Ferroelastic twin wall mediated ferro-flexoelectricity and bulk photovoltaic effect in SrTiO$_3$

Ferroelastic twin walls in nonpolar materials can give rise to a spontaneous polarization due to symmetry breaking. Nevertheless, the bi-stable polarity of twin walls and its reversal have not yet been demonstrated. Here, we report that the polarity of SrTiO$_3$ twin walls can be switched by ultra-low strain gradient. Using first-principles-based machine-learning potential, we demonstrate that the twin walls can be deterministically rotated and realigned in specific directions under strain gradient, which breaks the inversion symmetry of a sequence of walls and leads to a macroscopic polarization. The system can maintain polarity even after the strain gradient is removed. As a result, the polarization of twin walls can exhibit ferroelectric-like hysteresis loop upon cyclic bending, namely ferro-flexoelectricity. Finally, we propose a scheme to experimentally detect the polarity of twin wall by measuring the bulk photovoltaic responses. Our findings suggest a twin-wall-mediated ferro-flexoelectricity in SrTiO$_3$, which could be potentially exploited as functional elements in nano-electronic devices design.