Microscopic theory of the lattice dynamics of hcp rare-earth metals

Abstract

A microscopic theory of the lattice dynamics of the rare-earth metals based on the model-potential method is developed and applied to the hexagonal close-packed metals, Tb and Ho. The electron-phonon interaction is represented in the rigid-ion approximation by a rare-earth-metal model potential (REMMP) of the Heine-Abarenkov-Animalu type which incorporates formally the $s\ensuremath{-}f$ hybridization in the energy bands of the lanthanides through an $l=3$ model-potential well depth of the resonance form, ${A}_{3}(E)\ensuremath{\propto}\frac{1}{2}\frac{{W}_{f}}{({E}_{f}\ensuremath{-}E)}$, where ${W}_{f}$ and ${E}_{f}$ are, respectively, the width and the position of the narrow $f$ band. Physical effects due to the nonlocality of the REMMP, spin-orbit coupling, local-field corrections, and three-body forces are investigated but only the nonlocality of the REMMP was included explicitly in the numerical calculation. Calculated phonon dispersion curves for Tb and Ho are in reasonable agreement with the experimental data of Houmann and Nicklow and of Nicklow et al. This work represents a successful completion of the program of extending the pseudopotential and model-potential methods to all metals throughout the Periodic Table.