- 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
  • Editors' Suggestion
  • Open Access

Magnetoelastic honeycomb fragmentation in VI3

Enlin Shen1, Tiberiu I. Popescu1, Nishwal Gora1, Guratinder Kaur1, Edmond Chan1, Harry Lane1, Jose A. Rodriguez-Rivera2,3, Guangyong Xu2, Peter M. Gehring2 et al.

Russell A. Ewings4, Andy N. Fitch5, and Chris Stock1

PDF

Phys. Rev. B 113, 014439 – Published 29 January, 2026

DOI: https://doi.org/10.1103/pkc4-vyj8

Abstract

The unexpected discovery of ordered magnetism in two-dimensional van der Waals materials at the monolayer limit [B. Huang et al., Nature (London) 546, 270 (2017)] challenges the Mermin-Wagner theorem [N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 133 (1966)], which forbids spontaneous breaking of continuous symmetries in two dimensions at finite temperatures. The persistence of static magnetism in low dimensions is fundamentally influenced by magnetic anisotropy which is tied to the local single-ion crystalline electric field. Crucially, spin-orbit coupling connects the structural properties with spin degrees of freedom. We investigate the magnetic single-ion properties in the two-dimensional van der Waals magnet VI3. Utilizing neutron and x-ray diffraction, we map out the symmetry breaking phase transitions in VI3 and argue for the presence of a single structural transition at TS∼80 K, driven by an orbital degeneracy, followed by a ferromagnetic transition at a lower temperature, TC∼50 K. Through a comparative analysis of samples prepared under varying conditions, we suggest that lower temperature transitions reported near ∼30 K are not intrinsic to VI3. A group theoretical analysis suggests a structural transition from rhombohedral R3¯ to triclinic P1¯ or P1. This transition is significant as it suggests the formation of two distinct crystallographically inequivalent V3+ sites on the honeycomb lattice, each with distinct spin-orbital properties. Neutron spectroscopy provides evidence for dominant magnetic exchange coupling only between symmetry-equivalent sites in the triclinic unit cell. We suggest this breaks up the low-temperature two-dimensional honeycomb VI3 lattice into two interpenetrating approximately hexagonal planes resulting in a fragmentated honeycomb. Our findings highlight the critical role of magnetoelastic coupling in determining the magnetic and structural phases in two-dimensional van der Waals magnets.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (85)

