Toward accurate measurement of electromagnetic field by retrieving and refining the center position of non-uniform diffraction disks in Lorentz 4D-STEM.

Recent advancement in scanning transmission electron microscopy (STEM) allows the use of 4D-STEM, a technique that captures an electron diffraction pattern at each scan point in STEM, to measure electrostatic and magnetic potential and field in materials. However, accurate measurement, separation of the magnetic and electric signals, and removal of artifacts remain challenging, especially in the presence of complex non-uniform diffraction contrast within the disks. Here, based on dynamic simulations of 4D-STEM patterns built upon superstructures consisting of millions of atoms to account for different sample thickness and edge geometries, we show how the shape and intensity distribution of the central disk are affected by multiple scattering. We propose a robust refinement procedure through iteration of the spin-sensitive peak position of the disk-center in the circular Hough transform filtered images from experimental Lorentz 4D-STEM dataset after minimizing the possible artifacts, such as those due to the change of thickness, dynamic scattering, and scanning process. We verify that caution must be taken as in practice the rigid-disk-shift model used to reconstruct induction maps can easily break down due to disk-protrusion when there exists a nonconstant phase gradient or thickness within the width of the probe. Through quantitative analysis and comparing experiment with calculation the effect of the non-spin-related intensity distribution inside the disk as well as that causes the disk shift due to the intensity-protrusion can be removed, and high-quality magnetic field mapping is possible.