Ferromagnetic Resonance in Ruthenium-Doped Gadolinium Iron Garnet

Ferromagnetic-resonance measurements on single crystals of gadolinium iron garnet doped with ruthenium were carried out at 9.25 GHz in the temperature range 4.2-500 °K. The single-ion model is used to calculate the anisotropy contributions $\Delta K_1$ and $\Delta K_2$ and the field for ferromagnetic resonance. By fitting the theory to the experimental anisotropy data one finds $g{H}_e=1.2\mathrm{}\times {10}^7$ Oe and $\frac{v}{\xi }=-0.4\mathrm{}$, where $g$, $H_e$, $v$, and $\xi$ are the $g$ factor, the exchange field, the one-electron trigonal-field parameter, and the one-electron spin-orbit-coupling parameter, respectively. The linewidth could be interpreted in terms of the longitudinal-relaxation model assigning a short relaxation time of $\tau =3.3\mathrm{}\times {10}^{-12\mathrm{}}$ sec to the ${\mathrm{Ru}}^{3+}$ ions.