4fn→4fn-1 5d transitions of the heavy lanthanides: Experiment and theory

The 4⁢𝑓𝑛 →4⁢𝑓𝑛−1⁢5⁢𝑑⁡(fd) excitation spectra of the heavy lanthanides (Tb3+, Dy3+, Ho3+, Er3+, Tm3+, and Yb3+) incorporated in LiYF4, CaF2, and YPO4 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 5⁢𝑑 electron can be clearly observed. Fine structure (zero-phonon lines and vibronic lines) is observed for the transition to the lowest 5⁢𝑑 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 4⁢𝑓𝑛 states. A good agreement between experimental and simulated spectra is obtained, using parameters that describe the 5⁢𝑑 crystal-field splitting (from the spectra of Ce3+), the parameters for the splitting of the 4⁢𝑓𝑛−1 core (from the literature on energy-level calculations for 4⁢𝑓𝑛 states) and parameters for the spin-orbit coupling of the 5⁢𝑑 electron and the Coulomb interaction between 4⁢𝑓 and 5⁢𝑑 electrons (from atomic ab initio calculations using the computer code of Cowan). To improve the agreement between the model and experiment, the 5⁢𝑑 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.