Electromechanical properties of the 180° domain wall in PbTiO3

TL;DR

This work addresses how $180^{\circ}$ domain walls in PbTiO3 contribute to electromechanical strain. By combining ab initio density-functional theory with a continuum LGD framework that includes gradient (inhomogeneous) electrostriction, the authors extract wall parameters and decompose the wall-induced length change into conventional and gradient components. They find that gradient electrostriction dominates, producing a localized, wall-core elongation with a gradient coefficient $I_R\approx -6\times10^{-21}$ m$^{6}$C$^{-2}$, while the conventional term is small and negative. The results underscore the necessity of gradient couplings in LGD models to stabilize Bloch-like walls and provide a transferable method to quantify gradient effects in ferroic domain walls.

Abstract

We analyze the electromechanical response of the 180 degree ferroelectric domain wall in tetragonal PbTiO3 by combining first-principles calculations with a Landau-Ginzburg-Devonshire (LGD) description. Using regular multidomain structures with varying domain-wall density, we extract polarization profiles and lattice distortions and map them onto the continuum model to determine conventional (homogeneous) and gradient (inhomogeneous) electrostriction. Conventional electrostriction yields only a small negative length change of the sample, whereas gradient electrostriction--arising from the coupling between strain and polarization gradients--produces a positive contribution nearly an order of magnitude larger and localized at the wall core. Our results demonstrate that gradient electrostriction dominates the electromechanical response of 180 degree walls in PbTiO3, supporting its inclusion in LGD models that stabilize Bloch-type domain wall structures.

Figures (4)

• Figure 1: Schematic illustration of the periodic supercell containing two ${180}^{\circ}$ domain walls in PbTiO$_3$. The supercell is repeated along the $x$ axis, forming an equidistant array of DWs separated by $n/2$ unit cells.
• Figure 2: (Color online) Layer-resolved polarization components across the Bloch-type ${180}^{\circ}$ DW for $n=20$. Integer indices correspond to Pb planes, while half-integer indices (e.g., 0.5, 1.5, …) correspond to Ti planes.
• Figure 3: (Color online) Dependence of the domain polarization $P_{3,\mathrm{max}}$, the Bloch component $P_{2,\mathrm{max}}$, and the inverse DW thickness $k$ on the DW density $\rho$. (a) Ising case; (b) Bloch case. The values for independent DWs occur at $\rho = 0$.
• Figure 4: (Color online) The longitudinal elongation $\Delta L$, as well as the transverse expansion $\Delta b$ and contraction $\Delta c$, are shown as functions of $\rho$ for the Ising domain wall (DW). The corresponding Bloch DW curves are very similar; only $\Delta L$ for the Bloch case at $\rho = 0$ is shown. The values for independent DWs occur at $\rho = 0$.