Investigations of the local structures and the EPR g factors for V4+ and Cr4+ in Bi4Ge3O12 crystals

The local structures and the electron paramagnetic resonance (EPR) g factors $g_{\parallel }$ and $g_{\perp }$ for the substitutional V⁴⁺ and Cr⁴⁺ at the Ge⁴⁺ sites in Bi₄Ge₃O₁₂ are theoretically investigated from the perturbation formulas of the g factors for 3d¹ and 3d² ions under tetragonally elongated tetrahedra. In the calculations, the ligand orbital and spin–orbit coupling contributions are taken into account from the cluster approach in view of the covalency of the systems. The local impurity-ligand bond angles β related to the C₄ axis in the V⁴⁺ and Cr⁴⁺ centers are found to be about 5° and 6°, respectively, lower than the host angle β_H in the pure crystal. So the ligand tetrahedra transform from original compression at the host Ge⁴⁺ site into elongation in the impurity centers due to the size mismatching substitution of the smaller Ge⁴⁺ by the larger impurities. Meanwhile, the Jahn–Teller effect also brings forward some contribution to the local structure of the V⁴⁺ center. The calculated g factors are in good agreement with the experimental data. The local structures of both centers are discussed.