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Sub-10-nm quantification of spin and orbital magnetic moment across the metamagnetic phase transition in FeRh using EMCD

Jan Hajduček1,*, Veronica Leccese2,*, Ján Rusz3, Jon Ander Arregi1, Alexey Sapozhnik2, Jáchym Štindl4, Francesco Barantani2, Paolo Cattaneo2, Antoine Andrieux2 et al.

Vojtěch Uhlíř1,4, Fabrizio Carbone2, and Thomas LaGrange2,†

  • *These authors contributed equally to this work.
  • †Contact author: thomas.lagrange@epfl.ch
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Phys. Rev. Materials 10, 013801 – Published 26 January, 2026

DOI: https://doi.org/10.1103/m3vy-18hn

Abstract

Electron magnetic circular dichroism (EMCD) in transmission electron microscopy (TEM) enables element-specific measurement of spin and orbital magnetic moments, analogous to x-ray magnetic circular dichroism (XMCD). While the EMCD technique offers unmatched spatial resolution, its quantitative accuracy remains under scrutiny, particularly in beam-splitter geometries with convergent probes. Here, we systematically evaluate the limits of quantitative EMCD analysis using the first-order magnetostructural transition in the functional phase-change material FeRh as a tunable magnetic reference. Unlike previous EMCD studies primarily focused on elemental ferromagnets such as Fe, we demonstrate its applicability to a correlated material exhibiting coupled structural and magnetic order. We demonstrate that the extracted orbital-to-spin moment ratio (mL/mS) remains within the same order of magnitude as XMCD benchmarks, despite a systematic reduction in absolute value, for TEM probes down to approximately 6 nm, thereby establishing the validity range for reliable quantification. For nanometer-sized probes with higher convergence angles, we observe an enhanced mL/mS, which we attribute to a combination of instrumental factors and sensitivity to nanoscale heterogeneity within the probed volume. Our results confirm that EMCD provides quantitative agreement with macroscale techniques under suitable conditions, while uniquely enabling spatially confined measurements of local magnetic moments in functional magnetic materials, and allowing the study of interfacial, defect-mediated, or phase-separated magnetism that is inaccessible to photon-based methods.

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New Insights into Functional Materials through Advanced Electron Microscopy

The Editors of Physical Review Materials are pleased to present the Collection on New Insights into Functional Materials through Advanced Electron Microscopy, highlighting cutting-edge microscopy techniques and the extraordinary advances in materials science and engineering that they enable. The Collection is being guest-edited by Joanne Etheridge from Monash University (Australia) and Yimei Zhu from Brookhaven National Laboratory (USA). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.

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References (71)

