Influence of Band and Orbital Degeneracies on Ferromagnetism in the Periodic Anderson Model

We investigate the influence of degeneracies of the conduction band and the $f$-orbital on the stability of ferromagnetism in the periodic Anderson model. To this end we calculate the temperature dependence of the inverse susceptibility for different degeneracies $D^c, D^f$ and conduction electron densities $n^c$ within the dynamical mean-field theory. A strong increase of the Curie temperature $T_c$ with the degeneracy $D^f$ of the localized $f$-level is found. For $D^c \leq D^f$ a simple \emph{ansatz} based on a mean-field treatment of the RKKY interaction is shown to imply a scaling behavior of $T_c$ as a function of the conduction electron density per band which is well obeyed by the numerical results. In particular, $T_c$ is found to have a maximum at $n^c / D^c\approx 0.3$.