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# Magnetism and charge density wave order in kagome FeGe

## Abstract

Electron correlations often lead to emergent orders in quantum materials, and one example is the kagome lattice materials where topological states exist in the presence of strong correlations between electrons. This arises from the features of the electronic band structure that are associated with the kagome lattice geometry: flat bands induced by destructive interference of the electronic wavefunctions, topological Dirac crossings and a pair of van Hove singularities. Various correlated electronic phases have been discovered in kagome lattice materials, including magnetism, charge density waves, nematicity and superconductivity. Recently, a charge density wave was discovered in the magnetic kagome FeGe, providing a platform for understanding the interplay between charge order and magnetism in kagome materials. Here we observe all three electronic signatures of the kagome lattice in FeGe using angle-resolved photoemission spectroscopy. The presence of van Hove singularities near the Fermi level is driven by the underlying magnetic exchange splitting. Furthermore, we show spectral evidence for the charge density wave as gaps near the Fermi level. Our observations point to the magnetic interaction-driven band modification resulting in the formation of the charge density wave and indicate an intertwined connection between the emergent magnetism and charge order in this moderately correlated kagome metal.

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## Data availability

Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding authors upon reasonable request.

## Code availability

The band structure and phonon calculations used in this study are available from the corresponding authors upon reasonable request.

## References

1. Paschen, S. & Si, Q. Quantum phases driven by strong correlations. Nat. Rev. Phys. 3, 9–26 (2021).

2. Keimer, B. et al. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

3. Fernandes, R. M. et al. Iron pnictides and chalcogenides: a new paradigm for superconductivity. Nature 601, 35–44 (2022).

4. Yi, M., Zhang, Y., Shen, Z.-X. & Lu, D. Role of the orbital degree of freedom in iron-based superconductors. npj Quantum Mater. 2, 57 (2017).

5. Mielke, A. Ferromagnetic ground states for the Hubbard model on line graphs. J. Phys. A 24, L73 (1991).

6. Kiesel, M. L., Platt, C. & Thomale, R. Unconventional Fermi surface instabilities in the kagome Hubbard model. Phys. Rev. Lett. 110, 126405 (2013).

7. Lin, Z. et al. Flatbands and emergent ferromagnetic ordering in Fe3Sn2 kagome lattices. Phys. Rev. Lett. 121, 096401 (2018).

8. Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).

9. Kang, M. et al. Dirac fermions and flat bands in the ideal kagome metal FeSn. Nat. Mater. 19, 163–169 (2020).

10. Xie, Y. et al. Spin excitations in metallic kagome lattice FeSn and CoSn. Commun. Phys. 4, 240 (2021).

11. Yin, J.-X. et al. Quantum-limit Chern topological magnetism in TbMn6Sn6. Nature 583, 533–536 (2020).

12. Li, M. et al. Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6. Nat. Commun. 12, 3129 (2021).

13. Morali, Noam et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).

14. Liu, D. F. et al. Magnetic Weyl semimetal phase in a kagomé crystal. Science 365, 1282–1285 (2019).

15. Wang, Q. et al. Field-induced topological Hall effect and double-fan spin structure with a c-axis component in the metallic kagome antiferromagnetic compound YMn6Sn6. Phys. Rev. B 103, 014416 (2021).

16. Yin, J.-X. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019).

17. Ortiz, B. R. et al. CsV3Sb5: a Z2 topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).

18. Zhao, H. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021).

19. Chen, Hui et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).

20. Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

21. Jiang, Y.-X. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).

22. Mielke, C. et al. Time-reversal symmetry-breaking charge order in a correlated kagome superconductor. Nature 602, 245–250 (2022).

23. Feng, X., Jiang, K., Wang, Z. & Hu, J. Chiral flux phase in the Kagome superconductor AV3Sb5. Sci. Bull. 66, 1384–1388 (2021).

24. Denner, M. M., Thomale, R. & Neupert, T. Analysis of charge order in the kagome metal AV3Sb5 (A = K, Rb, Cs). Phys. Rev. Lett. 127, 217601 (2021).

25. Lin, Y.-P. & Nandkishore, R. M. Complex charge density waves at van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A = K, Rb, Cs). Phys. Rev. B 104, 045122 (2021).

26. Park, T., Ye, M. & Balents, L. Electronic instabilities of kagome metals: saddle points and Landau theory. Phys. Rev. B 104, 035142 (2021).

27. Tan, H. et al. Charge density waves and electronic properties of superconducting kagome metals. Phys. Rev. Lett. 127, 046401 (2021).

28. Setty, C., Hu, H. Chen, L. & Si, Q. Electron correlations and T-breaking density wave order in a Z2 kagome metal. Preprint at https://arxiv.org/abs/2105.15204 (2021).

29. Sales, B. C. et al. Tuning the flat bands of the kagome metal CoSn with Fe, In, or Ni doping. Phys. Rev. Mater. 5, 044202 (2021).

30. Li, H. et al. Conjoined charge density waves in the kagome superconductor CV3Sb5. Nat. Commun. 13, 6348 (2022).

31. Qian, T. et al. Revealing the competition between charge density wave and superconductivity in CsV3Sb5 through uniaxial strain. Phys. Rev. B 104, 144506 (2021).

32. Teng, X. et al. Discovery of charge density wave in a correlated kagome lattice antiferromagnet. Nature 609, 490–495 (2022).

33. Yin, J.-X. et al. Discovery of charge order and corresponding edge state in kagome magnet FeGe. Phys. Rev. Lett. 129, 166401 (2022).

34. Ohoyama, T., Kanematsu, K. & Yasukōchi, K. A new intermetallic compound FeGe. J. Phys. Soc. Jpn 18, 589–589 (1963).

35. Bernhard, J., Lebech, B. & Beckman, O. Neutron diffraction studies of the low-temperature magnetic structure of hexagonal FeGe. J. Phys. F 14, 2379–2393 (1984).

