Hall coefficient of dilute Cu-Au(Fe) alloys. II. Theory

We study the resistivity $\rho$ and the Hall coefficient $R$ for a polycrystalline metallic host which possesses carriers with a variety of transport properties, particularly an anisotropy over the Fermi surface in the background defect scattering rate. Using the $s-d$ model we derive general expressions for $\rho$ and $R$ when the metallic host contains a dilute concentration of magnetic impurities. Our theory when applied to Cu-Au(Fe) correctly predicts the dependence of $\rho$ and $R$ on temperature, magnetic field, and Fe concentration $C$. The formulas can be expanded in powers of the concentration and we find that the terms in $\rho$ and $R$ which are linear and quadratic in $C$ are consistent with each other and agree with experimental findings reported in a preceding paper.