ArticleNature nanotechnology2026
Atomic-scale visualization of three-dimensional magnetization vectors with competing spin Hamiltonian interactions.
Article in Nature nanotechnology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
The spin Hamiltonian describes the energy of a magnetic system, which originates from interactions between electron spins that have a three-dimensional (3D) vectorial nature and atomic-scale arrangement. It is crucial to know the energy contributions associated with spin behaviour, such as superexchange coupling, Dzyaloshinskii-Moriya interaction, Zeeman energy in external fields and single-ion anisotropy (SIA), for a fundamental understanding of the ground state and dynamics of magnetic materials. An experimental method, capable of resolving local 3D spin vectors on the atomic scale, is needed to provide direct correlation between the competing energy terms and corresponding atomic configurations. Here we demonstrate a beam-shift-based four-dimensional electron magnetic circular dichroism technique, which achieves quantitative 3D vector magnetometry and infers the energy contributions to the spin Hamiltonian on an individual atomic plane basis. The spatial resolution of 2.25 Å enables evaluation of spin Hamiltonian energy terms within individual atomic planes. In a canted antiferromagnet, YFeO
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