Variation of the Low-Temperature Resistivity in Dilute Magnetic Alloys

Abstract

We examine the effect of internal fields upon resistivity of dilute magnetic impurities in nonmagnetic metals, using the second Born approximation. Several distributions of internal fields are considered. We find that the internal field effects suppress the Kondo log T term at moderately low temperatures (several orders of magnitude above the Suhl—Abrikosov resonance temperature Tr). This low-temperature behavior is found to be sensitive to the variation of the probability distribution of the fields P (H) near zero field. When P (H) is proportional to Hn−1 for small H, the change in the low-temperature resistivity Δρ (T) is found to be proportional to Tn (1-α logT). α is about 0.06 for copper and gold alloys. More generally, we find that, except for the small logT term, Δρ(T) is proportional to that part of the low-temperature specific heat which arises from the magnetic disordering of the impurities. For an Ising model, n=1, and the resistivity is thus approximately linear in T for 0.01<T<1°K. This linearity has been observed for a 0.1% Au-Fe alloy where the resistivity has been measured to sufficiently low temperatures, thus giving additional support to the Ising-like internal field model of the specific heat and Δρ(T). The theory predicts the resistivity maximum as well as the disappearance of the minimum as a function of the impurity concentration in reasonable agreement with experiment. It is suggested that the low-temperature resistivity measurements be used to probe the distribution of the internal fields in the dilute alloy system.