Investigations of g factors for the ²E state of V²⁺ ions in Al₂O₃ crystals

The exchange charge model of crystal field was used to calculate the crystal filed parameters (CFPs) acting upon the V²⁺ electrons in the Al₂O₃ crystals. With those CFPs, the crystal field Hamiltonian was diagonalized in the complete space spanned by all wave functions of the 3d³ electron configuration of divalent vanadium. The obtained wave functions of the calculated energy levels were used to estimate the zero filed splitting (ZFS) of the ground state and g factors of ground and the first excited states for V²⁺ ion in Al₂O₃ crystals. The theoretical results are in good agreement with the corresponding experimental data. Numerical estimations of the contributions to the ZFS and g factors arising from the nearest ligands and ions from further coordination spheres were performed. It has been shown that consideration of a large cluster around an impurity ion leads to improvement of the calculated results.