The EPR g factors g // and g ⊥ for the six-coordinated Cu 2+(1) site in YBa 2 Cu 3 O 6+x are theoretically investigated from the perturbation formulas for a 3 d 9 ion in tetragonally elongated octahedra. The related tetragonal crystal-field parameters Ds and Dt are determined from the superposition model and the structural data for the Cu 2+(1) site, by considering the effective elongation of the oxygen octahedron due to the Jahn-Teller effect of the Cu 2+ cluster. Based on the calculations, the effective elongation (≈ 15%) of the ligand octahedron is obtained for the signals at 100K. As for the EPR signals at room temperature, the elongation declines to merely 4%, corresponding to the smaller anisotropy Δ g (= g // - g ⊥). The theoretical results for the g factors are in good agreement with the observed values, and the local tetragonal distortion due to the Jahn-Teller effect is discussed.

The superhyperfine parameters A′ and B′ for Cr 3+ ions in K 2 NaGaF 6 , K 2 NaCrF 6 , KMgF 3 and CsCdF 3 are theoretically studied from the cluster approach. In the present treatments, the orbital admixture coefficients and the unpaired spin densities in 2s, 2p s and 2p p 2 fluorine orbitals are obtained in a uniform way. The experimental A′ and B′ are reasonably explained, and the unpaired spin densities for the 2s, 2pσ and 2pπ orbitals of the ligand F − are also compared with those in the previous works.

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.

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The axial displacements for Co2+ and Ni3+ in Al2O3 are theoretically investigated starting from the perturbation formulas of the EPR parameters for a 3d7 ion with high spin (S=3/2) and low spin (S=1/2) in trigonal symmetry, respectively. Based upon these studies, the Co2+ is found to shift towards the center of the oxygen octahedron by an amount ZCo (≈ 0.03 Å) along the C3 axis, while the Ni3+ may suffer another axial displacement ZNi (≈ −0.38 Å) away from the center of the octahedron. The calculated EPR parameters based upon the above axial displacements show good agreement with the observed values. The differences in the EPR parameters and the axial displacements for the two 3d7 ions are discussed.