Magnetic susceptibility of mixed-valence rare-earth compounds

Many rare-earth compounds (e.g., Sm chalcogenides, ${\mathrm{YbAl}}_3$) exhibit temperature-independent magnetic susceptibility at low temperatures in their mixed valence phase despite the fact that the ionic configuration in at least one of the valences is such as to lead to a Curie-Weiss behavior. An essential feature of these compounds is that the Fermi level is pinned to the $f$ levels. We first examine the effect of this feature in the Anderson model for an isolated impurity and find through a strong-coupling variational wave function as well as through a simple Green's-function treatment that the susceptibility is finite at $T\to 0$°K and of order $\frac{{\mu }^2}{\Gamma }$ where $\Gamma$ is the virtual width of the $f$ level corrected for correlation effects. For the compounds, a two-band ("$f$" and "$d$" with orbital degeneracies neglected) Hubbard-like model leads in the same treatment to a finite susceptibility at $T=0\mathrm{}$, where now $\Gamma$ is essentially the $f-d$ hybridization energy. Order-of-magnitude agreement with experiments is obtained with a reasonable value of the $f-d$ mixing interaction. The physics of the finite susceptibility at $T=0\mathrm{}$ is the renormalization of the local moments by the conduction electrons which is strongest when the $f$ levels are at the Fermi level.