The excitation spectra of ferromagnetically and spirally ordered rare-earth alloys

A lattice of localized electronic spins, coupled by an exchange interaction, is considered. These spins may be either ferromagnetically or spirally ordered (as in heavy rare-earth metals) and each electronic spin is coupled via a hyperfine interaction to the nuclear spin on the same lattice site: a model is used in which only a fraction c of the sites are occupied by nuclear spins. The coupled mode spectrum is calculated for a nuclear spin concentration c << 1 for both types of magnetic ordering, and the results are shown to be those yielded by a 'virtual-crystal' treatment of the nuclear spins. An analysis of the self-energy shows that because the hyperfine coupling is very much less than the exchange coupling in any real system, the results obtained must hold for arbitrary c. The resonance strengths of the zero-wave-vector modes are calculated in this approximation and again display the virtual-crystal behaviour of the nuclear spins for all concentrations. (author)