Rare-Earth Ion Relaxation in Ferrimagnetic Resonance

The linewidths in ferrimagnetic resonance ΔH and the frequency dependence of the anisotropy field for iron garnets containing rare-earth ions are explained on the basis of a model for relaxation which was used by Clogston for nickel ferrous ferrite. It is assumed that the population of the rare-earth ion energy levels relaxes towards equilibrium with a finite relaxation time τ. Consequently for ωτ≳1, where ω is the measurement frequency, significant departures from equilibrium occur and give rise to the effects noted above. If the static torque, linewidth, and the resonant field can be measured in a temperature range where only the lowest two rare-earth ion energy levels are appreciably populated, τ can be deduced for the magnetization along [100] and [110]. The consequences of the model are described; they differ quite extensively from those of the fast relaxing ion model. A quantitative comparison with the theory for iron garnets containing ytterbium supported the theory and yielded values for τ. In the case of erbium, however, the static torque was found to be strongly field dependent and hence only a qualitative comparison is possible. It is nevertheless concluded that the effects observed support the model. At 55°K τ for the ground doublet is about 10−11 sec.