By considering weaker magnetic interactions (including spin-spin and spin-other-orbit interactions) in Hamiltonian, the spin-Hamiltonian parameters, including the zero-field splitting parameter D and g factors (g_∥, g_⊥) for 3d^{2(8)} ions in Al_2O_3 crystals have been investigated. The results show that the contributions to D, g_∥ and g_⊥ from the spin-orbit interaction are dominant. The contributions from weaker magnetic interactions to D decrease (increase) with increasing charge of impurity ions for 3d^2 (3d^8) ions.
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