Theoretical investigations of the EPR parameters for Cr3+ and Mn4+ ions in PbTiO3 crystals

The complete high-order perturbation formulas of EPR parameters (g factors g∥, g⊥ and zero-field splitting D), containing the crystal-field (CF) mechanism and charge-transfer (CT) mechanism (the latter is omitted in crystal-field theory which is often used to study the EPR parameters), are established from a cluster approach for 3d3 ions in tetragonal octahedral sites. According to the calculations based on these formulas, the EPR parameters g∥, g⊥ and zero-field splitting D for Cr3+ and Mn4+ ions in PbTiO3 crystals are explained reasonably. The calculations show that (i) the sign of g  -shift ΔgiCT (=gi − gs, where gs = 2.0023 is free-electron value and i = ∥ and ⊥) in CT mechanism is opposite to, but that of DCT is the same as, the corresponding signs in the CF mechanism and (ii) the relative importance of CT mechanism for the high valence state 3d3 ion (e.g., Mn4+) is large and so the contributions to EPR parameters from CT mechanism should be taken into account. The different sign of splitting D and the different defect structure for Cr3+ and Mn4+ impurity centers in PbTiO3 crystals are also suggested from the calculations. The results are discussed.