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Discovery of charge density wave in a kagome lattice antiferromagnet

Nature volume 609, pages 490–495 (2022)Cite this article

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Abstract

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies1,2. A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity1,2. Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons3,4, non-trivial topology5,6,7, chiral magnetic order8,9, superconductivity and CDW order10,11,12,13,14,15. Although CDW has been found in weakly electron-correlated non-magnetic AV3Sb5 (A = K, Rb, Cs)10,11,12,13,14,15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals4,16,17,18,19,20,21. Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs. 16,17,18,19). The CDW in FeGe occurs at wavevectors identical to that of AV3Sb5 (refs. 10,11,12,13,14,15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect22,23. Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase24,25,26,27,28, in stark contrast to strongly correlated copper oxides1,2 and nickelates29,30,31, in which the CDW precedes or accompanies the magnetic order.

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Fig. 1: Crystal and magnetic structure, phase diagram, sample characterization and schematic of flux phase in FeGe.
Fig. 2: BZ, canted AFM structure, neutron diffraction data and schematic in the [H, 0, L] plane.
Fig. 3: Order parameter of CDW and magnetic peaks, line shape of CDW peaks and STM results.
Fig. 4: Schematic and ARPES data of vHSs in AFM FeGe.

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The data that support the plots in this paper and other findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

We thank D. Xiao, Q. Si and C. Setty for helpful discussions. The neutron scattering and single-crystal synthesis work at Rice was supported by US NSF-DMR-2100741 and by the Robert A. Welch Foundation under grant no. C-1839, respectively. The ARPES work at Rice was supported by the U.S. Department Of Energy (DOE) grant no. DE-SC0021421, the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9470 and the Robert A. Welch Foundation grant no. C-2024. The transport experiment at the University of Washington was supported by the Air Force Office of Scientific Research under grant FA9550-21-1-0068 and the David and Lucile Packard Foundation. Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547 and GBMF9461; M.Z.H.) and the U.S. DOE under the Basic Energy Sciences programme (grant no. DOE/BES DE-FG-02-05ER46200). The work at the University of California, Berkeley was supported by the U.S. DOE under contract no. DE-AC02-05-CH11231 in the Quantum Materials Program (KC2202). 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 Oak Ridge National Laboratory.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Rice University, Houston, TX, USA

    Xiaokun Teng, Lebing Chen, Ji Seop Oh, Kelly J. Neubauer, Bin Gao, Yaofeng Xie, Ming Yi & Pengcheng Dai

  2. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Feng Ye

  3. Department of Physics, University of Washington, Seattle, WA, USA

    Elliott Rosenberg, Zhaoyu Liu & Jiun-Haw Chu

  4. Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton, NJ, USA

    Jia-Xin Yin, Yu-Xiao Jiang & M. Zahid Hasan

  5. Department of Physics, University of California, Berkeley, Berkeley, CA, USA

    Ji Seop Oh & Robert J. Birgeneau

  6. Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Makoto Hashimoto & Donghui Lu

  7. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Chris Jozwiak, Aaron Bostwick & Eli Rotenberg

  8. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Robert J. Birgeneau

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Contributions

P.D. and M.Y. conceived and managed the project. The single-crystal FeGe samples were grown by X.T. and B.G. Neutron scattering and X-ray diffraction experiments were carried out by F.Y. in remote discussion with P.D. and X.T. Neutron refinements were carried out by X.T., L.C., and K.J.N. Magnetic susceptibility and heat capacity measurements were performed by X.T. and Y.X. Transport measurements were carried out by E.Rosenberg, Z.L. and J.-H.C. STM measurements were carried out by J.-X.Y., Y.-X.J. and M.Z.H. ARPES experiments were carried out by X.T., J.S.O., R.J.B. and M.Y., with the assistance of M.H., D.L., C.J., A.B. and E.Rotenberg. The paper is written by P.D., M.Y., J.-H.C., J.-X.Y., X.T. and L.C., and all co-authors made comments on the paper.

Corresponding authors

Correspondence to Ming Yi or Pengcheng Dai.

