Abstract

Electronic systems with flat bands are predicted to be a fertile ground for hosting emergent phenomena including unconventional magnetism and superconductivity1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, but materials that manifest this feature are rare. Here, we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2 (refs. 16,17,18,19,20). We observe a pronounced peak at the Fermi level, which we identify as arising from the kinetically frustrated kagome flat band. On increasing the magnetic field up to ±8 T, this state exhibits an anomalous magnetization-polarized many-body Zeeman shift, dominated by an orbital moment that is opposite to the field direction. Such negative magnetism is induced by spin–orbit-coupling quantum phase effects21,22,23,24,25 tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of a kagome magnet where the low-energy physics can be dominated by the spin–orbit-coupled flat band.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Additional information

Journal peer review information: Nature Physics thanks Oleg Yazyev and other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

  1. 1.

    Soumyanarayanan, A., Reyren, N., Fert, A. & Panagopoulos, C. Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces. Nature 539, 509–517 (2016).

  2. 2.

    Wang, J. & Zhang, S.-C. Topological states of condensed matter. Nat. Mater. 16, 1062–1067 (2017).

  3. 3.

    Hasan, M. Z., Xu, S.-Y. & Bian, G. Topological insulators, topological superconductors and Weyl fermion semimetals. Phys. Scr. T164, 014001 (2015).

  4. 4.

    Hasan, M. Z., Xu, S.-Y., Belopolski, I. & Huang, S.-M. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8, 289–309 (2017).

  5. 5.

    Sachdev, S. Topological order, emergent gauge fields, and Fermi surface reconstruction. Rep. Prog. Phys. 82, 014001 (2019).

  6. 6.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

  7. 7.

    Yin, J.-X. et al. Giant and anisotropic spin–orbit tunability in a strongly correlated kagome magnet. Nature 562, 91–95 (2018).

  8. 8.

    Belopolski, I. et al. Topological Weyl lines and drumhead surface states in a room-temperature magnet. Preprint at https://arxiv.org/abs/1712.09992 (2017).

  9. 9.

    Si, Q. & Steglich, F. Heavy fermions and quantum phase transitions. Science 329, 1161–1166 (2010).

  10. 10.

    Mielke, A. Exact ground states for the Hubbard model on the Kagome lattice. J. Phys. Rev. Lett. 69, 1608 (1992).

  11. 11.

    Wu, C., Bergan, D., Balents, L. & Sarma, S. D. Flat bands and Wigner crystallization in the honeycomb optical lattice. Phys. Rev. Lett. 99, 070401 (2007).

  12. 12.

    Leykam, D., Andreanov, A. & Flach, S. Artificial flat band systems: from lattice models to experiments. Adv. Phys. X 3, 1473052 (2018).

  13. 13.

    Tang, E., Mei, J. W. & Wen, X. G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).

  14. 14.

    Sun, K. et al. Nearly flat bands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

  15. 15.

    Neupert, T. et al. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

  16. 16.

    Vaqueiro, P. & Sobany, G. G. A powder neutron diffraction study of the metallic ferromagnet Co3Sn2S2. Solid State Sci. 11, 513–518 (2009).

  17. 17.

    Dedkov, Y. S., Holder, M., Molodtsov, S. L. & Rosner, H. Electronic structure of shandite Co3Sn2S2. J. Phys. Conf. Ser. 100, 072011 (2008).

  18. 18.

    Schnelle, W. et al. Ferromagnetic ordering and half-metallic state of Sn2Co3S2 with the Shandite-type structure. Phys. Rev. B 88, 144404 (2013).

  19. 19.

    Wang, Qi et al. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions. Nat. Commun. 9, 3681 (2018).

  20. 20.

    Liu, E. et al. Giant anomalous Hall angle in a half-metallic magnetic Weyl semimetal. Nat. Phys. 14, 1125–1131 (2018).

  21. 21.

    Karplus, R. & Luttinger, J. M. Hall effect in ferromagnetics. Phys. Rev. 95, 1154–1160 (1954).

  22. 22.

    Xiao, D., Chang, M. C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).

  23. 23.

    Resta, R. Electrical polarization and orbital magnetization: the modern theories. J. Phys. Condens. Matter 22, 123201 (2010).

  24. 24.

    Thonhauser, T. Theory of orbital magnetization in solids. Int. J. Mod. Phys. B 25, 1429 (2011).

  25. 25.

    Vanderbilt, D. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge University Press, Cambridge, 2018).

  26. 26.

    Fischer, Ø. et al. Scanning tunneling spectroscopy of high-temperature superconductors. Rev. Mod. Phys. 79, 353 (2007).

  27. 27.

    Ternes, M., Heinrich, Andreas., J. & Schneider, W.-D. Spectroscopic manifestations of the Kondo effect on single adatoms. J. Phys. Condens. Matter 21, 053001 (2009).

