Contribution of Some4dand5dTransition-Metal Ions on Octahedral Sites to the Anisotropy of Ferrites and Garnets

The contribution to the magnetocrystalline anisotropy of transition-metal ions in ferrites on octahedral sites is calculated for the strong crystalline-field case for $d^1$, $d^2$, $d^4$, and $d^5$ configurations. The single-ion model is used which requires small concentrations of such ions. Good agreement with experiment was found for trivalent ruthenium. For this case, anisotropy measurements of ${\mathrm{Ru}}^{3+}$ ($4d^5$)-doped yttrium-iron garnet of the composition ${\mathrm{Y}}_{3-y}{\mathrm{Ca}}_y{\mathrm{Fe}}_{5-x}{\mathrm{Ru}}_x{\mathrm{O}}_{12}$ were carried out in the temperature range of 4.2-500°K. By fitting the theory to the measured anisotropy data, one finds for the product of the $g$ factor times the exchange field, $g{H}_e=1.1\mathrm{}\times {10}^7$ Oe and the ratio of the trigonal field to the spin-orbit energy $\frac{v}{\xi =-1\mathrm{}}$.