Spin-Spin and Spin-Other-Orbit Interactions of Spin-Hamiltonian Parameters for $3d^{2(8)}$ Ions in $Al_2O_3$ Crystals

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.