On the Multi-channel Anderson Impurity Model of Uranium Compounds

In this talk we will present the solution of the two-channel Anderson impurity model, proposed in the context of the heavy fermion compound UBe13, and discuss briefly the more general multi-channel case. We will show results for the thermodynamics in the full range of temperature and fields and make the connection with the current experimental situation. 1. Models of Uranium ions During the last two decades, there has been growing interest in materials whose desciption falls outside the framework of Landau’s Fermi Liquid Theory. Examples are the high Tc superconductors, heavy fermions and quasi-1D conductors. Uranium heavy fermion compounds provide very interesting examples, exhibiting unusual specific heat temperature dependence, γ = CV /T ∼ lnT . This behavior is often related to multichannel Kondo physics, occasioned in the case of Uranium by the ground state configuration which is degenerate and non-magnetic, so that one is lead to consider a quadrupolar Kondo scenario (1, 2). The starting point is to consider the energies of the uranium ion in its different states of valence. They fall on a parabola depicted in Fig. 1. The ground state corresponds to a U ionization state, with a 5f shellconfiguration. Considering the spin-orbit Hund’s coupling, the lowest multiplet corresponds to J = 4. Taking, further, into account the splitting due to a cubic crystal field (as is the case for the heavy fermion compound UBe13) one finds that the lowest multiplet corresponds to a non-Kramers Γ3 doublet (see Fig. 1). A similar analysis for the neighboring states of valence indicates that they corresponds to: (i) U: a 5f shell-configuration that splits giving a J = 9/2 lowest multiplet configuration, that further splits giving a lowest Γ6 Kramer’s doublet and (ii) U: a 5f shell-configuration that splits giving