Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4

Nature Physics volume 13, pages 157–161 (2017)Cite this article

Subjects

Abstract

Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc2S4 by directly observing the ‘spiral surface’—a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behaviour of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the J1–J2 Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc2S4, and also demonstrate a new way to realize a magnetic vortex lattice through frustrated interactions.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Spiral spin-liquid.
Figure 2: Multi-step ordering towards the helical ground state.
Figure 3: Spin structures and their magnetic field response.
Figure 4: Phase diagram of MnSc2S4 under a magnetic field along the [001] direction.

Similar content being viewed by others

References

  1. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  ADS  Google Scholar 

  2. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001).

    Article  ADS  Google Scholar 

  3. Henley, C. L. The Coulomb phase in frustrated systems. Annu. Rev. Condens. Matter Phys. 1, 179–210 (2010).

    Article  ADS  Google Scholar 

  4. Reimers, J. N., Berlinsky, A. J. & Shi, A. C. Mean-field approach to magnetic ordering in highly frustrated pyrochlores. Phys. Rev. B 43, 865–878 (1991).

    Article  ADS  Google Scholar 

  5. Tchernyshyov, O., Moessner, R. & Sondhi, S. L. Order by distortion and string modes in pyrochlore antiferromagnets. Phys. Rev. Lett. 88, 067203 (2002).

    Article  ADS  Google Scholar 

  6. Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism (Clarendon, 1991).

    Google Scholar 

  7. Cheong, S.-W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007).

    Article  ADS  Google Scholar 

  8. Mostovoy, M. Ferroelectricity in spiral magnets. Phys. Rev. Lett. 96, 067601 (2006).

    Article  ADS  Google Scholar 

  9. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotech. 8, 899–911 (2013).

    Article  ADS  Google Scholar 

  10. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    Article  ADS  Google Scholar 

  11. Kézsmárki, I. et al. Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8 . Nat. Mater. 14, 1116–1122 (2015).

    Article  ADS  Google Scholar 

  12. Tokunaga, Y. et al. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat. Commun. 6, 7638 (2015).

    Article  ADS  Google Scholar 

  13. Bergman, D., Alicea, J., Gull, E., Trebst, S. & Balents, L. Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets. Nat. Phys. 3, 487–491 (2007).

    Article  Google Scholar 

  14. Lee, S. B. & Balents, L. Theory of the ordered phase in A-site antiferromagnetic spinels. Phys. Rev. B 78, 144417 (2008).

    Article  ADS  Google Scholar 

  15. Savary, L. et al. Impurity effects in highly frustrated diamond-lattice antiferromagnets. Phys. Rev. B 84, 064438 (2011).

    Article  ADS  Google Scholar 

  16. Villain, J., Bidaux, R., Carton, J.-P. & Conte, R. Order as an effect of disorder. J. Phys. 41, 1263–1272 (1980).

    MathSciNet  Google Scholar 

  17. Henley, C. L. Ordering due to disorder in a frustrated vector antiferromagnet. Phys. Rev. Lett. 62, 2056–2059 (1989).

    Article  ADS  Google Scholar 

  18. Suzuki, T., Nagai, H., Nohara, M. & Takagi, H. Melting of antiferromagnetic ordering in spinel oxide CoAl2O4 . J. Phys. Condens. Matter 19, 145265 (2007).

    Article  ADS  Google Scholar 

  19. Tristan, N. et al. Geometric frustration in the cubic spinels MAl2O4 (M = Co, Fe, and Mn). Phys. Rev. B 72, 174404 (2005).

    Article  ADS  Google Scholar 

  20. Krimmel, A., Mutka, H., Koza, M. M., Tsurkan, V. & Loidl, A. Spin excitations in frustrated A-site spinels investigated with inelastic neutron scattering. Phys. Rev. B 79, 134406 (2009).

    Article  ADS  Google Scholar 

  21. Zaharko, O. et al. Spin liquid in a single crystal of the frustrated diamond lattice antiferromagnet CoAl2O4 . Phys. Rev. B 84, 094403 (2011).

