Comparative study of the absorption spectrum of Li_2CaSiO_4:Cr~(4+): First-principles fully relativistic and crystal field calculations

摘要

Systematic analysis of the energy level scheme and ground state absorption of the Cr~(4+) ion in Li_2CaSiO_4 crystal was performed using the exchange charge model of the crystal field [B.Z. Malkin, in: A.A. Kaplyanskii, B.M. Macfarlane (Eds.), Spectroscopy of Solids Containing Rare-earth Ions, North-Holland, Amsterdam, 1987, pp. 33-50] and recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multielectron (DVME) method [K. Ogasawara, T. Iwata, Y. Koyama, T. Ishii, I. Tanaka, H. Adachi, Phys. Rev. B 64 (2001) 115413]. Using the former method, the values of parameters of crystal field acting on the Cr~(4+) ion valence electrons were calculated using the Li_2CaSiO_4 crystal structure data. Energy levels of the Cr~(4+) ion obtained after diagonalizing the crystal field Hamiltonian are in good agreement with those obtained from the experimental spectra. The latter method is based on the numerical solution of the Dirac equation; therefore, all relativistic effects are automatically considered. As a result, energy level scheme of Cr~(4+) and its absorption spectra in both polarizations were calculated, assigned and compared with experimental data; energy of the lowest charge transfer transition was evaluated and compared with theoretical predictions for the CrO_4~(4-) complex available in the literature. The main features of the experimental spectra shape are reproduced well by the calculations. By performing analysis of the molecular orbitals (MO) population, it was shown that the covalent effects play an important role in formation of the spectral properties of Cr~(4+) ion in the considered crystal.