Theoretical investigations of the local structure and the g factors for the tetragonal Ru3+ center in PbTiO3

The local structure and the g factors for the tetragonal Ru³⁺ center in PbTiO₃ are theoretically studied from the perturbation formulas of the g factors for a 4d⁵ ion in tetragonally distorted octahedra. From the studies, the distance between the impurity Ru³⁺ and the center of the oxygen octahedron is found to be about 0.283 Å, which is smaller than that (≈0.3 Å) for the host Ti⁴⁺ site. It appears that the impurity may not occupy exactly the host Ti⁴⁺ site but suffer a slight inward shift toward the center of the oxygen octahedron. The calculated g factors based on the above local structure show good agreement with the experimental values.