The method, called beam-shift-based four-dimensional electron magnetic circular dichroism, builds on a phenomenon first demonstrated in a transmission electron microscope in 2006. When electrons pass through a magnetic material, the energy-loss spectra of the transmitted beam differ subtly depending on the relative orientation of the electron beam and the local magnetization, an effect known as electron magnetic circular dichroism, or EMCD. The dichroic signal is sensitive to the spin and orbital magnetic moments of the atoms in the beam path. Earlier work by Jan Rusz and collaborators showed theoretically and experimentally that EMCD could, in favorable geometries, deliver magnetic information at atomic-plane resolution, but extracting a full three-dimensional vector from such data remained a formidable challenge.

The innovation of the new study lies in how the electron probe is manipulated. By deliberately shifting the incident beam within the convergent beam geometry of a three-beam diffraction condition, the researchers gain access to different Cartesian components of the magnetization vector. In a three-beam condition, a systematic row of diffraction spots is strongly excited, and the dynamical diffraction of the electrons through the crystal makes the EMCD signal selectively sensitive to particular magnetization components. Shifting the beam and analyzing the resulting four-dimensional data set, which records a full energy-loss spectrum at every probe position, allows the team to separate the out-of-plane component along the beam direction from the two in-plane components. Simulations of the relative dynamical diffraction coefficients guided the choice of detector integration windows, and the team demonstrated that in each optimized configuration the target magnetic component dominates the extracted signal, keeping crosstalk between components under control.

To validate the approach, the researchers turned to yttrium orthoferrite, YFeO3, a canted antiferromagnet that has fascinated physicists since the 1960s. In an ideal antiferromagnet, neighboring spins point in exactly opposite directions and cancel out. In YFeO3, the Dzyaloshinskii–Moriya interaction tilts, or cants, the two antiferromagnetically coupled spin sublattices slightly toward each other, producing a weak net magnetization. The material also undergoes a field-induced spin reorientation transition, in which an external magnetic field forces the spins to swing toward the field direction. Because several competing interactions of comparable strength are at play, YFeO3 is an ideal test bed for a technique that claims to read out the energetics of the spin Hamiltonian directly.

The crystals used in the study were grown at the Shanghai Institute of Ceramics by Anhua Wu, Wenhao Di and Liangbi Su. At the TRACE electron microscopy centre at City University of Hong Kong, Qi Wang and Miao Zhang, the two co-first authors, recorded atomic-resolution imaging and compositional maps of the YFeO3 structure along multiple zone axes, confirming the positions of the yttrium, iron and oxygen atoms. They then acquired four-dimensional EMCD data sets in two distinct three-beam conditions, one exciting the (022) systematic reflections and the other the (202) reflections. In each condition, raw positive and negative electron energy-loss spectra were extracted from individual, consecutively numbered iron atomic planes, and their difference yielded the EMCD signal plane by plane.

The results were striking. The EMCD signals from the odd-numbered and even-numbered iron planes were almost exactly reversed, confirming the antiferromagnetic coupling between adjacent planes along both in-plane directions. More importantly, when the researchers converted the relative EMCD strengths into quantitative magnetization directions, they found that the two spin sublattices were not canted symmetrically. The moments on the odd-numbered planes were tilted by 11.6 degrees from the [100] direction, while those on the even-numbered planes were tilted by 19.5 degrees from the opposite direction. This asymmetry in the spin reorientation angles had been inferred indirectly in earlier bulk studies using Mössbauer spectroscopy and nuclear magnetic resonance, but it had never been seen directly at the level of individual atomic planes.

Why should the two sublattices respond differently to the same external field? The answer, according to the team’s analysis, lies in the interplay of the spin Hamiltonian terms on adjacent, antiferromagnetically coupled atomic planes. Because the two sublattices carry nearly opposite moments, the Zeeman energy of an applied field acts with opposite sign on the two sets of planes, while the single-ion anisotropy, which pins each moment to the crystal lattice, contributes differently depending on the local orientation. The researchers inferred the superexchange coupling, Dzyaloshinskii–Moriya interaction, single-ion anisotropy and Zeeman energy contributions from their measured spin configurations and found that the observed asymmetry arises primarily from the single-ion anisotropy and the opposite Zeeman energies of the adjacent planes. The net effect is that both magnetic moments end up nearly aligned with the external magnetic field, exactly as expected for the field-induced spin reorientation transition, but through a pathway that is visibly asymmetric at the atomic scale.

The quantitative work was supported by an extensive simulation effort. Miao Zhang performed the dynamical diffraction calculations that connect the measured dichroic signals to intrinsic magnetization components, solving a system of linear equations in which a matrix of simulation coefficients relates the experimental spectra of each sublattice to the underlying out-of-plane and in-plane magnetization. Gustav Bihlmayer of Forschungszentrum Jülich carried out density functional theory calculations of the electronic and magnetic structure of YFeO3, providing independent theoretical grounding for the inferred energy terms. Statistical analysis across five odd-numbered and five even-numbered planes, with error bars representing the standard error of the mean, gave the quantitative claims a firm footing. The team also extracted the orbital-to-spin magnetic moment ratio of the iron atoms, finding a value of 0.046, which confirms that the orbital moment in YFeO3 is almost completely quenched, as expected for iron oxide systems with strong crystal-field effects.

The significance of the technique extends well beyond one material. Three-dimensional nanomagnetism has become one of the liveliest frontiers in condensed matter physics, driven by applications in antiferromagnetic spintronics, skyrmionics and topological spin textures such as hopfions. Existing three-dimensional imaging methods, including X-ray vector nanotomography, electron holographic vector field tomography and Lorentz ptychography, can map magnetic textures with impressive fidelity, but none of them simultaneously resolve the magnetization vector in three dimensions and the atomic positions that host it. By bridging that resolution gap, the beam-shift-based 4D EMCD method allows experimentalists to correlate specific atomic configurations with specific energy contributions, which is precisely the correlation needed to test and refine spin Hamiltonian models rather than simply fitting them to bulk measurements.

There are practical implications as well. Canted antiferromagnets such as YFeO3 are candidates for ultrafast, low-dissipation spintronic devices because their antiferromagnetic resonance frequencies are high and their net stray fields are small, and recent work has demonstrated anisotropic long-range spin transport in this very material. Engineering such devices requires knowing exactly how anisotropy, exchange and Dzyaloshinskii–Moriya terms compete at the atomic scale, particularly at defects, interfaces and domain walls. A method that can now watch spins rotate plane by plane under an applied field, and assign the energetic cost of each rotation to its microscopic origin, turns the spin Hamiltonian from a fitting device into something closer to a measurable map. The raw experimental data have been released on Zenodo, and the authors suggest that the approach opens an avenue for the atomic-scale characterization and engineering of the energetics described by the spin Hamiltonian, a capability that magnetic materials researchers have sought since the Hamiltonian itself was first written down.

Subject of Research: Atomic-scale 3D vector magnetometry of competing spin Hamiltonian interactions in canted antiferromagnets

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

Article References: Atomic-scale visualization of three-dimensional magnetization vectors with competing spin Hamiltonian interactions. (n.d.). https://doi.org/10.1038/s41565-026-02270-6

Image Credits: AI Generated

DOI: 10.1038/s41565-026-02270-6

Keywords: electron magnetic circular dichroism, 4D EMCD, spin Hamiltonian, antiferromagnetism, YFeO3, Dzyaloshinskii–Moriya interaction, single-ion anisotropy, superexchange, Zeeman energy, spin reorientation, atomic-resolution microscopy, 3D magnetization