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Broken inversion symmetry in the charge density wave phase in EuAl4

Surya Rohith Kotla1, Leila Noohinejad2, Preeti Pokhriyal2, Martin Tolkiehn2, Harshit Agarwal1,3, Sitaram Ramakrishnan4, and Sander van Smaalen1,*

  • *Contact author: smash@uni-bayreuth.de
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Phys. Rev. B 112, 064113 – Published 28 August, 2025

DOI: https://doi.org/10.1103/kl2z-brms

Abstract

EuAl4 exhibits a complex phase diagram, including the development of a charge density wave (CDW) below TCDW=145K. Below TN=15.4K, a series of antiferromagnetically (AFM) ordered phases appear, while nontrivial topological phases, like skyrmion lattices, are stabilized under an applied magnetic field. The symmetries of the variously ordered phases are a major issue concerning the understanding of the stabilization of the ordered phases as well as concerning the interplay between the various types of order. EuAl4 at room temperature has tetragonal symmetry with space group I4/mmm. The CDW phase has an incommensurately modulated crystal structure described by the modulation wave vector q≈0.17c*. On the basis of various experiments, including elastic and inelastic x-ray scattering, and second-harmonic generation, it has been proposed that the symmetry of the CDW phase of EuAl4 could be centrosymmetric orthorhombic, noncentrosymmetric orthorhombic or noncentrosymmetric tetragonal. Here, we report temperature-dependent, single-crystal x-ray diffraction experiments that show that the CDW is a transverse CDW with phason disorder, and with noncentrosymmetric symmetry according to the orthorhombic superspace group F222(00σ)00s. Essential for this finding is the availability of a sufficient number of second-order (2q) satellite reflections in the x-ray diffraction data set. The broken inversion symmetry implies that skyrmions might form due to Dzyaloshinskii-Moriya (DM) interactions, instead of a more exotic mechanism as it is required for centrosymmetric structures.

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References (48)

