- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Nonchiral 1T−TiSe2 creates circular dichroism in resonant x-ray diffraction via multipole scattering interference

Hiroki Ueda1,2,*, Yves Joly3, and Urs Staub1,†

  • *Contact author: hiroki.ueda@psi.ch
  • †Contact author: urs.staub@psi.ch
PDF

Phys. Rev. B 111, L081114 – Published 25 February, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L081114

Abstract

Resonant x-ray diffraction (RXD) provides a unique capability to investigate electronically ordered states in matter. Importantly, circular dichroism in RXD can determine the absolute chirality formed by anisotropic multipole arrangement. Here, we demonstrate that the scattering interference between distinct atomic electric multipoles can create circular contrast in resonant RXD even in a nonchiral crystal. These general considerations are applied to 1T−TiSe2, where recently reported circular dichroism in RXD was used to claim a chiral charge density wave order. We show that the experimental observations are well reproduced by our ab initio calculations based on the centrosymmetric crystal structure. Our results not only illuminate a way for a better understanding of possible chiral electronic order but also propose a general approach to extract buried high-order atomic multipoles via circular contrast in RXD. Besides, we discuss the difference in the circular dichroism of RXD originated by crystal chirality in chiral crystals and the interference effect in nonchiral crystals.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. C. Sutter, G. Grübel, C. Vettier, F. de Bergevin, A. Stunault, D. Gibbs, and C. Giles, Helicity of magnetic domains in holmium studied with circularly polarized x rays, Phys. Rev. B 55, 954 (1997).
  2. 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).
  3. 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).
  4. Q. Xiao, O. Janson, S. Francoual, Q. Qiu, Q. Li, S. Zhang, W. Xie, P. Bereciartua, J. van den Brink, J. van Wezel, and Y. Peng, Observation of circular dichroism induced by electronic chirality, Phys. Rev. Lett. 133, 126402 (2024).
  5. J. Ishioka, Y. H. Liu, K. Shimatake, T. Kurosawa, K. Ichimura, Y. Toda, M. Oda, and S. Tanda, Chiral charge-density waves, Phys. Rev. Lett. 105, 176401 (2010).
  6. J.-P. Castellan, S. Rosenkranz, R. Osborn, Q. Li, K. E. Gray, X. Luo, U. Welp, G. Karapetrov, J. P. C. Ruff, and J. van Wezel, Chiral phase transition in charge ordered 1T-TiSe2, Phys. Rev. Lett. 110, 196404 (2013).
  7. B. Hildebrand, T. Jaouen, M.-L. Mottas, G. Monney, C. Barreteau, E. Giannini, D. R. Bowler, and P. Aebi, Local real-space view of the achiral 1T-TiSe2 2×2×2 charge density wave, Phys. Rev. Lett. 120, 136404 (2018).
  8. M.-K. Lin, J. A. Hlevyack, P. Chen, R.-Y. Liu, and T.-C. Chiang, Comment on Chiral phase transition in charge ordered 1T-TiSe2, Phys. Rev. Lett. 122, 229701 (2019).
  9. S.-Y. Xu, Q. Ma, A. Kogar, A. Zong, A. M. Mier Valdivia, T. H. Dinh, S.-M. Huang, B. Singh, C.-H. Hsu, T.-R. Chang, J. P. C. Ruff, K. Watanabe, T. Taniguchi, H. Lin, G. Karapetrov, D. Xiao, P. Jarillo-Herrero, and N. Gedik, Spontaneous gyrotropic electronic order in a transition-metal dichalcogenide, Nature (London) 578, 545 (2020).
  10. H. Ueda, M. Porer, J. R. L. Mardegan, S. Parchenko, N. Gurung, F. Fabrizi, M. Ramakrishnan, L. Boie, M. J. Neugebauer, B. Burganov, M. Burian, S. L. Johnson, K. Rossnagel, and U. Staub, Correlation between electronic and structural orders in 1T-TiSe2, Phys. Rev. Res. 3, L022003 (2021).
  11. R. Zhang, W. Ruan, J. Yu, L. Gao, H. Berger, L. Forró, K. Watanabe, T. Taniguchi, A. Ranjbar, R. V. Belosludov, T. D. Kühne, M. S. Bahramy, and X. Xi, Second-harmonic generation in atomically thin 1T-TiSe2 and its possible origin from charge density wave transitions, Phys. Rev. B 105, 085409 (2022).
  12. K. Kim, H.-W. J. Kim, S. Ha, H. Kim, J.-K. Kim, J. Kim, J. Kwon, J. Seol, S. Jung, C. Kim, D. Ishikawa, T. Manjo, H. Fukui, A. Q. R. Baron, A. Alatas, A. Said, M. Merz, T. L. Tacon, J. M. Bok, K.-S. Kim, and B. J. Kim, Origin of the chiral charge density wave in transition-metal dichalcogenide, Nat. Phys. 20, 1919 (2024).
  13. H. Kim, K.-H. Jin, and H. W. Yeom, Electronically seamless domain wall of chiral charge density wave in 1T-TiSe2, Nano Lett. 24, 14323 (2024).
