  Recent realizations of ultrathin freestanding perovskite oxides offer a
unique platform to probe novel properties in two-dimensional oxides. Here, we
observed a giant flexoelectric response in freestanding BiFeO3 and SrTiO3 in
their bent state arising from strain gradients up to 4x10e7/m, suggesting a
promising approach for realizing extremely large polarizations. Additionally, a
substantial reversible change in thickness was discovered in bent freestanding
BiFeO3, which implies an unusual bending-expansion/shrinkage and
thickness-dependence Poisson's ratios in this ferroelectric membrane that has
never been seen before in crystalline materials. Our theoretical modeling
reveals that this unprecedented flexural deformation within the membrane is
attributable to a flexoelectricity-piezoelectricity interplay. The finding
unveils intriguing nanoscale electromechanical properties and provides guidance
for their practical applications in flexible nanoelectromechanical systems.
