Crystal-field determination for trivalent thulium in yttrium orthoaluminate

The polarized absorption spectra of ${\mathrm{YAlO}}_{3}$:${\mathrm{Tm}}^{3+}$ were analyzed at 77\ifmmode^\circ\else\textdegree\fi{}K. A free-ion calculation was performed by fitting the centers of gravity of the $J$ manifolds. The coefficients which gave the best least-squares deviation of the calculated "free-ion" spectra from the observed "free-ion" spectra were ${E}^{1}=7075.5$, ${E}^{2}=33.8$, ${E}^{3}=654.3$, $\ensuremath{\zeta}=2631.8$, $\ensuremath{\alpha}=8.0$, $\ensuremath{\beta}=\ensuremath{-}764.9$; where all parameters have units of ${\mathrm{cm}}^{\ensuremath{-}1}$. A crystal-field calculation was also carried out by fitting Stark splittings and irreducible representations to the observed spectra. In order to obtain good starting parameters for fitting a ${C}_{s}$ (${C}_{1h}$) symmetry Hamiltonian, a descending symmetries technique was used. The results of a least-squares fit of the crystal-field Hamiltonian to the observed $^{3}F_{4}$, $^{3}F_{3}$, $^{1}G_{4}$, and $^{1}D_{2}$ Stark splittings gave the following parameters for the ${C}_{s}$ Hamiltonian: ${B}_{0}^{2}=\ensuremath{-}434.9$, $\mathrm{Re}{B}_{2}^{2}=420.8$, $\mathrm{Im}{B}_{2}^{2}=199.4$, ${B}_{0}^{4}=\ensuremath{-}691.6$, $\mathrm{Re}{B}_{2}^{4}=444.9$, $\mathrm{Im}{B}_{2}^{4}=114.2$, $\mathrm{Re}{B}_{4}^{4}=501.2$, $\mathrm{Im}{B}_{4}^{4}=\ensuremath{-}389.2$, ${B}_{0}^{6}=\ensuremath{-}260.4$, $\mathrm{Re}{B}_{2}^{6}=175.6$, $\mathrm{Im}{B}_{2}^{6}=229.7$, $\mathrm{Re}{B}_{4}^{6}=92.7$, $\mathrm{Im}{B}_{4}^{6}=542.4$, $\mathrm{Re}{B}_{6}^{6}=410.5$, $\mathrm{Im}{B}_{6}^{6}=113.4$; where all units are in ${\mathrm{cm}}^{\ensuremath{-}1}$.