Theory of Magnetic Resonance in the Heavy Rare-Earth Metals

Abstract

The spin-wave spectrum has been calculated from a Hamiltonian including anisotropic exchange, axial and hexagonal anisotropy, and magnetic fields for the various types of magnetic order which are known to occur in the heavy rare-earth metals Tb-Tm. Particular attention is paid to those spin waves which can be excited by radiation. Because of the high anisotropy, most resonances will occur in the infrared where they will be difficult to observe. However, those phases which show either ferromagnetic ordering with moments in the hexagonal planes, or spiral configurations of the moments in those planes, should display a microwave resonance when a suitably chosen magnetic field is applied in that plane. In the spiral phases an additional resonance with $\ensuremath{\omega}\ensuremath{\propto}{H}^{2}$ may also be observed.