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Extended data figures and tables

Extended Data Fig. 1 X-ray pattern, structure refinement, EDX spectroscopy analysis and sample pictures of FeGe.

a, X-ray diffraction pattern of the (0, 0, 1) plane. The strongest intensity is around 1,000 and the minimum is zero. b, Calculated structure factor Fcalc versus observed structure factor Fobs from X-ray diffraction. The X-ray experiment is performed at 150 K. c,d, X-ray diffraction patterns of the (0, 0, 0.5) plane at 150 K and 50 K. The strongest intensity at L = 0.5 is around 10 and the minimum is zero. e, EDX spectroscopy analysis in a FEI Nano 450 scanning electron microscope, which shows that the atomic ratios of Fe and Ge are 52 ± 3% and 48 ± 5%, respectively. Measurement is performed at room temperature using a voltage of 20 kV. Counting time is 30 s. Inset of e shows a piece of FeGe single crystal. Tick size is 1 mm.

Extended Data Fig. 2 Magnetic susceptibility, phase diagram and heat capacity of FeGe single crystal.

a,b, Magnetic susceptibility with field perpendicular to the c-axis \({\chi }_{\perp }\) (a) and parallel to the c-axis \({\chi }_{| | }\) (b) versus magnetic field at various temperatures. Spin-flop field keeps decreasing with decreasing temperature. At TCDW (100 K), the \({\chi }_{\perp }\) curve begins to have a shoulder directly under the spin-flop field instead of a sharp spin-flop transition. c, Magnetic moment at different temperatures and fields. Dashed lines are phase boundaries. d, Heat capacity versus temperature. A kink is observed at TCDW.

Extended Data Fig. 3 Electron density, electron mobility and Hall resistivity at various temperatures and fields.

a,b, Field dependence of Hall resistivity ρxy at various temperatures. The step-like feature at high field that corresponds to spin-flop transition becomes less prominent below TCDW (100 K) but is present nevertheless. c, Red dots show the electron density ne versus temperature (left axis). With decreasing temperature, a sudden decrease is observed at TCDW. Blue dots show the electron mobility μe versus temperature. An increase in slope occurs at TCDW. d,e, Colour plot of ρxy and dρxy/dB at different temperatures and fields. Spin-flop transition becomes less clear below TCDW. f, Temperature dependence of dρxy/dB for fields above and below spin-flop transition. g,h, The absence of hysteresis in ρxy either below (T = 10 K) or above (T = 120 K) the TCDW.

Extended Data Fig. 4 Line shape of selected lattice, magnetic and CDW peaks and neutron diffraction map at 6 K.

Cuts of lattice peak (2, 0, 1) (a,b), (4, 0, 2) (c,d), AFM magnetic peak (2, 0, 1.5) (e,f), CDW peak (2.5, 0, 2) (g,h) and CDW peak (3.5, 0, 1.5) (i–l) along the L and H directions, respectively. Integration range is ±0.1 r.l.u. Black dots are 70-K data. Grey, red and blue dots are 140-K data. Dashed lines in panels a–j are Gaussian fits and solid lines in panels k and l are Lorentzian fits. m, [H, 0, L] plane map is taken at 6 K, in canted AFM + CDW phase. Clear CDW peaks at QCDW1 = (0.5, 0, 0.5) and QCDW2 = (0.5, 0, 0) are observed.

Extended Data Fig. 5 Form factors of the flux phase, magnetic and CDW peaks.

a, A flux hexagon in the real space. b, The 2D Fourier transform of the hexagon. c, A cut along Qy in b with Qx = 0, showing the magnetic form factor of the flux hexagon, with a comparison of the magnetic form factor of Fe atom. d–f, The flux triangle in the real space, its Fourier transform and the form factor along the [0, Qy] direction compared with Fe magnetic form factor, respectively. g, Wavevector dependence of the magnetic Bragg peak intensity in the [H, 0, L] plane at 140 K and the extra intensity induced by CDW (calculated by subtracting 140 K intensity over 70 K). The CDW-induced intensity shows similar Q dependence as Fe atom. h, Wavevector dependence of the CDW peak intensity in the [H, 0, L] plane at 70 K.

