Flexoelectricity and ferroelectric domain wall structures: Phase-field modeling and DFT calculations

We show that flexoelectric effect is responsible for the non-Ising character of a 180^∘{} ferroelectric domain wall. The wall, long considered being of Ising type, contains both Bloch- and N\'eel-type polarization components. Using the example of classic ferroelectric BaTiO₃, and by incorporating the flexoelectric effect into a phase-field model, it is demonstrated that the flexoelectric effect arising from stress inhomogeneity around the domain wall leads to the additional Bloch and N\'eel polarization components. The magnitudes of these additional components are two or three magnitudes smaller than the Ising component, and they are determined by the competing depolarization and flexoelectric fields. Our results from phase-field model are consistent with the atomistic scale calculations. The results prove the critical role of flexoelectricity in defining the internal structure of ferroelectric domain walls.