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.

Keywords:

• defect structure
• electron paramagnetic resonance
• crystal-field and ligand theory
• Ti³⁺
• BaTiO₃