Nonreciprocal Bending in Ferroelectric Membranes Driven by Flexoelectricity

Nonreciprocity reflects the asymmetric propagation or motion of an object in two opposite directions and can achieve directional transport in physics. However, nonreciprocity in natural quasi-static mechanical systems, including nonreciprocal bending, has rarely been explored. Here we demonstrate nonreciprocal bending in a freestanding ferroelectric single-crystalline PbTiO₃ membrane using suspended-membrane nanoindentation. The mechanical bending of the ferroelectric membrane is strongly asymmetric in the two opposite bending directions with a difference in effective elastic modulus of up to 33%. The elastic recovery of bending deformation also becomes polarity-dependent. Such unconventional nonreciprocal bending originates from the asymmetric ferroelectric domain switching driven by the crucial flexoelectricity, as revealed by phase-field simulations. This work enriches the nonreciprocal functionalities of ferroelectrics and presents a route for exploring more nonreciprocal effects by flexoelectric engineering.