Spin waves in terbium. III. Magnetic anisotropy at zero wave vector

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Abstract
The energy gap at zero wave vector in the spin-wave dispersion relation of ferromagnetic. Tb has been studied by inelastic neutron scattering. The energy was measured as a function of temperature and applied magnetic field, and the dynamic anisotropy parameters were deduced from the results. The axial anisotropy is found to depend sensitively on the orientation of the magnetic moments in the basal plane. This behavior is shown to be a convincing indication of considerable two-ion contributions to the magnetic anisotropy at zero wave vector. With the exception of the sixfold basal-plane anisotropy of the unstrained lattice, the dynamic anisotropy parameters deduced from our results agree with macroscopic measurements both with respect to the magnitudes (at zero temperature) and the temperature dependences. The deviations observed cannot be explained by existing theories which include the effects of zero-point deviations from the fully aligned ground state, and we tentatively propose polarization-dependent two-ion couplings as their origin.