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
  • Letter
  • Open Access

Circular dichroism in resonant inelastic x-ray scattering from birefringence in CuO

Abhishek Nag1,2,*,†, Gérard Sylvester Perren1,*, Hiroki Ueda1, A. T. Boothroyd3, D. Prabhakaran3, M. García-Fernández4, S. Agrestini4, Ke-Jin Zhou4, and Urs Staub1,‡

  • *These authors contributed equally to this work.
  • †Contact author: abhishek.nag@ph.iitr.ac.in
  • ‡Contact author: urs.staub@psi.ch

Phys. Rev. Research 7, L022047 – Published 30 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022047

Abstract

Resonant inelastic x-ray scattering (RIXS) has become a prominent technique to study quasiparticle excitations. With advances in polarization analysis capabilities at different facilities, RIXS offers exceptional potential for investigating symmetry-broken quasiparticles such as chiral phonons and magnons. At optical wavelengths, birefringence can severely affect polarization states in low-symmetry systems. Here we show its importance for soft x-ray resonances. Given the growing interest in circular dichroism (CD) in RIXS, it is important to evaluate how birefringence may affect the RIXS spectra of anisotropic systems. We investigate CuO, a well-known anisotropic material, using Cu L3-edge RIXS and detect significant CD in both magnetic and orbital excitations in the collinear antiferromagnetic phase. We demonstrate that the CD can be modeled by a proper treatment of RIXS scattering amplitudes derived from single-ion calculations with birefringence. Recognizing these effects is crucial for unambiguous identification of subtle dichroic effects induced by symmetry-broken quasiparticles. Furthermore, the combined sensitivity of RIXS and birefringence to local symmetry presents an opportunity to study microscopic changes driven by external perturbations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, Cambridge, 1999).
  2. J. Stöhr, K. Baberschke, R. Jaeger, R. Treichler, and S. Brennan, Orientation of chemisorbed molecules from surface-absorption fine-structure measurements: CO and NO on Ni(100), Phys. Rev. Lett. 47, 381 (1981).
  3. G. van der Laan, Magnetic linear x-ray dichroism as a probe of the magnetocrystalline anisotropy, Phys. Rev. Lett. 82, 640 (1999).
  4. G. Schütz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G. Materlik, Absorption of circularly polarized x rays in iron, Phys. Rev. Lett. 58, 737 (1987).
  5. L. Alagna, T. Prosperi, S. Turchini, J. Goulon, A. Rogalev, C. Goulon-Ginet, C. R. Natoli, R. D. Peacock, and B. Stewart, X-ray natural circular dichroism, Phys. Rev. Lett. 80, 4799 (1998).
  6. Y. Tanaka, T. Takeuchi, S. W. Lovesey, K. S. Knight, A. Chainani, Y. Takata, M. Oura, Y. Senba, H. Ohashi, and S. Shin, Right handed or left handed? Forbidden x-ray diffraction reveals chirality, Phys. Rev. Lett. 100, 145502 (2008).
  7. H. Ueda, E. Skoropata, M. Burian, V. Ukleev, G. S. Perren, L. Leroy, J. Zaccaro, and U. Staub, Conical spin order with chiral quadrupole helix in CsCuCl3, Phys. Rev. B 105, 144408 (2022).
  8. J. C. Lang, D. R. Lee, D. Haskel, and G. Srajer, Imaging spiral magnetic domains in Ho metal using circularly polarized Bragg diffraction, J. Appl. Phys. 95, 6537 (2004).
  9. N. Ortiz Hernández, E. Skoropata, H. Ueda, M. Burian, J. A. Alonso, and U. Staub, Magnetoelectric effect in multiferroic nickelate perovskite YNiO3, Commun. Mater. 5, 154 (2024).
  10. A. M. Mulders, S. M. Lawrence, A. J. Princep, U. Staub, Y. Bodenthin, M. García-Fernández, M. Garganourakis, J. Hester, R. Macquart, and C. D. Ling, Circularly polarized soft x-ray diffraction study of helical magnetism in hexaferrite, Phys. Rev. B 81, 092405 (2010).
  11. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
  12. F. M. F. de Groot, M. W. Haverkort, H. Elnaggar, A. Juhin, K.-J. Zhou, and P. Glatzel, Resonant inelastic X-ray scattering, Nat. Rev. Methods Primers 4, 45 (2024).
