Atomic-scale visualization of three-dimensional magnetization vectors with competing spin Hamiltonian interactions

Abstract
Three-dimensional (3D) spin textures underpin a wide range of magnetic phenomena, yet atomically resolving their vector orientations remains challenging. Here we report a beam-shift-based four-dimensional electron magnetic circular dichroism (EMCD) approach that enables quantitative 3D vector magnetometry at atomic-scale resolution. Applied to the canted antiferromagnet YFeO₃, the method maps competing spin Hamiltonian interactions—including super-exchange coupling, Dzyaloshinskii–Moriya interaction (DMI), single-ion anisotropy (SIA), and Zeeman energy—across individual atomic planes, providing a direct experimental link between local atomic structure and magnetic energetics.
Reference
Wang, Q., Zhang, M., Bihlmayer, G. et al. Atomic-scale visualization of three-dimensional magnetization vectors with competing spin Hamiltonian interactions. Nature Nanotechnology (2026). Published 8 October 2026. https://doi.org/10.1038/s41565-026-02270-6.