Magnetotransport properties of noble metals containing rare-earth impurities. II. Theory

Abstract

Rare-earth impurities in noble metals induce an anisotropic magnetoresistance and a skew scattering contribution to the Hall resistivity. These effects are due to anisotropic terms of the $4f$---conduction-electron interaction, but an estimate of these terms based on conduction electrons in plane-wave states gives values too small to explain the experimental data. We have taken into account the admixture of $5d$ screening electrons into the conduction band, and we obtain a $4f$---conduction-electron interaction which has large anisotropic terms in addition to the conventional spin interaction. We have used in this calculation atomic $4f\ensuremath{-}5d$ Slater integrals, and we also had to estimate the width of the $5d$ virtual bound state. When we assume that the $5d$ electrons are in ${t}_{2g}$ states, we find that our estimate of the anisotropy of the magnetoresistance and of the skew scattering effect are in fair agreement with the experimental data. However, we find too large a negative isotropic magnetoresistance.