  1. K. Burch, D. Mandrus, and J. G. Park, Magnetism in two-dimensional van der Waals materials, Nature (London) 563, 47 (2018).
  2. N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966).
  3. N. D. Mermin, Crystalline order in two dimensions, Phys. Rev. 176, 250 (1968).
  4. P. C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev. 158, 383 (1967).
  5. J. Als-Nielsen, J. D. Litster, R. J. Birgeneau, M. Kaplan, C. R. Safinya, A. Lindegaard-Andersen, and S. Mathiesen, Observation of algebraic decay of positional order in a smectic liquid crystal, Phys. Rev. B 22, 312 (1980).
  6. J. P. Hill, T. R. Thurston, R. W. Erwin, M. J. Ramstad, and R. J. Birgeneau, Transition to long-range order in the three-dimensional random-field Ising model, Phys. Rev. Lett. 66, 3281 (1991).
  7. J. P. Hill, Q. Feng, Q. J. Harris, R. J. Birgeneau, A. P. Ramirez, and A. Cassanho, Phase-transition behavior in the random-field antiferromagnet Fe0.5Zn0.5F2, Phys. Rev. B 55, 356 (1997).
  8. Y. Imry and S.-k. Ma, Random-field instability of the ordered state of continuous symmetry, Phys. Rev. Lett. 35, 1399 (1975).
  9. K. Yosida, Theory of Magnetism (Springer, New York, 1996).
  10. K. Yang, F. Fan, H. Wang, D. I. Khomskii, and H. Wu, VI3: A two-dimensional ising ferromagnet, Phys. Rev. B 101, 100402(R) (2020).
  11. T. Kong, K. Stolze, E. I. Timmons, J. Tao, D. Ni, S. Guo, Z. Yang, R. Prozorov, and R. J. Cava, VI3 - A new layered ferromagnetic semiconductor, Adv. Mater. 31, 1808074 (2019).
  12. G. A. Gehring and K. A. Gehring, Co-operative Jahn Teller effects, Rep. Prog. Phys. 38, 1 (1975).
  13. L. Camerano and G. Profeta, Symmetry breaking in vanadium trihalides, 2D Mater. 11, 025027 (2024).
  14. Y. Tian, M. Gu, K. Zhang, Y. Yang, Z. Yang, L. Chen, J. Yang, W. Wang, J. Wang, and Y. Zhang, Ferromagnetic van der Waals crystal VI3, J. Am. Chem. Soc. 141, 5326 (2019).
  15. H. Lane, E. Pachoud, J. A. Rodriguez-Rivera, M. Songvilay, G. Xu, P. M. Gehring, J. P. Attfield, R. A. Ewings, and C. Stock, Two-dimensional ferromagnetic spin-orbital excitations in honeycomb VI3, Phys. Rev. B 104, L020411 (2021).
  16. S. Son, M. J. Coak, N. Lee, J. Kim, T. Y. Kim, H. Hamidov, H. Cho, C. Liu, D. M. Jarvis, P. A. C. Brown, J. H. Kim, C.-H. Park, D. I. Khomskii, S. S. Saxena, and J.-G. Park, Bulk properties of the van der Waals hard ferromagnet VI3, Phys. Rev. B 99, 041402(R) (2019).
  17. Z. Lin, B. Huang, K. Hwangbo, Q. Jiang, Q. Zhang, Z. Liu, Z. Fei, H. Lv, A. Millis, M. McGuire, D. Xiao, J.-H. Chu, and X. Xu, Magnetism and its structural coupling effects in 2DIsing ferromagnetic insulator VI3, Nano Lett. 21, 9180 (2021).
  18. Y. Liu, M. Abeykoon, and C. Petrovic, Critical behavior and magnetocaloric effect in VI3, Phys. Rev. Res. 2, 013013 (2020).
  19. P. Doležal, M. Kratochvílová, V. Holý, P. Čermák, V. Sechovský, M. Dušek, M. Míšek, T. Chakraborty, Y. Noda, S. Son, and J.-G. Park, Crystal structures and phase transitions of the van der Waals ferromagnet VI3, Phys. Rev. Mater. 3, 121401(R) (2019).
  20. T. Marchandier, N. Dubouis, F. Fauth, M. Avdeev, A. Grimaud, J.-M. Tarascon, and G. Rousse, Crystallographic and magnetic structures of the VI3 and LiVI3 van der Waals compounds, Phys. Rev. B 104, 014105 (2021).