  1. B. T. Thole, P. Carra, F. Sette, and G. Van Der Laan, X-ray circular dichroism as a probe of orbital magnetization, Phys. Rev. Lett. 68, 1943 (1992).
  2. P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-ray circular dichroism and local magnetic fields, Phys. Rev. Lett. 70, 694 (1993).
  3. B. Rösner, S. Finizio, F. Koch, F. Döring, V. A. Guzenko, M. Langer, E. Kirk, B. Watts, M. Meyer, J. Loroña Ornelas, A. Späth, S. Stanescu, S. Swaraj, R. Belkhou, T. Ishikawa, T. F. Keller, B. Gross, M. Poggio, R. H. Fink, J. Raabe, et al., Soft x-ray microscopy with 7 nm resolution, Optica 7, 1602 (2020).
  4. M. J. Robertson, C. J. Agostino, A. T. N'Diaye, G. Chen, M. Y. Im, and P. Fischer, Quantitative x-ray magnetic circular dichroism mapping with high spatial resolution full-field magnetic transmission soft x-ray spectro-microscopy, J. Appl. Phys. 117, 17D145 (2015).
  5. C. Hébert and P. Schattschneider, A proposal for dichroic experiments in the electron microscope, Ultramicroscopy 96, 463 (2003).
  6. P. Schattschneider, S. Rubino, C. Hébert, J. Rusz, J. Kuneš, P. Novák, E. Carlino, M. Fabrizioli, G. Panaccione, and G. Rossi, Detection of magnetic circular dichroism using a transmission electron microscope, Nature (London) 441, 486 (2006).
  7. P. Schattschneider, Linear and Chiral Dichroism in the Electron Microscope, edited by P. Schattschneider (Jenny Stanford Publishing, New York, 2012).
  8. P. Schattschneider, C. Hébert, S. Rubino, M. Stöger-Pollach, J. Rusz, and P. Novák, Magnetic circular dichroism in EELS: Towards 10 nm resolution, Ultramicroscopy 108, 433 (2008).
  9. T. Thersleff, S. Muto, M. Werwiński, J. Spiegelberg, Y. Kvashnin, B. Hjörvarsson, O. Eriksson, J. Rusz, and K. Leifer, Towards sub-nanometer real-space observation of spin and orbital magnetism at the fe/MgO interface, Sci. Rep. 7, 44802 (2017).
  10. S. Löffler and W. Hetaba, Convergent-beam EMCD: Benefits, pitfalls and applications, Microscopy 67, i60 (2018).
  11. J. Verbeeck, H. Tian, and P. Schattschneider, Production and application of electron vortex beams, Nature (London) 467, 301 (2010).
  12. M. Uchida and A. Tonomura, Generation of electron beams carrying orbital angular momentum, Nature (London) 464, 737 (2010).
  13. B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, Electron vortex beams with high quanta of orbital angular momentum, Science 331, 192 (2011).
  14. E. Rotunno, M. Zanfrognini, S. Frabboni, J. Rusz, R. E. Dunin Borkowski, E. Karimi, and V. Grillo, Orbital angular momentum resolved electron magnetic chiral dichroism, Phys. Rev. B 100, 224409 (2019).
  15. J. Rusz, S. Muto, J. Spiegelberg, R. Adam, K. Tatsumi, D. E. Bürgler, P. M. Oppeneer, and C. M. Schneider, Magnetic measurements with atomic-plane resolution, Nat. Commun. 7, 12672 (2016).
  16. H. Ali, D. Negi, T. Warnatz, B. Hjörvarsson, J. Rusz, and K. Leifer, Atomic resolution energy-loss magnetic chiral dichroism measurements enabled by patterned apertures, Phys. Rev. Res. 2, 023330 (2020).
  17. Z. Wang, A. H. Tavabi, L. Jin, J. Rusz, D. Tyutyunnikov, H. Jiang, Y. Moritomo, J. Mayer, R. E. Dunin-Borkowski, R. Yu, J. Zhu, and X. Zhong, Atomic scale imaging of magnetic circular dichroism by achromatic electron microscopy, Nat. Mater. 17, 221 (2018).
  18. J. Rusz, O. Eriksson, P. Novák, and P. M. Oppeneer, Sum rules for electron energy loss near edge spectra, Phys. Rev. B 76, 060408(R) (2007).
  19. L. Calmels, F. Houdellier, B. Warot-Fonrose, C. Gatel, M. J. Hÿtch, V. Serin, E. Snoeck, and P. Schattschneider, Experimental application of sum rules for electron energy loss magnetic chiral dichroism, Phys. Rev. B 76, 060409(R) (2007).
