- 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
  • Open Access

Noncollinear spin order, field-induced transitions, and short-range correlations in Cu4SO4(OH)6

Oleksandr Prokhnenko1, Koji Kaneko2,3, Chihiro Tabata2,3, Mitsuru Akaki4, Chanhyeon Lee4, Takayoshi Yamanaka4, Hironori Sakai3, Yusuke Hirose2,3, Alsu Gazizulina1 et al.

Yoshifumi Tokiwa3, Yoshinori Haga3, Motoi Kimata3, Masaki Fujita4, Hiroyuki Nojiri4, Lawrence M. Anovitz5, and Andrey Podlesnyak6

PDF

Phys. Rev. B 114, 014414 – Published 10 July, 2026

DOI: https://doi.org/10.1103/l362-1h1r

Abstract

We report a comprehensive study of spin-12 quantum magnet brochantite, Cu4SO4(OH)6, combining high-field thermodynamic measurements, polarized neutron diffraction, inelastic neutron scattering, and nuclear magnetic resonance spectroscopy. Using bulk magnetization and specific heat measurements we construct the magnetic H−T phase diagram for magnetic fields applied along main crystallographic directions up to 24.1 T. Polarized neutron diffraction reveals a noncollinear magnetic ground state confined to the ab plane. A field-induced transition is observed for magnetic fields in the ab plane whose critical field and character evolve continuously with field direction in the ab plane. While the transition for H∥b might be a spin-flop-like transition, the one for H∥a resembles the short-range correlated state above TN, suggesting a magnetic configuration related to the quasi-two-dimensional correlations in the bc planes. The experimental results demonstrate that the ground-state and field-induced phases cannot be explained by a simple XXZ model with a single dominant exchange interaction and that weaker interchain and anisotropic interactions have to be taken into account. Our work establishes brochantite as a low-symmetry Cu-based quantum magnet with noncollinear order and complex field-induced behavior.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (49)