  21. D. Juza, D. Giegling, and H. Schäfer, Über die vanadinjodide VJ2 und VJ3, Z. Anorg. Allg. Chem. 366, 121 (1969).
  22. M. Kratochvílová, K. Uhlirova, M. Misek, V. Holy, J. Zazvorka, M. Veis, J. Pospisil, S. Son, J. G. Park, and V. Sechovsky, The surface degradation and its impact on the magnetic properties of bulk VI3, Mater. Chem. Phys. 278, 125590 (2022).
  23. J. A. Rodriguez, D. M. Adler, P. C. Brand, C. Broholm, J. C. Cook, C. Brocker, R. Hammond, Z. Huang, P. Hundertmakr, J. W. Lynn, N. C. Maliszewskyj, J. Moyer, J. Orndorff, D. Pierce, T. D. Pike, G. Scharfstein, S. A. Smee, and R. Vilaseca, MACS—a new high intensity cold neutron spectrometer at NIST, Meas. Sci. Technol. 19, 034023 (2008).
  24. T. Osakabe, Principles and applications of multilayer mirror optics for X-ray diffraction measurements - CBO series for Smartlab, Rigaku J. 33, 15 (2017).
  25. E. Gati, Y. Inagaki, T. Kong, R. J. Cava, Y. Furukawa, P. C. Canfield, and S. L. Bud'ko, Multiple ferromagnetic transitions and structural distortion in the van der waals ferromagnet VI3 at ambient and finite pressures, Phys. Rev. B 100, 094408 (2019).
  26. D. Moses, J. E. Kardontchik, R. Brener, and H. Shechter, Magnetic phase diagram of antiferromagnetic CoCl2, J. Phys. C: Solid State Phys. 13, 3903 (1980).
  27. E. W. Lee and M. A. Asgar, Magnetostriction of nickel, Proc. R. Soc. London A 326, 73 (1971).
  28. E. du Tremolet de Lacheisserie and R. Mendia Monterroso, Magnetostriction of iron, J. Magn. Magn. Mater. 31-34, 837 (1983).
  29. M. Kratochvílová, P. Dolezal, D. Hovancik, J. Pospisil, A. Bendova, M. Dusek, V. Holy, and V. Sechovsky, Crystal structure evolution in the van der Waals vanadium trihalides, J. Phys.: Condens. Matter 34, 294007 (2022).
  30. A. L. Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffr. 20, 316 (2005).
  31. B. H. Toby and R. B. V. Dreele, GSAS-II: The genesis of a modern open-source all purpose crystallography software package, J. Appl. Crystallogr. 46, 544 (2013).
  32. M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov, and H. Wondratschek, Bilbao crystallographic server I: Databases and crystallographic computing programs, Z. Kristallogr.-Cryst. Mater 221, 15 (2006).
  33. M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato, and H. Wondratschek, Bilbao crystallographic server II: Representations of crystallographic point groups and space groups, Acta Crystallogr. A 62, 115 (2006).
  34. S. Ivantchev, E. Kroumova, G. Madariaga, J. M. Pérez-Mato, and M. I. Aroyo, SUBGROUPGRAPH: A computer program for analysis of group–subgroup relations between space groups, J. Appl. Crystallogr. 33, 1190 (2000).
  35. S. Ivantchev, E. Kroumova, M. I. Aroyo, J. M. Perez-Mato, J. M. Igartua, G. Madariaga, and H. Wondratschek, SUPERGROUPS – a computer program for the determination of the supergroups of the space groups, J. Appl. Crystallogr. 35, 511 (2002).
  36. H. T. Stokes and D. M. Hatch, Group-subgroup structural phase transitions: A comparison with existing tables, Phys. Rev. B 30, 4962 (1984).
