Giant Superelastic Piezoelectricity in Flexible Ferroelectric $BaTiO_3$ Membranes

Mechanical displacement in commonly used piezoelectric materials is typically restricted to linear or biaxial in nature and to a few percent of the material dimensions. Here, we show that free-standing BaTiO$_3$ membranes exhibit non-conventional electromechanical coupling. Under an external electric field, these superelastic membranes undergo controllable and reversible 'sushi-rolling-like' 180$^\circ$ folding-unfolding cycles. This crease-free folding is mediated by charged ferroelectric domains, leading to a giant > 3.8 and 4.6 $\mu$m displacements for a 30-nm thick membrane at room temperature and 60$^\circ$C, respectively. Further increasing the electric field above the coercive value changes the fold curvature, hence augmenting the effective piezoresponse. Finally, it is found that the membranes fold with increasing temperature followed by complete immobility of the membrane above the Curie temperature, allowing us to model the ferroelectric-domain origin of the effect.