- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Magnetically modified double-slit-based x-ray interferometry

S. Atkar1, Z. Tumbleson2,3, S. A. Morley4, N. Burdet5, A. Islegen-Wojdyla4, K. A. Goldberg4, A. Scholl4, S. A Montoya6, Trinanjan Datta7 et al.

S. Roy4,3,*

  • *Contact author: sroy@lbl.gov
PDF

Phys. Rev. Research 8, 023092 – Published 29 April, 2026

DOI: https://doi.org/10.1103/5njk-mhwg

Abstract

We demonstrate an experimental approach to determine magneto-optical effects that combines x-ray magnetic circular dichroism (XMCD) with x-ray interferometry, based on the concepts of Young's canonical double slit. By covering one of two slits with a magnetic thin film and employing XMCD, we show that it is possible to determine both the real and the imaginary parts of the complex refractive index by measuring the fringe shifts that occur due to a change in the sample magnetization. Our hybrid spectroscopic-interferometric methodology provides a means to probe changes in the magnetic refractive index in terms of the electron spin moment.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (30)

  1. J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (John Wiley & Sons, Ltd, Chichester, UK, 2011).
  2. J. Stöhr and H. C. Siegmann, Magnetism: From Fundamentals to Nanoscale Dynamics (Springer Science and Business Media, London, 2007).
  3. P. Norman and A. Dreuw, Simulating x-ray spectroscopies and calculating core-excited states of molecules, Chem. Rev. 118, 7208 (2018).
  4. A. Sakdinawat and D. Attwood, Nanoscale x-ray imaging, Nat. Photon. 4, 840 (2010).
  5. C. Sanchez-Cano, R. A. Alvarez-Puebla, J. M. Abendroth, T. Beck, R. Blick, Y. Cao, F. Caruso, I. Chakraborty, H. N. Chapman, C. Chen, et al., X-ray-based techniques to study the nano–bio interface, ACS Nano 15, 3754 (2021).
  6. Q. Saadeh, V. Philipsen, J. Meersschaut, V. S. K. Channam, K.-A. Kantre, A. Sokolov, B. Kupper, T. Wiesner, D. O. na García, Z. Salami, C. Buchholz, F. Scholze, and V. Soltwisch, Optical constants of TiN, amorphous SiO2, and SiN in the extreme ultraviolet range, Appl. Opt. 63, 9210 (2024).
  7. J. Kas, F. Vila, C. Pemmaraju, M. Prange, K. Persson, R. Yang, and J. Rehr, Full spectrum optical constant interface to the materials project, Comput. Mater. Sci. 201, 110904 (2022).
  8. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research. Springer Series in Optical Sciences (Springer-Verlag Berlin Heidelberg, 2005), Vol. 110, pp. 162.
  9. M. Blume and D. Gibbs, Polarization dependence of magnetic x-ray scattering, Phys. Rev. B 37, 1779 (1988).
  10. J. P. Hill and D. F. McMorrow, Resonant exchange scattering: Polarization dependence and correlation function, Acta Crystallogr. Sect. A: Found. 52, 236 (1996).
  11. 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).
  12. C. Kao, J. B. Hastings, E. D. Johnson, D. P. Siddons, G. C. Smith, and G. A. Prinz, Magnetic-resonance exchange scattering at the iron LII and LIII edges, Phys. Rev. Lett. 65, 373 (1990).
  13. A. Scherz, W. F. Schlotter, K. Chen, R. Rick, J. Stöhr, J. Lüning, I. McNulty, C. Günther, F. Radu, W. Eberhardt, O. Hellwig, and S. Eisebitt, Phase imaging of magnetic nanostructures using resonant soft x-ray holography, Phys. Rev. B 76, 214410 (2007).
  14. S. Eisebitt, M. Lörgen, W. Eberhardt, J. Lüning, J. Stöhr, C. T. Rettner, O. Hellwig, E. E. Fullerton, and G. Denbeaux, Polarization effects in coherent scattering from magnetic specimen: Implications for x-ray holography, lensless imaging, and correlation spectroscopy, Phys. Rev. B 68, 104419 (2003).
