Kondo-Resistivity Suppression Due to Inelastic Scattering of Conduction Electrons by Magnetic Impurities in Alloys

The interaction of localized magnetic moments of a magnetic impurity with the lattice causes relaxation of the states of that localized moment. The lifetime is represented as a broadening $\gamma$ of the states of the localized moment. The introduction of this broadening changes the scatering of the conduction electrons by the localized moment from an elastic scattering to an inelastic one plus negligible elastic scattering. Thus, the electron of the average excitation energy above the Fermi level $\epsilon \approx T$ may take part in all inelastic allowed scattering processes only if $\epsilon \gtrsim \gamma$, i.e., $T\gtrsim \gamma$. For $T<\mathrm{}\gamma$ this number of processes is reduced, and it vanishes for $T\to 0$. This effect was in fact found for the terms of the order $J^2$ and $J^3$ in the perturbation expansion, and the correct temperature dependence of the Kondo resistivity was obtained for $J<\mathrm{}0\mathrm{}$. The resistivity for $J>\mathrm{}0\mathrm{}$ is also discussed.