Resonant Frequency Shift in Ellipsoidal Samples

A polished, ellipsoidal, single crystal, yttrium iron garnet sample with rotation axis along a [100] direction and $\text{ΔH\hspace{0.17em}=\hspace{0.17em}1.0\hspace{0.17em}}\mathrm{oe}$ was prepared. X-band measurements of the microwave resonant frequency were made as a function of rf power. The resonant frequency was found to shift at the rate of 41 Mc/w. The shift of the resonant frequency was related to the number of $\text{k\hspace{0.17em}=\hspace{0.17em}0}$ magnons ${\mathrm{(n}}_0)$ and the number of $\text{k\hspace{0.17em}≠\hspace{0.17em}0}$ magnons ${\mathrm{(n}}_k)$ by means of spin-wave theory. From this relation and the experimental data the value of $n_k{\mathrm{/n}}_0$ was determined to be 2.7.