Homogeneous dynamical susceptibilities of dilute magnetic alloys

The four longitudinal and four transverse dynamical susceptibilities for zero wave number of the coupled system of conduction electrons and impurity spins in metals are discussed within the s-d model. The susceptibilities are expressed in terms of two well-behaved relaxation functions which are then calculated in lowest order perturbation theory. As a result closed expressions for the dynamical susceptibilities are found valid for all frequencies, magnetic fields, and temperatures under the restriction that Kondo anomalies are quenched. A Bloch equation description is found to be valid in the transverse case, whereas in the longitudinal case large deviations from the Bloch-type behavior may occur (provided the bottleneck is broken) whenever the thermal energy is small compared to the Zeeman energy of the impurities. However, these anomalies do not cause a breaking of the bottleneck.