  1. G. Grüner, Charge Density Waves in Solids (Addison-Wesley, Reading, Massachusetts, 1994).
  2. P. Monceau, Electronic crystals: an experimental overview, Adv. Phys. 61, 325 (2012).
  3. J.-P. Pouget and E. Canadell, Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding, Rep. Prog. Phys. 87, 026501 (2024).
  4. D. I. Khomskii and S. V. Streltsov, Orbital effects in solids: Basics, recent progress, and opportunities, Chem. Rev. 121, 2992 (2021).
  5. H. D. Yang, P. Klavins, and R. N. Shelton, Competition between superconductivity and charge-density-waves in the pseudoternary system (Lu1−xScx)5Ir4Si10, Phys. Rev. B 43, 7681 (1991).
  6. S. Ramakrishnan and S. van Smaalen, Unusual ground states in R5T4X10 (R = rare earth; T = Rh, Ir; and X = Si, Ge, Sn): a review, Rep. Prog. Phys. 80, 116501 (2017).
  7. Q. Wang, P. Kong, W. Shi, C. Pei, C. Wen, L. Gao, Y. Zhao, Q. Yin, Y. Wu, G. Li, H. Lei, J. Li, Y. Chen, S. Yan, and Y. Qi, Charge density wave orders and enhanced superconductivity under pressure in the kagome metal CsV3Sb5, Adv. Mater. 33, 2102813 (2021).
  8. Y. Xie, Y. Li, P. Bourges, A. Ivanov, Z. Ye, J.-X. Yin, M. Z. Hasan, A. Luo, Y. Yao, Z. Wang, G. Xu, and P. Dai, Electron-phonon coupling in the charge density wave state of CsV3Sb5, Phys. Rev. B 105, L140501 (2022).
  9. K. K. Kolincio, M. Roman, M. J. Winiarski, J. Strychalska-Nowak, and T. Klimczuk, Magnetism and charge density waves in RNiC2 (R = Ce, Pr, Nd), Phys. Rev. B 95, 235156 (2017).
  10. M. Roman, M. Fritthum, B. Stöger, D. T. Adroja, and H. Michor, Charge density wave and crystalline electric field effects in TmNiC2, Phys. Rev. B 107, 125137 (2023).
  11. S. Shimomura, C. Hayashi, G. Asaka, N. Wakabayashi, M. Mizumaki, and H. Onodera, Charge-density-wave destruction and ferromagnetic order in SmNiC2, Phys. Rev. Lett. 102, 076404 (2009).
  12. A. Wölfel, L. Li, S. Shimomura, H. Onodera, and S. van Smaalen, Commensurate charge-density wave with frustrated interchain coupling in SmNiC2, Phys. Rev. B 82, 054120 (2010).
  13. S. Ramakrishnan, A. Schönleber, T. Rekis, N. van Well, L. Noohinejad, S. van Smaalen, M. Tolkiehn, C. Paulmann, B. Bag, A. Thamizhavel, D. Pal, and S. Ramakrishnan, Unusual charge density wave transition and absence of magnetic ordering in Er2Ir3Si5, Phys. Rev. B 101, 060101(R) (2020).
  14. Y. Singh, D. Pal, and S. Ramakrishnan, Low-temperature studies of the magnetic and superconducting properties of the R2Ir3Si5 (R = Y, La, Ce–Nd, Gd–Tm) system, Phys. Rev. B 70, 064403 (2004).
  15. J. M. Moya, S. Lei, E. M. Clements, C. S. Kengle, S. Sun, K. Allen, Q. Li, Y. Y. Peng, A. A. Husain, M. Mitrano, M. J. Krogstad, R. Osborn, A. B. Puthirath, S. Chi, L. Debeer-Schmitt, J. Gaudet, P. Abbamonte, J. W. Lynn, and E. Morosan, Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric EuGa2Al2 system, Phys. Rev. Mater. 6, 074201 (2022).
  16. A. M. Vibhakar, D. D. Khalyavin, J. M. Moya, P. Manuel, F. Orlandi, S. Lei, E. Morosan, and A. Bombardi, Competing charge and magnetic order in the candidate centrosymmetric skyrmion host EuGa2Al2, Phys. Rev. B 108, L100404 (2023).
  17. R. Takagi, N. Matsuyama, V. Ukleev, L. Yu, J. S. White, S. Francoual, J. R. L. Mardegan, S. Hayami, H. Saito, K. Kaneko, K. Ohishi, Y. Ōnuki, T.-h. Arima, Y. Tokura, T. Nakajima, and S. Seki, Square and rhombic lattices of magnetic skyrmions in a centrosymmetric binary compound, Nat. Commun. 13, 1472 (2022).
  18. M. Gen, R. Takagi, Y. Watanabe, S. Kitou, H. Sagayama, N. Matsuyama, Y. Kohama, A. Ikeda, Y. Onuki, T. Kurumaji, T.-h. Arima, and S. Seki, Rhombic skyrmion lattice coupled with orthorhombic structural distortion in EuAl4, Phys. Rev. B 107, L020410 (2023).
  19. R. Yang, C. C. Le, P. Zhu, Z. W. Wang, T. Shang, Y. M. Dai, J. P. Hu, and M. Dressel, Charge density wave transition in the magnetic topological semimetal EuAl4, Phys. Rev. B 109, L041113 (2024).
  20. S. Shimomura, H. Murao, S. Tsutsui, H. Nakao, A. Nakamura, M. Hedo, T. Nakama, and Y. Ōnuki, Lattice modulation and structural phase transition in the antiferromagnet EuAl4, J. Phys. Soc. Jpn. 88, 014602 (2019).
  21. S. Ramakrishnan, S. R. Kotla, T. Rekis, J.-K. Bao, C. Eisele, L. Noohinejad, M. Tolkiehn, C. Paulmann, B. Singh, R. Verma, B. Bag, R. Kulkarni, A. Thamizhavel, B. Singh, S. Ramakrishnan, and S. van Smaalen, Orthorhombic charge density wave on the tetragonal lattice of EuAl4, IUCrJ 9, 378 (2022).
  22. A. N. Korshunov, A. S. Sukhanov, S. Gebel, M. S. Pavlovskii, N. D. Andriushin, Y. Gao, J. M. Moya, E. Morosan, and M. C. Rahn, Phonon softening and atomic modulations in EuAl4, Phys. Rev. B 110, 045102 (2024).
  23. A. S. Sukhanov, S. Gebel, A. N. Korshunov, N. D. Andriushin, M. S. Pavlovskii, Y. Gao, J. M. Moya, K. Allen, E. Morosan, and M. C. Rahn, Electron-phonon coupling in EuAl4 under hydrostatic pressure, Phys. Rev. B 111, 195150 (2025).
  24. H. Agarwal, S. R. Kotla, L. Noohinejad, B. Bag, C. Eisele, S. Ramakrishnan, M. Tolkiehn, C. Paulmann, A. Thamizhavel, S. Ramakrishnan, and S. van Smaalen, I-centered versus F-centered orthorhombic symmetry and negative thermal expansion of the charge density wave of EuAl2Ga2, Phys. Rev. B 111, 155144 (2025).
