First-principles calculations of domain wall energies of prototypical ferroelectric perovskites

Ferroelectric domain walls play a critical role in determining the polarization switching kinetics and physical properties in ferroelectric materials. There have been extensive studies on identifying the domain wall structures and domain wall energies. Nevertheless, the predicted domain wall energies tend to vary a lot for the same type of domain walls, and it remains elusive under what conditions the non-Ising type domain wall is more stable than the Ising type. In this work, we performed first-principles calculations to evaluate the structures and energetics of several types of domain walls for two prototypical tetragonal ferroelectric perovskites, PbTiO₃ and BaTiO₃, including charge-neutral 90° domain walls, Ising-type and Ising-Bloch-type 180° domain walls with various orientations. We adopted three schemes of structural optimization to optimize the domain wall structures and extract the domain wall energies by carefully eliminating the contribution from strain energies. We discussed how the choice of the schemes influence the calculation results and their applicable conditions. We found that the anisotropy of domain wall energy for Ising-type 180° walls is larger in BaTiO₃ than that in PbTiO₃. The emergence of Bloch component in PbTiO₃ can lower the domain wall energy and reduce its anisotropy. This work offers a more accurate method for predicting the domain wall structures and energetics of ferroelectrics. The calculation results can be useful for understanding of stability of ferroelectric domain walls with high-index orientations and non-Ising characteristics, which is of critical importance in developing domain wall nanoelectronics.