Theoretical investigations of the EPR parameters for Cr 3+ and Mn 4+ ions in PbTiO 3 crystals

Abstract

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 3d 3 ions in tetragonal octahedral sites. According to the calculations based on these formulas, the EPR parameters g ∥, g ⊥ and zero-field splitting D for Cr 3+ and Mn 4+ ions in PbTiO 3 crystals are explained reasonably. The calculations show that (i) the sign of g-shift Δ g i CT (= g i − g s, where g s = 2.0023 is free-electron value and i = ∥ and ⊥) in CT mechanism is opposite to, but that of D CT is the same as, the corresponding signs in the CF mechanism and (ii) the relative importance of CT mechanism for the high valence state 3d 3 ion (e.g., Mn 4+) 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 Cr 3+ and Mn 4+ impurity centers in PbTiO 3 crystals are also suggested from the calculations. The results are discussed.