Spin Waves and Magnetic Resonance in Rare-Earth Metals: Thermal, Applied-Field, and Magnetoelastic Effects

Abstract

The theory is developed for the temperature and magnetic field dependence expected for the energy of long-wavelength spin waves in ferromagnetic heavy rare-earth metals. Emphasis is placed on examining magnetoelastic effects on the spin-wave energies. The resulting theory is applied to understanding recent neutron inelastic-scattering and ferromagnetic-resonance experiments in Tb and Dy. For Tb and Dy, comparison of theoretical predictions with the experimental results, especially the magnetic field dependence of the uniform-mode spin-wave energy, precludes the applicability of the frozen-lattice approximation suggested by Turov and Shavrov for magnetoelastic effects on spin-wave energies. The most striking point found in the present work is the contrast between the behavior of Tb and that of Dy. For Tb, the magnitude of the planar anisotropy constant found in static measurements is much smaller than the value necessary for agreement with the spin-wave experiments, i.e., neutron inelastic scattering and ferromagnetic resonance, which are mutually consistent. In contrast to this puzzling discrepancy for Tb, for Dy the static measured planar anisotropy constant gives absolute calculated values for the spin-wave behavior in excellent agreement with the results of ferromagnetic-resonance experiments.