A theoretical investigation of 4f→5d transition of trivalent rare earth ions in fluorides and complex oxides

We have investigated 4fn→4fn−15d excitation energies for trivalent rare earth ions in LaF3, LiYF4, YF3, LiGdF4, K2YF5, YAlO3, LaBO3 and YPO4 using a spin density functional procedure based on the atomic sphere approximation (computer code ASW). The local relaxation of the activator ions in the host lattices has been calculated by the projector augmented wave method (computer code VASP). The experimentally observed 4fn→4fn−15d excitation energies are shown to depend linearly on the calculated energy difference between the one-electron f- and d-like states of the rare earth ions Δεf−d. The linear relationship, ΔE=mΔε+εshift, involves two empirical parameters m and εshift. m is found to be the same for all ions and hosts, and εshift is different for the different ions but independent of the host lattice. In the present case, m and εshift have been determined empirically by a least-square fitting procedure from the experimental and calculated ΔE for the hosts LaF3, YF3 and LiYF4. The error of the predicted excitation energies is lower than 0.3 eV for the systems. This error increases up to 0.6 eV for some heavy rare earth ions for which the calculated occupied one-electron f-like states overlap energetically with the host valence band states (Er and Tm in the hosts LaF3, YPO4 and LiYF4).