Theoretical Studies of the Local Structures and EPR Spectra for $VO^{2+}$ in $MB_4O_7$ (M = Zn, Cd) Glasses

Electron spin resonance spectral parameters (g factors $g_{∥}$, $g_{⊥}$ and hyperfine structure constants $A_{∥}$, $A_{⊥}$) of a tetragonal $V^{4+}$ centers in $MB_4O_7$ (M = Zn, Cd) are theoretically investigated by using the perturbation formulae for a $3 d^1$ ion in tetragonally compressed octahedra. In these formulae, the contributions to the g factors from the tetragonal distortion, characterized by the tetragonal field parameters $D_{s}$ and $D_{t}$ are taken into account by considering the local structures of the ligand octahedron around the $V^{4+}$ due to the Jahn-Teller effect. Based on the calculations, the ligand octahedra around $V^{4+}$ are suggested to suffer about 5.7% and 4.3% relative compression along $C_4$ axis for $MB_4O_7$ glasses with M = Zn and Cd, respectively, and negative signs of the hyperfine structure constants $A_{∥}$ and $A_{⊥}$ for $V^{4+}$ centers in $MB_4O_7$ glasses were suggested in the discussion.