Crystal Field in Dysprosium Garnets

The crystal-field splittings of the ${}_{}{}^6{}_{}{}^{}H$ and ${}_{}{}^6{}_{}{}^{}F$ multiplets of ${\mathrm{Dy}}^{3+}$ in yttrium gallium garnet and yttrium aluminum garnet have been determined from absorption and emission spectra. In addition, the $g$ factors of some crystal-field levels have been determined from Zeeman-effect measurements. All these experimental data are used to derive a set of crystal-field parameters for the two garnet systems. In these calculations, the full Hamiltonian appropriate for the $D_2$ symmetry at the rare-earth sites and also the mixing of the different $J$ states by the crystal field were taken into account. The agreement between experimental results and calculations is very satisfactory, and of the same quality as for the case of ${\mathrm{Yb}}^{3+}$, where far fewer experimental results had to be fitted.