Theoretical Studies on the Local Structure and Spin Hamiltonian Parameters for Single Cu²⁺ Ion in BaF₂

The spin Hamiltonian parameters (g-factors and the hyperfine structure constants) and local structure are theoretically studied for single Cu²⁺ ion in BaF₂ from the high-order perturbation formulae of these parameters for 3d⁹ ions in tetragonally elongated octahedra. In the calculations, the ligand orbital and spin-orbit coupling of the impurity Cu²⁺ are taken into account, based on the cluster approach. Due to the Jahn-Teller effect and size mismatching substitution, the impurity Cu²⁺ is found to be located at a distance of about 0.2 Å from the nearest fluorine plane. The signs of the hyperfine structure constants $A_∥ $ and $ A_⊥ $ are suggested. The theoretical spin Hamiltonian parameters based on the above local structure are in good agreement with the observed values.