Magnetic-field dependence of the specific heat of a heavy-fermion system

Abstract

We use the lattice Anderson model on a small cluster to calculate the effect of an external magnetic field on the specific heat of a heavy-fermion system. The suppression of the specific heat results from the spreading of a manifold that contains states of different spins through the Zeeman effect. Our results are compared qualitatively with experiments on CeCu6.A defining characteristic of heavy-fermion metals is the extraordinarily large size of the electronic specific heat at low temperatures.If one writes, in a standard way, C, -yT, then the specific-heat coefficient y can be as large as 2 J/mol (deg) . Additionally, it is sometimes found that specific heat can be drastically reduced by an external magnetic field at very 1ow temperatures and enhanced at slightly larger temperatures. ' We will show here that this behavior can be reproduced in a simple calculation for a finite cluster, although the simplicity of the cluster model does not permit quantitative comparison with experiment. This problem has been discussed from a single-particle viewpoint by Schotte and Schotte and Edelstein in terms of an enhanced density of states around the Fermi energy. Because we consider a small system, we can work with many-body states. Our calculation is essentially exact for a given model cluster, the only caveat being that we ignore the effect of a field on the single-particle hopping.The physical picture which emerges from our calculations is simple. The system is characterized at low energies by a narrow, dense manifold of states which are mostly spin rearrangements of the f electrons. These states are responsible for the high specific heat. We believe this is also true for large (bulk) systems, whether or not the material is ordered magnetically. Although the ground state is a singlet, the manifold contains states with differing values of the total spin quantum number. Application of a magnetic field separates the Zeeman components and broadens the energy distribution.The specific heat will be decreased at some temperatures, generally the lowest, and increased at higher temperature.For temperatures large compared to the width of the manifold, the entropy and specific heat are unaffected by the field.The model is one we have considered previously: a four-site Anderson lattice, with two nondegenerate orbitals (c and f) on each site. The four sites are arranged to form a tetrahedron. We believe this geometry is more appropriate for application to three-dimensional systems than other simple four-site arrangements such as the square or rhombus. Crystal fields and spin-orbit coupling are ignored. These restrictions, which are necessary for our computations, inhibit us from trying to fit experiment data numerically.We are content to demonstrate hereThe last term describes the interaction with an external magnetic field. Let S, = gS;, , r 0.0014r r L / r r r r / I r / r I r / I r r r / r r r 0.0012--3.P t r 0.0010 -,' ; r' rN 'i~/ r r %

Magnetic and Thermodynamic Properties of Ce4RuAl

“…It evolves from the 158 to 180 mJ/(Ce mol K 2 ) for (H) increasing from 0 to 5 T. The obtained γ behavior is consistent with the Anderson model-based theoretical predictions [8].…”

Heat Capacity of Heavy Fermion Compound CeCu4Ga in High Magnetic Fields

“…5 shows such a fit on the example of H = 0 T, 3 T and 6 T. Figures 5 and 6 show the field dependence of T * and γ 0 , respectively. The values of γ 0 behave in a manner consistent with the Anderson model based on the theoretical predictions of Kim et al [9] and other calculations [10], i.e., it depends strongly on the applied magnetic field. The value of T * = 2.4 K is in good agreement with results of paper [5] and T K derived above from the paramagnetic Curie temperature.…”

Valence fluctuations in YbNiAl4 compound

“…The mixed valence ͑MV͒ state is a dynamical effect resulting from a temporal residence of electron in two different states, the nonmagnetic 4f 0 for Ce and 4f 14 for Yb and magnetic 4f 1 for Ce and 4f 13 for Yb. There are two main models of the MV state.…”