Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling

Abstract

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.

Formation of polarization needle-like domain and its unusual switching in compositionally graded ferroelectric thin films: an improved phase field model

“…Note that, as the elastic coefficients slightly change with the change of mole fraction x, the elastic coefficients of Flexoelectricity, the electromechanical coupling between the polarization and strain gradient (direct effect) or mechanical stress and electric eld gradient (converse effect), is a property of all insulators. 48 The exoelectric coupling energy density is expressed as: [48][49][50][51] f…”

USID and Pycroscopy – Open Source Frameworks for Storing and Analyzing Imaging and Spectroscopy Data

“…Other imaging modes such as 4D STEM, promise further increases in both spatial resolution and data dimensionality. [7][8][9] The data can be much more precise [10][11][12] and quantitative 13,14 allowing, subtle details, such as changes in shape, to be directly related to various physical properties 13,[15][16][17] .…”

Hidden symmetry of flexoelectric coupling

“…ilkj ijkl f f = It has been shown that the static flexocoupling induces imprint [14,15,16], internal bias [17,18] and dead layer effect [19,20] in ferroelectric thin films, and vortices in superlattices [21].…”