36. Huang, L. & Lu, H. Signatures of Hundness in kagome metals. Phys. Rev. B 102, 125130 (2020).

37. Setty, C. et al. Electron correlations and charge density wave in the topological kagome metal FeGe. Preprint at https://arxiv.org/abs/2203.01930 (2022).

38. Ptok, A. et al. Chiral phonons in the honeycomb sublattice of layered CoSn-like compounds. Phys. Rev. B 104, 054305 (2021).

39. Sobota, J., He, Y. & Shen, Z.-X. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).

40. Kang, M. et al. Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5. Nat. Phys. 18, 301–308 (2021).

41. Yu, T. L. et al. Colossal band renormalization and Stoner ferromagnetism induce by electron–antiferromagnetic–magnon coupling. Nat. Commun. 13, 6560 (2020).

42. Wray, L. et al. Momentum dependence of superconducting gap, strong-coupling dispersion kink, and tightly bound Cooper pairs in the high-Tc (Sr,Ba)1−x(K,Na)xFe2As2 superconductors. Phys. Rev. B 78, 184508 (2008).

43. Grimvall, G. in Metals (ed Wohlfarth, E.) (North-Holland, 1981).

44. Plummer, E. W., Shi, J. R., Tang, S. J., Rotenberg, E. & Kevan, S. D. Enhanced electron–phonon coupling at metal surfaces. Prog. Surf. Sci. 74, 251–268 (2003).

45. Luo, H. et al. Electronic nature of charge density wave and electron–phonon coupling in kagome superconductor KV3Sb5. Nat. Commun. 13, 273 (2022).

46. Xie, Y. et al. Electron–phonon coupling in the charge density wave state of CsV3Sb5. Phys. Rev. B 105, L140501 (2022).

47. Li, H. et al. Observation of unconventional charge density wave without acoustic phonon anomaly in kagome superconductors AV3Sb5 (A = Rb, Cs). Phys. Rev. X 11, 031050 (2021).

48. Wu, S. et al. Charge density wave order in kagome metal AV3Sb5 (A = Cs, Rb, K). Phys. Rev. B 105, 155106 (2022).

49. Wang, C. et al. Origin of charge density wave in the layered kagome metal CsV3Sb5. Phys. Rev. B 105, 045135 (2022).

50. Liu, Z. et al. Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor RbV3Sb5. Phys. Rev. X 11, 041010 (2021).

51. Abernathy, D. L. et al. Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source. Rev. Sci. Instrum. 83, 15114 (2012).

52. Arnold, O. et al. Mantid—data analysis and visualization package for neutron scattering and μSR experiments. Nucl. Instrum. 764, 156–166 (2014).

53. Ewings, R. A. et al. Horace: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods Phys. Res. A 834, 132 (2016).

54. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

55. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

56. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. L 77, 3865 (1996).

57. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1 (2015).

58. Mostofi, A. A. et al. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685 (2008).

59. Johannes, M. D. & Mazin, I. I. Fermi surface nesting and the origin of charge density waves in metals. Phys. Rev. B 77, 165135 (2008).

## Acknowledgements

We thank J. Zhu, C. Lane, Q. Si and C. Setty for helpful discussions. The ARPES work is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9470 (M.Y.), Robert A. Welch Foundation grant no. C-2024 (M.Y.) and U.S. Department of Energy (DOE) grant bo. DE-SC0021421 (M.Y.). The neutron scattering and single-crystal synthesis work at Rice was supported by US NSF-DMR-2100741 (P.D.) and by the Robert A. Welch Foundation under grant no. C-1839 (P.D.), respectively. The work at the University of California, Berkeley was supported by the U.S. DOE under contract no. DE-AC02-05-CH11231 within the Quantum Materials Program (KC2202) (R.J.B.). This research used resources of the Advanced Light Source and the Stanford Synchrotron Radiation Lightsource, both U.S. DOE Office of Science User Facilities under contract nos. DE-AC02-05CH11231 and AC02-76SF00515, respectively. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by ORNL. B.Y. acknowledges financial support from the European Research Council (ERC Consolidator grant “NonlinearTopo”, no. 815869) and an ISF personal research grant (no. 2932/21). JSO acknowledges the support of the NSF Grants Nos. DMR-1921798 and DMR-1921847.

## Author information

Authors

### Contributions

M.Y., P.D. and R.J.B. managed the project. The single-crystal FeGe samples were grown by X.T. and B.G. under the guidance of P.D. APRES experiments were carried out by J.S.O., X.T., J.H. and M.Y. with the assistance of M.H., D.L., C.J., A.B. and E.R. First-principles calculations were performed by H.T. and B.Y. Neutron scattering measurements and analysis were carried out by G.G., X.T., L.C. and P.D. The paper was written by M.Y., P.D., X.T., J.S.O. and L.C. with input from and significant discussions with all co-authors.

### Corresponding authors

Correspondence to Robert J. Birgeneau, Pengcheng Dai or Ming Yi.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Physics thanks Niels Schröter and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. S1–S11 and Sections 1–8.

## Source data

### Source Data Fig. 1

DFT calculations and script to extract spin-resolved calculations.

### Source Data Fig. 3

Raw data for Fig. 3b–d,f–h.

### Source Data Fig. 4

Raw data for Fig. 4g,h,j,l.

### Source Data Fig. 5

Raw data for Fig. 5b–d and fitted data for Fig. 5h,i.

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Reprints and Permissions

Teng, X., Oh, J.S., Tan, H. et al. Magnetism and charge density wave order in kagome FeGe. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-01985-w

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• DOI: https://doi.org/10.1038/s41567-023-01985-w