High-order perturbation formulae for the zero-field splitting of a6S ion in C3symmetry and its application to Mn(I):Ca5(PO4)3F

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Abstract
The relationship between the zero-field splitting parameter D and the C3 crystalline potential components for 6S ions is established with the use of the high-order perturbation method. It is found that the effect of the spin-spin interaction within the d5 configuration is comparable with the mechanism suggested by Orbach et al. (1962). By using the d-orbital theory proposed by Zhao et al. (1982, 1983, 1984) the optical levels and the zero-field splitting of Mn(I):Ca5(PO4)3F are calculated. The results agree well with the values measured experimentally.