Research on the spin-Hamiltonian parameters for the approximately trigonal Mn5+ tetrahedral center in Sr5(PO4)3Cl crystal

The spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) of the approximately trigonal Mn5+ tetrahedral cluster in Sr5(PO4)3Cl crystal are computed from the complete high-order perturbation formulas established on the two-mechanism model, in which in addition to the contributions due to the frequently-applied crystal-field (CF) mechanism in the CF theory, those due to the commonly-ignored charge-transfer (CT) mechanism are contained. The calculated results are in rational accordance with the experimented values. The calculations demonstrate that for the high valence state dn clusters in crystals, the contributions to spin-Hamiltonian parameters from the CT mechanism should also be considered. The negative sign of zero-field splitting D and the defect structure of the approximately trigonal Mn5+ center in Sr5(PO4)3Cl are proposed from the calculations.