  13. H. Ueda, M. García-Fernández, S. Agrestini, C. P. Romao, J. van den Brink, N. A. Spaldin, K.-J. Zhou, and U. Staub, Chiral phonons in quartz probed by x-rays, Nature (London) 618, 946 (2023).
  14. M. Schüler, T. Schmitt, and P. Werner, Probing magnetic orbitals and Berry curvature with circular dichroism in resonant inelastic X-ray scattering, npj Quantum Mater. 8, 6 (2023).
  15. P. Marra, K. Wohlfeld, and J. van den Brink, Unraveling orbital correlations with magnetic resonant inelastic X-ray scattering, Phys. Rev. Lett. 109, 117401 (2012).
  16. L. Šmejkal, A. Marmodoro, K.-H. Ahn, R. González-Hernández, I. Turek, S. Mankovsky, H. Ebert, S. W. D'Souza, O. Šipr, J. Sinova, and T. Jungwirth, Chiral magnons in altermagnetic RuO2, Phys. Rev. Lett. 131, 256703 (2023).
  17. S. P. Collins, I. Dolbnya, B. A. Palmer, G. R. Edwards-Gau, A. Morte-Ródenas, B. M. Kariuki, G. K. Lim, K. D. M. Harris, and Y. Joly, X-ray birefringence in highly anisotropic materials, J. Phys.: Conf. Ser. 425, 132015 (2013).
  18. S. W. Lovesey, V. Scagnoli, A. N. Dobrynin, Y. Joly, and S. P. Collins, Effects of dispersion and absorption in resonant Bragg diffraction of x-rays, J. Phys.: Condens. Matter 26, 125504 (2014).
  19. S. W. Lovesey and S. P. Collins, X-ray birefringence and dichroism obtained from magnetic materials, J. Synchrotron Radiat. 8, 1065 (2001).
  20. B. A. Palmer, A. Morte-Ródenas, B. M. Kariuki, K. D. M. Harris, and S. P. Collins, X-ray birefringence from a model anisotropic crystal, J. Phys. Chem. Lett. 2, 2346 (2011).
  21. Y. Joly, S. P. Collins, S. Grenier, H. C. N. Tolentino, and M. De Santis, Birefringence and polarization rotation in resonant x-ray diffraction, Phys. Rev. B 86, 220101(R) (2012).
  22. H.-C. Mertins, P. M. Oppeneer, S. Valencia, W. Gudat, F. Senf, and P. R. Bressler, X-ray natural birefringence in reflection from graphite, Phys. Rev. B 70, 235106 (2004).
  23. A. Petcov, A. Kirfel, and K. Fischer, X-ray birefringence and dichroism in lithium niobate, LiNbO3, Acta Crystallogr. A 46, 754 (1990).
  24. Y. Joly, Y. Tanaka, D. Cabaret, and S. P. Collins, Chirality, birefringence, and polarization effects in α-quartz studied by resonant elastic x-ray scattering, Phys. Rev. B 89, 224108 (2014).
  25. B. A. Palmer, G. R. Edwards-Gau, B. M. Kariuki, K. D. M. Harris, I. P. Dolbnya, and S. P. Collins, X-ray birefringence imaging, Science 344, 1013 (2014).
  26. F. Karbstein and C. Sundqvist, Probing vacuum birefringence using x-ray free electron and optical high-intensity lasers, Phys. Rev. D 94, 013004 (2016).
  27. H. Jacobsen, S. M. Gaw, A. J. Princep, E. Hamilton, S. Tóth, R. A. Ewings, M. Enderle, E. M. H. Wheeler, D. Prabhakaran, and A. T. Boothroyd, Spin dynamics and exchange interactions in CuO measured by neutron scattering, Phys. Rev. B 97, 144401 (2018).
  28. T. Kimura, Y. Sekio, H. Nakamura, T. Siegrist, and A. P. Ramirez, Cupric oxide as an induced-multiferroic with high-Tc, Nat. Mater. 7, 291 (2008).
  29. N. Terada, D. D. Khalyavin, P. Manuel, F. Orlandi, C. J. Ridley, C. L. Bull, R. Ono, I. Solovyev, T. Naka, D. Prabhakaran, and A. T. Boothroyd, Room-temperature type-II multiferroic phase induced by pressure in cupric oxide, Phys. Rev. Lett. 129, 217601 (2022).
  30. S. L. Johnson, R. A. de Souza, U. Staub, P. Beaud, E. Möhr-Vorobeva, G. Ingold, A. Caviezel, V. Scagnoli, W. F. Schlotter, J. J. Turner, O. Krupin, W.-S. Lee, Y.-D. Chuang, L. Patthey, R. G. Moore, D. Lu, M. Yi, P. S. Kirchmann, M. Trigo, P. Denes et al., Femtosecond dynamics of the collinear-to-spiral antiferromagnetic phase transition in CuO, Phys. Rev. Lett. 108, 037203 (2012).
  31. R. Masuda, Y. Kaneko, Y. Tokura, and Y. Takahashi, Electric field control of natural optical activity in a multiferroic helimagnet, Science 372, 496 (2021).
  32. P. Babkevich, A. Poole, R. D. Johnson, B. Roessli, D. Prabhakaran, and A. T. Boothroyd, Electric field control of chiral magnetic domains in the high-temperature multiferroic CuO, Phys. Rev. B 85, 134428 (2012).
