K) PrOs4Sb12 single crystals disordered by fast neutron irradiation. Disordering leads to very fast suppression of superconductivity and to large increase in low-temperature values of both r and RH. Kondo-like magnetic scattering is observed in disordered crystals. Positive magnetoresistance in the crystals with different values of disordering is observed only at To10 K: It is an evidence of magnetic field influence on the band of conduction electrons. It is shown that the electronic transport in a PrOs4Sb12 can be described by two-band model including heavy and light holes. r 2005 Elsevier B.V. All rights reserved. PACS: 72.15.Gd; 74 Keywords: Heavy fermions; Neutron irradiation; Transport properties
It is considered that the ground state of heavy fermion (HF) systems emerges under continuous transition from a high-T phase, in which felectrons behave as if they were localized with well-defined magnetic moments, to a low-T HF liquid phase, in which f-electrons seem to be delocalized with large effective electron mass m : At low T, the resistivity r1 ðTÞ ¼ r01 þ AT 2 with relatively large A, while at high T, it usually is r2 ðTÞ ¼ r02 B lnðTÞ; where the last term deCorresponding author. Tel.: +7 3433 744494;
fax: +7 3433 740003. E-mail address: [email protected] (A. Karkin).
scribes the magnetic scattering of Kondo type. In fact, other light carriers can also make a significant contribution to conductivity even at low T. To reveal the features of the electronic transport, we studied an influence of atomic irradiation-induced disordering on r and Hall coefficient RH in single crystals of the recently discovered HF system PrOs4Sb12 with m 50me ; which has attracted interest because of the superconductivity observed at T C ¼ 1:85 K [1]. Single crystals PrOs4Sb12 were grown from a solution in a melt of antimony [1]. Initial components in the ratio of 1.5(Pr):4(Os):25(Sb) were placed in a graphite container with a cover,
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.261
ARTICLE IN PRESS A. Karkin et al. / Physica B 359– 361 (2005) 913–916
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which, in its turn, was placed in an evacuated quartz tube. The tube was slowly (20 h) heated up to 950 1C, held so for 3–5 h and then cooled down to 640 1C at a rate of 2–5 1C h1. The crystals had a cubic structure [2] with lattice parameter a0 ¼ 9:301 A˚ (compared with ˚ a0 ¼ 9:3017 A in [1]) and relatively small residual resistivity r0 5 mO cm. Superconductivity was observed at T C ¼ 1:8 K: Crystals 1.0 0.6 0.1 mm3 in size were irradiated with fast neutrons (fluence F ¼ 2 1019 cm2 ) at T ¼ ð330 10Þ K: The irradiated sample was isochronally (20 min.) annealed within a temperature range of 100–45001C. The initial sample shows a very complex temperature dependence of rðTÞ (Fig. 1). At To5 K; the value rðTÞ has approximately linear dependence instead of the expected squared one; in
addition, low-T resistivity is strongly affected by the magnetic field. At T ¼ ð10250Þ K; rðTÞ shows square-law dependence, while, again, at T4200 K; it is rather linear. Radiation-induced disordering leads to considerable modification of the transport properties. High-T resistivity slope is transformed from positive dr=dT40 in the initial sample to dr=dTo0 in the irradiated one, and is restored after annealing at T ann ¼ 200 1C: Low T part of rðTÞ shows a large increase in residual resistivity r0, similar to the increase in dr=dT: Magnetic field H leads to a qualitative change in low-T dependence of rðTÞ: from roughly linear at H¼0 to approximately logarithmic at H ¼ 13:6 T (Fig. 1). The Hall coefficient RH ðTÞ also shows significant transformations under irradiation (Fig. 2),
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Fig. 1. Resistivity rðTÞ for initial (1), irradiated by F ¼ 2 1019 cm2 and annealed at T ann ¼100 1C (2), 150 1C (3), 200oC (4), 250 1C % (5), 300 1C (6), 350 1C (7), 400 1C (8) and 450 1C (9) sample PrOs4Sb12 at H ¼ 0 (blank symbols) and H ¼ 13:6 T (filled symbols). Curves on the right panel are shifted for clarity.
ARTICLE IN PRESS A. Karkin et al. / Physica B 359– 361 (2005) 913–916 14
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RH, 10-3 cm3/C
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T,K Fig. 2. Hall coefficient RH ðTÞ for initial (1), irradiated by F ¼ 2 1019 cm2 (2) and annealed at Tann ¼ 100 oC (3), 200 1C (4), 300 1C (5) and 400 1C (6) sample PrOs4%Sb12 at H ¼ 13:6 T.
low-T Hall number nH ¼ ðRH eÞ1 decreases from 2.8 to 0.46 1021 cm3. Evidently, the strong T-dependence of RH ðTÞ appears because of the multi-band origin of the electronic states with at least two types of carriers with qualitatively different temperature dependences of their resistivities. To describe T-dependences of RH ðTÞ measured at H ¼ 13:6 T, resistivities and RH may be represented in the form r1 ¼ r0 þ A1 T 2 , r2 ¼ r02 þ A2 T B lnðTÞ, RH ¼ ðRH1 =r21 þ RH2 =r22 =ð1=r1 þ 1=r2 Þ2 , where indexes 1 and 2 are related to holes of two types (heavy and light holes). Fitting (solid lines in Fig. 2) shows that RH2 remains approximately constant while RH1 increases, i.e. the heavy holes
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concentration nH1 ¼ 1=RH1 decreases under irradiation. A satisfactory description of experimental rðTÞ curves in H ¼ 13:6 T (Fig. 1) can be achieved (using for conductivity an expression 1=r ¼ 1=r1 þ 1=r2 ) with roughly the same parameters r01, A1, r02, A2 and B. Zero field curves cannot be described by two-band model because of the sharp features in low-T resistivity at To5 K: To understand the large values of positive magnetoresistance, we estimate the values of inverse mobility m1 ; because a normal magnetoresistance (related to the distortion of electronic paths by magnetic field) is determined by the parameter ðH=m1 Þ2 : Using low-T values of r 1200 mO cm and RH 14 cm3 C1 for the irradiated sample, we obtain m1 103 T, therefore these effects are neglected in the fields up to 13.6 T. The origin of the influence of H on the low-T resistivity (so called high-field ordered phase), observed in the sample with different disorder, may be attributed to Zeeman splitting of Pr3+ J ¼ 4 states which affects the interaction between 4-f and conduction electrons [3]. The initial state is almost completely restored after annealing at 450 1C, however, superconductivity does not appear at T41:45 K: Therefore superconductivity is extremely sensitive to atomic disordering. In conclusion, we have shown that (i) Atomic disordering leads to a significant rearrangement of band structure: it decreases charge carrier concentration (heavy holes). At that, superconductivity is suppressed and Kondo-like magnetic scattering is observed in disordered crystals. The initial state is almost completely restored upon annealing at 450 1C. However, superconductivity does not appear at T41:45 K: (ii) Positive magnetoresistance observed at low temperatures only in the crystals with different values of disorder is an evidence of magnetic field influence on the band of conduction electrons; (iii) The electronic transport in a PrOs4Sb12 sample can be described by two-band model including heavy and light holes. Work was carried out with the financial support of the Ministry of Industry, Science and Technologies of the Russian Federation (State contracts
ARTICLE IN PRESS 916
A. Karkin et al. / Physica B 359– 361 (2005) 913–916
Nos. 40.020.1.1.1166, 40.012.1.1.1356) and the Special Federal Program of Basic Research at Russian Academy of Science ‘‘Quantum macrophysics’’ (State contract no 1000-251/P-03/040348-11054-269, Project UB RAS no 3).
References [1] E.D. Bauer, et al., Phys. Rev. B 65 (2002) 100506(R). [2] W. Jeitscho, et al., Acta Crystallogr. B 33 (1977) 3401. [3] P.-C. Ho, et al., Phys. Rev. B 67 (2003) 180508(R).
