Electron scattering on magnetic impurities in metals and anomalous resistivity effects

A special quantum field theory technique for a system of spins was used to evaluate the resistivity of metals containing paramagnetic impurities, assuming J/₅1, for an arbitrary value of (J/₅) ln (₅/T), where J is the exchange scattering amplitude and ₅ the Fermi energy. The first term of this series has been found earlier by Kondo1. It is shown that exchange and ordinary interactions give independent contributions to the resistivity. For a ferromagnetic sign of the exchange interaction between the electron and the impurity (J>0), the exchange component of resistivity decreases with temperature and disappears at T=0. In the reverse case (J<0), the resistivity starts increasing when the temperature decreases. After going through a maximum (for T=T₌₀ₗ), where the exchange resistivity, due to a local impurity atom, is of the same order of magnitude as the usual resistivity, the exchange resistivity, even in this case, goes to zero at T=0. Such a behavior is related to the resonant nature of the scattering amplitude for J<0. The calculation assumes that the impurity spins are completely disordered, i. e. , the temperature is higher than the Curie temperature of the impurity ferromagnetism. Since the latter is proportional to the concentration, while T₌₀ₗ does not depend on concentration, the results obtained are reasonable for sufficiently small concentration.