  33. S. Asbrink and A. Waskowska, CuO: X-ray single-crystal structure determination at 196 K and room temperature, J. Phys.: Condens. Matter 3, 8173 (1991).
  34. A. Urru, J.-R. Soh, N. Qureshi, A. Stunault, B. Roessli, H. M. Rønnow, and N. A. Spaldin, Neutron scattering from local magnetoelectric multipoles: A combined theoretical, computational, and experimental perspective, Phys. Rev. Res. 5, 033147 (2023).
  35. V. Scagnoli, U. Staub, Y. Bodenthin, R. A. De Souza, M. García-Fernández, M. Garganourakis, A. T. Boothroyd, D. Prabhakaran, and S. W. Lovesey, Observation of orbital currents in CuO, Science 332, 696 (2011).
  36. R. Misawa, K. Arakawa, H. Ueda, H. Nakajima, S. Mori, Y. Tanaka, and T. Kimura, Magnetic domains in two distinct antiferromagnetic phases of CuO, Phys. Rev. B 106, 104401 (2022).
  37. K.-J. Zhou, A. Walters, M. Garcia-Fernandez, T. Rice, M. Hand, A. Nag, J. Li, S. Agrestini, P. Garland, H. Wang, S. Alcock, I. Nistea, B. Nutter, N. Rubies, G. Knap, M. Gaughran, F. Yuan, P. Chang, J. Emmins, and G. Howell, I21: An advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source, J. Synchrotron Radiat. 29, 563 (2022).
  38. D. Prabhakaran and A. Boothroyd, Single crystal growth of Zn-doped CuO by the floating-zone method, J. Cryst. Growth 250, 77 (2003).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022047 for additional experimental information, RIXS CD in paramagnetic phase, single-ion parameters, comparison to REXS CD, and more information on energy-dependent RIXS CD calculations.
  40. W. B. Wu, N. Hiraoka, D. J. Huang, S. W. Huang, K. D. Tsuei, M. van Veenendaal, J. van den Brink, Y. Sekio, and T. Kimura, Effective orbital symmetry of CuO: Examination by nonresonant inelastic x-ray scattering, Phys. Rev. B 88, 205129 (2013).
  41. G. Ghiringhelli, A. Piazzalunga, X. Wang, A. Bendounan, H. Berger, F. Bottegoni, N. Christensen, C. Dallera, M. Grioni, J.-C. Grivel, M. Moretti Sala, L. Patthey, J. Schlappa, T. Schmitt, V. Strocov, and L. Braicovich, Crystal field and low energy excitations measured by high resolution RIXS at the L3 edge of Cu, Ni and Mn, Eur. Phys. J. Spec. Top. 169, 199 (2009).
  42. H.-Y. Huang, N. A. Bogdanov, L. Siurakshina, P. Fulde, J. van den Brink, and L. Hozoi, Ab initio calculation of d−d excitations in quasi-one-dimensional Cu d9 correlated materials, Phys. Rev. B 84, 235125 (2011).
  43. Y. L. Wang, G. Fabbris, M. P. M. Dean, and G. Kotliar, EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering, Comput. Phys. Commun. 243, 151 (2019).
  44. H. C. Robarts, M. García-Fernández, J. Li, A. Nag, A. C. Walters, N. E. Headings, S. M. Hayden, and K.-J. Zhou, Dynamical spin susceptibility in La2CuO4 studied by resonant inelastic x-ray scattering, Phys. Rev. B 103, 224427 (2021).
  45. S. Di Matteo and M. R. Norman, Orbital currents, anapoles, and magnetic quadrupoles in CuO, Phys. Rev. B 85, 235143 (2012).
  46. R. C. Jones, A new calculus for the treatment of optical systems. VII. Properties of the N-matrices, J. Opt. Soc. Am. 38, 671 (1948).
  47. S. W. Lovesey, Photon scattering by magnetic solids, Rep. Prog. Phys. 56, 257 (1993).
  48. B. Henke, E. Gullikson, and J. Davis, X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 ev, Z = 1–92, At. Data Nucl. Data Tables 54, 181 (1993).
  49. H. Ueda, Y. Joly, and U. Staub, Non-chiral 1T-TiSe2 creates circular dichroism in resonant X-ray diffraction via multipole scattering interference, Phys. Rev. B 111, L081114 (2025).
  50. M. W. Haverkort, N. Hollmann, I. P. Krug, and A. Tanaka, Symmetry analysis of magneto-optical effects: The case of x-ray diffraction and x-ray absorption at the transition metal L2,3 edge, Phys. Rev. B 82, 094403 (2010).
  51. A. Nag, G. S. Perren, H. Ueda, A. T. Boothroyd, D. Prabhakaran, M. García-Fernández, S. Agrestini, K.-J. Zhou, and U. Staub, Database SCICAT (2025), doi:10.16907/ef016403-9a76-44c7-94d2-cd6bccd0e9f9.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation