Anisotropy and magnetostriction of cobalt-substituted yttrium iron garnet

The anisotropy, magnetostriction, and ferromagnetic resonance linewidth of cobalt-substituted yttrium iron garnets of composition ${\mathrm{Y}}_3{\mathrm{Fe}}_{5-x-y}{\mathrm{Co}}_x{\mathrm{Ge}}_y{\mathrm{O}}_{12}$ have been investigated by means of ferromagnetic resonance at 9.15 GHz in the temperature range $4.2\le T\le 500$ K. The impurities, the valence states, and the site distribution of the cobalt ions in the measured crystals have been determined by chemical analysis, optical absorption, and spin-echo measurements. The measured temperature dependence of both the anisotropy constants and the magnetostriction constants are compared with calculations performed in the framework of the single-ion theory. The behavior of the ferromagnetic resonance linewidth can be well interpreted on the basis of the calculated orientation dependence of the energy-level diagram within the longitudinal relaxation mechanism.