J.W. Rasul

Theoretical and experimental progress in intermediate valence systems (invited)

Recent experimental measurements such as susceptibility, specific heat, thermopower, and UPS on a wide range of intermetallic intermediate valence systems, e.g. YbCuAl, CeSn3, support a high degree of universality in the properties of such materials which apparently form a unique class of metallic compounds. The ratio χ(0)/γ≂g2μ2B (J+1) (J+1/2)/π2k2B is a good constant for compounds of a given rare earth (though g and J are rare earth dependent). A class of compounds of a given IV rare earth ion shows scaling of properties in terms of an effective temperature, or energy, scale TF, which is strong function of valence. We review the success of theoretical approaches such as perturbation theory, local Fermi liquid theory, the Bethe Ansatz technique, and large‐N perturbation theory in understanding these experimental facts. A challenge continues to be the understanding of the ground state, in which lattice periodicity plays a fundamental role, giving rise to ραT2 in some metallic, and a several meV gap in ins...

Theory of a Tm impurity in metals in a jj-coupling model

A Tm magnetic impurity with U= infinity is considered in the jj-coupling scheme in the limit of zero j.j coupling. The model has SU(N) symmetry. The spin-fluctuation energy scale is found in the f12 and f13 Kondo limits via Haldane scaling arguments. The model possesses a 1/N expansion; selecting the leading-N diagrams in perturbation theory, the Yafet-Varma integral equation is derived. This is solved analytically in the f1 and f2 Kondo limits and the results for N to infinity are found to be in accord with scaling theory. The energy separation between the singlet ground state and the N-fold-degenerate excited state is found as a function of f occupation in the large-N limit. The results are found to differ significantly with data on LaTmSe and YTmSe. A model with large j.j coupling is also considered and does not significantly improve the agreement.

The magnetic field dependence of the magnetization of the SU(4) and SU(6) Kondo models

Abstract The zero temperature impurity magnetization as a function of magnetic field strength has been calculated numerically for the SU(4) and SU(6) Kondo models using the integral equations derived from recent exact results for the linear dispersion model.

YbCuAl - A yardstick of progress in IV theory

Abstract The extensive data on YbCuAl is examined, on the assumption it lies close to the Kondo limit, using the results for the j = 7/2 Coqblin-Schrieffer model. Features well explained with a single parameter fit are χ(0), γ, M ( H ) curves, position of the maximum in χ( T ) and the reduction of the high T moment. The apparent success of the impurity model is discussed in the large N approach to the lattice model.

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.

Magnetic isotherm for YbCuAl — Comparison with exact results for the Coqblin-Schrieffer model

Abstract We give an exact calculation for the magnetic isotherm for YbCuAl based on an impurity model which treats the valence fluctuations as virtual. With a single parameter derived from χ(0) we can fit χ(0), γ and the magnetic isotherm extremely accurately.

Ground state properties of the two impurity Anderson model in a 1/N expansion☆

Abstract The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/ N . The dependence of this contribution on the interimpurity separation has an R −1 or R −3 envelope for distances smaller or larger than a length ν F / T A ranges from a value equal to the bare ƒ-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).

Models for Intermediate Valence Systems and Kondo Lattices — Applications to Cerium and Ytterbium Compounds

For sometime now there has been a group of us at Imperial College (increasing in number but now dispersing) concerned with the theoretical problems of intermediate valency and Kondo lattices. Some of our recent results based on the 1/N expansion, the Bethe ansatz and mean field approach with applications to cerium and ytterbium will be presented here. However, by way of introduction I shall review some of the earlier work concentrating on its motivation and the way the early ideas have been developed and clarified with time.

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.

A 1/N expansion for the two impurity Anderson model

Abstract The leading order intersite contribution to the partition function in a 1/ N expansion is obtained by resumming all relevant diagrams in perturbation theory. Competition between RKKY and single impurity behaviour can be discussed in such a formalism. The zero temperature intersite contribution to the ground state energy is examined.