  15. J. Neethirajan, B. J. Daurer, M. D. P. Martínez, A. Hrabec, L. Turnbull, R. Yamamoto, M. R. Ferreira, A. Štefančič, D. A. Mayoh, G. Balakrishnan, Z. Pei, P. Xue, L. Chang, E. Ringe, R. Harrison, S. Valencia, M. Kazemian, B. Kaulich, and C. Donnelly, Soft x-ray phase nanomicroscopy of micrometer-thick magnets, Phys. Rev. X 14, 031028 (2024).
  16. P. Hessing, Interference-basedspectroscopy with XUV radiation, Ph.D. thesis, Technischen Universität Berlin, 2021.
  17. P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-ray circular dichroism and local magnetic fields, Phys. Rev. Lett. 70, 694 (1993).
  18. C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. Attwood, Direct measurement of index of refraction in the extreme-ultraviolet wavelength region with a novel interferometer, Opt. Lett. 27, 1028 (2002).
  19. J. W. Freeland, K. Bussmann, Y. U. Idzerda, and C.-C. Kao, Understanding correlations between chemical and magnetic interfacial roughness, Phys. Rev. B 60, R9923 (1999).
  20. S. Roy, M. R. Fitzsimmons, S. Park, M. Dorn, O. Petracic, I. V. Roshchin, Z.-P. Li, X. Batlle, R. Morales, A. Misra, X. Zhang, K. Chesnel, J. B. Kortright, S. K. Sinha, and I. K. Schuller, Depth profile of uncompensated spins in an exchange bias system, Phys. Rev. Lett. 95, 047201 (2005).
  21. See Supplemental Material at http://link.aps.org/supplemental/10.1103/5njk-mhwg for comprehensive details regarding the analytical derivation of the interference-diffraction intensity profiles, the data processing pipeline, and the implementation of the image registration algorithm, which includes Refs. [23, 25, 26, 27].
  22. J. C. T. Lee, J. J. Chess, S. A. Montoya, X. Shi, N. Tamura, S. K. Mishra, P. Fischer, B. J. McMorran, S. K. Sinha, E. E. Fullerton, S. D. Kevan, and S. Roy, Synthesizing skyrmion bound pairs in Fe-Gd thin films, Appl. Phys. Lett. 109, 022402 (2016).
  23. H. Foroosh, J. Zerubia, and M. Berthod, Extension of phase correlation to subpixel registration, IEEE Trans. Image Process. 11, 188 (2002).
  24. K. A. Goldberg and J. Bokor, Fourier-transform method of phase-shift determination, Appl. Opt. 40, 2886 (2001).
  25. M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, Cambridge, 1999).
  26. D. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, Subtleties with Young's double-slit experiment: Investigation of spatial coherence and fringe visibility, Am. J. Phys. 86, 683 (2018).
  27. A. Savitzky and M. J. E. Golay, Smoothing and differentiation of data by simplified least squares procedures., Anal. Chem. 36, 1627 (1964).
  28. J. B. Kortright and S.-K. Kim, Resonant magneto-optical properties of Fe near its 2p levels: Measurement and applications, Phys. Rev. B 62, 12216 (2000).
  29. P. Rudolf, F. Sette, L. Tjeng, G. Meigs, and C. Chen, Magnetic moments in a gadolinium iron garnet studied by soft-x-ray magnetic circular dichroism, J. Magn. Magn. Mater. 109, 109 (1992).
  30. S. Atkar, Z. Tumbleson, S. A. Morley, N. Burdet, A. Islegen-Wojdyla, K. A. Goldberg, A. Scholl, S. A. Montoya, T. Datta, and S. Roy, Magnetically modified double slit based x-ray interferometry (2026), https://doi.org/10.5061/dryad.4tmpg4frb.

Outline

Information

Phys. Rev. Research 8, 023092– Published 29 April, 2026
  • Received 26 February 2025
  • Revised 19 June 2025
  • Accepted 26 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation