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CeNi2Ge2
Physica B 281&282 (2000) 3}4
Oral Presentation
Anomalous low-temperature normal state of CeIn 3 and CePd Si /CeNi Ge 2 2 2 2 F.M. Grosche!,", M.J. Steiner!,*, P. Agarwal!, I.R. Walker!, D.M. Freye!, S.R. Julian!, G.G. Lonzarich! !Low Temperature Physics, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK "MPI Chemische Physik fester Stowe, Bayreuther Stra}e 40, D-01187 Dresden, Germany
Abstract Metals on the border of magnetism have attracted great attention in recent times, as a number of them exhibit a superconducting phase at low temperatures in the vicinity of the critical pressure at which the magnetic transition temperature is suppressed to zero. We present a brief overview and comparison of the body centred tetragonal compounds CePd Si and CeNi Ge , and the simple cubic CeIn . In spite of the di!erences in structure and the detailed 2 2 2 2 3 behaviour in the unconventional normal state near the critical pressure, these compounds share the existence of superconductivity at the border of antiferromagnetic order, and therefore are prime candidates for the study of a possible magnetic pairing mechanism. In this paper, we will solely present a comparison of the normal state properties of these materials. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: CeIn ; Unconventional normal state; Superconductivity 3
The unusual metallic states and low-temperature phase transitions exhibited by strongly correlated electron systems remain only partly understood. Distinct regimes can be identi"ed through the temperature dependence of thermodynamic and transport properties, in particular the resistivity. The high-temperature regime is characterised by a weakly temperature-dependent, large resistivity with scattering o! disordered local magnetic moments. Below a characteristic temperature, the resistivity drops with decreasing temperature. In a number of systems, the then expected crossover to a Fermi liquid regime is either suppressed to very low temperatures or even masked by the onset of superconductivity or other forms of order. The unconventional normal state in these particular systems might in "rst instance be examined in terms of a phenomenological model based on #uctuations of the local order parameter, in the cases discussed here spin #uctuations. The implications of such a model
* Corresponding author. Fax: #44-1223-337-351. E-mail address: [email protected] (M.J. Steiner)
are discussed for example in Ref. [1]. The present paper will concentrate on a brief discussion of experimental results. The phase diagram as measured in these systems is displayed for example in Fig. 1 for CeIn . The corre3 sponding phase diagrams for CePd Si and CeNi Ge 2 2 2 2 near the critical density are similar (see [2]). A striking similarity is that in both cases, the superconducting phase around the critical pressure of the antiferromagnetically ordered state is very narrow in pressure. The fact that CePd Si has an isostructural and isoelectronic 2 2 &high-pressure' phase in form of the compound CeNi Ge allows the investigation of a pressure region 2 2 normally not accessible with the clamp cells used. A very remarkable feature is the reentrance of superconductivity together with some other phase transition at higher temperatures which is clearly visible as a kink in the resistivity data [2]. Another notable feature is the unconventional exponent of the electrical resistivity in the vicinity of the critical pressure. In clean samples, the resistivity exponent at the critical density for CeIn is near 1.5 in 3 a temperature range of about 1 to 10 K, for CePd Si 2 2
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 1 1 1 6 - 3
4
F.M. Grosche et al. / Physica B 281&282 (2000) 3}4
Fig. 1. Temperature}pressure phase diagram of high-purity single-crystal CeIn . Superconductivity is observed in a narrow 3 window near the critical pressure. The existence of the antiferromagnetic phase has been demonstrated in Ref. [3].
change in pressure, the cross-over region in the CePd Si /CeNi Ge systems is much broader. 2 2 2 2 On "rst sight, the unusual exponents appear to be consistent within a simple spin #uctuation picture. In the simplest case with a dynamical exponent of 2 and a spatial dimension of 3, a resistivity exponent of 1.5 as seen in CeIn would be expected. Assuming the spatial 3 dimension closer to 2 in the CePd Si /CeNi Ge as 2 2 2 2 suggested in Ref. [1], this same picture would lead to an expected exponent of 1. However, for the CePd Si /CeNi Ge system, there 2 2 2 2 are major di$culties with this simple picture, one being that it assumes that essentially all carriers are scattered o! excited spin #uctuations, a picture which cannot be justi"ed within the usual Born approximation in the presence of harmonic spin #uctuations in an ideally pure system. Under these conditions, carriers not satisfying the &Bragg' condition for scattering from critical spin #uctuations near the magnetic ordering wave vector Q are only weakly perturbed, and at low temperatures lead to a Fermi liquid behaviour of the resistivity, a prediction not consistent with our "ndings. This di$culty, however, might be cured by including residual impurities, anharmonicity in the spin #uctuations, and corrections to the Born approximation. A proposal for the inclusion of residual impurities has recently been reported in Ref. [4] in an extension of earlier work [5,6], but it is too early to assess whether it could account for the features we observed, both in the tetragonal and the cubic systems, in a consistent way. Although the behaviour of CePd Si and CeNi Ge is qualitatively well described, 2 2 2 2 the higher-temperature behaviour seems not to "t quantitatively, a feature possibly due to high-temperature effects not accounted for in an essentially low-temperature theory. A crucial test, however, for the validity of this theory will be the precise form of the resistivity exponent in a simple system like CeIn . The model described in 3 Ref. [4] predicts a dramatic downturn in the resistivity exponent from a value of 1.5 as shown in Fig. 2 towards unity below 1 K.
References Fig. 2. Plot of the resistivity exponent of CeIn (above) and 3 CePd Si (below) at the critical pressure. In both cases, the 2 2 observed exponent di!ers signi"cantly from the conventional Fermi liquid exponent of 2.
and CeNi Ge , it is around 1.2 for temperature below 2 2 40 K, whereas &dirty' samples of CePd Si exhibit an 2 2 exponent close to 1.5. Fig. 2 compares the dependence of the resistivity exponent at the critical pressure in CeIn and CePd Si . 3 2 2 Whereas in CeIn , the conventional Fermi liquid 3 exponent of 2 is easily recovered by a relatively small
[1] N.D. Mathur, F.M. Grosche, S.R. Julian, I.R. Walker, D.M. Freye, R.K.W. Haselwimmer, G.G. Lonzarich, Nature 394 (1998) 39; I.R. Walker, F.M. Grosche, D.M. Freye, G.G. Lonzarich, Physica C 282 (1997) 303. [2] F.M. Grosche, P. Agarwal, S.R. Julian, N.J. Wilson, R.K.W. Haselwimmer, S.J.S. Lister, N.D. Mathur, F.V. Carter, S.S. Saxena, G.G. Lonzarich, condmat/9812133. [3] J. Flouquet, P. Haen, P. Lejay, D. Jaccard, J. Schweizer, C. Vettier, R.A. Fisher, N.E. Phillips, J. Magn. Magn. Mater. 90 (1) (1990) 377. [4] A. Rosch, Phys. Rev. Lett. 82 (1999) 4280. [5] K. Ueda, J. Phys. Soc. Japan 43 (1977) 1497. [6] R. Hlubina, T.M. Rice, Phys. Rev. B 53 (1996) 8241.
Oral Presentation
Anomalous low-temperature normal state of CeIn 3 and CePd Si /CeNi Ge 2 2 2 2 F.M. Grosche!,", M.J. Steiner!,*, P. Agarwal!, I.R. Walker!, D.M. Freye!, S.R. Julian!, G.G. Lonzarich! !Low Temperature Physics, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK "MPI Chemische Physik fester Stowe, Bayreuther Stra}e 40, D-01187 Dresden, Germany
Abstract Metals on the border of magnetism have attracted great attention in recent times, as a number of them exhibit a superconducting phase at low temperatures in the vicinity of the critical pressure at which the magnetic transition temperature is suppressed to zero. We present a brief overview and comparison of the body centred tetragonal compounds CePd Si and CeNi Ge , and the simple cubic CeIn . In spite of the di!erences in structure and the detailed 2 2 2 2 3 behaviour in the unconventional normal state near the critical pressure, these compounds share the existence of superconductivity at the border of antiferromagnetic order, and therefore are prime candidates for the study of a possible magnetic pairing mechanism. In this paper, we will solely present a comparison of the normal state properties of these materials. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: CeIn ; Unconventional normal state; Superconductivity 3
The unusual metallic states and low-temperature phase transitions exhibited by strongly correlated electron systems remain only partly understood. Distinct regimes can be identi"ed through the temperature dependence of thermodynamic and transport properties, in particular the resistivity. The high-temperature regime is characterised by a weakly temperature-dependent, large resistivity with scattering o! disordered local magnetic moments. Below a characteristic temperature, the resistivity drops with decreasing temperature. In a number of systems, the then expected crossover to a Fermi liquid regime is either suppressed to very low temperatures or even masked by the onset of superconductivity or other forms of order. The unconventional normal state in these particular systems might in "rst instance be examined in terms of a phenomenological model based on #uctuations of the local order parameter, in the cases discussed here spin #uctuations. The implications of such a model
* Corresponding author. Fax: #44-1223-337-351. E-mail address: [email protected] (M.J. Steiner)
are discussed for example in Ref. [1]. The present paper will concentrate on a brief discussion of experimental results. The phase diagram as measured in these systems is displayed for example in Fig. 1 for CeIn . The corre3 sponding phase diagrams for CePd Si and CeNi Ge 2 2 2 2 near the critical density are similar (see [2]). A striking similarity is that in both cases, the superconducting phase around the critical pressure of the antiferromagnetically ordered state is very narrow in pressure. The fact that CePd Si has an isostructural and isoelectronic 2 2 &high-pressure' phase in form of the compound CeNi Ge allows the investigation of a pressure region 2 2 normally not accessible with the clamp cells used. A very remarkable feature is the reentrance of superconductivity together with some other phase transition at higher temperatures which is clearly visible as a kink in the resistivity data [2]. Another notable feature is the unconventional exponent of the electrical resistivity in the vicinity of the critical pressure. In clean samples, the resistivity exponent at the critical density for CeIn is near 1.5 in 3 a temperature range of about 1 to 10 K, for CePd Si 2 2
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 1 1 1 6 - 3
4
F.M. Grosche et al. / Physica B 281&282 (2000) 3}4
Fig. 1. Temperature}pressure phase diagram of high-purity single-crystal CeIn . Superconductivity is observed in a narrow 3 window near the critical pressure. The existence of the antiferromagnetic phase has been demonstrated in Ref. [3].
change in pressure, the cross-over region in the CePd Si /CeNi Ge systems is much broader. 2 2 2 2 On "rst sight, the unusual exponents appear to be consistent within a simple spin #uctuation picture. In the simplest case with a dynamical exponent of 2 and a spatial dimension of 3, a resistivity exponent of 1.5 as seen in CeIn would be expected. Assuming the spatial 3 dimension closer to 2 in the CePd Si /CeNi Ge as 2 2 2 2 suggested in Ref. [1], this same picture would lead to an expected exponent of 1. However, for the CePd Si /CeNi Ge system, there 2 2 2 2 are major di$culties with this simple picture, one being that it assumes that essentially all carriers are scattered o! excited spin #uctuations, a picture which cannot be justi"ed within the usual Born approximation in the presence of harmonic spin #uctuations in an ideally pure system. Under these conditions, carriers not satisfying the &Bragg' condition for scattering from critical spin #uctuations near the magnetic ordering wave vector Q are only weakly perturbed, and at low temperatures lead to a Fermi liquid behaviour of the resistivity, a prediction not consistent with our "ndings. This di$culty, however, might be cured by including residual impurities, anharmonicity in the spin #uctuations, and corrections to the Born approximation. A proposal for the inclusion of residual impurities has recently been reported in Ref. [4] in an extension of earlier work [5,6], but it is too early to assess whether it could account for the features we observed, both in the tetragonal and the cubic systems, in a consistent way. Although the behaviour of CePd Si and CeNi Ge is qualitatively well described, 2 2 2 2 the higher-temperature behaviour seems not to "t quantitatively, a feature possibly due to high-temperature effects not accounted for in an essentially low-temperature theory. A crucial test, however, for the validity of this theory will be the precise form of the resistivity exponent in a simple system like CeIn . The model described in 3 Ref. [4] predicts a dramatic downturn in the resistivity exponent from a value of 1.5 as shown in Fig. 2 towards unity below 1 K.
References Fig. 2. Plot of the resistivity exponent of CeIn (above) and 3 CePd Si (below) at the critical pressure. In both cases, the 2 2 observed exponent di!ers signi"cantly from the conventional Fermi liquid exponent of 2.
and CeNi Ge , it is around 1.2 for temperature below 2 2 40 K, whereas &dirty' samples of CePd Si exhibit an 2 2 exponent close to 1.5. Fig. 2 compares the dependence of the resistivity exponent at the critical pressure in CeIn and CePd Si . 3 2 2 Whereas in CeIn , the conventional Fermi liquid 3 exponent of 2 is easily recovered by a relatively small
[1] N.D. Mathur, F.M. Grosche, S.R. Julian, I.R. Walker, D.M. Freye, R.K.W. Haselwimmer, G.G. Lonzarich, Nature 394 (1998) 39; I.R. Walker, F.M. Grosche, D.M. Freye, G.G. Lonzarich, Physica C 282 (1997) 303. [2] F.M. Grosche, P. Agarwal, S.R. Julian, N.J. Wilson, R.K.W. Haselwimmer, S.J.S. Lister, N.D. Mathur, F.V. Carter, S.S. Saxena, G.G. Lonzarich, condmat/9812133. [3] J. Flouquet, P. Haen, P. Lejay, D. Jaccard, J. Schweizer, C. Vettier, R.A. Fisher, N.E. Phillips, J. Magn. Magn. Mater. 90 (1) (1990) 377. [4] A. Rosch, Phys. Rev. Lett. 82 (1999) 4280. [5] K. Ueda, J. Phys. Soc. Japan 43 (1977) 1497. [6] R. Hlubina, T.M. Rice, Phys. Rev. B 53 (1996) 8241.