Theory for the Phonon Dispersion of Mixed-ValentSm0.75Y0.25S

The phonon dispersion and elastic constants of mixed-valent ${\mathrm{Sm}}_{0.75}$ ${\mathrm{Y}}_{0.25}$ S are calculated. The microscopic model takes into account interactions of localized $4f$ electrons with lattice vibrations and phonon-induced $4f\leftrightarrows 5d$ transitions leading to a breathing of the rare-earth ionic radius. The resulting three-parameter model yields a quantitative overall agreement with quite anomalous experimental dispersion curves. As input data the unrenormalized frequencies are obtained from a second-neighbor Born-von Kármán model.