4fn→4fn−15dtransitions of the heavy lanthanides: Experiment and theory

The ${4f}^n\to {4f}^{n-1}5d\left(\mathrm{fd}\right)\mathrm{}$ excitation spectra of the heavy lanthanides $({\mathrm{Tb}}^{3+},$ ${\mathrm{Dy}}^{3+},$ ${\mathrm{Ho}}^{3+},$ ${\mathrm{Er}}^{3+},$ ${\mathrm{Tm}}^{3+},$ and ${\mathrm{Yb}}^{3+})$ incorporated in ${\mathrm{LiYF}}_4,$ ${\mathrm{CaF}}_2,$ and ${\mathrm{YPO}}_4$ are investigated in the ultraviolet and vacuum-ultraviolet spectral region (100–275 nm). Spin-forbidden transitions as well as spin-allowed transitions are observed for all heavy lanthanides. In the excitation spectra the crystal-field splitting of the $5d$ electron can be clearly observed. Fine structure (zero-phonon lines and vibronic lines) is observed for the transition to the lowest $5d$ crystal-field component, for both the high-spin and low-spin fd bands. Energy-level and intensity calculations are performed by an extension of the commonly used model for energy-level calculations of ${4f}^n$ states. A good agreement between experimental and simulated spectra is obtained, using parameters that describe the $5d$ crystal-field splitting (from the spectra of ${\mathrm{Ce}}^{3+}),$ the parameters for the splitting of the ${4f}^{n-1}$ core (from the literature on energy-level calculations for ${4f}^n$ states) and parameters for the spin-orbit coupling of the $5d$ electron and the Coulomb interaction between $4f$ and $5d$ electrons (from atomic ab initio calculations using the computer code of Cowan). To improve the agreement between the model and experiment, the $5d$ crystal-field parameters were adjusted slightly to correct for the decreasing crystal-field strength for the heavier rare earths due to the lanthanide contraction. The f-d interaction parameters in the fluoride host lattices were reduced to about 67% of the calculated free-ion values in order to compensate for the nephelauxetic effect.