Resistance Minimum in Dilute Magnetic Alloys

Based on the s-d interaction model for dilute magnetic alloys we have calculated the scattering probability of the conduction electrons to the second Born approximation. Because of the dynamical character of the localized spin system, the Pauli principle should be taken into account in the intermediate states of the second order terms. Thus the effect of the Fermi sphere is involved in the scattering probability and gives rise to a singular term in the resistivity which involves c log T as a factor, where c is the concentration of impurity atoms. When combined with the lattice resistivity, this gives rise to a resistance minimum, provided the s-d exchange integral J is negative. The temperature at which the minimum ccurs is proportional to c1/5 and the depth of the minimum to c, as is observed. The predicted log T dependence is tested with available experiments and is confirmed. The value of J to have fit with experiments is about -0.2 ev, which is of reasonable magnitude. Our conclusion is that J should be negative in alloys which show a resistance minimum. It is argued that the resistance minimum is a result of the sharp Fermi surface.