High-order perturbation formulas of the zero-field splitting for 3d5 ion in tetragonal symmetry

The third- and fourth-order perturbation formulas based on the dominant spin-orbit coupling mechanism for the zero-field splitting D of 3d(5) ion in tetragonal symmetry have been established from the strong-field scheme. From the formulas, the spin-lattice coupling coefficient G(11) (which is related to the zero-field splitting D due to the slight tetragonal distortion under stress) of MgO:Mn2+ and the zero-field splitting D of the tetragonal Mn2+ -V-O center in SrTiO3 are calculated. The results suggest that in the cases of 3d(5) clusters with small tetragonal distortion, the lowest (third)-order perturbation formula is applicable; however, in the cases of large tetragonal distortion, the higher (fourth)-order contribution is comparable with the third-order one and should be taken into account. The displacement of Mn2+ in the Mn2+ -V-O center and hence the microstructures of this centre in SrTiO3 are also obtained. The relaxation pattern is consistent with that of the isoelectronic Fe3+-V-O center in KNbO3 crystal obtained from both the shell-model simulations and the embedded-cluster calculations. (C) 2001 Elsevier Science B.V. All rights reserved.