Extended Data Fig. 6 Estimation of lattice components on the magnetic Bragg peak positions.

a, Comparison of integrated scattering intensity at all (H, 0, L+1/2) magnetic Bragg peak positions at 140 K after accounting for the A-type AFM structural factor but not the magnetic form factor. b, Integrated intensity at all (H, 0, L+1/2) magnetic Bragg peak positions at 70 K. The orange solid lines in a and b are Fe magnetic form factors discussed in Extended Data Fig. 5. Green dots highlight unexpected Bragg peak positions that deviate from the Fe magnetic form factor (orange lines). White-shaded blue dots indicate Bragg peaks markedly contaminated with aluminium powder ring. c, Comparison between the integrated scattering intensity at all (H, 0, L+1/2) magnetic (blue, green) and superlattice (H+1/2, 0, L+1/2) (orange) Bragg peak positions at 70 K. These are raw data without any correction and, thus, should be the most accurate description of the scattering intensity at both positions. The integrated intensity of the (2, 0, 0.5) peak at 140 K is shown in the solid black circle. The solid green circles indicate anomalous data at (H, 0, 4.5) positions. d, Expanded view of integrated scattering intensity at (H, 0, L+1/2) positions at 70 K (blue, green) and 140 K (purple). The green bars in c and d near 3 Å−1 indicate the estimated lattice component at (2, 0, 0.5), if present, compared with the intensity gain between 70 K and 140 K shown in the dashed yellow lines.

Extended Data Fig. 7 [H, K, 0.5] plane neutron diffraction maps at various temperatures.

a–c, [H, K, 0.5] plane diffraction maps at 440 K, 140 K and 70 K, respectively. At 440 K (T > TN), no magnetic peak is observed; at 140 K (TCDW < T < TN), AFM peaks emerge at H, K = 1, 2, 3…. At 70 K (T < TCDW), further CDW peaks emerge at H, K = 0.5, 1.5, 2.5…. d–f, [H, K, 4] plane diffraction maps at 440 K, 140 K and 70 K, respectively. Colour bar is in log scale. At 440 K (T > TN) and 140 K (TCDW < T < TN), structural peaks are present at H, K = 1, 2, 3…; at 70 K (T < TCDW), CDW peaks emerge at H, K = 0.5, 1.5, 2.5….

Extended Data Fig. 8 Structure refinement results and possible lattice distortion for CDW order.

a–c, The refinement result on lattice and magnetic Bragg peaks at 300 K, 140 K and 70 K, respectively. d,e, Comparison of calculated and experimental magnetic peak intensity in the incommensurate phase at 6 K. f, Schematic diagram of the crystal structure of FeGe with two independent iron positions plotted. g, Refinement results using a simple model discussed in Methods.

Extended Data Fig. 9 Extended STM and ARPES data.

a, STM topographic data taken at V = −30 mV and I = 0.1 nA. The inset shows its Fourier transform, in which the red circles mark the 2 × 2 CDW vector peaks. b, Photon-energy-dependent ARPES measurement of FeGe. Electron-like pockets are observed at A points. Inner potential is determined to be 16 eV. Thick red lines mark out in-plane high-symmetry cuts at various photon energies: hν = 69 eV corresponds to kz = 0 (Γ-K-M); hν = 47 eV and 102 eV correspond to the kz = π plane (A-H-L). Measurement is performed at 8 K.

Extended Data Table 1 Crystal data and structure refinement for FeGe
Full size table
Extended Data Table 2 Atomic positions of FeGe
Full size table
Extended Data Table 3 Atomic displacement factors
Full size table
Extended Data Table 4 Positions of atoms in the CDW phase of FeGe
Full size table

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Teng, X., Chen, L., Ye, F. et al. Discovery of charge density wave in a kagome lattice antiferromagnet. Nature 609, 490–495 (2022). https://doi.org/10.1038/s41586-022-05034-z

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