Physica B 359–361 (2005) 913–916 www.elsevier.com/locate/physb
Transport properties in PrOs4Sb12 single crystals probed by radiation-induced disordering A. Karkin, A. Krivoshchekov, S. Naumov, N. Kostromitina, B. Goshchitskii Institute of Metal Physics, S. Kovalevskoi Str. 18, Ekaterinburg 620219, Russian Federation
Abstract Resistivity rðTÞ and Hall coefficient RH ðTÞ in magnetic fields H up to 13.6 T were studied in superconducting (T C ¼ 1:8 K) PrOs4Sb12 single crystals disordered by fast neutron irradiation. Disordering leads to very fast suppression of superconductivity and to large increase in low-temperature values of both r and RH. Kondo-like magnetic scattering is observed in disordered crystals. Positive magnetoresistance in the crystals with different values of disordering is observed only at To10 K: It is an evidence of magnetic field influence on the band of conduction electrons. It is shown that the electronic transport in a PrOs4Sb12 can be described by two-band model including heavy and light holes. r 2005 Elsevier B.V. All rights reserved. PACS: 72.15.Gd; 74 Keywords: Heavy fermions; Neutron irradiation; Transport properties
It is considered that the ground state of heavy fermion (HF) systems emerges under continuous transition from a high-T phase, in which felectrons behave as if they were localized with well-defined magnetic moments, to a low-T HF liquid phase, in which f-electrons seem to be delocalized with large effective electron mass m : At low T, the resistivity r1 ðTÞ ¼ r01 þ AT 2 with relatively large A, while at high T, it usually is r2 ðTÞ ¼ r02 B lnðTÞ; where the last term deCorresponding author. Tel.: +7 3433 744494;
fax: +7 3433 740003. E-mail address: [email protected] (A. Karkin).
scribes the magnetic scattering of Kondo type. In fact, other light carriers can also make a significant contribution to conductivity even at low T. To reveal the features of the electronic transport, we studied an influence of atomic irradiation-induced disordering on r and Hall coefficient RH in single crystals of the recently discovered HF system PrOs4Sb12 with m 50me ; which has attracted interest because of the superconductivity observed at T C ¼ 1:85 K [1]. Single crystals PrOs4Sb12 were grown from a solution in a melt of antimony [1]. Initial components in the ratio of 1.5(Pr):4(Os):25(Sb) were placed in a graphite container with a cover,
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.261
ARTICLE IN PRESS A. Karkin et al. / Physica B 359– 361 (2005) 913–916
914
which, in its turn, was placed in an evacuated quartz tube. The tube was slowly (20 h) heated up to 950 1C, held so for 3–5 h and then cooled down to 640 1C at a rate of 2–5 1C h1. The crystals had a cubic structure [2] with lattice parameter a0 ¼ 9:301 A˚ (compared with ˚ a0 ¼ 9:3017 A in [1]) and relatively small residual resistivity r0 5 mO cm. Superconductivity was observed at T C ¼ 1:8 K: Crystals 1.0 0.6 0.1 mm3 in size were irradiated with fast neutrons (fluence F ¼ 2 1019 cm2 ) at T ¼ ð330 10Þ K: The irradiated sample was isochronally (20 min.) annealed within a temperature range of 100–45001C. The initial sample shows a very complex temperature dependence of rðTÞ (Fig. 1). At To5 K; the value rðTÞ has approximately linear dependence instead of the expected squared one; in
addition, low-T resistivity is strongly affected by the magnetic field. At T ¼ ð10250Þ K; rðTÞ shows square-law dependence, while, again, at T4200 K; it is rather linear. Radiation-induced disordering leads to considerable modification of the transport properties. High-T resistivity slope is transformed from positive dr=dT40 in the initial sample to dr=dTo0 in the irradiated one, and is restored after annealing at T ann ¼ 200 1C: Low T part of rðTÞ shows a large increase in residual resistivity r0, similar to the increase in dr=dT: Magnetic field H leads to a qualitative change in low-T dependence of rðTÞ: from roughly linear at H¼0 to approximately logarithmic at H ¼ 13:6 T (Fig. 1). The Hall coefficient RH ðTÞ also shows significant transformations under irradiation (Fig. 2),
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ρ, µΩcm
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T,K
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Fig. 1. Resistivity rðTÞ for initial (1), irradiated by F ¼ 2 1019 cm2 and annealed at T ann ¼100 1C (2), 150 1C (3), 200oC (4), 250 1C % (5), 300 1C (6), 350 1C (7), 400 1C (8) and 450 1C (9) sample PrOs4Sb12 at H ¼ 0 (blank symbols) and H ¼ 13:6 T (filled symbols). Curves on the right panel are shifted for clarity.
