KONDO RESISTIVITY DUE TO A PAIR OF INTERACTING IMPURITIES

The Kondo-type resistivity due to the scattering of conduction electrons by a pair of interacting magnetic impurities of spin dissolved in a nonmagnetic host is calculated as a function of the distance R between the impurities and their coupling W. The Kondo Hamiltonian is used, and the scattering amplitudes are calculated up to third order in energy. For small WkBT and large R, the resistivity of the pair reduces to twice the Kondo resistivity of one isolated impurity; for large WkBT and small R, the pair acts practically as one single spin, and gives a Kondo resistivity corresponding to spin of 1, or (depending on the sign of W), no spin-dependent resistivity at all corresponding to a spin of 0. For intermediate W, one verifies (taking for W the Rudermann-Kittel-Yosida indirect interaction) that the anomalous Kondo resistivity of two correlated impurities increases less rapidly (for decreasing temperature) than the resistivity of two isolated noninteracting impurities; this is in agreement with experiments. Therefore, it is suggested that this simple procedure may be useful to describe the resistivity of dilute alloys of CuMn type, when the concentration is not sufficiently small to neglect the correlations between the impurities. © 1969 The American Physical Society.