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Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet

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.

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Fig. 1: Atomic-scale visualization of the cleavage surface of Co3Sn2S2.
Fig. 2: Observation of a sharp peak around the Fermi energy.
Fig. 3: Magnetic kagome flat band nature of the density-of-state peak.
Fig. 4: Negative orbital magnetism of the flat band peak.

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.

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).

    Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 3.

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  5. 5.

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

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  10. 10.

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

    Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  12. 12.

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

    Google Scholar 

  13. 13.

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

    ADS  Article  Google Scholar 

  14. 14.

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

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 17.

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

    Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  20. 20.

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

    Article  Google Scholar 

  21. 21.

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

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

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

    ADS  Article  Google Scholar 

  24. 24.

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  29. 29.

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

    ADS  Article  Google Scholar 

  30. 30.

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

    Article  Google Scholar 

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.

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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.

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Correspondence to M. Zahid Hasan.

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

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Supplementary information

Supplementary Information

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

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Yin, JX., Zhang, S.S., Chang, G. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019). https://doi.org/10.1038/s41567-019-0426-7

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