Detecting linear dichroism with atomic resolution

Nature Materials (2026) Cite this article X-ray linear dichroism has been pivotal for probing electronic anisotropies, but its inherent limited spatial resolution precludes the atomic-scale investigations of orbital polarization. Here we introduce a versatile electron linear dichroism methodology in scanning transmission electron microscopy that overcomes these constraints. Using electron energy loss spectroscopy with an atomic-sized probe and selecting momentum transfers along two orthogonal directions, we directly visualize orbital occupation at individual atomic columns in real space. Using strained La0.7Sr0.3MnO3 thin films as a model system, we resolve the Mn3d eg orbital polarization with sub-ångström precision. We show that compressive strain stabilizes 3z2–r2 occupation whereas tensile strain favours x2–y2. These results validate our approach against established X-ray measurements, achieving the ultimate single-atomic-column sensitivity. We further demonstrate two optimized signal extraction protocols that adapt to experimental constraints without compromising sensitivity. This generalizable platform opens unique opportunities to study symmetry-breaking phenomena at individual defects, interfaces and in quantum materials where atomic-scale electronic anisotropy governs emergent functionality.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data that support the findings of this study are available from the corresponding authors on request.All of the codes used in this work are available from the corresponding authors on request.Van Der Laan, G. & Thole, B. 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Ultramicroscopy 177, 20–25 (2017).Article CAS PubMed Google Scholar Download referencesR.G., A.L. and W.Z. acknowledge support from the Beijing Outstanding Young Scientist Program (number BJJWZYJH01201914430039), the National Natural Science Foundation of China (grant number 52373231) and the CAS Project for Young Scientists in Basic Research (YSBR-003).

This research benefited from resources and support from the Electron Microscopy Center at the University of Chinese Academy of Sciences. R.G. and J.G. also acknowledge financial support from project numbers PID2020-118479RB-I00, PID2023-152225NB-I00 and PID2023-14947NB-I00, from Severo Ochoa MATRANS42 (number CEX2023-001263-S) of the Spanish Ministry of Science, Innovation and Universities/AEI (grant number MICIU/AEI/10.13039/501100011033 and FEDER, EU) and from Generalitat de Catalunya (2021 SGR 00445). J.R. acknowledges the Swedish Research Council (grant numbers 2021-03848 and 2025-04514), Olle Engkvist Foundation (grant number 214-0331), STINT (grant number CH2019-8211), Knut and Alice Wallenberg Foundation (grant number 2022.0079) and eSSENCE for financial support. The simulations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially financed by the Swedish Research Council through grant agreement number 2022-06725. J.C.I. acknowledges the US Department of Energy (DOE), Office of Science (SC), Basic Energy Sciences, Material Sciences and Engineering Division, Electron and Scanning Probe Microscopies Program, FWP 83244.Roger GuzmanPresent address: Institute of Materials Science of Barcelona (ICMAB-CSIC), Cerdanyola del Vallès, SpainSchool of Physical Sciences, University of Chinese Academy of Sciences, Beijing, ChinaRoger Guzman, Ang Li (李昂) & Wu Zhou (周武)Department of Physics and Astronomy, Uppsala University, Uppsala, SwedenJán RuszDepartment of Materials Science and Engineering, University of Washington, Seattle, WA, USAJuan Carlos IdroboPhysical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA, USAJuan Carlos IdroboInstitute of Materials Science of Barcelona (ICMAB-CSIC), Cerdanyola del Vallès, SpainJaume GazquezSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarJ.G., J.C.I. and J.R. conceived the project. J.G., J.C.I. and W.Z. supervised the research. R.G. and W.Z. designed the research and microscopy experiments with input from J.G. and J.C.I. R.G. prepared the TEM specimens, performed the STEM experiments and data processing under the supervision of W.Z. A.L. wrote support codes for spectral data processing under the supervision of W.Z. J.R. designed and carried out the dynamical diffraction calculations. The paper was prepared by R.G. with contributions from all other co-authors.Correspondence to Juan Carlos Idrobo, Wu Zhou (周武) or Jaume Gazquez.The authors declare no competing interests.Nature Materials thanks Peter Rez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Top panels: MnO6 octahedral distortions as a function of strain for (001)-oriented LSMO, where green, orange and red spheres represent La/Sr, Mn and O, respectively. Bottom panels: the effects of symmetry breaking on the Mn eg levels of Mn3+ ions. Strain induces a tetragonal crystal field in which compressive strain (c > a) favors 3z2-r2 occupancy whereas tensile strain (c < a) favors x2-y2 occupancy.a, Quadrant of a Mn-L2,3 energy-filtered spectrum image, indicating horizontal (Ih, blue) and vertical (Iv, red) integration regions for the line-integration method. Pixel numbering begins at the Mn column center (0). b, Position-dependent ELD signal peaking ~3 pixels from the column center (green shading: Mn-L2 integration window). c, Coordinate map of the Mn-L spectrum image. d, e, Orbital polarization maps for compressively strained (LAO, d) and tensile strained (STO, e) LSMO, showing sign reversal of the area under ELD19,20, with maxima displaced from atomic nuclei. Color denotes the integrated ELD value at each beam position, calculated as the difference between horizontal (Ih(x)) and vertical (Iv(z)) coordinate positions at each pixel. Non-integrated pixels are set to zero (black). f, g, Comparison of the line-integration (f) and two-window integration (g) methods for the same dataset, demonstrating enhanced contrast with the latter. The scale bars in the insets are 0.1 nm.a, left: HAADF-STEM image of unstrained SrTiO3, acquired during ELNES-SI collection. Right: magnified view of a single SrTiO3 unit cell, with white and blue dashed circles marking Sr and Ti atoms, respectively. b, Left: corresponding Ti-L energy filtered map to the image in a. Right: magnified unit cell with blue and red markers indicating the 2 × 3-pixel2 integration windows used to extract the Ih and Iv signals. c, Normalized ELNES spectra for in-plane (Ih= L + R, blue) and out-of-plane (Iv=T + B, red) orientations in bulk-SrTiO3. The ELD signal Ih – Iv is negligible, as expected for Ti-3d orbitals under a cubic crystal field.a) Structure model of a lateral 3x3 supercell. The Mn atoms are in orange color. The surrounding of the central Mn column, highlighted by the bright blue square, has been partially scanned in simulations. b) A zoom-in of the scanned area. Each small block of 3 × 3 pixels represents one beam position, with the individual pixels encoding the ELD contribution from the individual 3 × 3 Mn atomic columns at this beam position. c), d) Percentual contributions of individual Mn atomic columns to the total ELD for the two summation strategies over beam positions: the ‘line integration method’ (Fig. 1c), and the ‘two-window integration method (L, R, T, B, Fig. 1i)’.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsGuzman, R., Rusz, J., Li, A. et al. Detecting linear dichroism with atomic resolution. Nat. Mater. (2026). https://doi.org/10.1038/s41563-026-02606-6Download citationReceived: 21 October 2025Accepted: 14 April 2026Published: 12 May 2026Version of record: 12 May 2026DOI: https://doi.org/10.1038/s41563-026-02606-6Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative