Static and Dynamic Effects of the Magnetoelastic Interaction in Terbium and Dysprosium Metals

Abstract

A detailed theoretical study has been made of the magnetoelastic perturbation of the spectra of elementary spin and lattice excitations in Tb and Dy metals. The theory was formulated on the basis of an interaction formed from bilinear products of local spin and strain functions. Previous ad hoc models appear in certain limits of the theory, giving a coherence to the theoretical picture of magnetoelastic coupling. It is found that uniform magnetostriction causes a smooth transition from "free-lattice" to "frozen-lattice" perturbation of the magnon spectrum depending on the wave vector of the state. The microwave absorption versus magnetic field applied along the hard planar axis of Tb and Dy is calculated. It is found that free-lattice magnons are primarily responsible for low-frequency absorption in Tb below 140 K, and for both low- and high-frequency absorption in Dy below the Curie temperature of that metal. It is shown that the transition from free- to frozen-lattice behavior of the magnon spectrum is essential to the explanation of existing data on the temperature dependence of absorption-peak positions in Tb. The dynamic interaction between spin and lattice waves is derived and used to calculate the mixed-mode splittings in regions of the Brillouin zone of Tb where phonon and magnon dispersion curves cross. The theory predicts well the splitting which occurs where the acoustical-magnon and phonon branches touch, but fails to account for the splitting between the acoustical-magnon and optical-phonon branches. A different coupling mechanism is proposed which may account for the mixing of these branches.