Abstract
Abstract The high (fourth) order perturbation formulas based on the dominant spin-orbit coupling mechanism for the zero-field splittings Dtri of a 6S-state ion in trigonal symmetry and Erho in rhombic symmetry are derived from the strong field scheme. Two analytic expressions of the spin-lattice coupling coefficient G44 obtained from the formulas of and Erho are established by using a simple and uniform method. Based on the two expressions, the coefficients G44 for KMgF3:Mn2+ are calculated in two cases. The results show that the lowest (third) order perturbation formulas of D(3) tri and E(3) rho are too simple and too approximate to give reasonable and consistent values of G44, whereas when the fourth-order perturbation terms D(4) tri and E(4) rho are considered, the calculated values of G44 (= G(3) 44 + G(4) 44) in both cases are not only close to each other, but also in agreement with the observed value. So, the fourth-order perturbation terms cannot be neglected.
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