Anisotropic Exchange Interaction in the Conical Magnetic Phase of Erbium

From a general two ion spin Hamiltonian, an expression is deduced for the energies of spin waves propagating in a hexagonal solid in which the magnetic moments are ordered in a conical or helical structure. The spin wave dispersion relation in the c direction of Er in its conical magnetic phase at 4.5K, which has been studied by Nicklow et al (1971) is reanalysed. In this analysis an alternative kind of anisotropic coupling between the total angular moments (Ji and Jj) on the sites i and j is introduced which is proportional to the following combination of Racah operators: O2, -2(Ji), O2, -2(Jj), expressed with respect to a coordinate system with the z axis along the c direction. The resulting anisotropy (both the constant and the q dependent part) is reduced by an order of magnitude in comparison with that deduced by Nicklow et al (1971). The constant anisotropy is found to be equal to about 20 meV (a rough estimate from magnetization measurements gives 5-10 meV). The anisotropic part of the exchange interaction is found to be of the same order of magnitude as the isotropic part.