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

Goldstone-Mediated Polar Instability in Hexagonal Barium Titanate

Struan Simpson1,*, Urmimala Dey2,3, Robin Sjökvist4, Jonathan Wright5, Clemens Ritter6, Richard Beanland4, Nicholas C. Bristowe2, and Mark S. Senn1,†

  • *Contact author: struan.simpson@warwick.ac.uk
  • †Contact author: m.senn@warwick.ac.uk

Phys. Rev. Lett. 136, 116101 – Published 17 March, 2026

DOI: https://doi.org/10.1103/9mdh-2b5w

Abstract

We discover a rare structural manifestation of the Goldstone paradigm in a hexagonal polytype of the prototypical ferroelectric BaTiO3. First-principles calculations confirm the Goldstone character of the order parameter, while our high-resolution diffraction measurements unveil an unusual reentrant Goldstone regime manifesting as a quasicontinuous domain texture in the vicinity of the ferroelectric transition. We develop a minimal Landau model that encapsulates these observations, illustrating how U(1) symmetry can be restored at the ferroelectric transition. Our findings demonstrate how exotic Goldstone physics can be unlocked in systems dominated by highly anharmonic interactions, presenting a promising pathway to stabilize emergent polar topologies in bulk materials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (54)

  1. D. Meier, J. Seidel, A. Cano, K. Delaney, Y. Kumagai, M. Mostovoy, N. A. Spaldin, R. Ramesh, and M. Fiebig, Nat. Mater. 11, 284 (2012).
  2. Y. S. Oh, X. Luo, F.-T. Huang, Y. Wang, and S.-W. Cheong, Nat. Mater. 14, 407 (2015).
  3. R. G. P. McQuaid, M. P. Campbell, R. W. Whatmore, A. Kumar, and J. M. Gregg, Nat. Commun. 8, 15105 (2017).
  4. S. Das, Y. L. Tang, Z. Hong, M. A. P. Gonçalves, M. R. McCarter, C. Klewe, K. X. Nguyen, F. Gómez-Ortiz, P. Shafer, E. Arenholz et al., Nature (London) 568, 368 (2019).
  5. R. Zhu, Z. Jiang, X. Zhang, X. Zhong, C. Tan, M. Liu, Y. Sun, X. Li, R. Qi, K. Qu et al., Phys. Rev. Lett. 129, 107601 (2022).
  6. T. Choi, Y. Horibe, H. T. Yi, Y. J. Choi, W. Wu, and S.-W. Cheong, Nat. Mater. 9, 253 (2010).
  7. S. C. Chae, N. Lee, Y. Horibe, M. Tanimura, S. Mori, B. Gao, S. Carr, and S.-W. Cheong, Phys. Rev. Lett. 108, 167603 (2012).
  8. G. Sánchez-Santolino, V. Rouco, S. Puebla, H. Aramberri, V. Zamora, M. Cabero, F. A. Cuellar, C. Munuera, F. Mompean, M. Garcia-Hernandez et al., Nature (London) 626, 529 (2024).
  9. J. M. Gregg, Ferroelectrics 433, 74 (2012).
  10. J. Junquera, Y. Nahas, S. Prokhorenko, L. Bellaiche, J. Íñiguez, D. G. Schlom, L.-Q. Chen, S. Salahuddin, D. A. Muller, L. W. Martin, and R. Ramesh, Rev. Mod. Phys. 95, 025001 (2023).
  11. H. Fu and L. Bellaiche, Phys. Rev. Lett. 91, 257601 (2003).
  12. I. I. Naumov, L. Bellaiche, and H. Fu, Nature (London) 432, 737 (2004).
  13. J. Yin, H. Zong, H. Tao, X. Tao, H. Wu, Y. Zhang, L.-D. Zhao, X. Ding, J. Sun, J. Zhu, J. Wu, and S. J. Pennycook, Nat. Commun. 12, 3632 (2021).
  14. K. W. Kirby and B. A. Wechsler, J. Am. Ceram. Soc. 74, 1841 (1991).
  15. J. S. O. Evans, Mater. Sci. Forum 651, 1 (2010).
  16. B. J. Campbell, J. S. O. Evans, F. Perselli, and H. T. Stokes, IUCr Comput. Comm. Newsl. 8, 81 (2007).
  17. B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, J. Appl. Crystallogr. 39, 607 (2006).
  18. H. T. Stokes, D. M. Hatch, and B. J. Campbell, isodistort, https://iso.byu.edu/.
  19. H. T. Stokes, D. M. Hatch, and B. J. Campbell, invariants, https://iso.byu.edu/.
  20. D. M. Hatch and H. T. Stokes, J. Appl. Crystallogr. 36, 951 (2003).
  21. J. Wright, C. Giacobbe, and M. Majkut, Curr. Opin. Solid State Mater. Sci. 24, 100818 (2020).
