Ground and excited state absorption of Ni²⁺ ions in MgAl₂O₄: Crystal field analysis

The exchange charge model (ECM) of crystal field is utilized to provide the theoretical explanation of the ground state absorption and the excited state absorption observed for the octahedrally coordinated Ni²⁺ ions in the spinel MgAl₂O₄. The ECM enables modeling of the crystal field parameters (CFPs) for the impurity ions based on the crystal structure data of the host lattice. To ensure the reliability of the CFPs, the convergence of the CFP values with the increasing number of the coordination spheres taken into account in the ECM calculations is considered. The trigonal CFPs B₂ ⁰, B₄ ⁰ and B₄ ^{- 3} determined by the ECM, together with the appropriate Racah parameters B and C, serve as input to two crystal field analysis computer packages, which compute the energy level schemes within the whole 3d⁸ configuration. The cubic approximation utilizing only one CFP Dq is also discussed. Basic features of the ground and excited state absorption spectra observed for MgAl₂O₄:Ni²⁺ are satisfactorily explained by our crystal field analysis. In order to model the pressure dependence of the CFPs (and thus of the absorption spectra when relevant experimental data become available), the variation of the CFPs induced by possible distortions of the lattice due to, e.g. overall relaxation of the ions or accommodation of the impurity ions in the lattice, is studied. Analysis of the experimental absorption spectra enables us to evaluate also the Huang-Rhys parameter, the effective phonon energy, and the zero-phonon line position.