Paramagnetic impurities in metals at finite temperatures

Abstract

Dispersion theory is combined with the Green's function technique to discuss the scattering of electrons by paramagnetic impurities in normal metals at finite temperatures. The thermodynamic Green's function is derived from an approximate solution of an equation for a modified (non-unitary) scattering matrix. As a check on the consistency of our theory, we generalize it to arbitrary impurity spin $S$, and show that in the limit $S\ensuremath{\rightarrow}\ensuremath{\infty}$, it reduces to ordinary potential scattering of electrons with spin parallel or antiparallel to a localized fixed Zeemann field. Some observations are made on the problem of the residual resistance. The effect of additional non-magnetic scattering is briefly considered. Finally, a justification is given for the neglect of multiparticle intermediate states in the dispersion equations.