Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit

Nanoscale spin textures, especially magnetic skyrmions, have attracted intense interest as candidate high-density and power-efficient information carriers for spintronic devices^1,2. Facilitating a deeper understanding of sub-hundred-nanometre to atomic-scale spin textures requires more advanced magnetic imaging techniques^3-5. Here we demonstrate a Lorentz electron ptychography method that can enable high-resolution, high-sensitivity magnetic field imaging for widely available electron microscopes. The resolution of Lorentz electron ptychography is not limited by the usual diffraction limit of lens optics, but instead is determined by the maximum scattering angle at which a statistically meaningful dose can still be recorded-this can be an improvement of up to 2-6 times depending on the allowable dose. Using FeGe as the model system, we realize a more accurate magnetic field measurement of skyrmions with an improved spatial resolution and sensitivity by also correcting the probe-damping effect from the imaging optics via Lorentz electron ptychography. This allows us to directly resolve subtle internal structures of magnetic skyrmions near the skyrmion cores, boundaries and dislocations in an FeGe single crystal. Our study establishes a quantitative, high-resolution magnetic microscopy technique that can reveal nanoscale spin textures, especially magnetization discontinuities and topological defects in nanomagnets⁶. The technique's high-dose efficiency should also make it well suited for the exploration of magnetic textures in electron radiation-sensitive materials such as organic or molecular magnets⁷.