Flexoelectricity is a property of dielectric materials whereby they exhibit electric polarization induced by strain gradients; while this effect can be negligible at the macroscale, it can become dominant at the nanoscale, where strain gradients can turn out to be tremendous. Previous works have demonstrated that flexoelectricity coupled with piezoelectricity enables the mechanical writing of ferroelectric polarization. When considering ferroelectric materials with out-of-plane polarization, the coupling of piezoelectricity with flexoelectricity can insert a mechanical asymmetry to the system and enable the distinction of oppositely polarized domains, based on their nanomechanical response. Using atomic force microscopy and, more specifically, contact resonance techniques, the coupling of flexoelectricity to piezoelectricity can be exploited to mechanically read the sign of ferroelectric polarization in a non-destructive way. We have measured a variety of ferroelectric materials, from a single crystal to thin films, and domains that are polarized down always appear to be stiffer than oppositely polarized domains. In this article, we demonstrate experimentally that the phenomenon is size-dependent and strongly enhanced when the dimension of the material is reduced to nanoscale in thin films. Ultimately, we demonstrate how the sensitivity in mechanical reading of ferroelectric polarization can be improved by appropriately tuning the mechanical stiffness of the cantilevers.
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