Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO3/SrTiO3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO3 and SrTiO3. Our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.

Variable temperature band-excitation atomic force microscopy in conjunction with I-V spectroscopy was used to investigate the crystalline superionic proton conductor CsHSO4 during proton exchange induced by a Pt-coated conductive scanning probe. At a sample temperature of 150 °C and under an applied bias <1 V, reduction currents of up to 1 nA were observed. Simultaneously, we show that the electrochemical reactions are accompanied by a reversible decrease in the elastic modulus of CsHSO4, as seen by a contact resonance shift, and find evidence for superplasticity during scanning. These effects were not observed in the room-temperature phase of CsHSO4 or in the case of catalytically inactive conductive probes, proving the utility of this technique for monitoring electrochemical processes on the nanoscale, as well as the use of local contact stiffness as a sensitive indicator of electrochemical reactions.