Atomic Structure of Steps on 180^o Ferroelectric Domain Walls in PbTiO_3

TL;DR

This study uses anharmonic lattice statics to analyze the atomic structure of steps on 180° ferroelectric domain walls in PbTiO_3, revealing localized distortions, domain wall thickening, and polarization rotation effects.

Contribution

It provides the first detailed atomic-level analysis of different step types on ferroelectric domain walls in PbTiO_3 using anharmonic lattice statics.

Findings

Steps broaden the domain wall but distortions are localized

Pb-Pb steps have the lowest static energy

Steps cause polarization to rotate out of the wall plane

Abstract

Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180^o ferroelectric domain walls (DW) in PbTiO_3. 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 domain wall; the defective domain wall is two to three times thicker than the perfect domain wall depending on the step type. We also observe that steps distort the polarization distribution in a mixed Bloch-N\'{e}el like way; polarization rotates out of the domain wall plane near the steps. Our calculations show that Pb-Pb steps have the lowest static energy.