Imaging Topological Textures from the Pico to Micro Scale with Electron Ptychography

The discovery of non-trivial topological textures, including flux-closure, vortices, skyrmions, merons and hopfion in both ferromagnetic and ferroelectric systems have required electron microscopy to resolve their internal structures. Here, enabled by a new design of electron detector [1] that is capable of measuring the complete distribution of momentum transfers at every probe position, we construct a 4-dimensional phase space from which we solve the inverse multiple scattering problem and retrieve the underlying 3-dimensional potential of the sample. The lateral resolution of less than 20 pm is now limited not by the instrument, but by the thermal vibrations of the atoms themselves, and the precision is improved to well below 1 pm [2]. The resulting ptychographic reconstructions have allowed us to image the internal structures of both magnetic and ferroelectric vortices, skyrmions and merons, including their singular points that are critical for accurately describing the topological properties of these field textures. [3]<br/><br/>[1] H. Philipp et al., <i>Microscopy and Microanalysis</i> <b>28</b> (2022), p. 425-440.<br/>[2] Z. Chen et al., <i>Science</i> <b>372</b> (2021), p. 826-831.<br/>[3] In collaboration with Harikrishnan K. P. , Yu-Tsun Shao, Zhen Chen and Yi Jiang. Funding from the U.S. Army Research Office under the MURI ETHOS (W911NF-21-2-0162). Facility support from the Cornell Center for Materials Research (National Science Foundation grants MRI-1429155, DMR-1719875, DMR-1539918).