Theoretical Studies Of The EPR Parameters For 3d～1 Ions In Tetragonal Octahedral Crystals

3d¹ ions, such as Ti³⁺ and V⁴⁺, are important transition-metal ions. Some laser crystals, luminescence crystals, nonlinear optical crystals, minerals and even life bodies contain 3d¹ ions, so, a great deal of studies for the electron paramagnetic resonance (EPR) spectra of 3d¹ -doped crystals were made and many experimental data of EPR parameters were reported. However, in comparison with the 3d⁹ ions which is also D-state ions, the theoretical studies are not satisfactory. For example,(i)in many theoretical studies of EPR parameters, the rough second-order perturbation formulas were often used, and especially, (ii) only the contribution to EPR parameters (g factors and the hyperfine structure constants A factors) from the spin-orbit (SO) coupling parameter of central 3d¹ ion is considered, but the contribution due to the SO coupling parameter of ligand ion via covalency effect is neglected. Thus, some experimental data were not explained reasonably. In addition, since the EPR parameters are sensitive to the defect structures of 3d¹ impurity centers, the information on the defect structures of 3d¹ impurity centers has not been obtained yet. The SO coupling parameters of 3d¹ ions are small, such as ζ_d⁰(Ti³⁺) ≈154cm^-1 and ζ_d⁰(V⁴⁺) ≈248 cm^-1. Even for the ligands with the small SO coupling parameters, such as O^2-(ζ_p⁰ ≈150 cm^-1), F^-(ζ_p⁰ ≈220 cm^-1) and Cl^-(ζ_p⁰ ≈587 cm^-1), their SO coupling parameters are comparable with that of the 3d¹ ions. So, we should apply the two-SO -parameter model which contains the contribution due to the SO coupling parameter of 3d¹ ions and that of ligand ions. In this paper, we apply a semiempirical molecular orbital method to establish the high-order perturbation formulas based on the two-SO-parameter model for the EPR parameters of 3d¹ ions in the compressed tetragonal octahedral crystal fields. These formulas were not reported in previous papers. By applying these formulas, the EPR parameters of 3d1 ions have been studied in the following materials and some information on the defect structures of these impurity centers is obtained: (1) For Ti3+ ions in cubic ABF3 perovskites (including the perovskites KMgF3 and KZnF3 and the inverse perovskite LiBaF3), because of charge compensation, an O2? ion will replace F? in the nearest-neighbors site of Ti3+. Through the calculation of EPR parameters in these Ti3+ centers, the useful information on the defect structures of Ti3+ centers is obtained. (2) By calculating the g factors g//, g⊥and hyperfine structure constants A//, A⊥of tetragonal Ti3+ center in CaO crystals, the information on the defect structures of the Ti3+ center is obtained. (3) By studying the EPR parameters of V4+ ions in tetragonal phase of SrTiO3, we found that the (VO6)8? octahedron turns into the compressed octahedron from the elongated octahedron of the pure SrTiO3 crystal because of the Jahn-Teller effect.