Spin-Magnon Relaxation in Rare-Earth Iron Garnets

Abstract

The relaxation of paramagnetic ions coupled to a magnetic lattice is investigated. The exchange interaction is separated into static and dynamic parts. The dynamic part is responsible for the relaxation process. The relaxation occurs via the absorption and emission of magnons in a manner analogous to spin-lattice relaxation. The spin-magnon relaxation time is calculated for ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Eu}}^{3+}$ ions in the iron garnets. Comparisons are made with the corresponding spin-lattice relaxation times. In each case the two relaxation mechanisms make nearly comparable contributions to the ferrimagnetic resonance linewidth and shift. The possibility of a contribution to the resonance linewidth and shift of the iron garnet from the presence of ${\mathrm{Gd}}^{3+}$ ions is also examined. It is found that probably neither relaxation mechanism makes an appreciable contribution to either the width or the shift. Finally, a discussion is given of the conditions under which the effects of the spin-magnon relaxation process might be uniquely observed.