Single crystals of 1% ${\mathrm{Er}}^{3+}$-doped ${\mathrm{Cs}}_3{\mathrm{Lu}}_2{\mathrm{Cl}}_9$ were grown using the Bridgman technique. From highly resolved polarized absorption spectra measured at 10 and 16 K, and upconversion luminescence and excitation spectra measured at 4.2 K, 114 crystal-field levels from 27 ${}^{2S+1}{L}_J{(4f}^{11})$ multiplets of ${\mathrm{Er}}^{3+}$ were assigned. 111 of these were used for a semiempirical computational analysis. A Hamiltonian including only electrostatic, spin-orbit, and one-particle crystal-field interactions ${(C}_{3v})$ yielded a root-mean-square standard deviation of $159.8{\mathrm{cm}}^{\mathrm{-}1}$ and could not adequately reproduce the experimental crystal-field energies. The additional inclusion of two- and three-body atomic interactions, giving a Hamiltonian with 16 atomic and 6 crystal-field parameters, greatly reduced the rms standard deviation to $22.75{\mathrm{cm}}^{\mathrm{-}1}.$ The further inclusion of the correlation crystal-field interaction $g_{10A}^4$ again lowered the rms standard deviation to a final value of $17.98{\mathrm{cm}}^{\mathrm{-}1}$ and provided substantial improvement in the calculated crystal-field splittings of mainly the $J=9/2\mathrm{}$ or $J=11/2\mathrm{}$ multiplets. However, the calculated baricenter energies of some excited-state multiplets deviate from their respective experimental values, and improvements in the atomic part of the effective Hamiltonian are required to correct this deficiency of the model. On the basis of the calculated electronic wave functions, the 12 electric-dipole intensity parameters ${(C}_{3v})$ of the total transition dipole strength were obtained from a fit to 95 experimental crystal-field transition intensities. The overall agreement between experimental and calculated intensities is fair. The discrepancies are most likely a result of using the approximate $C_{3v}$ rather than the actual $C_3$ point symmetry of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Cs}}_3{\mathrm{Lu}}_2{\mathrm{Cl}}_9$ in the calculations.

• Received 16 January 1998

DOI:https://doi.org/10.1103/PhysRevB.57.15229