Comparative analysis ofNd3+(4f3) energy levels in four garnet hosts

As many as thirty-seven ${}_{}{}^{2\mathit{S}+1\mathrm{}}{}_{}{}^{}$ ${\mathit{L}}_{\mathit{J}}$ multiplet manifolds of ${\mathrm{Nd}}^{3+}$(4${\mathit{f}}^3$) have been analyzed in the garnets ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$ (YAG), ${\mathrm{Y}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Al}}_3$ ${\mathrm{O}}_{12}$ (YSAG), ${\mathrm{Gd}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Ga}}_3$ ${\mathrm{O}}_{12}$ (GSGG), and ${\mathrm{La}}_3$ ${\mathrm{Lu}}_2$ ${\mathrm{Ga}}_3$ ${\mathrm{O}}_{12}$ (LLGG). The majority of ${\mathrm{Nd}}^{3+}$ ions substitute for ${\mathrm{Y}}^{3+}$, ${\mathrm{Gd}}^{3+}$, or ${\mathrm{La}}^{3+}$ ions in sites of ${\mathit{D}}_2$ point-group symmetry in the lattice. Individual Stark levels within each manifold have been identified experimentally up to 40 000 ${\mathrm{cm}}^{\mathrm{-}1}$ and compared with results obtained from a theoretical calculation. The model Hamiltonian includes Coulombic, spin-orbit, and interconfiguration interaction terms for the 4${\mathit{f}}^3$ atomic configuration of ${\mathrm{Nd}}^{3+}$ and crystal-field terms in ${\mathit{D}}_2$ symmetry, including spin-correlated crystal-field (SCCF) contributions. The Hamiltonian was diagonalized within the complete 4${\mathit{f}}^3$ ${\mathit{SLJM}}_{\mathit{J}}$ basis set which includes 364 states. Comparison between 148...