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The aim of this paper is to model the crystal field parameters (CFPs) and spin-Hamiltonian parameters (g factors g | | , g ⊥ and hyperfine structure constants A | | , A ⊥ ) for the Ti3+:MgO system. The CFPs were modeled in the frame of superposition model of the crystal field theory, based on ab initio supercell calculations of Ti3+:MgO geometry and crystal field parameter 10Dq. The obtained values were used to simulate the energy levels scheme, by diagonalizing the full energy matrix of the Hamiltonian. The EPR parameters have been calculated from both the complete diagonalization method and the perturbation theory method. All the obtained results (optical and EPR) were compared with experimental data and a good agreement is observed.

The spin-Hamiltonian parameters (g factors g∥, g⊥ and hyperfine structure constants 143A∥, 143A⊥, 145A∥ and 145A⊥) of the tetragonal Nd3+ center in the low-temperature (T≈4.2 K) tetragonal phase of SrTiO3 are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term 4HJ (J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd3+ center is attributed to Nd3+ occupying the 12-fold coordinated Sr2+ site in SrTiO3. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd3+ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd3+ and the Nd3+ displacement Δz along C4 axis, we suggest that it is due to the distortion of SrTiO3 lattice in the tetragonal phase. The calculated g factors g∥ and g⊥ show good agreement with the experimental values, suggesting that our defect model of Nd3+ center in SrTiO3 is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.

In this paper, the third-order perturbation formulas of EPR g factors g(i) (i=x, y, z) for d(9) ions in rhombic symmetry where the ground state being an vertical bar d(x2-y2)> admixture of and vertical bar d(z2)> states are derived. These formulas are based on a two-spin-orbit-parameter model in which the contributions to g factors due to both the spin-orbit parameter of the central 3d(n) ion and that of ligand ion are included. From these formulas, the g factors g(i) for the rhombic CuCl(6)(4-) clusters in (3-chloroanilinium)(8)[CdCl(6)]CL(4):Cu(2+) crystal are calculated. The calculated values are in good agreement with those obtained by the complete diagonalization (of energy matrix) method and experimental values. Results are discussed. (C) 2010 Elsevier B.V. All rights reserved.