  25. F. Z. Yang, K. F. Luo, W. Zhang, X. Guo, W. R. Meier, H. Ni, H. X. Li, P. M. Lozano, G. Fabbris, A. H. Said, C. Nelson, T. T. Zhang, A. F. May, M. A. McGuire, R. Juneja, L. Lindsay, H. N. Lee, J. M. Zuo, M. F. Chi, X. Dai et al., Incommensurate transverse Peierls transition, arXiv:2410.10539.
  26. J. Pérez-Mato, G. Madariaga, and L. Elcoro, Influence of phason dynamics on atomic Debye-Waller factors of incommensurate modulated structures and quasicrystals, Solid State Commun. 78, 33 (1991).
  27. H. Ni, W. R. Meier, H. Miao, A. F. May, B. C. Sales, J.-M. Zuo, and M. Chi, Real-space visualization of atomic displacements in a long-wavelength charge density wave using cryogenic 4D-STEM, Phys. Rev. Mater. 8, 104414 (2024).
  28. S. Ramakrishnan, S. R. Kotla, H. Pi, B. B. Maity, J. Chen, J.-K. Bao, Z. Guo, M. Kado, H. Agarwal, C. Eisele, M. Nohara, L. Noohinejad, H. Weng, S. Ramakrishnan, A. Thamizhavel, and S. van Smaalen, Noncentrosymmetric, transverse structural modulation in SrAl4, and elucidation of its origin in the BaAl4 family of compounds, Phys. Rev. Res. 6, 023277 (2024).
  29. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
  30. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  31. Y. Tokura and N. Kanazawa, Magnetic skyrmion materials, Chem. Rev. 121, 2857 (2021).
  32. A. M. Vibhakar, D. D. Khalyavin, F. Orlandi, J. M. Moya, S. Lei, E. Morosan, and A. Bombardi, Spontaneous reversal of spin chirality and competing phases in the topological magnet EuAl4, Commun. Phys. 7, 313 (2024).
  33. A. Nakamura, T. Uejo, F. Honda, T. Takeuchi, H. Harima, E. Yamamoto, Y. Haga, K. Matsubayashi, Y. Uwatoko, M. Hedo, T. Nakama, and Y. Ōnuki, Transport and magnetic properties of EuAl4 and EuGa4, J. Phys. Soc. Jpn. 84, 124711 (2015).
  34. D. Pennicard, S. Lange, S. Smoljanin, H. Hirsemann, and H. Graafsma, LAMBDA–large area Medipix3-based detector array, J. Instrum. 7, C11009 (2012).
  35. Rigaku, CrysAlisPro version 171.40.53, Rigaku Oxford diffraction (2019), https://rigaku.com/products/crystallography/x-ray-diffraction/crysalispro.
  36. A. M. M. Schreurs, X. Xian, and L. M. J. Kroon-Batenburg, EVAL15: a diffraction data integration method based on ab initio predicted profiles, J. Appl. Crystallogr. 43, 70 (2010).
  37. G. M. Sheldrick, SADABS, Version 2008/1 (Germany Bruker AXS Inc., Karlsruhe, 2008).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/kl2z-brms for details on the diffraction experiments and values of the structural parameters.
  39. V. Petříček, L. Palatinus, J. Plasil, and M. Dusek, jana2020–a new version of the crystallographic computing system jana, Z. Kristallogr. Cryst. Mater. 238, 271 (2023).
  40. H. T. Stokes, B. J. Campbell, and S. van Smaalen, Generation of (3+d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures, Acta Crystallogr. A 67, 45 (2011).
  41. T. Shang, Y. Xu, S. Gao, R. Yang, T. Shiroka, and M. Shi, Experimental progress in Eu(Al,Ga)4 topological antiferromagnets, J. Phys.: Condens. Matter 37, 013002 (2025).
  42. S. van Smaalen, Incommensurate Crystallography (Oxford University Press, Oxford, 2012).
  43. T. Janssen, G. Chapuis, and M. de Boissieu, Aperiodic Crystals: From Modulated Phases to Quasicrystals, 2nd ed. (Oxford University Press, Oxford, 2018).
  44. W. J. Schutte, F. Disselborg, and J. L. de Boer, Determination of the two-dimensional incommensurately modulated structure of Mo2S3, Acta Crystallogr. B 49, 787 (1993).
  45. D. E. Bugaris, C. D. Malliakas, F. Han, N. P. Calta, M. Sturza, M. J. Krogstad, R. Osborn, S. Rosenkranz, J. P. C. Ruff, G. Trimarchi, S. L. Bud'ko, M. Balasubramanian, D. Y. Chung, and M. G. Kanatzidis, Charge density wave in the new polymorphs of RE2Ru3Ge5 (RE = Pr, Sm, Dy), J. Am. Chem. Soc. 139, 4130 (2017).
  46. V. Sharma, S. Ramakrishnan, J. SS, S. R. Kotla, B. Maiti, C. Eisele, H. Agarwal, L. Noohinejad, M. Tolkiehn, D. Bansal, S. van Smaalen, and T. Arumugam, Room temperature charge density wave in a tetragonal polymorph of Gd2Os3Si5 and study of its origin in the RE2T3X5 (RE = rare earth, T = transition metal, X = Si, Ge) series, Chem. Mater. 36, 6888 (2024).
  47. M. Kobata, S.-i. Fujimor, Y. Takeda, T. Okane, Y. Saitoh, K. Kobayashi, H. Yamagami, A. Nakamura, M. Hedo, T. Nakama, and Y. Onuki, Electronic structure of EuAl4 studied by photoelectron spectroscopy, J. Phys. Soc. Jpn. 85, 094703 (2016).
  48. K. Kaneko, T. Kawasaki, A. Nakamura, K. Munakata, A. Nakao, T. Hanashima, R. Kiyanagi, T. Ohhara, M. Hedo, T. Nakama, and Y. Ōnuki, Charge-density-wave order and multiple magnetic transitions in divalent europium compound EuAl4, J. Phys. Soc. Jpn. 90, 064704 (2021).

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Phys. Rev. B 112, 064113– Published 28 August, 2025
  • Received 4 June 2025
  • Revised 24 July 2025
  • Accepted 15 August 2025
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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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