The attached paper was recently accepted for publicaiton in Applied Physics Letters. Here we try to speculate on the origins of a type of electromechanical indentation size-effect. Although we have decent supporting evidence, I think that our assertions are still on the speculative side and hope that future experiments can shed further light on this.

Abstract: Metals exhibit a size-dependent hardening when subject to indentation. Mechanisms for this phenomenon have been intensely researched in recent times. Does such a size-effect also exist in the electromechanical behavior of ferroelectrics?---if yes, what are the operative mechanisms? Our experiments on BaTiO3 indeed suggest an elastic electromechanical sizeeffect. We argue, through theoretical calculations and differential experiments on another nonferroelectric piezoelectric (Quartz), that the phenomenon of flexoelectricity (as opposed to dislocation activity) is most likely responsible for our observations. Flexoelectricity is the coupling of strain gradients to polarization and exists in both ordinary and piezoelectric dielectrics. In particular, ferroelectrics exhibit an unusually large flexoelectric response.