Selection rules for inelastic neutron scattering by magnetic crystals. I. The symmetries of magnetoelastic waves and the determination of selection rules for magnon-phonon interactions, with an application to antiferromagnetic FeF2

Abstract

It is shown how theory given by Herring concerning accidental degeneracies in the electronic band structure of a crystalline solid can be adapted to the case of magnetoelastic waves in a magnetically-ordered crystal. From this it is possible to determine selection rules governing magnon-phonon interactions for dispersion relations along special lines of symmetry in the Brillouin zone. The theory is illustrated for antiferromagnetic FeF₂, on which inelastic neutron scattering studies of magnon-phonon interactions have recently been performed by Rainford, Houmann and Guggenheim.