  37. Y. Gu, Y. Hao, Z. Kao, Y. Gu, F. Liu, S. Zheng, H. Cao, L. He, and J. Zhao, Lattice and magnetic structure in the van der Waals antiferromagnet VBr3, Phys. Rev. B 110, 064403 (2024).
  38. S. R. Kuindersma, C. Haas, J. P. Sanchez, and R. Al, Magnetic structures and properties of VI2, Solid State Commun. 30, 403 (1979).
  39. J. A. Schneeloch, S. Liu, P. V. Balachandran, Q. Zhang, and D. Louca, Helimagnetism in the candidate ferroelectric CrI2, Phys. Rev. B 109, 144403 (2024).
  40. J. A. Schneeloch, A. A. Aczel, and D. Louca, Helimagnetism in CrBr2 and CrIBr, Phys. Rev. B 111, 054403 (2025).
  41. S. Zhang, F. Tang, X. Song, and X. Zhang, Structural phase transitions and raman identifications of the layered van der Waals magnet CrI2, Phys. Rev. B 105, 104105 (2022).
  42. C. Stock, R. J. Birgeneau, S. Wakimoto, J. S. Gardner, W. Chen, Z.-G. Ye, and G. Shirane, Universal static and dynamic properties of the structural transition in Pb(Zn1/3Nb2/3)O3, Phys. Rev. B 69, 094104 (2004).
  43. T. Y. Koo, P. M. Gehring, G. Shirane, V. Kiryukhin, S.-G. Lee, and S.-W. Cheong, Anomalous transverse acoustic phonon broadening in the relaxor ferroelectric Pb(Mg1/3Nb2/3)0.8Ti0.2O3, Phys. Rev. B 65, 144113 (2002).
  44. C. Stock, G. Xu, P. M. Gehring, H. Luo, X. Zhao, H. Cao, J. F. Li, D. Viehland, and G. Shirane, Neutron and x-ray diffraction study of cubic [111] field-cooled PbMg1/3Nb2/3O3, Phys. Rev. B 76, 064122 (2007).
  45. F. Yao, D. Rossi, I. A. Gabrovski, V. Multian, N. Hua, K. Watanabe, T. Taniguchi, M. Gibertini, I. Gutierrez-Lezama, L. Rademaker, and A. F. Morpurgo, Moire magnetism in CrBr3 multilayers emerging from differential strain, Nat. Commun. 15, 10377 (2024).
  46. R. A. Cowley, W. J. L. Buyers, C. Stock, Z. Yamani, C. Frost, J. W. Taylor, and D. Prabhakaran, Neutron scattering investigation of the d−d excitations below the mott gap of CoO, Phys. Rev. B 88, 205117 (2013).
  47. P. M. Sarte, R. A. Cowley, E. E. Rodriguez, E. Pachoud, D. Le, V. García-Sakai, J. W. Taylor, C. D. Frost, D. Prabhakaran, C. MacEwen, A. Kitada, A. J. Browne, M. Songvilay, Z. Yamani, W. J. L. Buyers, J. P. Attfield, and C. Stock, Disentangling orbital and spin exchange interactions for Co2+ on a rocksalt lattice, Phys. Rev. B 98, 024415 (2018).
  48. P. M. Sarte, M. Songvilay, E. Pachoud, R. A. Ewings, C. D. Frost, D. Prabhakaran, K. H. Hong, A. J. Browne, Z. Yamani, J. P. Attfield, E. E. Rodriguez, S. D. Wilson, and C. Stock, Spin-orbit excitons in CoO, Phys. Rev. B 100, 075143 (2019).
  49. P. M. Sarte, C. Stock, B. R. Ortiz, K. H. Hong, and S. D. Wilson, Van Vleck excitons in Ca2RuO4, Phys. Rev. B 102, 245119 (2020).
  50. T. I. Popescu, N. Gora, F. Demmel, Z. Xu, R. Zhong, T. J. Williams, R. J. Cava, G. Xu, and C. Stock, Zeeman split Kramers doublets in spin-supersolid candidate Na2BaCo(PO4)2, Phys. Rev. Lett. 134, 136703 (2025).
  51. D. S. McClure, Electronic Spectra of Molecules and Ions in Crystals Part II. Spectra of Ions in Crystals (Academic Press, New York, 1959), pp. 399–525.
  52. A. Abragam and B. Bleany, Electron Paramagnetic Resonance of Transition Ions (Oxford University Press, Oxford, 1970).
  53. D. Hovančík, J. Pospisil, K. Carva, V. Sechovskyu, and C. Piamonteze, Large orbital magnetic moment in VI3, Nano Lett. 23, 1175 (2023).
