The impurity displacements for Fe 3+ and Ru 3+ in corundum (Al2O3) are theoretically studied using the perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and anisotropic g factors) for a 3d 5 (with high spin S = 5/2) and a 4d 5 (with low spin S = 1/2) ion in trigonal symmetry, respectively. According to the investigations, the nd 5 (n = 3 and 4) impurity ions may not locate at the ideal Al 3+ site but undergo axial displacements by about 0.132Å and 0.170Å for Fe 3+ and Ru 3+ , respectively, away from the center of the ligand octahedron along the C3 axis. The calculated spin Hamiltonian parameters based on the above axial displacements show good agreement with the observed values. The validity of the results is discussed.

The electron paramagnetic resonance (EPR) parameters (g factors and the hyperfine structure constants) for Ni 2+ and Co + in MgO are theoretically studied from the perturbation formulas of these parameters for a 3d 8 ion in octahedral crystal-fields. In the computations, the ligand orbital and spin-orbit coupling contributions are taken into account using the cluster approach. The calculated EPR parameters are in good agreement with the experimental data. The larger g factor and the smaller magnitude of the hyperfine structure constant for Ni 2+ as compared with those for Co + can be attributed to the higher spin-orbit coupling coefficient and the lower dipolar hyperfine structure parameter of the former, respectively.

The local structure and the spin Hamiltonian parameters g factors gi (i =x, y and z) and the hyperfine structure constants Ai for Co2+ in orthorhombic CaTiO3 are theoretically investigated from diagonalization of 6 × 6 energy matrix within the 4T1 ground state for a 3d7 ion in orthorhombic symmetry. In the calculations, the contributions from the admixtures of various J states (J=1/2, 3/2, 5/2), the ligand orbitals and spin-orbit coupling and the fourth-order orthorhombic field parameter, which were usually neglected in the previous works, are taken into account. The crystal-field parameters are determined from the superposition model in consideration of the suitable lattice distortion due to the charge and size mismatching substitution of Ti4+ by Co2+. Based on the studies, the bond lengths R1 and R2 in the xy plane are estimated to suffer the relative alternation R ≈ 5.4%, yielding more significant orthorhombic distortion in the impurity center as compared with that for the host Ti4+ site in pure crystal. The calculation results based on the above local lattice distortion show reasonable agreement with the observed values. The various contributions to the spin Hamiltonian parameters are discussed. Present studies may theoretically verify that the impurity Co2+ occupies the 6-fold coordinated Ti4+ site rather than the 12-fold coordinated Ca2+ site, associated with the enhanced orthorhombic distortion due to the mismatching substitution.