Intrinsic threshold electric field for domain wall motion in ferroelectrics based on a discretized phase-field model

With the development of ferroelectric memories, it is becoming increasingly important to understand the ferroelectric switching behaviors at small applied electric fields. In this paper we use discretized phase-field models to systematically investigate the intrinsic threshold electric field (TEF) to drive flat ${180}^{\ensuremath{\circ}}$ and ${90}^{\ensuremath{\circ}}$ domain walls (DWs), which cannot be captured by continuum models. The results show that this TEF increases as the ratio of DW width to unit-cell size decreases, and it becomes significant if the DW width is thinner than two unit cells. The results are qualitatively consistent with existing first-principles studies and cryogenic experiments. In addition, this work proposes a conceptual model to explain the activation electric field (AEF) observed in experiments at room temperature. This work improves the understanding of DW motion kinetics at small applied fields and shows that the mesh size and orientation are both important for the phase-field modeling of the above process.