  54. A. De Vita, T. T. P. Nguyen, R. Sant, G. M. Pierantozzi, D. Amoroso, C. Bigi, V. Polewczyk, G. Vinai, L. T. Nguyen, T. Kong, J. Fujii, I. Vobornik, N. B. Brookes, G. Rossi, R. J. Cava, F. Mazzola, K. Yamauchi, S. Picozzi, and G. Panaccione, Influence of orbital character on the ground state electronic properties in the van der Waals transition metal iodides VI3 and CrI3, Nano Lett. 22, 7034 (2022).
  55. A. De Vita, R. Sant, V. Polewczyk, G. van der Laan, N. B. Brookes, T. Kong, R. J. Cava, G. Rossi, G. Vinai, and G. Panaccione, Evidence of temperature-dependent interplay between spin and orbital moment in van der Waals ferromagnet VI3, Nano Lett. 24, 1487 (2024).
  56. X. Zhang, L. W. H. Su, X. Xia, C. Liu, B. Lyu, J. Lin, M. Huang, Y. Cheng, J. W. Mei, and J. F. Dai, Strain tunability of perpendicular magnetic anisotropy in van der Waals ferromagnets VI3, Nano Lett. 22, 9891 (2022).
  57. L. M. Sandratskii and K. Carva, Interplay of spin magnetism, orbital magnetism, and atomic structure in layered van der Waals ferromagnet VI3, Phys. Rev. B 103, 214451 (2021).
  58. Y. Hao, Y. Gu, Y. Gu, E. Feng, H. Cao, S. Chi, H. Wu, and J. Zhao, Magnetic order and its interplay with structure phase transition in van der Waals ferromagnetic VI3, Chin. Phys. Lett. 38, 096101 (2021).
  59. L. Camerano, A. O. Fumega, G. Profeta, and J. L. Lado, Multicomponent magneto-orbital order and magneto-orbitons in monolayer VCl3, Nano Lett. 25, 4825 (2025).
  60. K. Xu, S. Lei, P. Wang, W. Wang, Y. Feng, and J. Feng, Unraveling the microscopic origin of out of plane magnetic anisotropy in VI3, Chin. Chem. Lett. 36, 110257 (2025).
  61. H. Zhang, C. Xu, C. Carnahan, M. Sretenovic, N. Suri, D. Xiao, and X. Ke, Anomalous thermal hall effect in an insulating van der Waals magnet, Phys. Rev. Lett. 127, 247202 (2021).
  62. D. Hovančík, D. Repcek, F. Borodavka, C. Kadlec, K. Carva, P. Dolezal, M. Kratochvilova, P. Kuzel, S. Kamba, V. Sechovsky, and J. Pospisil, Terahertz magnetic and lattice excitations in van der Waals ferromagnet VI3, J. Phys. Chem. Lett. 13, 11095 (2022).
  63. Y. Gu, Y. Gu, F. Liu, S. Ohira-Kawamura, N. Murai, and J. Zhao, Signatures of Kitaev interactions in the van der Waals ferromagnet VI3, Phys. Rev. Lett. 132, 246702 (2024).
  64. W. Moffitt, G. Goodman, M. Fred, and B. Weinstock, The colours of transition metal hexafluorides, Mol. Phys. 2, 109 (1959).
  65. Y. Tanabe and S. Sugano, On the absorption spectra of complex ions I, J. Phys. Soc. Jpn. 9, 753 (1954).
  66. Y. Tanabe and S. Sugano, On the absorption spectra of complex ions II, J. Phys. Soc. Jpn. 9, 766 (1954).
  67. A. S. Chakravarty, On the magnetic susceptibility and anisotropy of trivalent vanadium alum under the crystalline electric field having predominantly cubic symmetry with a small trigonal symmetry, Proc. Phys. Soc. 74, 711 (1959).
  68. H. Lane, P. M. Sarte, K. Guratinder, A. M. Arevalo-Lopez, R. S. Perry, E. C. Hunter, T. Weber, B. Roessli, A. Stunault, Y. Su, R. A. Ewings, S. D. Wilson, P. Böni, J. P. Attfield, and C. Stock, Spin-orbital correlations from complex orbital order in MgV2O4, Phys. Rev. Res. 5, 043146 (2023).
