Stefan R. Lüthi, Hans U. Güdel, M. P. Hehlen and J. R. Quagliano
Electronic energy-level structure, correlation crystal-field effects, and f-f transition intensities of Er³⁺ in Cs₃Lu₂Cl₉
Phys. Rev. B 57, 15229-15241 (1998)                 

Abstract: Single crystals of 1% Er³⁺-doped Cs₃Lu₂Cl₉ 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+1L_J(4f¹¹) multiplets of Er³⁺ 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 cm^–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 cm^–1. The further inclusion of the correlation crystal-field interaction g⁴_10A again lowered the rms standard deviation to a final value of 17.98 cm^–1 and provided substantial improvement in the calculated crystal-field splittings of mainly the J=9/2 or J=11/2 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 C₃ point symmetry of Er³⁺ in Cs₃Lu₂Cl₉ in the calculations.