Coupled nuclear and electronic spin wave modes in non-commensurate spiral and conical spin structures

Abstract

A discussion is given of the coupled nuclear-electronic spin wave modes which arise when one has strong hyperfine coupling in a system with an unperturbed electronic spin wave branch starting from zero frequency, such as is the case in spiral, conical, or fan spin structures of wave vector incommensurate with the lattice. Such systems with strong hyperfine interactions are found in certain rare-earth metals (for example). The coupled bands differ markedly from the unperturbed bands at small momenta and exhibit forbidden energy gaps. In the absence of quadrupolar terms the k=0 mode of the upper band is proportional to the hyperfine constant, is temperature-dependent through the average nuclear magnetization, and is excited with an amplitude determined by the Bohr, rather than the nuclear, magneton. This leads to the possibility of measuring the hyperfine constant by observing the temperature dependence of a ferromagnetic resonance experiment.