The high (fourth) order perturbation formulas based on the dominant spin-orbit coupling mech anism for the zero-field splittings D m of a 6S-state ion in trigonal symmetry and E [ha in rhombic symmetry are derived from the strong field scheme. Two analytic expressions of the spin-lattice coupling coefficient G 4 4 obtained from the formulas of and E rho are established by using a simple and uniform method. Based on the two expressions, the coefficients G 4 4 for KMgF3:Mn2+ are calculated in two cases. The results show that the lowest (third) order perturbation formulas of and E ^ 0 are too simple and too approximate to give reasonable and consistent values of G 44, whereas when the fourth-order perturbation terms D (^ and E ^ 0 are considered, the calculated values of G 44 (= G 44 + G '^) 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.