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Absorption spectra of ${\mathrm{Tm}}^{3+}$:${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ are reported between 1.9 and 0.26 \ensuremath{\mu}m at 15 and 90 K, and between 0.80 and 0.35 \ensuremath{\mu}m at 1.6 K. Laser-excited emission obtained at 80 K is also reported from the ${\mathrm{Tm}}^{3+}$ manifolds $^{1}\mathrm{D}_{2}$, $^{1}\mathrm{G}_{4}$, $^{3}\mathrm{H}_{4}$, and $^{3}\mathrm{F}_{4}$ to the ground-state manifold, $^{3}\mathrm{H}_{6}$. The emission from $^{1}\mathrm{D}_{2}$ also includes transitions to Stark levels in manifolds $^{3}\mathrm{F}_{4}$, $^{3}\mathrm{F}_{3}$, and $^{3}\mathrm{F}_{2}$. Analysis of the emission spectra confirms the experimental crystal-field splitting deduced from an analysis of the hot-band absorption data. Both emission and absorption spectra indicate that ${\mathrm{Tm}}^{3+}$ ions occupy several different sites although the majority of ${\mathrm{Tm}}^{3+}$ ions appear to substitute for ${\mathrm{Y}}^{3+}$ ions in dodecahedral lattice sites (${D}_{2}$ point-group symmetry). The most intense spectra are analyzed assuming selection rules for ${D}_{2}$ symmetry. A lattice-sum calculation predicts a symmetry of ${\ensuremath{\Gamma}}_{2}$ for the ground state. Using this result the symmetries of 20 ${\ensuremath{\Gamma}}_{1}$, 11 ${\ensuremath{\Gamma}}_{2}$, 17 ${\ensuremath{\Gamma}}_{3}$, and 18 ${\ensuremath{\Gamma}}_{4}$ Stark levels were identified experimentally and compared with results from a crystal-field splitting calculation. A Hamiltonian consisting of Coulombic, spin-orbit, interconfiguration-interaction, and crystal-field (${D}_{2}$ symmetry) terms was parametrized and diagonalized for all manifolds of the ${\mathrm{Tm}}^{3+}$(4${\mathrm{f}}^{12}$) configuration. The rms deviation between 66 experimental and calculated Stark levels was 11 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.

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