  1. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  2. M. Hermanns, I. Kimchi, and J. Knolle, Physics of the Kitaev model: Fractionalization, dynamic correlations, and material connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018).
  3. D. A. Tennant, R. A. Cowley, S. E. Nagler, and A. M. Tsvelik, Measurement of the spin-excitation continuum in one-dimensional KCuF3 using neutron scattering, Phys. Rev. B 52, 13368 (1995).
  4. M. Mourigal, M. Enderle, A. Klöpperpieper, J.-S. Caux, A. Stunault, and H. M. Rønnow, Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain, Nat. Phys. 9, 435 (2013).
  5. B. Lake, A. M. Tsvelik, S. Notbohm, D. Alan Tennant, T. G. Perring, M. Reehuis, C. Sekar, G. Krabbes, and B. Büchner, Confinement of fractional quantum number particles in a condensed-matter system, Nat. Phys. 6, 50 (2010).
  6. C. Rüegg, N. Cavadini, A. Furrer, H.-U. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3, Nature (London) 423, 62 (2003).
  7. T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Bose–Einstein condensation in magnetic insulators, Nat. Phys. 4, 198 (2008).
  8. M. Takigawa and F. Mila, Magnetization plateaus, in Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer, Berlin, 2010), pp. 241–267.
  9. A. Barman, G. Gubbiotti, S. Ladak, A. O. Adeyeye, M. Krawczyk, J. Gräfe, C. Adelmann, S. Cotofana, A. Naeemi, V. I. Vasyuchka, et al., The 2021 magnonics roadmap, J. Phys.: Condens. Matter 33, 413001 (2021).
  10. P. Pirro, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Adva- nces in coherent magnonics, Nat. Rev. Mater. 6, 1114 (2021).
  11. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  12. Y. Tokura, M. Kawasaki, and N. Nagaosa, Emergent functions of quantum materials, Nat. Phys. 13, 1056 (2017).
  13. I. Buluta and F. Nori, Quantum simulators, Science 326, 108 (2009).
  14. Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Coherent coupling between a ferromagnetic magnon and a superconducting qubit, Science 349, 405 (2015).
  15. A. Chiesa, E. Macaluso, F. Petiziol, S. Wimberger, P. Santini, and S. Carretta, Molecular nanomagnets as qubits with embedded quantum-error correction, J. Phys. Chem. Lett. 11, 8610 (2020).
  16. S. Vilminot, M. Richard-Plouet, G. André, D. Swierczynski, F. Bourée-Vigneron, and M. Kurmoo, Nuclear and magnetic structures and magnetic properties of synthetic brochantite, Cu4(OH)6SO4, Dalton Trans. 1455 (2006).
  17. V. A. Ginga, B. Shen, E. Uykur, N. Giordano, P. Gegenwart, and A. A. Tsirlin, Pressure-tuned spin chains in brochantite, cu4so4(OH)6, Phys. Rev. Mater. 9, 094412 (2025).
  18. Y. Li, B. Pan, S. Li, W. Tong, L. Ling, Z. Yang, J. Wang, Z. Chen, Z. Wu, and Q. Zhang, Gapless quantum spin liquid in the S = 1/2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4, New J. Phys. 16, 093011 (2014).
  19. M. Gomilšek, M. Klanjšek, M. Pregelj, F. C. Coomer, H. Luetkens, O. Zaharko, T. Fennell, Y. Li, Q. M. Zhang, and A. Zorko, Instabilities of spin-liquid states in a quantum kagome antiferromagnet, Phys. Rev. B 93, 060405(R) (2016).
  20. M. Gomilšek, M. Klanjšek, R. Žitko, M. Pregelj, F. Bert, P. Mendels, Y. Li, Q. M. Zhang, and A. Zorko, Field-induced instability of a gapless spin liquid with a spinon Fermi surface, Phys. Rev. Lett. 119, 137205 (2017).
  21. R. A. Gallardo, P. Alvarado-Seguel, T. Schneider, C. Gonzalez-Fuentes, A. Roldán-Molina, K. Lenz, J. Lindner, and P. Landeros, Spin-wave non-reciprocity in magnetization-graded ferromagnetic films, New J. Phys. 21, 033026 (2019).
  22. G. Gitgeatpong, Y. Zhao, P. Piyawongwatthana, Y. Qiu, L. W. Harriger, N. P. Butch, T. J. Sato, and K. Matan, Nonreciprocal magnons and symmetry-breaking in the noncentrosymmetric antiferromagnet, Phys. Rev. Lett. 119, 047201 (2017).
  23. M. Helliwell and J. V. Smith, Brochantite, Acta Crys. C 53, 1369 (1997).
  24. S. Merlino, N. Perchiazzi, and D. Franco, Brochantite, Cu4SO4(OH)6: OD character, polytypism and crystal structures, Eur. J. Mineral. 15, 267 (2003).
  25. S. E. Nikitin, T. Xie, A. Gazizulina, B. Ouladdiaf, J. A. R. Velamazán, I. F. Díaz-Ortega, H. Nojiri, L. M. Anovitz, A. M. dos Santos, O. Prokhnenko, and A. Podlesnyak, Helical spin dynamics in commensurate magnets: A study on brochantite, Cu4SO4(OH)6, Phys. Rev. Res. 5, 033111 (2023).
  26. S. E. Nikitin, T. Xie, A. Gazizulina, B. Ouladdiaf, J. A. Rodriguez Velamazán, I. F. Díaz-Ortega, H. Nojiri, L. M. Anovitz, A. M. d. Santos, O. Prokhnenko, and A. Podlesnyak, Erratum: Helical spin dynamics in commensurate magnets: A study on brochantite, Cu4SO4(OH)6 [Phys. Rev. Res. 5, 033111 (2023)], Phys. Rev. Res. 6, 039001(E) (2024).
  27. A. M. Chakkingal, C. Fuller, M. Avdeev, R. Gumeniuk, K. K. Parui, M. C. Rahn, F. Pabst, Y. Wang, S. Granovsky, A. Korshunov, D. Chernyshov, D. S. Inosov, and D. C. Peets, Stacking disorder in novel ABAC-stacked brochantite, Cu4SO4(OH)6, Phys. Rev. Mater. 9, 054407 (2025).
  28. M. R. Bissengaliyeva, N. S. Bekturganov, D. B. Gogol, S. T. Taimassova, T. A. Koketai, and M. A. Bespyatov, Heat capacities of natural antlerite and brochantite at low temperature, J. Chem. Eng. Data 58, 2904 (2013).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/l362-1h1r for a brief description of sample characterization, magnetic structure refinement, and additional polarized neutron data.
  30. M. Kimata, T. Moriyama, K. Oda, and T. Ono, Distinct domain reversal mechanisms in epitaxial and polycrystalline antiferromagnetic NiO films from high-field spin Hall magnetoresistance, Appl. Phys. Lett. 116, 192402 (2020).
  31. O. Tanaka, Y. Mizukami, R. Harasawa, K. Hashimoto, K. Hwang, N. Kurita, H. Tanaka, S. Fujimoto, Y. Matsuda, E.-G. Moon, and T. Shibauchi, Thermodynamic evidence for a field-angle-dependent Majorana gap in a Kitaev spin liquid, Nat. Phys. 18, 429 (2022).
  32. K. Kaneko, C. Tabata, M. Hagihala, H. Yamauchi, Y. Oba, T. Kumada, M. Kubota, Y. Kojima, N. Nabatame, M. Sasaki, Y. Shimojo, K. Kodama, and T. Osakabe, New standard for low temperature sample environment at JAEA/JRR-3, JPS Conf. Proc. 41, 011015 (2024).
  33. G. Ehlers, A. Podlesnyak, J. L. Niedziela, E. B. Iverson, and P. E. Sokol, The new cold neutron chopper spectrometer at the spallation neutron source: Design and performance, Rev. Sci. Instrum. 82, 085108 (2011).
  34. G. Ehlers, A. Podlesnyak, and A. I. Kolesnikov, The cold neutron chopper spectrometer at the spallation neutron source: A review of the first 8 years of operation, Rev. Sci. Instrum. 87, 093902 (2016).
  35. O. Arnold, J. C. Bilheux, J. M. Borreguero, A. Buts, S. I. Campbell, L. Chapon, M. Doucet, N. Draper, R. F. Leal, M. A. Gigg, et al., Mantid–data analysis and visualization package for neutron scattering and µSR experiments, Nucl. Instrum. Methods Phys. Res. Sect. A 764, 156 (2014).
  36. J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Phys. B (Amsterdam) 192, 55 (1993).
  37. K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Cryst. 44, 1272 (2011).
  38. A. T. Boothroyd, Principles of Neutron Scattering from Condensed Matter (Oxford University Press, Oxford, 2020).
  39. B. Fauqué, Y. Sidis, V. Hinkov, S. Pailhès, C. T. Lin, X. Chaud, and P. Bourges, Magnetic order in the pseudogap phase of high-TC superconductors, Phys. Rev. Lett. 96, 197001 (2006).
  40. T. P. Croft, E. Blackburn, J. Kulda, R. Liang, D. A. Bonn, W. N. Hardy, and S. M. Hayden, No evidence for orbital loop currents in charge-ordered YBa2Cu3O6+x from polarized neutron diffraction, Phys. Rev. B 96, 214504 (2017).
  41. M. Kenzelmann, A. Zheludev, S. Raymond, E. Ressouche, T. Masuda, P. Böni, K. Kakurai, I. Tsukada, K. Uchinokura, and R. Coldea, Spin waves and magnetic ordering in the quasi-one-dimensional S=12 antiferromagnet BaCu2Si2O7, Phys. Rev. B 64, 054422 (2001).
  42. J. B. Forsyth, P. J. Brown, and B. M. Wanklyn, Magnetism in cupric oxide, J. Phys. C: Solid State Phys. 21, 2917 (1988).
  43. T. Freltoft, G. Shirane, S. Mitsuda, J. P. Remeika, and A. S. Cooper, Magnetic form factor of Cu in La2CuO4, Phys. Rev. B 37, 137 (1988).
  44. O. Zaharko, H. M. Ronnow, A. Daoud-Aladine, S. Streule, F. Juranyi, J. Mesot, H. Berger, and P. J. Brown, Incommensurate magnetism in the coupled spin tetrahedra system Cu2Te2O5Cl2, Low Temp. Phys. 31, 814 (2005).
  45. B. Pato-Doldán, L. C. Gómez-Aguirre, A. P. Hansen, J. Mira, S. Castro-García, M. Sánchez-Andújar, M. A. Señarís-Rodríguez, V. S. Zapf, and J. Singleton, Magnetic transitions and isotropic versus anisotropic magnetic behaviour of [CH3NH3][M(HCOO)3]M=Mn2+, Co2+, Ni2+, Cu2+ metal–organic perovskites, J. Mater. Chem. C 4, 11164 (2016).
  46. O. Prokhnenko, G. Marmorini, S. E. Nikitin, D. Yamamoto, A. Gazizulina, M. Bartkowiak, A. N. Ponomaryov, S. A. Zvyagin, H. Nojiri, I. F. Díaz-Ortega, L. M. Anovitz, A. I. Kolesnikov, and A. Podlesnyak, High-field spin-flop state in green dioptase, Phys. Rev. B 103, 014427 (2021).
  47. Z. Seidov, T. P. Gavrilova, R. M. Eremina, L. E. Svistov, A. A. Bush, A. Loidl, and H.-A. Krug von Nidda, Anisotropic exchange in LiCu2O2, Phys. Rev. B 95, 224411 (2017).
  48. K. Tanaka, K. Hirota, S. Nitta, and K. Motizuki, Anisotropy of g-factor and magnetic anisotropy energy of antiferromagnetic Li2CuO2, in Electronic Properties of Transition Metal Compounds, edited by K. Motizuki et al. (CRC Press, Boca Raton, FL, 2020), pp. 1–15.
  49. H.-A. Krug von Nidda, L. E. Svistov, M. V. Eremin, R. M. Eremina, A. Loidl, V. Kataev, A. Validov, A. Prokofiev, and W. Aßmus, Anisotropic exchange in LiCuVO4 probed by ESR, Phys. Rev. B 65, 134445 (2002).

Outline

Information

Phys. Rev. B 114, 014414– Published 10 July, 2026
  • Received 16 February 2026
  • Revised 23 April 2026
  • Accepted 12 June 2026
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