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 Er**^{3+} in
Cs_{3}Lu_{2}Cl_{9}

*Phys. Rev. B* __57__, 15229-15241 (1998)

**Abstract:**
Single crystals of 1% Er^{3+}-doped
Cs_{3}Lu_{2}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}(4*f*^{11})
multiplets of 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 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 *g*^{4}_{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
*C*_{3} point symmetry of Er^{3+} in
Cs_{3}Lu_{2}Cl_{9}
in the calculations.