Theory of Ferromagnetic Resonance in Rare Earth Garnets. III. Giant Anisotropy Anomalies

Abstract

The giant sharp anisotropy anomalies in YIG discovered by Dillon and attributed to rare earth ions are explained in terms of the crossovers or, most probably, near crossovers of the energy levels of the rare earth ions in the combined crystal and exchange fields. The central consequence deduced by the theory, independent of the detailed behavior of the energy levels, is that $-H_{\alpha }{\left(\Delta {\theta }_{\frac{1}{2}}\right)}^2\approx \frac{\mathrm{kT}{N}^{\prime }}{M}$, where $H_{\alpha }$ is the anisotropy field; $\Delta {\theta }_{\frac{1}{2}}$ the angular width of the peak; $N^{\prime }$ the concentration of rare earth ions at the crossover; $M$ is the total magnetization; the result assumes $\mathrm{kT}\gg \mathrm{level}$ splitting at apparent crossover. This and other results appear to be in satisfactory agreement with the available experimental data. Crystals with giant anomalies have useful properties for adiabatic demagnetization experiments—the ferric-rare earth exchange field of 100 koe can be effectively turned on or off by rotation of the magnetic moment of the crystal. In an appendix we examine the validity of the molecular field approximation to the ferric-rare earth ion interaction, and we find that the approximation is excellent. A further appendix discusses the question of crossing or noncrossing of energy levels in static fields.