Spectroscopy of Ca₄GdO(BO₃)₃ (GdCOB): Pr³⁺ single crystals

A complex spectroscopic study of Ca₄GdO(BO₃)₃ (GdCOB) doped with Pr³⁺ has been performed experimentally and theoretically using the ab initio configuration interaction (CI) calculation method. This approach is based on the numerical discrete-variational Dirac-Slater cluster calculations and numerical solution of the Dirac equation using the local density approximation. All relativistic effects are considered automatically by virtue of the relativistic Hamiltonian. The principal novelty of the approach is that during the calculations the molecular orbitals (MO) consisting of the atomic wave functions of the central ion (in this case, Pr³⁺) and its nearest ligands (O^2-) are used. The principal advantage of the method consists in ab initio approach not requiring the fitting parameters like in the widely used crystal field approach or FLAPW requiring the muffin tin orbitals. Such a complete basis set allows not only to evaluate the main energy terms, but also to analyze the covalent charge transfer effects and to evaluate the energy separations between different MO groups. Using the GdCOB:Pr single crystals as good probes to check the introduced theoretical model, we report the calculations of the complete energy terms (including unoccupied excited MO) for the principal [PrO₆]^9- cluster. Theoretical simulations are verified by comparison with both the ground and excited state absorption. A particular interest presents estimations of the crystal field splitting of the localized Pr³⁺ 5d orbitals (10 Dq) (about 20,800 cm^-1) and energy separations between the 2p (O^2-)-4f (Pr³⁺), 2p (O^2-)-5d (Pr³⁺), and 2p (O^2-)-6s (Pr³⁺) MO (13,300, 40,050, and 78,900 cm^-1, respectively). These values are in sufficient agreement with performed excited state absorption experimental data and available ground state absorption data including the low temperatures study at 4.2 K. Several discrepancies between the calculated and measured intensities of the optical transitions can be explained by contribution of electron-phonon coupling and sample's imperfections. In addition to the first principles calculations, crystal field theory was used to calculate the Pr³⁺ energy levels; a set of crystal field parameters for Pr³⁺ ion in GdCOB crystal is suggested.