AFM-tip written normal and anomalous domains in PMN-0.4PT crystals

At present, crystals of the solid solutions Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-xPT) are under intensive investigation due to their excellent piezoelectric characteristics. Studies in domain engineering are of importance for an insight into the contribution from the domain formation and resulting domain-wall density to piezoelectric coefficients. In this work, the fabrication of domains by dc AFM-tip voltages was studied in the tetragonal PMN-0.4PT crystals. Two types of domains were observed, either uniformly polarized along the poling field (the "normal" ones), or, following the commonly accepted term, "anomalous" ones containing a small area with the polarization directed oppositely to the poling field. In this work, for the first time, the correlation between the domain shape and the local piezoelectric hysteresis loops H_ω-U_tip was found, namely, the larger is the local bias voltage U_b, the higher is the tip voltage U_tip at which the anomalous domains appear. This finding relates the observed scatter in the exposure conditions corresponding to the anomalous domains formation, to the nonuniform spatial distribution of the local bias fields. The domain diameter D vs U_tip and pulse duration t_p were investigated for U_tip ≤ 50 V and t_p from 10 ms to 10 s. The exposure characteristics are independent of the domain shape. For a given t_p, D(U_tip) is described by a unified linear function in the whole U_tip range. The curves D(t_p) follow a power law D ∼ t p k with the exponent k varying very weakly with U_tip. The relaxation kinetics of anomalous domains depends on the writing conditions. The normal domains are found to decay significantly faster than the anomalous ones, with the decay kinetics depending on the domain spacing.