Absorption spectra and energy levels of ${\mathrm{Gd}}^{3+}$, ${\mathrm{Nd}}^{3+}$, and ${\mathrm{Cr}}^{3+}$ in the garnet ${\mathrm{Gd}}_3$${\mathrm{Sc}}_2$${\mathrm{Ga}}_3$${\mathrm{O}}_{12}$

Absorption spectra measured between 0.3 and 6.7 μm are reported for ${\mathrm{Gd}}^{3+}$, ${\mathrm{Nd}}^{3+}$, and ${\mathrm{Cr}}^{3+}$ in single-crystal gadolinium scandium gallium garnet, ${\mathrm{Gd}}_3$${\mathrm{Sc}}_2$${\mathrm{Ga}}_3$${\mathrm{O}}_{12}$, at various temperatures. Energy levels split by the crystal field are identified between 1500 and 35 000 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{Gd}}^{3+}$(4$f^7$), ${\mathrm{Nd}}^{3+}$(4$f^3$), and ${\mathrm{Cr}}^{3+}$(3$d^3$). The rare-earth ions occupy sites of $D_2$ point-group symmetry, and chromium ions are found primarily in sites of $C_{3i}$ point-group symmetry. A Hamiltonian consisting of Coulombic, spin-orbit, and crystal-field terms is diagonalized to obtain theoretical energy levels for each symmetry. Empirical crystal-field parameters $B_{\mathrm{km}}$ were determined by fitting calculated energy levels to observed levels through a variation of the $B_{\mathrm{km}}$; these were compared with a lattice-sum calculation. The rms deviations between calculated and observed levels are 1.7 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{Nd}}^{3+}$ (45 levels), 4.0 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{Gd}}^{3+}$ (14 levels), and 87.7 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{Cr}}^{3+}$ (35 levels).