Low-Lying Spectrum of Rare-Earth Iron Garnets

The spin-wave spectra of simplified two- and three-sublattice models of the rare-earth iron garnets are obtained, and shown to contain an iron spin-wave spectrum similar to that in ytrrium iron garnet, together with one and two optical branches, respectively. Intensities for optical excitation of $k=0\mathrm{}$ spin waves are computed, and the effect of an external magnetic field on the resonant frequencies is also found. The consequences of anisotropic $g$ values, which can be very different from the Landé $g_J$, are explored. Whereas frequencies are determined by the $g$ values along the exchange field produced by the iron, selection rules depend on transverse $g$ values. This results in absorption at single-ion splitting frequencies as well as at the Kaplan-Kittel exchange resonance frequency ${\omega }_e=\lambda ({\gamma }_2{M}_1-{\gamma }_1{M}_2)$. The anisotropy in the $g$ values also produces a shift in the exchange resonance frequency, which can be related to the macroscopic anisotropy energy deduced from the anisotropic single-ion exchange splittings. Agreement with experimental data on ytterbium iron garnet, given in an accompanying paper, is excellent. Application of the theory to anisotropy effects in ferrimagnetic resonance of rare-earth-doped yttrium iron garnet is also considered. Finally, the specific heat capacity is considered and shown to be well approximated by the single-ion Shottky anomaly approximation used by Meyer and Harris.