Role of electron-electron interactions in the RKKY theory of magnetism

The theory of magnetism in heavy rare earth metals is based on the RKKY theory. In this formalism the indirect exchange interaction between the local 4f spins is mediated by the conduction electrons. When carried to second order in the 4f-conduction electron interaction, traditional pertubation theory leads to a Heisenberg-like interaction between the local spins which depends on the electronic energy bands and 4f-conduction electron exchange matrix elements. This derivation neglects the detailed behavior of electron-electron interaction within the conduction band, which is known to be important in metallic systems. By using an equation of motion method, an expression for the inelastic neutron scattering cross-section has been derived which includes, in an approximate way, this electron-electron interaction. The results of this calculation indicate that spin-wave peaks can be broadened and shifted if the spin-wave band lies near the conduction electron Stoner continuum. The origin of this effect is similar to that found in itinerant electron systems where the spin-wave band actually intersects the Stoner continuum, resulting in the disappearance of the spin-wave mode.