Nucleation process on the 180${^\circ}$ domain wall of PbTiO$_{3}$ by the external electric field

Ferroelectric oxides are extremely useful as nonvolatile memory storage materials, and the speed at which polar domains can be reversed is a critical characteristic for future development of these materials. However, the size of the critical nucleus during the polarization reversal is still unknown experimentally. If we assume that the magnitudes of local polarizations are the same and their directions are along the external field, it will be triangular and the height of the nucleus along the external field should be much larger than its width following the Miller and Weinreich's study in 1960s. We made an atomic potential for perovskite ferroelectrics based on the first-principles calculation, and performed molecular-dynamics simulations to understand the nucleation and growth process of ferroelectric domains. We find that its shape is close to a square not a triangle and its size much smaller than Miller and Weinreich's. It stems from the small polarizations and the voltex-like flow around the nucleus. To increase the system size we used the stochastic study using the nucleation and growth rates which were obtained from the molecular dynamics simulations. The overall speed of the domain wall motion can be estimated from this stochastic calculation.