  22. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
  23. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9mdh-2b5w for further details on the synthesis, diffraction experiments, DFT calculations, symmetry analysis, and microscopy experiments, which includes Refs. [25–39].
  25. D. C. Sinclair, J. M. S. Skakle, F. D. Morrison, R. I. Smith, and T. P. Beales, J. Mater. Chem. 9, 1327 (1999).
  26. P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
  27. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
  28. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 100, 136406 (2008).
  29. A. Togo and I. Tanaka, Scr. Mater. 108, 1 (2015).
  30. X. Gonze, J.-C. Charlier, D. C. Allan, and M. P. Teter, Phys. Rev. B 50, 13035 (1994).
  31. X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997).
  32. S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001).
  33. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Phys. Rev. B 73, 045112 (2006).
  34. G. H. Kwei, A. C. Lawson, S. J. L. Billinge, and S. W. Cheong, J. Phys. Chem. 97, 2368 (1993).
  35. imaged11, https://github.com/FABLE-3DXRD/ImageD11.
  36. J. P. Wright, C. Giacobbe, and E. Lawrence Bright, Crystals 12, 255 (2022).
  37. A. Bonnin, J. P. Wright, R. Tucoulou, and H. Palancher, Appl. Phys. Lett. 105, 084103 (2014).
  38. A. Henningsson and S. A. Hall, Acta Crystallogr. Sect. A 79, 542 (2023).
  39. W. van Aarle, W. J. Palenstijn, J. Cant, E. Janssens, F. Bleichrodt, A. Dabravolski, J. D. Beenhouwer, K. J. Batenburg, and J. Sijbers, Opt. Express 24, 25129 (2016).
  40. R. D. Burbank and H. T. Evans, Acta Crystallogr. 1, 330 (1948).
  41. E. Sawaguchi, Y. Akishige, and M. Kobayashi, Jpn. J. Appl. Phys. 24, 252 (1985).
  42. Y. Noda, K. Akiyama, T. Shobu, Y. Kuroiwa, H. Nakao, Y. Morii, and H. Yamaguchi, Ferroelectrics 217, 1 (1998).
  43. Y. Noda, K. Akiyama, T. Shobu, Y. Morii, N. Minakawa, and H. Yamaguchi, J. Phys. Chem. Solids 60, 1415 (1999).
  44. D. M. Hatch and H. T. Stokes, Phys. Rev. B 40, 4198 (1989).
  45. M. S. Senn, D. A. Keen, T. C. A. Lucas, J. A. Hriljac, and A. L. Goodwin, Phys. Rev. Lett. 116, 207602 (2016).
  46. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).
  47. F. Mayer, M. N. Popov, D. M. Evans, S. Krohns, M. Deluca, and J. Spitaler, Phys. Rev. B 106, 064108 (2022).
  48. S.-Z. Lin, X. Wang, Y. Kamiya, G.-W. Chern, F. Fan, D. Fan, B. Casas, Y. Liu, V. Kiryukhin, W. H. Zurek et al., Nat. Phys. 10, 970 (2014).
  49. Q. N. Meier, A. Stucky, J. Teyssier, S. M. Griffin, D. van der Marel, and N. A. Spaldin, Phys. Rev. B 102, 014102 (2020).
  50. J. A. McNulty, T. T. Tran, P. S. Halasyamani, S. J. McCartan, I. MacLaren, A. S. Gibbs, F. J. Y. Lim, P. W. Turner, J. M. Gregg, P. Lightfoot, and F. D. Morrison, Adv. Mater. 31, 1903620 (2019).
  51. X. Zhang, Q.-J. Ye, and X.-Z. Li, Phys. Rev. B 103, 024101 (2021).
  52. M. Edwards and S. Simpson, Resolving the mechanism of ferroelectricity in hexagonal barium titanate [Dataset], European Synchrotron Radiation Facility, 10.15151/ESRF-ES-1302904542 (2026).
  53. W. T. Chen, E. Ladbrook, M. S. Senn, and S. Simpson, Mapping the structural domains associated with the suppression of the 3D superconducting state in the high-Tc layered cuprate [Dataset], European Synchrotron Radiation Facility, 10.15151/ESRF-ES-1734554406 (2027).
  54. M. S. Senn, M. Edwards, C. Ritter, S. Simpson, and B. Tragheim, Resolving the mechanism of ferroelectricity in hexagonal barium titanate, Institut Laue-Langevin (ILL), 10.5291/ILL-DATA.5-24-716 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation