Investigations of the local structures and the EPR g factors for V 4+ and Cr 4+ in Bi 4Ge 3O 12 crystals

Abstract

The local structures and the electron paramagnetic resonance (EPR) g factors g ∥ and g ⊥ for the substitutional V 4+ and Cr 4+ at the Ge 4+ sites in Bi 4Ge 3O 12 are theoretically investigated from the perturbation formulas of the g factors for 3d 1 and 3d 2 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 C 4 axis in the V 4+ and Cr 4+ 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 Ge 4+ site into elongation in the impurity centers due to the size mismatching substitution of the smaller Ge 4+ by the larger impurities. Meanwhile, the Jahn–Teller effect also brings forward some contribution to the local structure of the V 4+ center. The calculated g factors are in good agreement with the experimental data. The local structures of both centers are discussed.