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.
Bibliographical noteFunding Information:
The research was performed at the Center for Nanophase Materials Sciences, a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory. R.R. and L.W.M. acknowledge support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, under grant no. GBMF5307. A.R.D. acknowledges support from the Army Research Office under grant no. W911NF-14-1-0104 and the Department of Energy, Office of Basic Energy Sciences under grant no. DE-SC0012375 for synthesis and structural study of the materials. Q.L. thanks Dr. Ye Cao and Dr. Jiawang Hong for helpful discussions.