  28. 28.

    Nayak, A. K. et al. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2, e1501870 (2016).

  29. 29.

    Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090–1095 (2017).

  30. 30.

    Aivazian, G. et al. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys. 11, 148–152 (2015).

Download references

Acknowledgements

STM experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547/M.Z.H.). ARPES characterization of the sample is supported by the United States Department of Energy (US DOE) under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02–05ER46200). Work at Renmin University was supported by the Ministry of Science and Technology of China (2016YFA0300504), the National Natural Science Foundation of China (nos. 11574394, 11774423 and 11822412), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (15XNLF06, 15XNLQ07 and 18XNLG14). S.S.T. and T.N. acknowledge support from the European Union’s Horizon 2020 research and innovation programme (ERC-StG-Neupert-757867-PARATOP). Z.W. and K.J. acknowledge US DOE grant DE-FG02–99ER45747. We also acknowledge the Natural Science Foundation of China (grant nos. 11790313 and 11774007), the Key Research Program of the Chinese Academy of Sciences (grant no. XDPB08-1), the National Key R&D Program of China (grant nos. 2016YFA0300403 and 2018YFA035601), the Princeton Center for Theoretical Science and the Princeton Institute for the Science and Technology of Materials Imaging and Analysis Center at Princeton University. Muon spin rotation (µSR) experiments were performed at the πE3 beamline of the Paul Scherrer Institute, using the HAL-9500 µSR spectrometer. Z.G. acknowledges R. Scheuermann for support in the µSR experiments. M.Z.H. acknowledges support from Lawrence Berkeley National Laboratory and the Miller Institute of Basic Research in Science at the University of California, Berkeley in the form of a Visiting Miller Professorship.

Author information

Author notes

  1. These authors contributed equally: Jia-Xin Yin, Songtian S. Zhang, Guoqing Chang.

Affiliations

  1. Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, NJ, USA

    • Jia-Xin Yin
    • , Songtian S. Zhang
    • , Guoqing Chang
    • , Zurab Guguchia
    • , Ilya Belopolski
    • , Nana Shumiya
    • , Daniel Multer
    • , Maksim Litskevich
    • , Tyler A. Cochran
    •  & M. Zahid Hasan
  2. Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, China

    • Qi Wang
    •  & Hechang Lei
  3. Department of Physics, University of Zurich, Zurich, Switzerland

    • Stepan S. Tsirkin
    •  & Titus Neupert
  4. Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, Villigen PSI, Switzerland

    • Zurab Guguchia
  5. Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA

    • Biao Lian
  6. International Center for Quantum Materials and School of Physics, Peking University, Beijing, China

    • Huibin Zhou
    •  & Shuang Jia
  7. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China

    • Huibin Zhou
    •  & Shuang Jia
  8. Department of Physics, Boston College, Chestnut Hill, MA, USA

    • Kun Jiang
    •  & Ziqiang Wang
  9. Institute of Physics, Academia Sinica, Taipei, Taiwan

    • Hsin Lin
  10. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    • M. Zahid Hasan
  11. Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ, USA

    • M. Zahid Hasan

Authors

  1. Search for Jia-Xin Yin in:

  2. Search for Songtian S. Zhang in:

  3. Search for Guoqing Chang in:

  4. Search for Qi Wang in:

  5. Search for Stepan S. Tsirkin in:

  6. Search for Zurab Guguchia in:

  7. Search for Biao Lian in:

  8. Search for Huibin Zhou in:

  9. Search for Kun Jiang in:

  10. Search for Ilya Belopolski in:

  11. Search for Nana Shumiya in:

  12. Search for Daniel Multer in:

  13. Search for Maksim Litskevich in:

  14. Search for Tyler A. Cochran in:

  15. Search for Hsin Lin in:

  16. Search for Ziqiang Wang in:

  17. Search for Titus Neupert in:

  18. Search for Shuang Jia in:

  19. Search for Hechang Lei in:

  20. Search for M. Zahid Hasan in:

Contributions

J.-X.Y. and S.S.Z. conducted the STM and STS experiments in consultation with M.Z.H.; Q.W., H.Lei, H.Z. and S.J. synthesized and characterized the sequence of samples; Z.G. performed µSR measurements in consultation with M.Z.H.; G.C., T.N., S.S.T., B.L., K.J., H.Lin and Z.W. carried out theoretical analysis in consultation with J.-X.Y. and M.Z.H.; I.B., N.S., D.M., M.L. and T.A.C. contributed to sample characterization and instrument calibration; J.-X.Y., S.S.Z. and M.Z.H. performed the data analysis and figure development and wrote the paper with contributions from all authors; M.Z.H. supervised the project. All authors discussed the results, interpretation and conclusion.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to M. Zahid Hasan.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–7, additional theoretical details and Supplementary References 31–35.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/s41567-019-0426-7

Further reading