Direct evidence of coupling between charge density wave and Kondo lattice in ferromagnet Fe5GeTe2

Abstract

d-electronic heavy fermion systems have sparked interest in exploring the connection between electronic and spin degrees of freedom in Kondo systems. Nevertheless, the coexistence of charge order on a Kondo lattice has yet to be discovered. Fe₅GeTe₂, a two-dimensional ferromagnet, intriguingly provides a promising avenue to bridge the gap, as this d-electronic Kondo system facilitates the ordering of charge and magnetic behaviors due to the influence of itinerant magnetism on local electronic band structure. Here, we present direct evidence for the coherent interplay between Kondo interaction and charge density wave (CDW) phenomena in Fe₅GeTe₂ using scanning tunneling microscopy/spectroscopy (STM/STS). From the electronic structure, we observe a $\sqrt{3}\times \sqrt{3}R30^{\circ }$ modulation accompanied by phase inversion, indicative of CDW. Concurrently, the presence of a Fano-like peak near the Fermi level corroborates the Kondo lattice behavior. Furthermore, formations of Kondo holes at defect sites underscore the influence of Kondo interaction on local electronic structures. To unveil the robust correlation between CDW and Kondo lattice behavior, we analyze the CDW modulation and develop a theoretical model to interpret their robust coupling. Our findings advance the understanding of Kondo physics in d-electronic ferromagnetic systems and highlight Fe₅GeTe₂ as a promising platform for exploring low-dimensional magnetism.

Fig. 1. STM Topography of Fe₅GeTe₂ lattice structure.

a Schematic three-dimensional diagram of Fe₅GeTe₂ showing the hexagonal lattice structure, with the Fe(I) atoms highlighted in red. b Schematic side view of the crystal structure of Fe₅GeTe₂, cutting along the blue plane in (a). The possible configurations include Fe(I)_up, Fe(I)_down, and Fe(I)_vac (denoted by U, D, and X, respectively). c Large-scale topographic STM image of the surface of Fe₅GeTe₂ (+10 mV, 250 nA). d Atomic-resolution topographic STM image of Region I. (+40 mV, 400 pA) The inset shows the fast Fourier transform (FFT) of the STM image. e, f Upward and downward scanned topographic STM images at the same field of view, showing the diffusion of Fe(I) vacancies. g Height line profile analysis at the pristine and defect sites, demonstrating that Region I is composed of Fe(I) vacancies with a background of UUU configuration. Source data are provided as a Source Data file.

Fig. 2. dI/dV spectra, Kondo resonance, and Kondo hole.

a Magnified image of the Fe(I) vacancy structure at the energy of +0.04 eV. The red arrow marks the Fe(I) vacancy (Fe(I)_vac) site, while the gray arrow marks a pristine site away from the Fe(I)_vac site. b dI/dV spectra measured at Fe(I)_vac sites (red) and pristine sites (gray). The experimental dI/dV spectrum at pristine areas is theoretically simulated by a Fano resonance (purple dashed curve) and a Lorentzian curve (orange dashed curve). The inset depicts the schematic diagram for the tunneling process in STS measurements, showing the additional pathway owing to the Kondo resonance states. c Spatially averaged dI/dV spectra acquired at various temperatures. d Temperature dependence of the Fano resonance width $\Gamma$ extracted by the fitting model in (b). The error bars are from the Fano fitting. e Waterfall plot of successive dI/dV spectra measured across the Fe(I)_vac in (a). f Spatial profiles of the tunneling ratio q and rectification R values, extracted from the curves in (e). Source data are provided as a Source Data file.

Fig. 3. Emergence of charge density wave.

a, b dI/dV maps at the energies of +0.20 eV and +0.04 eV, respectively. c, d Corresponding fast Fourier transform (FFT) images of the dI/dV maps in (a, b), respectively. The green dashed hexagon marks the first Brillouin zone, and the Q_c modulation is labeled by the blue arrow. e Schematic of the conductive electronic band (red) and the Kondo resonance states (purple) in momentum space. f Voltage-dependent FFT amplitudes extracted along the directions of the yellow and orange line/arrow marked in (c). The red and purple dashed lines label the conductive band and the Kondo resonance states, respectively.

Fig. 4. Characteristics of CDW and the coherent Kondo lattice behavior.

a, b dI/dV maps at the energies of +60 meV and −80 meV, respectively, with the $\sqrt{3}\times \sqrt{3}$ CDW signal enhanced. c dI/dV band alignment across the orange arrow in (b). The blue arrow marks the length of the Q_c modulation. d Energy dependence of the CDW phases. e Oscillating dI/dV values at the energies of +0.10 eV (gray) and −0.04 eV (black), demonstrating the phase inversion. f–h Oscillations of tunneling ratio q (purple), rectification R (blue), and amplitudes of ferromagnetic (FM) states (orange). The gray dashed lines label the peak positions, demonstrating that these parameters oscillate with the same periodicity as the CDW. i Intensities of the FFT signals along $\mathrm{M}-\mathrm{K}-\mathrm{G}$ direction for q, FM, +0.04 eV dI/dV, and +0.20 eV dI/dV maps. The amplitudes are normalized by the maximum value of each curve. The blue dashed line marks the Q_c modulation vector. Source data are provided as a Source Data file.

Fig. 5. Coupling between the 3×3 CDW and Kondo interactions.

a Spin frustration scenario in which the localized spin moments on the triangular vertices cannot simultaneously satisfy all pairwise antiferromagnetic interactions. b Inhomogeneous charge carrier density on the triangular lattice. c Modified spin arrangements due to the inhomogeneous Kondo effect. The initially frustrated spin moment S₃ is screened by the enhanced Kondo effect. d Schematic of consequent charge distribution on the entire Fe(I) triangular lattice, exhibiting a $\sqrt{3}\times \sqrt{3}$ periodicity, labeled by the blue diamond. Fe(I) vacancy manifests as a Kondo hole, where the impact range is consistent with the experimental observation in (e). e dI/dV image of Fe(I) vacancies. The vacancies are orderly positioned at the $\sqrt{3}\times \sqrt{3}$ grid.