Electron Interaction in Rare-Earth Metals

Abstract

We discuss from a unified point of view various aspects of the $s-f(s-d)\mathrm{}$ exchange interaction in the ferro-magnetically spin-ordered states of rare-earth metals, such as (1) the indirect Ruderman-Kittel-Kasuya-Yosida-type exchange interaction between localized $4f$ spins, (2) the spin-wave spectrum of the localized spins, and (3) the interaction between conduction electrons mediated by the exchange of spin waves of the localized spins. The present problem is very similar to that of the electron-phonon interaction in metals, and to obtain the electron-electron interaction we employ a similar method of using a cononical transformation. The electron interaction obtained leads to a repulsion between electrons of opposite spins at the same atomic site in the vicinity of the Fermi surface. The self-energy due to this effective electron interaction is calculated for a simplified model, and we discuss the possibility of an appreciable enhancement of the specific heat.