    Article  ADS  Google Scholar 

  22. MacDougall, G. J. et al. Kinetically inhibited order in a diamond-lattice antiferromagnet. Proc. Natl Acad. Sci. USA 108, 15693–15698 (2011).

    Article  ADS  Google Scholar 

  23. Nair, H. S., Fu, Z., Voigt, J., Su, Y. X. & Brückel, Th. Approaching the true ground state of frustrated A-site spinels: a combined magnetization and polarized neutron scattering study. Phys. Rev. B 89, 174431 (2014).

    Article  ADS  Google Scholar 

  24. Fritsch, V. et al. Spin and orbital frustration in MnSc2S4 and FeSc2S4 . Phys. Rev. Lett. 92, 116401 (2004).

    Article  ADS  Google Scholar 

  25. Chen, G., Balents, L. & Schnyder, A. P. Spin-orbital singlet and quantum critical point on the diamond lattice: FeSc2S4 . Phys. Rev. Lett. 102, 096406 (2009).

    Article  ADS  Google Scholar 

  26. Krimmel, A. et al. Magnetic ordering and spin excitations in the frustrated magnet MnSc2S4 . Phys. Rev. B 73, 014413 (2006).

    Article  ADS  Google Scholar 

  27. Mücksch, M. et al. Multi-step magnetic ordering in frustrated thiospinel MnSc2S4 . J. Phys. Condens. Matter 19, 145262 (2007).

    Article  ADS  Google Scholar 

  28. Giri, S., Nakamura, H. & Kohara, T. Classical antiferromagnetism in MnSc2S4: a 45Sc NMR study. Phys. Rev. B 72, 132404 (2005).

    Article  ADS  Google Scholar 

  29. Büttgen, N., Zymara, A., Kegler, C., Tsurkan, V. & Loidl, A. Spin and orbital frustration in FeSc2S4 probed by 45Sc NMR. Phys. Rev. B 73, 132409 (2006).

    Article  ADS  Google Scholar 

  30. Kalvius, G. M. et al. A μSR magnetic study of frustrated FeSc2S4 and MnSc2S4 . Physica B 378–380, 592–593 (2006).

    Article  ADS  Google Scholar 

  31. Batista, C. D., Lin, S.-Z., Hayami, S. & Kamiya, Y. Frustration and chiral orderings in correlated electron systems. Rep. Prog. Phys. 79, 084504 (2016).

    Article  ADS  Google Scholar 

  32. Kamiya, Y. & Batista, C. D. Magnetic vortex crystals in frustrated Mott insulator. Phys. Rev. X 4, 011023 (2014).

    Google Scholar 

  33. Wang, Z., Kamiya, Y., Nevidomskyy, A. H. & Batista, C. D. Three-dimensional crystallization of vortex strings in frustrated quantum magnets. Phys. Rev. Lett. 115, 107201 (2015).

    Article  ADS  Google Scholar 

  34. Okubo, T., Chung, S. & Kawamura, H. Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields. Phys. Rev. Lett. 108, 017206 (2012).

    Article  ADS  Google Scholar 

  35. Leonov, A. O. & Mostovoy, M. Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet. Nat. Commun. 6, 8275 (2015).

    Article  ADS  Google Scholar 

  36. Hayami, S., Lin, S.-Z. & Batista, C. D. Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy. Phys. Rev. B 93, 184413 (2016).

    Article  ADS  Google Scholar 

  37. Reimers, J. N. Diffuse-magnetic-scattering calculations for frustrated antiferromagnets. Phys. Rev. B 46, 193–202 (1992).

    Article  ADS  Google Scholar 

  38. Fennell, T. et al. Magnetic Coulomb phase in the spin ice Ho2Ti2O7 . Science 326, 415–417 (2009).

    Article  ADS  Google Scholar 

  39. Brown, P. J. in Neutron Scattering from Magnetic Materials (ed. Chatterji, T.) (Elsevier, 2006).

    Google Scholar 

  40. Mochizuki, M. & Furukawa, N. Microscopic model and phase diagrams of the multiferroic perovskite manganites. Phys. Rev. B 80, 134416 (2009).