  20. C. Hébert, P. Schattschneider, S. Rubino, P. Novak, J. Rusz, and M. Stöger-Pollach, Magnetic circular dichroism in electron energy loss spectrometry, Ultramicroscopy 108, 277 (2008).
  21. X. Fu, K. Wu, V. Serin, B. Warot-Fonrose, Q. He, R. Yang, L. Zhang, and X. Huang, Electron energy-loss magnetic chiral dichroism of magnetic iron film affected by an underlayer in a double-layer structure, Appl. Phys. Lett. 115, 112401 (2019).
  22. Z. Zeng, X. Fu, Q. Hu, G. Liu, J. Li, and X. Huang, The influence of residual plural scattering after deconvolution in electron magnetic chiral dichroism, Ultramicroscopy 253, 113806 (2023).
  23. S. Rubino, P. Schattschneider, M. Stöger-Pollach, C. Hébert, J. Rusz, L. Calmels, B. Warot-Fonrose, F. Houdellier, V. Serin, and P. Novak, Energy-loss magnetic chiral dichroism (EMCD): Magnetic chiral dichroism in the electron microscope, J. Mater. Res. 23, 2582 (2008).
  24. M. Fallot and R. Hocart, Sur l'apparition du ferromagnétisme par élévation de température dans des alliages de fer et de rhodium, Revue Scientifique 77, 498 (1939).
  25. S. Maat, J. U. Thiele, and E. E. Fullerton, Temperature and field hysteresis of the antiferromagnetic-to-ferromagnetic phase transition in epitaxial FeRh films, Phys. Rev. B 72, 214432 (2005).
  26. G. Shirane, R. Nathans, and C. W. Chen, Magnetic moments and unpaired spin densities in the Fe-Rh alloys, Phys. Rev. 134, A1547 (1964).
  27. N. Kunitomi, M. Kohgi, and Y. Nakai, Diffuse scattering of neutrons in the antiferromagnetic phase of FeRh, Phys. Lett. A 37, 333 (1971).
  28. Y. Ohtani and I. Hatakeyama, Features of broad magnetic transition in FeRh thin film, J. Magn. Magn. Mater. 131, 339 (1994).
  29. I. Suzuki, T. Koike, M. Itoh, T. Taniyama, and T. Sato, Stability of ferromagnetic state of epitaxially grown ordered FeRh thin films, J. Appl. Phys. 105, 07E501 (2009).
  30. L. H. Lewis, C. H. Marrows, and S. Langridge, Coupled magnetic, structural, and electronic phase transitions in FeRh, J. Phys. D 49, 323002 (2016).
  31. V. Uhlíř, J. A. Arregi, and E. E. Fullerton, Colossal magnetic phase transition asymmetry in mesoscale FeRh stripes, Nat. Commun. 7, 13113 (2016).
  32. J. A. Arregi, O. Caha, and V. Uhlíř, Evolution of strain across the magnetostructural phase transition in epitaxial FeRh films on different substrates, Phys. Rev. B 101, 174413 (2020).
  33. J. Hajduček, A. Andrieux, J. A. Arregi, M. Tichý, P. Cattaneo, B. Ferrari, F. Carbone, V. Uhlíř, and T. LaGrange, Dislocation-Driven nucleation type switching across repeated ultrafast magnetostructural phase transition, Phys. Rev. B 113, 014414 (2026).
  34. C. Stamm, J. U. Thiele, T. Kachel, I. Radu, P. Ramm, M. Kosuth, J. Minár, H. Ebert, H. A. Dürr, W. Eberhardt, and C. H. Back, Antiferromagnetic-ferromagnetic phase transition in FeRh probed by x-ray magnetic circular dichroism, Phys. Rev. B 77, 184401 (2008).
  35. H. Ali, J. Rusz, D. E. Bürgler, J. V. Vas, L. Jin, R. Adam, C. M. Schneider, and R. E. Dunin-Borkowski, Visualizing subatomic orbital and spin moments using a scanning transmission electron microscope, Nat. Mater. 24, 1215 (2025).
  36. T. Edler and S. G. Mayr, Film lift-off from MgO: Freestanding single crystalline Fe-Pd films suitable for magnetic shape memory actuation - and beyond, Adv. Mater. 22, 4969 (2010).
  37. L. Motyčková, J. A. Arregi, M. Staňo, S. Průša, K. Částková, and V. Uhlíř, Preserving metamagnetism in self-assembled FeRh nanomagnets, ACS Appl. Mater. Interfaces 15, 8653 (2023).
  38. S. Gorji, A. Kashiwar, L. S. Mantha, R. Kruk, R. Witte, P. Marek, H. Hahn, C. Kübel, and T. Scherer, Nanowire facilitated transfer of sensitive TEM samples in a FIB, Ultramicroscopy 219, 113075 (2020).
  39. J. Rusz, Modified automatic term selection v2: A faster algorithm to calculate inelastic scattering cross-sections, Ultramicroscopy 177, 20 (2017).
  40. C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, Experimental confirmation of the x-ray magnetic circular dichroism sum rules for Iron and cobalt, Phys. Rev. Lett. 75, 152 (1995).
  41. L. Honghong, W. Jie, L. Ruipeng, G. Yuxian, W. Feng, and H. Zhiwei, X-ray magnetic circular dichroism: Orbital and spin moments of iron single-crystal thin film deposited on MgO substrate, Chin. Sci. Bull. 50, 950 (2005).
  42. W. L. O'Brien, B. P. Tonner, G. R. Harp, and S. S. Parkin, Experimental investigation of dichroism sum rules for V, Cr, Mn, Fe, Co, and Ni: Influence of diffuse magnetism, J. Appl. Phys. 76, 6462 (1994).
  43. O. Zaharko, A. Cervellino, H.-C. Mertins, H. Grimmer, F. Schäfers, and D. Arvanitis, Soft x-ray magnetic circular dichroism in fe and Fe0.50Co0.48V0.02 films: Quantitative analysis of transmission, Eur. Phys. J. B 23, 441 (2001).
  44. H. Lidbaum, J. Rusz, A. Liebig, B. Hjörvarsson, P. M. Oppeneer, E. Coronel, O. Eriksson, and K. Leifer, Quantitative magnetic information from reciprocal space maps in transmission electron microscopy, Phys. Rev. Lett. 102, 037201 (2009).
  45. B. Warot-Fonrose, C. Gatel, L. Calmels, V. Serin, and P. Schattschneider, Effect of spatial and energy distortions on energy-loss magnetic chiral dichroism measurements: Application to an iron thin film, Ultramicroscopy 110, 1033 (2010).
  46. J. Rusz, H. Lidbaum, S. Rubino, B. Hjörvarsson, P. M. Oppeneer, O. Eriksson, and K. Leifer, Influence of plural scattering on the quantitative determination of spin and orbital moments in electron magnetic chiral dichroism measurements, Phys. Rev. B 83, 132402 (2011).
  47. T. Thersleff, J. Rusz, S. Rubino, B. Hjörvarsson, Y. Ito, N. J. Zaluzec, and K. Leifer, Quantitative analysis of magnetic spin and orbital moments from an oxidized iron (1 1 0) surface using electron magnetic circular dichroism, Sci. Rep. 5, 13012 (2015).
  48. H. Ali, T. Warnatz, L. Xie, B. Hjörvarsson, and K. Leifer, Quantitative EMCD by use of a double aperture for simultaneous acquisition of EELS, Ultramicroscopy 196, 192 (2019).
  49. H. Ali, J. Rusz, T. Warnatz, B. Hjörvarsson, and K. Leifer, Simultaneous mapping of EMCD signals and crystal orientations in a transmission electron microscope, Sci. Rep. 11, 2180 (2021).
  50. S. Muto, J. Rusz, K. Tatsumi, R. Adam, S. Arai, V. Kocevski, P. M. Oppeneer, D. E. Bürgler, and C. M. Schneider, Quantitative characterization of nanoscale polycrystalline magnets with electron magnetic circular dichroism, Nat. Commun. 5, 3138 (2014).
  51. Average value obtained for nine atomic planes. Value of mL/mS on Fe atomic planes reaches 0.26±0.17 and values in the middle of atomic planes reach 0.08±0.11 [35].
  52. J. Rusz, J. Spiegelberg, S. Muto, T. Thersleff, M. Ohtsuka, K. Leifer, and P. M. Oppeneer, Localization of magnetic circular dichroic spectra in transmission electron microscopy experiments with atomic plane resolution, Phys. Rev. B 95, 174412 (2017).
  53. J. Rusz, S. Bhowmick, M. Eriksson, and N. Karlsson, Scattering of electron vortex beams on a magnetic crystal: Towards atomic-resolution magnetic measurements, Phys. Rev. B 89, 134428 (2014).
  54. D. Pohl, S. Schneider, P. Zeiger, J. Rusz, P. Tiemeijer, S. Lazar, K. Nielsch, and B. Rellinghaus, Atom size electron vortex beams with selectable orbital angular momentum, Sci. Rep. 7, 934 (2017).
  55. P. Gambardella, S. Rusponi, M. Veronese, S. S. Dhesi, C. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P. H. Dederichs, K. Kern, C. Carbone, and H. Brune, Giant magnetic anisotropy of single Cobalt atoms and nanoparticles, Science 300, 1130 (2003).
  56. M. Tischer, O. Hjortstam, D. Arvanitis, J. H. Dunn, F. May, K. Baberschke, J. Trygg, J. M. Wills, B. Johansson, and O. Eriksson, Enhancement of orbital magnetism at surfaces: Co on Cu(100), Phys. Rev. Lett. 75, 1602 (1995).
  57. Y. B. Xu, M. Tselepi, C. M. Guertler, C. A. Vaz, G. Wastlbauer, J. A. Bland, E. Dudzik, and G. Van Der Laan, Giant enhancement of orbital moments and perpendicular anisotropy in epitaxial Fe/GaAs(100), J. Appl. Phys. 89, 7156 (2001).
  58. G. Autès, C. Barreteau, D. Spanjaard, and M. C. Desjonquères, Magnetism of iron: From the bulk to the monatomic wire, J. Phys.: Condens. Matter 18, 6785 (2006).
  59. K. Edmonds, C. Binns, S. Baker, M. Maher, S. Thornton, O. Tjernberg, and N. Brookes, Size dependence of the magnetic moments of exposed nanoscale iron particles, J. Magn. Magn. Mater. 231, 113 (2001).
  60. M.-C. Desjonquères, C. Barreteau, G. Autès, and D. Spanjaard, Orbital contribution to the magnetic properties of iron as a function of dimensionality, Phys. Rev. B 76, 024412 (2007).
  61. H.-J. Kim, J.-H. Park, and E. Vescovo, Oxidation of the Fe(110) surface: An Fe3O4(111)/Fe(110) bilayer, Phys. Rev. B 61, 15284 (2000).
  62. Y. Yonamoto, T. Yokoyama, K. Amemiya, D. Matsumura, and T. Ohta, Magnetism of an ultrathin mn film on Co(100) and the effect of oxidation studied by x-ray magnetic circular dichroism, Phys. Rev. B 63, 214406 (2001).
  63. V. Y. Irkhin and M. I. Katsnelson, Sum rules for x-ray magnetic circular dichroism spectra in strongly correlated ferromagnets, Eur. Phys. J. B 45, 1 (2005).
  64. G. van der Laan and A. I. Figueroa, X-ray magnetic circular dichroism—a versatile tool to study magnetism, Coord. Chem. Rev. 277-278, 95 (2014).
  65. L. Braicovich, G. Ghiringhelli, A. Tagliaferri, G. Van Der Laan, E. Annese, and N. B. Brookes, Femtosecond dynamics in ferromagnetic metals investigated with soft x-ray resonant emission, Phys. Rev. Lett. 95, 267402 (2005).
  66. L. Braicovich and G. Van Der Laan, Rationale for femtosecond magnetism explored with x-ray core-hole excitation, Phys. Rev. B 78, 174421 (2008).
  67. T. Böske, W. Clemens, C. Carbone, and W. Eberhardt, Circular magnetic x-ray dichroism of 3d impurities in Ni, Phys. Rev. B 49, 4003 (1994).
  68. T. LaGrange and V. Leccese, Sub-10 nm quantification of spin and orbital magnetic moment across the metamagnetic transition in FeRh using EMCD, [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17301296.
  69. J. Rusz, S. Muto, and K. Tatsumi, New algorithm for efficient Bloch-waves calculations of orientation-sensitive ELNES, Ultramicroscopy 125, 81 (2013).
  70. C. S. Smith and L. Guttman, Measurement of internal boundaries in three-dimensional structures by random sectioning, J. Met. 5, 81 (1953).
  71. R. K. Ham, The determination of dislocation densities in thin films, Philos. Mag. 6, 1183 (1961).

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Phys. Rev. Materials 10, 013801– Published 26 January, 2026
  • Received 28 October 2025
  • Accepted 2 January 2026
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