Strain Gradient Elasticity in SrTiO₃ Membranes: Bending versus Stretching

Young's modulus determines the mechanical loads required to elastically stretch a material and also the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. The associated energy cost can additionally contribute to elasticity via strain gradients, particularly at small length scales where they are geometrically enhanced. Here, we present nanomechanical measurements of freely suspended SrTiO₃ crystalline membrane drumheads. We observe an unexpected nonmonotonic thickness dependence of Young's modulus upon small deflections. Furthermore, the modulus inferred from a predominantly bending deformation is three times larger than that of a predominantly stretching deformation for membranes thinner than 20 nm. In this regime we extract a strain gradient elastic coupling of ∼2.2 μN, which could be used in new operational regimes of nanoelectro-mechanics.