Studies of EPR g factors for tetragonal and rhombic Cr⁵⁺ centers in ferroelectric PbTiO₃

Abstract

The anisotropic g factors (g x , g y , g z ) at low temperature and the motionally averaged isotropic g factor at high temperature for two Cr 5+ centers, the tetragonal t-Cr 5+ center and the rhombic O-Cr 5+ center, in ferroelectric PbTiO 3 are calculated from the high-order perturbation formulas based on a two-mechanism model. In the model, the contributions to g factors from both the crystal-field (CF) mechanism concerning the CF excited states and the charge-transfer (CT) mechanism (which is neglected in CF theory) concerning the CT excited states are contained. The calculated results are in reasonable agreement with the experimental values. From the calculations, the defect models of t-Cr 5+ center (which is attributed to Cr 5+ in the tetragonally-compressed octahedron caused by Jahn-Teller effect rather than in the tetragonally-elongated octahedron in the host PbTiO 3 ) and O-Cr 5+ center (which is due to the t-Cr 5+ center perturbated by the electrical polarization perpendicular to the C 4 axis) are confirmed, and the defect structure of t-Cr 5+ center is obtained. It is found that in the precise calculations of g factors for the high valence state d 1 ions in crystals, both the contributions due to CF and CT mechanisms should be taken into account.