  69. U. Walter, Treating crystal field parameters in lower than cubic symmetries, J. Phys. Chem. Solids 45, 401 (1984).
  70. M. T. Hutchings, Point-charge calculations of energy levels of magnetic ions in crystalline electric fields, Solid State Phys. 16, 227 (1964).
  71. W. Buyers, T. Holden, and A. Perreault, Temperature dependence of magnetic excitations in singlet-ground-state systems. II. Excited-state spin waves near the Curie temperature in Pr3Tl, Phys. Rev. B 11, 266 (1975).
  72. D. J. Brener, I. R. Mallo, H. Lane, J. A. Rodriguez-Rivera, K. Schmalzl, M. Songvilay, K. Guratinder, C. Petrovic, and C. Stock, Anisotropic excitonic magnetism from discrete C4 symmetry in CeRhIn5, Phys. Rev. B 110, 064434 (2024).
  73. H. Lane, E. E. Rodriguez, H. C. Walker, C. Niedermayer, U. Stuhr, R. I. Bewley, D. J. Voneshen, M. A. Green, J. A. Rodriguez-Rivera, P. Fouquet, S.-W. Cheong, J. P. Attfield, R. A. Ewings, and C. Stock, Metastable antiphase boundary ordering in CaFe2O4, Phys. Rev. B 104, 104404 (2021).
  74. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  75. C. Huang, F. Wu, S. Yu, P. Jena, and E. Kan, Discovery of twin orbital-order phases in ferromagnetic semiconducting VI3 monolayer, Phys. Chem. Chem. Phys. 22, 512 (2020).
  76. L. Chen, J.-H. Chung, B. Gao, T. Chen, M. B. Stone, A. I. Kolesnikov, Q. Huang, and P. Dai, Topological spin excitations in honeycomb ferromagnet CrI3, Phys. Rev. X 8, 041028 (2018).
  77. R. A. Ewings, J. R. Stewart, T. G. Perring, R. I. Bewley, M. D. Le, D. Raspino, D. E. Pooley, G. Škoro, S. P. Waller, D. Zacek, C. A. Smith, and R. C. Riehl-Shaw, Upgrade to the maps neutron time-of-flight chopper spectrometer, Rev. Sci. Instrum. 90, 035110 (2019).
  78. P. W. Anderson, Antiferromagnetism. Theory of superexchange interaction, Phys. Rev. 79, 350 (1950).
  79. J. Goodenough and A. Loeb, Theory of ionic ordering, crystal distortion, and magnetic exchange due to covalent forces in spinels, Phys. Rev. 98, 391 (1955).
  80. H. Kramers, L'interaction entre les atomes magnétogènes dans un cristal paramagnétique, Physica 1, 182 (1934).
  81. K. Tomiyasu, T. Inami, and N. Ikeda, Magnetic structure of CoO studied by neutron and synchrotron x-ray diffraction, Phys. Rev. B 70, 184411 (2004).
  82. I. V. Solovyev, R. Ono, and S. A. Nikolaev, Ferromagnetic ferroelectricity due to the Kugel-Khomskii mechanism of orbital ordering assisted by atomic Hund's second rule effects, Phys. Rev. B 110, 205116 (2024).
  83. L. Camerano, A. O. Fumega, J. L. Lado, A. Stroppa, and G. Profeta, Multiferroic nematic d-wave altermagnetism driven by orbital-order on the honeycomb lattice, 1D Mater. Appl. 9, 75 (2025).
  84. S. D. Mijin, A. M. M. Abeykoon, A. Solajic, A. Milosavljevic, J. Pesic, Y. Liu, C. Petrovic, X. V. Popovic, and N. Lazarevic, Short-range order in VI3, Inorg. Chem. 59, 16265 (2020).
  85. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yaho, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).

Outline

Information

Phys. Rev. B 113, 014439– Published 29 January, 2026
  • Received 17 September 2025
  • Accepted 22 December 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