Studies on the EPR parameters and local angular distortion for the tetragonal Cu²⁺ center in CaWO₄ crystal

The electron paramagnetic resonance (EPR) parameters-g factors g_i (i = || and ⊥) and hyperfine structure constants A_i (M) and A_i (N), with M and N belonging to isotopes ⁶³ Cu²⁺ and ⁶⁵ Cu²⁺ -and local structure of Cu²⁺ ion occupying W⁶⁺ site in CaWO₄ crystal are theoretically studied based on the perturbation formulas of these parameters for a 3d⁹ ion under tetragonally elongated tetrahedra. In these formulas, the ligand orbital (LO) and spin-orbit coupling (SOC) contributions are included due to the shorter impurity-ligand distance R (≈1.83 Å) and hence the strong covalency of the studied [CuO₄ ]^6- cluster, and the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way; meanwhile, the required crystal field (CF) parameters for the tetragonally distorted tetrahedron (TDT) are estimated from the superposition model and the local structure of the impurity Cu²⁺ center. According to the calculation, the bond angle θ between the four equivalent Cu²⁺ -O^2- bonds and the C₄ axis in the CaWO₄ :Cu²⁺ is found to be about 2.1° smaller than that (θ₀  ≈ 54.74°) for an ideal tetrahedron due to the Jahn-Teller (JT) effect and the size mismatch. The fitted results agree well with the observed values, and the validity of the present assignment for the local structure of the Cu²⁺ center is also discussed.