Theory of Ferromagnetic Resonance in Rare Earth Garnets. II. Line Widths

The spins of rare earth ions in the garnets are coupled strongly both to the lattice phonons and, by an exchange interaction, to the ferric spin lattice. The rare earth spins thus provide a powerful relaxation channel for the ferric lattice. Two contributions to the line width may be distinguished: a coherent process (in which the total magnetic moment of the ferric lattice relaxes without changing the magnitude of the moment) is dominant at temperatures from 0°K up to just below the Curie temperature. Near and above $T_c$ a fluctuation process (in which ferric spins flip locally) is dominant. The theoretical results describe the order of magnitude and the temperature dependence of the observed line widths in the rare earth garnets and in impure yttrium iron garnet, if one assumes in the absence of direct experimental knowledge that the relaxation frequency $\frac{1}{\tau }$ of the relevant rare earth ions is ∼${10}^{-12\mathrm{}}$ sec at 400°K. As the temperature is increased from 0°K, the width increases until a maximum is reached when $\frac{1}{\tau }$ becomes comparable with the ferric-rare earth exchange frequency. Above this temperature the width decreases until near $T_c$, where there is a sharp rise.