A C Hewson

Exact high- and low-temperature results for the Coqblin-Schreiffer model with applications to YbCuAl

The authors give numerical results for the asymptotic form of the magnetic isotherm M(H) at T=0 for weak and strong fields for the j=3/2, 5/2 and 7/2 Coqblin-Schrieffer model (1969). These are derived from integral equations based on the exact diagonalisation of the model. The low-field results indicate a clear change in qualitative behaviour of the model with j. They all show a positive initial curvature which increases with j and contrasts sharply with the behaviour of the standard Kondo model j=1/2. In high fields the leading terms in an asymptotic expansion in log (g mu H/T1) have been calculated. From these results the Wilson numbers, which relate the zero-temperature susceptibility to Kondo temperature TK, as defined by the high-temperature series expansion in log T/TK, have to be calculated for the j=3/2, 5/2 and 7/2 models. The j=7/2 results are applied to the compound YbCuAl. Using the single parameter determined from an earlier fit to the T=4.2K magnetic isotherm the authors find excellent agreement with the high-temperature susceptibility over a temperature range from 140 to 1000K. The results explain the apparent reduction of the moments of the Yb ions from their free-ion values.

On the local polaron model and its applications to intermediate valence systems

The local polaron problem in which a local electronic resonance in a wide conduction band is coupled to a local phonon mode is considered. Earlier work is extended by a more complete treatment of the case where a finite Fermi level is present which is important for intermediate valence materials. The authors demonstrate by variational and perturbational methods that there can be a renormalisation of the level width by a factor exp(-n), where n is the number of phonons in the polaron cloud. They discuss the conditions for this renormalisation to occur and in particular establish the importance of the closeness of the resonance to the Fermi level. The physical basis for the conditions and the relationship to the problem where only a single electron is present, where renormalisation only occurs if the level lies at the bottom of the band, are brought out. Renormalisation due to electron-hole pairs is also discussed. The authors suggest that in a lattice of resonances, renormalisation should lead to suppression of intersite scattering. The implications for intermediate valence systems are discussed.

Comparison of the 1/N expansion and Bethe ansatz results for the degenerate Anderson model

The authors find a relation for general N between the conduction band width D of the conventional N-fold-degenerate Anderson model (infinite U) and the cut-off D imposed on the Bethe ansatz solution of the linear dispersion version of the model. This enables them to compare the results of the 1/N expansion for the ground-state valence nv and the susceptibility chi with the exact Bethe ansatz results. They find complete agreement to leading and next-leading order in 1/N. The expansion to order 1/N is asymptotically exact as nv to 0 with chi varies as nv2, and as nv to 1 with chi varies as exp(1/N(1-nv)). Numerical comparison shows that the expansion to this order gives almost exact results for N=6 and 8 and excellent results for values of N as low as N=2. The authors find a Wilson number W(N) in complete agreement with their earlier calculations for Coqblin-Schrieffer mode.

Bethe ansatz and 1/N expansion results for N-fold degenerate magnetic impurity models

The authors calculate the ground state susceptibility chi 0, to leading and next-leading order in a 1/n expansion, for the N-fold degenerate Anderson model in the integral valent limit. From this and perturbational results they are able to calculate the Wilson numbers W(N), which relate to chi 0 and TK, to first order in 1/N.

Polaronic effects in mixed and intermediate-valence compounds

From an exact calculation of the density of states for one electron in the Sherrington-von Molnar model of an s-f resonance coupled to a local optical phonon mode the authors find the conditions necessary for a polaronic reduction in the width of the resonance. With the notation nu for the relaxation shift, Delta 0 for the resonance width in zero coupling, omega 0 the phonon frequency and W the conduction band width, they find for nu in the range W> nu > Delta 0 very little reduction in the resonance width, and obtain the polaronic reduction exp(- nu / omega 0) only if nu >W. This condition is too strong to be satisfied in intermediate-valence systems. However, the model is not an adequate description of intermediate-valence materials as it is an essentially one-site model. The authors generalise the model to include two sites coupled to phonons such that the sites compete a favourable local lattice distortion. In this model they can examine the dependence of the intersite transfer on lattice coupling strength. For w> nu > Delta 0 (the plausible physical region), this intersite transfer is reduced by a polaronic reduction factor leaving the widths of the virtual bound-state resonance almost unaffected.

Magnetic moment and valence fluctuations in a model for rare earth compounds

The ionic model proposed by Jefferson and Stevens (see ibid., vol.9, p.2151 (1976)) for the magnetic properties of rare earth compounds that display intermediate valence-behaviour is studied. The f-electrons of the rare earth ions are described by localised atomic-like configurations which are hybridised with a conduction band. The free energy and susceptibility are calculated perturbationally in powers of the hybridisation matrix element mod V mod to order mod V mod 4. When only virtual valence transitions are possible the leading correction to the Curie law susceptibility is due to the Kondo moment flip scattering. An effective interaction between the f- and conduction electrons is derived in this regime which is a generalisation of that given by Coqblin and Schrieffer (1969). The one-electron Green function is also calculated perturbationally and the results indicate that the spectral density has a virtual bound state resonance due to the incoherent scattering of the f-moments similar to that caused by impurity scattering.

Ground state properties of the Anderson model in the limit of large spin-orbit degeneracy

The spin-orbit degenerate Anderson model is investigated in the limit of large spin-orbit degeneracy (N). Low-temperature properties are discussed, yielding the full range of intermediate to local moment behaviour. The relation between ground state susceptibility and valence is examined to leading and next-leading orders in 1/N.

Ground state properties of the Anderson lattice in the large N limit

Ground state properties of the Anderson lattice are investigated in the limit of large orbital degeneracy (N) by examining perturbation theory to all orders in the d-f hybridisation V, keeping N mod V mod 2 constant. The effects of changes in the chemical potential are discussed, and expressions are derived for the susceptibility and linear specific heat.

A general derivation of Wiegmann's solution of the s-d exchange (Kondo) model

The author derives a general solution of the linear dispersion s-d exchange model which is not based on the Bethe ansatz. The spectrum of energy levels is the same as that obtained by Wiegmann but the solutions are shown to be very general. This derivation clarifies certain assumptions made by Wiegmann (1980) and the recent controversies on the completeness of the Wiegmann states.

A scaling approach to locally coupled electron-phonon systems

The authors give a brief outline of a poor mans scaling approach as applied to locally coupled electron-phonon systems. For these systems they show that the retardation of the effective interactions have to be taken into account. The approach is extended to the calculation of one-electron Green functions and applied to the spinless Anderson model coupled to phonons. A general expression is obtained for the renormalisation of the resonance width due to phonons. This gives the results of Hewson and Newns (1979, 1980) in the appropriate limits but is more general in being applicable to a continuum spectrum of local phonons and for all values of the coupling strength.