Investigation of the g factors and defect structures for the tetragonal Ti3+ and Ti3+–Nb5+ centers in the low-temperature rhombohedral phase of BaTiO3

Abstract

In this study, the electron paramagnetic resonance g factors g // and g ⊥ of two tetragonal Ti3+ defect centers, the isolated Ti3+ center and the Ti3+–Nb5+ center, in the low-temperature rhombohedral phase of BaTiO3 are calculated from the complete diagonalization (of energy matrix) method and the perturbation theory method. Both the methods are based on the two-spin–orbit (SO)-parameter model. In the model, the contributions to the g factors due to both the SO parameters of the central 3d1 ion and the ligand ion are included. The calculations are related to the defect models and defect structures of the two tetragonal Ti3+ centers. In the isolated Ti3+ center, the Ti3+ ion is assumed to occupy the approximately cubic octahedral Ti4+ site. The octahedron surrounding the Ti3+ undergoes a static Jahn–Teller distortion (characterized by the ligand displacement a) from approximately cubic to tetragonally compressed. In the Ti3+–Nb5+ center, the substitutional Ti3+ is charge compensated by an Nb5+ ion at the nearest neighboring Ti4+ site along the C 4-axis. The O2− ion intervening Ti3+ and Nb5+ has an additional displacement Δ z toward Nb5+ owing to the electrostatic interaction. From the calculations, the g factors of the two tetragonal Ti3+ centers are reasonably explained by either method. Also, the defect models of both the Ti3+ centers are confirmed and their defect structures (characterized by the ligand displacements a and Δ z) are obtained. The results are discussed.