Polarization of emission spectra from Ti³⁺-Doped oxide crystals: I. Molecular orbital theory

The photoluminescence spectra of Ti³⁺-doped YAlO₃, Y₃Al₅O₁₂ and Al₂O₃ crystals display weak zero-phonon lines and broad vibronic side bands. The zero-phonon lines are due to the splitting of the ²T_2g ground state into three Kramers' doublets by the combined effects of static axial crystal field, Jahn-Teller effect and spin-orbit interaction. A molecular orbital method is used to calculate the relative intensities and polarizations of both zero-phonon lines and broad band in terms of the mixing of odd-parity ligand wavefunctions into even-parity Ti³⁺ wavefunctions by odd-parity crystal fields of T_1u and T_2u symmetries at sites with tetragonal and trigonal symmetries. The odd-parity distortions may be static or dynamic and are of crucial relevance in determining the strength of vibronically induced transitions. In general, selection rules for optical spectra are uniquely determined by group theory. The relevance of the molecular orbit description of the d-d transitions is that it permits a physical interpretation of the strength of optical spectra in terms of the covalent charge transfer from ligand ions to central ions induced by odd-parity crystal field distortion.