Impact of ion-host interactions on the5d-to-4fspectra of lanthanide rare-earth-metal ions. I. A phenomenological crystal-field model

Dielectric crystals doped with ${\mathrm{Ce}}^{3+}$, ${\mathrm{Eu}}^{2+}$, ${\mathrm{Sm}}^{2+}$, and ${\mathrm{Yb}}^{2+}$ display broadband 5d-to-4f emission, and are candidate solid-state tunable laser materials. The absorption and emission wavelengths, however, are very host sensitive, and a better understanding of 5d crystal-field interactions is needed in order to design lasing materials. This paper focuses on the 5d energy levels of ${\mathrm{Ce}}^{3+}$ in an octahedral complex. A phenomenological model is proposed for the bond-distance dependence of these levels based on first-principles expressions derived by others for contributions to the crystal-field energies. The magnitudes of these contributions are estimated for the ${\mathrm{CeF}}_6$ complex.