Shear-strain gradient induced polarization reversal in ferroelectric BaTiO3 thin films: A first-principles total-energy study

Based on the first-principles total-energy calculation, we have studied the shear-strain gradient effect on the polarization reversal of ferroelectric ${\mathrm{BaTiO}}_{3}$ thin films. By calculating the energies of double-domain supercells for different electric polarization, shear-strain gradients, and domain-wall displacement, we extracted, in addition to the domain-wall energy, the polarization energy, elastic energy, and flexoelectric coefficient of a single domain. The constructed Landau-Devonshire phenomenological theory yields a critical shear-strain gradient of $9.091\ifmmode\times\else\texttimes\fi{}{10}^{7}/\text{m}$ (or a curvature radius ($R$) of 110 \AA{}) for reversing the ${180}^{\ensuremath{\circ}}$ domain at room temperature, which is on the same order of the experimentally estimated value of $3.333\ifmmode\times\else\texttimes\fi{}{10}^{7}/\text{m}$ ($R=300\phantom{\rule{0.16em}{0ex}}\AA{}$). In contrast to the commonly used linear response theory, the flexoelectric coefficient derived from fitting the total energy to a Landau-Devonshire energy functional does not depend on the specific pseudopotential. Thus, our method offers an alternative numerical approach to study the flexoelectric effect.