Spin-lattice coupling coefficient G(44) of KMgF3 : Mn2+ calculated from two cases

The high (fourth) order perturbation formulas based on the dominant spin-or bit coupling mechanism for the zero-field splittings D-tri of a S-6-state i on in trigonal symmetry and E-rho in rhombic symmetry are derived from the strong field scheme. Two analytic expressions of the spin-lattice coupling coefficient G(44) Obtained from the formulas of D-tri and E-rho are establi shed by using a simple and uniform method. Based on the two expressions, th e coefficients G(44) for KMgF3:Mn2+ are calculated in two cases. The result s show that the lowest (third) order perturbation formulas of D-tri((3)) an d E-rho((3)) are too simple and too approximate to give reasonable and cons istent values of G44, whereas when the fourth-order perturbation terms D-tr i((4)) and E-rho((4)) are considered, the calculated values of G(44) (= G(4 4)((3)) + G(44)((4))) in both cases are not only close to each other, but a lso in agreement with the observed value. So, the fourth-order perturbation terms cannot be neglected.