Flexoelectric\nEnhancement of Strain Gradient Elasticity\nAcross a Ferroelectric-to-Paraelectric Phase Transition

We study the temperature dependent elastic properties\nof Ba<sub>0.8</sub>Sr<sub>0.2</sub>TiO<sub>3</sub> freestanding membranes\nacross\nthe ferroelectric-to-paraelectric phase transition using an atomic\nforce microscope. The bending rigidity of thin membranes can be stiffer\ncompared to stretching due to strain gradient elasticity (SGE). We\nmeasure the Young’s modulus of freestanding Ba<sub>0.8</sub>Sr<sub>0.2</sub>TiO<sub>3</sub> drumheads in bending and stretching\ndominated deformation regimes on a variable temperature platform,\nfinding a peak in the difference between the two Young’s moduli\nobtained at the phase transition. This demonstrates a dependence of\nSGE on the dielectric properties of a material and alludes to a flexoelectric\norigin of an effective SGE.