  14. 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).
  15. S. Tardif, S. Takeshita, H. Ohsumi, J. Yamaura, D. Okuyama, Z. Hiroi, M. Takata, and T. Arima, All-in-all-out magnetic domains: X-ray diffraction imaging and magnetic field control, Phys. Rev. Lett. 114, 147205 (2015).
  16. H. Ueda, Y. Tanaka, Y. Wakabayashi, and T. Kimura, Observation of collinear antiferromagnetic domains making use of the circular dichroic charge-magnetic interference effect of resonant x-ray diffraction, Phys. Rev. B 98, 134415 (2018).
  17. R. Misawa, H. Ueda, K. Kimura, Y. Tanaka, and T. Kimura, Chirality and magnetic quadrupole order in Pb(TiO)Cu4(PO4)4 probed by interference scattering in resonant x-ray diffraction, Phys. Rev. B 103, 174409 (2021).
  18. R. Misawa, K. Arakawa, T. Yoshioka, H. Ueda, F. Iga, K. Tamasaku, Y. Tanaka, and T. Kimura, Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic TbB4, Phys. Rev. B 108, 134433 (2023).
  19. S. Kitou, A. Nakano, S. Kobayashi, K. Sugawara, N. Katayama, N. Maejima, A. Machida, T. Watanuki, K. Ichimura, S. Tanda, T. Nakamura, and H. Sawa, Effect of Cu intercalation and pressure on excitonic interaction in 1T-TiSe2, Phys. Rev. B 99, 104109 (2019).
  20. O. Bunau and Y. Joly, Self-consistent aspects of x-ray absorption calculations, J. Phys.: Condens. Matter 21, 345501 (2009).
  21. D. Cabaret, A. Bordage, A. Juhin, M. Arfaoui, and E. Gaudry, First-principles calculations of X-ray absorption spectra at the K-edge of 3d transition metals: An electronic structure analysis of the pre-edge, Phys. Chem. Chem. Phys. 12, 5619 (2010).
  22. S. Di Matteo, Resonant x-ray diffraction: Multipole interpretation, J. Phys. D: Appl. Phys. 45, 163001 (2012).
  23. V. E. Dmitrienko, Forbidden reflections due to anisotropic X-ray susceptibility of crystals, Acta Crystallogr. A39, 29 (1983).
  24. Y. Tanaka, T. Kojima, Y. Takata, A. Chainani, S. W. Lovesey, K. S. Knight, T. Takeuchi, M. Oura, Y. Senba, H. Ohashi, and S. Shin, Determination of structural chirality of berlinite and quartz using resonant x-ray diffraction with circularly polarized x-rays, Phys. Rev. B 81, 144104 (2010).
  25. 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).
  26. J. Igarashi and M. Takahashi, Resonant x-ray scattering from chiral materials: Α-quartz and α-berlinite, Phys. Rev. B 86, 104116 (2012).
  27. 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).
  28. J.-D. Su, A. R. Sandy, J. Mohanty, O. G. Shpyrko, and M. Sutton, Collective pinning dynamics of charge-density waves in 1T-TaS2, Phys. Rev. B 86, 205105 (2012).
  29. X. M. Chen, C. Mazzoli, Y. Cao, V. Thampy, A. M. Barbour, W. Hu, M. Lu, T. A. Assefa, H. Miao, G. Fabbris, G. D. Gu, J. M. Tranquada, M. P. M. Dean, S. B. Wilkins, and I. K. Robinson, Charge density wave memory in a cuprate superconductor, Nat. Commun. 10, 1435 (2019).
  30. Z. Shi, S. J. Kuhn, F. Flicker, T. Helm, J. Lee, W. Steinhardt, S. Dissanayake, D. Graf, J. Ruff, G. Fabbris, D. Haskel, and S. Haravifard, Incommensurate two-dimensional checkerboard charge density wave in the low-dimensional superconductor Ta4Pd3Te16, Phys. Rev. Res. 2, 042042(R) (2020).
  31. T. Usui, Y. Tanaka, H. Nakajima, M. Taguchi, A. Chainani, M. Oura, S. Shin, N. Katayama, H. Sawa, Y. Wakabayashi, and T. Kimura, Observation of quadrupole helix chirality and its domain structure in DyFe3(BO3)4, Nat. Mater. 13, 611 (2014).
  32. A. Tripathi, J. Mohanty, S. H. Dietze, and I. McNulty, Dichroic coherent diffractive imaging, Proc. Natl. Acad. Sci. USA 108, 13393 (2011).
  33. M. G. Kim, H. Miao, B. Gao, S.-W. Cheong, C. Mazzoli, A. Barbour, W. Hu, S. B. Wilkins, I. K. Robinson, M. P. M. Dean, and V. Kiryukhin, Imaging antiferromagnetic antiphase domain boundaries using magnetic Bragg diffraction phase contrast, Nat. Commun. 9, 5013 (2018).
  34. H. Ueda, Y. Joly, and U. Staub, Non-chiral 1T-TiSe2 creates circular dichroism in resonant x-ray diffraction via multipole scattering interference, PSI Public Data Repository (2024), https://doi.org/10.16907/d77e95b6-144f-4a61-9259-3b04888c718b.

Outline

Information

Phys. Rev. B 111, L081114– Published 25 February, 2025
  • Received 10 December 2024
  • Revised 4 February 2025
  • Accepted 12 February 2025
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