Atomic structure of steps on 180° ferroelectric domain walls in PbTiO3

Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180° ferroelectric domain walls (DWs) in PbTiO3. We consider three different types of steps: (i) Ti–Ti step that joins a Ti-centered DW to a Ti-centered DW, (ii) Pb–Pb step that joins a Pb-centered DW to a Pb-centered DW, and (iii) Pb–Ti step that joins a Pb-centered DW to a Ti-centered DW. We show that atomic distortions due to these steps broaden a DW but are localized, i.e., they are confined to regions with dimensions of a few lattice spacings. We see that a step locally thickens the DW; the defective DW is two to three times thicker than the perfect DW depending on the step type. We also observe that steps distort the polarization distribution in a mixed Bloch–Néel like way; polarization rotates out of the DW plane near the steps. Our calculations show that Pb–Pb steps have the lowest static energy.