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

TL;DR

This study examines how degeneracies in conduction bands and $f$-orbitals affect ferromagnetism in the periodic Anderson model, revealing that higher $f$-orbital degeneracy increases the Curie temperature and that $T_c$ scales with conduction electron density.

Contribution

It demonstrates the impact of band and orbital degeneracies on ferromagnetic stability and introduces a mean-field scaling approach validated by numerical results.

Findings

Curie temperature $T_c$ increases with $f$-orbital degeneracy $D^f$.

$T_c$ exhibits a maximum at conduction electron density per band $n^c / D^c \,\approx\, 0.3$.

Scaling behavior of $T_c$ as a function of conduction electron density is confirmed.

Abstract

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 $n^c / D^c\approx 0.3$.