Properties of model-valence-fluctuation heavy-electron systems in applied and molecular fields

Self-consistent large-orbital-degeneracy perturbation theory for the one-site Anderson model is used to compute the occupancy and magnetization as a function of field and temperature for both spin (1/2 and spin (5/2. The magnetization curves are in good agreement with exact Bethe-ansatz and high-field perturbation-theory results, although some systematic discrepancies are apparent between the two different approaches. The most novel result for the magnetization is that the ‘‘superlinear’’ behavior known for high-degeneracy impurities (and observed in YbCuAl) vanishes at precisely the temperature where the zero-field magnetic susceptibility peaks. The one-impurity results are extended to the lattice via perturbation theory in the intersite interactions, after which simple molecular field theory (excluding the possibilities of charge-density wave and superconducting phases) is applied to obtain magnetic-ordering phase boundaries for the spin-(1/2 and spin-(5/2 models which are in gross qualitative agreement with previous lattice calculations, including the so-called ‘‘Kondo necklace’’ and ‘‘resonant level’’ models. In particular, the criterion that the intersite coupling exceed the characteristic Kondo-effect energy scale is recovered. It is shown that the superlinear behavior obtained for high-degeneracy leads, within molecular field theory, to novel tricritical behavior without the inclusion of anisotropy terms. It is suggested that ${\mathrm{EuRh}}_3$ ${\mathrm{B}}_2$ and YbCuAl are likely candidates for observing this behavior. Detailed appendices indicate the approximations necessary to obtain the molecular field theory and thereby its limitations to finite temperatures away from the coherent regime of the Anderson lattice.