The spin scattering of conduction electrons by the local moments of transition-metal ions dissolved in metals, e.g., manganese in copper or silver, comes from the s-d mixing interaction. The characteristic energy and angular dependence of this scattering has a marked influence on the spin coupling between two local moments. We have derived expressions for this coupling due to s-d mixing. However, rather than evaluate the coupling itself, its envelope is much more relevant when one is interested in the range of the coupling. We have determined the envelope function by using only single-ion parameters. We find that in the range R<15a, the decay of the spin coupling is much slower than that of the Rudermen-Kittel-Kasuya-Yosida interaction, i.e., 1/$R^3$. This difference comes from the energy and angular dependence of the scattering which have been taken into account in the calculation. The calculations are made both with and without mean-free-path effects. We find that the preasymptotic corrections are far more important than mean-free-path effects for dilute systems. We have also calculated spin-interaction constants. Our results are very close to the values obtained from the low-field magnetization measurements.

• Received 5 March 1986

DOI:https://doi.org/10.1103/PhysRevB.34.1884