Self-Consistent Treatment of the Kondo Effect

We investigate the scattering of conduction electrons by magnetic impurities for arbitrary exchange and normal interaction using Nagaoka's self-consistent-field approach. The corresponding self-consistent equations are solved by iteration in the limit of high and low temperatures. One finds for an extended exchange interaction a series of Suhl-Abrikosov resonances corresponding to different partial waves, which determine the scattering at low temperatures. A part of these resonances is affected by the normal interaction. In the special case of a $\delta$-function exchange interaction corresponding to a single resonance, the exchange component of the resistivity goes to zero as $T\to 0$. For temperatures high compared to the temperature where the first resonance becomes possible, we find generalizations for Kondo's expressions for the resistivity and thermo-power. However, the exchange and normal interactions no longer give independent contributions to the resistivity. One finds for a sufficiently large normal interaction a resistivity minimum for ferromagnetic exchange coupling.