Ferrimagnetic Resonance of Rare-Earth-Doped Iron Garnets

Abstract

After a brief introductory sketch of the analogs in paramagnetic relaxation, the longitudinal and transverse (so-called ``slow'' and ``fast'' relaxing) mechanisms of line broadening as well as shifting by rare-earth impurities are described and compared, particularly for Kramers doublets. The longitudinal process is operative only if the rare-earth ions are anisotropically coupled to the iron magnetization, either because of the crystalline field or anisotropy in the exchange coupling tensor itself. Unless the anisotropy is small, the longitudinal process predominates when the splitting of the RE energy levels by the crystalline and exchange fields is large compared to the ferrimagnetic resonance frequency and to the relaxation frequency, as is usually the case at temperatures well below the Curie point. The longitudinal mechanism describes quite well the behavior of Yb in yttrium iron garnet except for one peculiar as yet unexplained peak in the linewidth at one angle at low temperatures. The line broadening with Eu comes from the excited state J=1, and its variation with temperature and frequency is explicable with the longitudinal model. The ``giant anisotropy frequency shifts'' with Tb are presumably caused by abnormally small rare-earth energy intervals for certain angles. The k=0 mode is mixed with other k modes by the rare-earth impurities. This effect is not ordinarily a major cause of line broadening, but may be for Tb at low temperatures.