Crystal-field splitting of some quintet states ofTb3+in aluminum garnets

A detailed crystal-field splitting analysis is reported for the quintet states ${}^{5}{D}_{J},$ ${}^{5}{G}_{J},$ and ${}^{5}{L}_{J}$ of ${\mathrm{Tb}}^{3+}{(4f}^{8})$ in the garnets ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}(\mathrm{YAG})$ and ${\mathrm{Tb}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}(\mathrm{TbAG}).$ In both garnets we assume that ${\mathrm{Tb}}^{3+}$ ions occupy sites of ${D}_{2}$ symmetry in the cubic structure. We have analyzed the optical spectra of ${\mathrm{Tb}}^{3+}$ between 487 and 349 nm. The absorption spectrum consist of transitions from the ground-state multiplet manifold, ${}^{7}{F}_{6},$ to individual energy (Stark) levels of the ${}^{5}{D}_{4},$ ${}^{5}{D}_{3},$ ${}^{5}{G}_{6},$ ${}^{5}{L}_{10},$ ${}^{5}{G}_{5},$ ${}^{5}{D}_{2},$ ${}^{5}{G}_{4},$ and ${}^{5}{L}_{9}$ multiplet manifolds. An algorithm used successfully by some of us earlier to analyze the spectra of ${\mathrm{Tm}}^{3+}{(4f}^{12})$ in YAG is helpful in the present study to establish the crystal quantum labels, ${\ensuremath{\Gamma}}_{n}(n=1,2,3,4)$ for individual Stark levels. A lattice-sum model is used to determine an initial set of crystal-field splitting parameters, ${B}_{\mathrm{nm}}.$ A combined free-ion and crystal-field Hamiltonian is diagonalized for the quintet and septet states. Considerable crystal-field mixing is found among all the quintet states investigated. A least-squares fitting analysis between 130 experimental-to-calculated Stark levels for ${\mathrm{Tb}}^{3+}$ in YAG gave a rms deviation of 9 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. A least-squares fitting analysis between 136 experimental-to-calculated Stark levels for ${\mathrm{Tb}}^{3+}$ in TbAG gave a rms deviation of 10 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.