Accuracy of Local Polarization Measurements by Scanning Transmission Electron Microscopy

Accurately determining local polarization at atomic resolution can unveil the mechanisms by which static and dynamical behaviors of the polarization occur, including domain wall motion, defect interaction, and switching mechanisms, advancing us toward the better control of polarized states in materials. In this work, we explore the potential of atomic-resolution scanning transmission electron microscopy to measure the projected local polarization at the unit cell length scale. ZnO and PbMg_1/3Nb_2/3O₃ are selected as case studies, to identify microscope parameters that can significantly affect the accuracy of the measured projected polarization vector. Different STEM imaging modalities are used to determine the location of the atomic columns, which, when combined with the Born effective charges, allows for the calculation of local polarization. Our results indicate that differentiated differential phase contrast (dDPC) imaging enhances the accuracy of measuring local polarization relative to other imaging modalities, such as annular bright-field or integrated-DPC imaging. For instance, under certain experimental conditions, the projected spontaneous polarization for ZnO can be calculated with 1.4% error from the theoretical value. Furthermore, we quantify the influence of sample thickness, probe defocus, and crystal mis-tilt on the relative errors of the calculated polarization.