Aberration-corrected electron microscopy can resolve the smallest atomic bond lengths in nature. However, the high-convergence angles that enable spectacular resolution in two dimensions have unknown three-dimensional (3D) resolution limits for all but the smallest objects (<∼8 nm). We show aberration-corrected electron tomography offers new limits for 3D imaging by measuring several focal planes at each specimen tilt. We present a theoretical foundation for aberration-corrected electron tomography by establishing analytic descriptions for resolution, sampling, object size, and dose - with direct analogy to the Crowther-Klug criterion. Remarkably, aberration-corrected scanning transmission electron tomography can measure complete 3D specimen structure of unbounded object sizes up to a specified cutoff resolution. This breaks the established Crowther limit when tilt increments are twice the convergence angle or smaller. Unprecedented 3D resolution is achievable across large objects. Atomic 3D imaging (1 Å) is allowed across extended objects larger than depth of focus (e.g., >20 nm) using available microscopes and modest specimen tilting (<3°). Furthermore, aberration-corrected tomography follows the rule of dose fractionation where a specified total dose can be divided among tilts and defoci.

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.