Imaging Topological Order at the Picometer-Scale by Electron Ptychography

Electron microscopy is often used to directly the image the atomic displacements in ferroelectrics, reaching a precision of a few picometers. As good as this is, it is still not sufficient to robustly measure many ferroic order parameters, including vorticity and higher order moments. Enabled by a new design of electron detector [1,2] 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 [3]. 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.<br/><br/>[1] M. W. Tate, P. Purohit, D. Chamberlain, K. X. Nguyen, R. Hovden, C. S. Chang, P. Deb, E. Turgut, J. T. Heron, D. G. Schlom, D. C. Ralph, G. D. Fuchs, K. S. Shanks, H. T. Philipp, D. A. Muller, and S. M. Gruner. “High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy” <i>Microscopy and Microanalysis</i> <b>22</b>, (2016): 237–249.<br/>[2] H. T. Philipp, H. T., M. W. Tate, K. S. Shanks, L. Mele, M. Peemen, P. Dona, R. Hartong, G. Van Veen, Y. T. Shao, Z. Chen, J. Thom-Levy, D. A. Muller, and S. M. Gruner. “Very-High Dynamic Range, 10,000 Frames/Second Pixel Array Detector for Electron Microscopy” <i>Microscopy and Microanalysis</i> <b>28</b>, (2022): 425–440.<br/>[3] Z. Chen, Y. Jiang, Y.-T. Shao, M. E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D. G. Schlom, and D. A. Muller. “Electron Ptychography Achieves Atomic-Resolution Limits Set by Lattice Vibrations” <i>Science</i> <b>372</b>, (2021): 826–831