High-order perturbation formulas of the zero-field splitting for 3d(5) ionin tetragonal symmetry

The third- and fourth-order perturbation formulas based on the dominant spi n-orbit coupling mechanism for the zero-field splitting D of 3d(5) ion in t etragonal symmetry have been established from the strong-field scheme. From the formulas, the spin-lattice coupling coefficient G(11) (which is relate d to the zero-field splitting D due to the slight tetragonal distortion und er 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 cas es of 3d(5) clusters with small tetragonal distortion, the lowest (third)-o rder perturbation formula is applicable; however, in the cases of large tet ragonal distortion, the higher (fourth)-order contribution is comparable wi th the third-order one and should be taken into account. The displacement o f 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 tha t 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.