Analysis of f-d excitation spectra of heavy lanthanide ions in various crystals based on the simple model for f-d transition and its correction caused by the 5d spin-orbit interaction

The simple model for f-d transitions of heavy lanthanide ions in crystals has been extended to more general cases applicable to the octahedral six-fold coordination compounds where the measured spectra involve the low-lying ²t ₂ component of 5d orbitals, for which the 5d spin-orbit splitting is considerable and can be as large as a few thousand wavenumbers for heavy lanthanide ions. A quasi-angular-momentum technique was employed to deal with the correction caused by the 5d spin-orbit interaction based on the equivalence between the t ₂ and p orbits. The extended and original models were successfully applied to the interpretations of the f-d excitation spectra of Tm ³⁺ ions in Cs ₂NaYF ₆ and CaF ₂ crystals. The impact of the 5d spin-orbit interaction on the f-d transition spectra was also discussed in more details.