Pair Description of Resistivity Maxima in Kondo Dilute Alloys

Abstract

Previous calculations, in the second Born approximation, of the electronic scattering rate in Kondo dilute alloys in the case when the spins of two impurities are coupled by an exchange energy -$W{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{2}$ are generalized to arbitrary spin values $S$. Under simple statistical assumptions we take into account the effect of all coupled pairs in the alloy. We study the limits of validity of this pair approximation and show how our results may possibly be extrapolated to hold for the most divergent term to any order of perturbation theory. The resulting expression for the resistivity accounts satisfactorily for the available experimental data when there are maxima well above the Kondo temperature. From comparison with such data pertaining to Mn in various matrices we can extract reasonable values for the characteristic parameters involved in the $s\ensuremath{-}d$ exchange Hamiltonian and for the amplitude of the indirect interaction between impurity spins.