Magnetic Symmetry and Spin Waves

Abstract

In general, the symmetry of the spin‐wave spectra is determined by the magnetic space group characteristic of the spin order in the crystal. For many magnetic materials, however, interactions such as dipole‐dipole, antisymmetric exchange, and higher‐order anisotropic exchange are quite small, so that most of their properties are essentially determined by isotropic Heisenberg exchange plus a few crystal field parameters. It was pointed out previously that this fact is reflected in the spin‐wave spectra in terms of additional symmetry not predicted by the magnetic‐space‐group theory and that this symmetry is describable in terms of spin‐space groups which include independent spin and space rotations. In this paper the theory of magnetic space groups and spin‐space groups and the characterization of the spin‐wave spectra in terms of their representations is briefly reviewed. The effect on the spin‐wave spectra of the various types of interactions that have been proposed for the rare‐earth metals is then analyzed in detail and compared with the recent experimental data for Tb. The calculation of selection rules for neutron scattering is also discussed and applied to Tb.