Theoretical Study of Gilbert Damping in Rare-Earth Permanent Magnets

Abstract

We investigate temperature dependence of the Gilbert damping of a magnetization of the Fe sublattice in rare-earth permanent magnets $R_{2}{\text {Fe}}_{14}{\text {B}}$ ( $R$ is a rare-earth element). Assuming that the spin angular moment of Fe dissipates to the phonon system via a localized 4f electron system, which interacts with the phonon system, we obtain the formulation of the Gilbert damping constant $\alpha $ on the basis of the ligand field theory and evaluate the temperature and material dependence of $\alpha $ . We show that the Gilbert damping of the magnetization arises only in certain temperature regions due to the discrete energy structure of the 4f electron system.