    Article  ADS  Google Scholar 

  41. Mulder, A., Ganesh, R., Capriotti, L. & Paramekanti, A. Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice. Phys. Rev. B 81, 214419 (2010).

    Article  ADS  Google Scholar 

  42. Rodrguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (1993).

    Article  ADS  Google Scholar 

  43. Bauer, B. et al. The ALPS project release 2.0: open source software for strongly correlated systems. J. Stat. Mech. Theory Exp. 2011, P05001 (2011).

    Google Scholar 

Download references

Acknowledgements

We acknowledge helpful discussions with L. Balents, B. Normand, J. H. Chen, A. Scaramucci, A. Cervellino, S. Tóth, S. Ward and M. Ruminy. Our neutron scattering experiments were performed at the Swiss Spallation Neutron Source SINQ, Paul Scherrer Institut, Villigen, Switzerland, the Heinz Maier-Leibnitz Zentrum MLZ, Garching, Germany, and the Institut Laue-Langevin ILL, Grenoble, France. The magnetization measurements were carried out in the Laboratory for Scientific Developments and Novel Materials, Paul Scherrer Institut, Villigen, Switzerland. This work was supported by the Swiss National Science Foundation under Grants Nos 200021-140862 and 200020-162626, and the SCOPES project No. IZ73Z0-152734/1. Our work was additionally supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) through a CRG-grant and via the Deutsche Forschungsgemeinschaft by the Transregional Collaborative Research Center TRR 80.

Author information

Authors and Affiliations

  1. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland

    Shang Gao, Oksana Zaharko, Jonathan S. White, Gregory S. Tucker, Bertrand Roessli, Romain Sibille, Tom Fennell & Christian Rüegg

  2. Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland

    Shang Gao & Christian Rüegg

  3. Experimental Physics V, University of Augsburg, D-86135 Augsburg, Germany

    Vladimir Tsurkan & Alois Loidl

  4. Institute of Applied Physics, Academy of Sciences of Moldova, MD-2028 Chisinau, Republic of Moldova

    Vladimir Tsurkan

  5. Jülich Center for Neutron Science JCNS-MLZ, Forshungszentrum Jülich GmbH, Outstation at MLZ, D-85747 Garching, Germany

    Yixi Su

  6. Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

    Gregory S. Tucker

  7. CEA et Université Grenoble Alpes, INAC-MEM-MDN, F-38000 Grenoble, France

    Frederic Bourdarot

  8. Laboratory for Scientific Developments and Novel Materials, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland

    Romain Sibille

  9. Swiss-Norwegian Beamlines at the European Synchrotron Radiation Facility, F-38000 Grenoble, France

    Dmitry Chernyshov

Authors
  1. Shang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oksana Zaharko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Tsurkan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yixi Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jonathan S. White
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Gregory S. Tucker
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Bertrand Roessli
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Frederic Bourdarot
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Romain Sibille
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Dmitry Chernyshov
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Tom Fennell
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Alois Loidl
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Christian Rüegg
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

O.Z. and C.R. designed and supervised the project. V.T. prepared the single crystals. S.G. and O.Z. performed the experiments with Y.S. as the local contact for DNS, J.S.W. and G.S.T. for TASP, B.R. for MuPAD, F.B. for CRYOPAD, D.C. for SNBL, and R.S. for the SQUID measurements. S.G. and O.Z. performed the calculations and analysed the data. The manuscript was written by S.G., O.Z., T.F. and C.R., with input from all co-authors.

Corresponding author

Correspondence to Oksana Zaharko.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 848 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, S., Zaharko, O., Tsurkan, V. et al. Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4. Nature Phys 13, 157–161 (2017). https://doi.org/10.1038/nphys3914

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3914

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing