Theory ofs−dScattering in Dilute Magnetic Alloys with Spin-½ Impurities

With the aid of a new Wick theorem for spin-½ operators, the properties of a single localized paramagnetic impurity in a metal are investigated, using diagrammatic techniques which are completely analogous to those of standard quantum field theory. Attention is directed at the high-temperature magnetic properties of this system. The present results include a new $\ln T$ term in the $g$ shift for the impurity spin and for the electronic susceptibility. In the high-field limit, the former logarithmic result is replaced by the logarithm of the Zeeman energy. A high-order equation is also obtained for the resistivity by a selective resummation of a complete subseries of electron self-energy diagrams. In this approximation, the resistivity exhibits a maximum for both ferro-and antiferromagnetic coupling (but at different temperatures) as the characteristic temperature is approached. The "bound-state" behavior appears in this theory as an anomalous correlation between the two spin systems, and first occurs at the characteristic temperature when the external magnetic field is zero.