Atomic-resolution differential phase contrast STEM on ferroelectric materials: A mean-field approach

The ultimate challenge in the investigation of ferroelectric properties lies in the quantitative measurements of their polarization at the unit cell scale. Such investigations are commonly performed using an indirect approach, by measuring the atomic displacements from atomic resolution images. Differential phase-contrast (DPC) scanning transmission electron microscopy (STEM) allows mapping the electric field with atomic resolution. This unique capability offers a direct way to study the polar properties in ferroelectrics. However, the effects of ferroelectric polarization on the contrast of high-resolution DPC-STEM imaging have not been addressed so far. In this work, we perform a theoretical study on the origin of the DPC-STEM contrast in ferroelectric materials and propose a modified multislice algorithm for STEM image simulations. Our results demonstrate that the mesoscopic polarization induces asymmetries in the detected electric fields, which are in line with our previous experimental observations. Moreover, we discuss the dependence of the DPC-STEM sensitivity on the polar field amplitude, specimen thickness, and defocus, and provide a route to discriminate between mesoscopic polarization and specimen misorientation.