ARTICLE IN PRESS A. Karkin et al. / Physica B 359– 361 (2005) 913–916 14
2
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RH, 10-3 cm3/C
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T,K Fig. 2. Hall coefficient RH ðTÞ for initial (1), irradiated by F ¼ 2 1019 cm2 (2) and annealed at Tann ¼ 100 oC (3), 200 1C (4), 300 1C (5) and 400 1C (6) sample PrOs4%Sb12 at H ¼ 13:6 T.
low-T Hall number nH ¼ ðRH eÞ1 decreases from 2.8 to 0.46 1021 cm3. Evidently, the strong T-dependence of RH ðTÞ appears because of the multi-band origin of the electronic states with at least two types of carriers with qualitatively different temperature dependences of their resistivities. To describe T-dependences of RH ðTÞ measured at H ¼ 13:6 T, resistivities and RH may be represented in the form r1 ¼ r0 þ A1 T 2 , r2 ¼ r02 þ A2 T B lnðTÞ, RH ¼ ðRH1 =r21 þ RH2 =r22 =ð1=r1 þ 1=r2 Þ2 , where indexes 1 and 2 are related to holes of two types (heavy and light holes). Fitting (solid lines in Fig. 2) shows that RH2 remains approximately constant while RH1 increases, i.e. the heavy holes
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concentration nH1 ¼ 1=RH1 decreases under irradiation. A satisfactory description of experimental rðTÞ curves in H ¼ 13:6 T (Fig. 1) can be achieved (using for conductivity an expression 1=r ¼ 1=r1 þ 1=r2 ) with roughly the same parameters r01, A1, r02, A2 and B. Zero field curves cannot be described by two-band model because of the sharp features in low-T resistivity at To5 K: To understand the large values of positive magnetoresistance, we estimate the values of inverse mobility m1 ; because a normal magnetoresistance (related to the distortion of electronic paths by magnetic field) is determined by the parameter ðH=m1 Þ2 : Using low-T values of r 1200 mO cm and RH 14 cm3 C1 for the irradiated sample, we obtain m1 103 T, therefore these effects are neglected in the fields up to 13.6 T. The origin of the influence of H on the low-T resistivity (so called high-field ordered phase), observed in the sample with different disorder, may be attributed to Zeeman splitting of Pr3+ J ¼ 4 states which affects the interaction between 4-f and conduction electrons [3]. The initial state is almost completely restored after annealing at 450 1C, however, superconductivity does not appear at T41:45 K: Therefore superconductivity is extremely sensitive to atomic disordering. In conclusion, we have shown that (i) Atomic disordering leads to a significant rearrangement of band structure: it decreases charge carrier concentration (heavy holes). At that, superconductivity is suppressed and Kondo-like magnetic scattering is observed in disordered crystals. The initial state is almost completely restored upon annealing at 450 1C. However, superconductivity does not appear at T41:45 K: (ii) Positive magnetoresistance observed at low temperatures only in the crystals with different values of disorder is an evidence of magnetic field influence on the band of conduction electrons; (iii) The electronic transport in a PrOs4Sb12 sample can be described by two-band model including heavy and light holes. Work was carried out with the financial support of the Ministry of Industry, Science and Technologies of the Russian Federation (State contracts
ARTICLE IN PRESS 916
A. Karkin et al. / Physica B 359– 361 (2005) 913–916
Nos. 40.020.1.1.1166, 40.012.1.1.1356) and the Special Federal Program of Basic Research at Russian Academy of Science ‘‘Quantum macrophysics’’ (State contract no 1000-251/P-03/040348-11054-269, Project UB RAS no 3).
References [1] E.D. Bauer, et al., Phys. Rev. B 65 (2002) 100506(R). [2] W. Jeitscho, et al., Acta Crystallogr. B 33 (1977) 3401. [3] P.-C. Ho, et al., Phys. Rev. B 67 (2003) 180508(R).