A phase-field simulation-based approach to determine flexoelectric coefficients from hysteresis loop of ferroelectrics

The flexoelectric effects in ferroelectric materials have attracted abundant attention in recent years due to the potential application in microscale mechanical-electrical devices. However, quantifying flexoelectric coefficients in ferroelectrics is still a challenge because of the complex electromechanical coupling in ferroelectric materials. Inspired by the flexoelectric effect-induced skew of the hysteresis curve, an indirect method is proposed in this article to determine the flexoelectric coefficient with reasonably high accuracy. Phase-field simulations show that such skew is stimulated only by the flexoelectric effect, which excludes the influence of other electromechanical coupling effects. In addition, the magnitude of such skew is in linear proportion to the flexoelectric coefficient. The four-point bending PbTiO₃ beam model is calculated as an example to obtain the transversal flexoelectric coefficient of $f1122$⁠.