Energy Levels ofYb3+in Gallium and Aluminum Garnets. II. Calculations

Abstract

Complete crystal-field calculations for ${\mathrm{Yb}}^{3+}$ in yttrium gallium and yttrium aluminum garnets have been performed. The energies and $g$ values obtained in the ten-parameter fits agree well with experiment. The calculated crystal fields are predominantly cubic with important sixth-order contributions. A five-parameter fit to these data was also computed, using point-charge-model constraints derived by Hutchings and Wolf. Results indicate that the point-charge model is a useful first approximation, but too crude for quantitative predictions. On the basis of the derived wave functions, the susceptibility was calculated over a wide temperature range. For yttrium gallium garnet, results agree well with experiment, but for the aluminum garnet, the calculated temperature-independent susceptibility is appreciably below the reported value.