Introduction

Kagome lattice, a two-dimensional hexagonal network of corner-sharing triangles (Fig. 1a), exhibits linearly dispersing Dirac cones at the Brillouin zone (BZ) corner K point and flat band (FB) through the rest of the BZ (Fig. 1b)1. These bands have been observed by angle-resolved photoemission spectroscopy (ARPES) in binary Kagome metal magnets TmXn (T: 3d transition metals, X: Sn, Ge, m:n = 3:1, 3:2, 1:1)2,3, and ternary ferromagnetic YMn6Sn64. Evidence of flat bands has been reported in FeSn thin films grown on SrTiO3(111) (STO) substrates in three-terminal planar Schottky tunneling measurements5. The interplay of spin-orbit-coupling and out-of-plane ferromagnetic order can further lead to Chern topological fermions, which have been observed in TbMn6Sn66. The band structure of the Kagome lattice also exhibits saddle points at the BZ boundary M1,4,7, which can lead to charge instabilities and symmetry-breaking electronic orders, including charge density waves (CDWs)7, bond order waves (BOWs)8,9,10,3a, b). Interestingly, the dI/dV intensities for the up- and down-triangles cross at 16.8 meV (marked by a red arrow in Fig. 3b), below which A site has higher intensity. At ∼100 meV, the intensity of the C site is the highest. These transitions are directly reflected in the energy-dependent dI/dV map** (Fig. 3c–l and additional data in Supplementary Fig. S8). Compared to the topographic image (Fig. 3a), the dI/dV maps in Fig. 3c–l reveal trimerization of the Kagome lattice, where the up and down triangles exhibit different contrasts. Below the crossing energy of 16.8 meV, the up-triangles have a much higher contrast compared to the down-triangles. Above the transition, the contrast reverses with the down triangle exhibiting higher contrast. At ∼100 meV, the central Sn site has the highest contrast, while the A and B sites are roughly similar. This energy-dependent contrast reversal between the up and down triangles indicates the trimerization of the Kagome lattice, breaking its six-fold rotational and mirror symmetry but not translational symmetry, as schematically illustrated in the inset of Fig. 3b.

Fig. 3: Trimerized Kagome lattice on the Fe3Sn layer.
figure 3

a Topographic STM image of the Fe3Sn layer. Setpoint: V = 0.2 V, I = 5.0 nA. b dI/dV spectra taken at three representative sites labeled A, B, and C (inset). The red arrow marks the intensity reversal for the up-and down-triangles at 16.8 meV. c–l Differential conductance maps of the same location at the energies marked. Setpoint: V = 0.2 V, I = 5.0 nA. A ball-and-stick model of the Kagome lattice is overlaid on the STM image (a) and differential conductance maps (c–l).

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Enhanced trimerization near single Sn vacancy

Additional evidence for this symmetry-breaking state is found near Sn vacancy defects, the most common type of defects on the Fe3Sn Kagome layer, as schematically shown in Fig. 4a and Supplementary Fig. S9. First, the topographic STM image indicates suppressed DOS at the Sn vacancy site (Fig. 4b), consistent with our DFT calculations (Supplementary Fig. S10). In the dI/dV map (Fig. 4c), the contrast of the up-triangle sites is enhanced significantly due to Sn-vacancy induced bound states, resulting in a three-lobe feature that can be more clearly seen by overlaying a Kagome lattice model on the image (Supplementary Fig. S11). This enhanced trimerization is also energy- and site-dependent. As shown in Fig. 4d–f, the dI/dV spectra taken on the three lobes reveal clear bound states at −49.8, −21.3, and −18.7 meV, respectively. The corresponding dI/dV maps recorded at these energies are shown in Fig. 4g–i and Supplementary Fig. S12. Three-fold symmetry is observed in dI/dV maps in the energy range [−200, −32 meV]. Interestingly, in maps with energy closer to the Fermi level, e.g., g(r, −21.3 meV) and g(r, −18.7 meV), the intensity at one of the up-triangles is suppressed, thus exhibiting a two-fold symmetry.

Fig. 4: Enhancement of trimerization by Sn vacancy induced bound states on the Fe3Sn layer.
figure 4

a Ball-and-stick model of a single Sn vacancy on the Fe3Sn Kagome layer. b Topographic STM image of the Kagome layer with Sn vacancies. Setpoint: V = 0.2 V, I = 5.0 nA. The white and yellow dashed squares mark the regions with and without Sn vacancy. c Differential conductance map taken at −101.3 meV of the same region as (b), setpoint: V = 0.2 V, I = 5.0 nA, Vmod = 3.0 meV. d–f dI/dV spectra (red) measured at one of the lobes marked by the red circles and away from the defect (black). Black arrows label the energy positions of the bound states. g–i Corresponding dI/dV maps recorded at the bound state energies indicated, setpoint: V = 0.2 V, I = 5.0 nA, Vmod = 3.0 meV.

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Tuning the stripe modulations by an in-plane magnetic field

Given that Fe atoms in the Kagome layer are ordered ferromagnetically, we now examine the impact of the magnetic field on trimerization. Note that non-spin-polarized tips are used for STM imaging and spectroscopy; magnetic information is not expected directly. Nevertheless, as presented below, we have observed energy-dependent stripe modulations of the trimerized Kagome lattice.

Figure 5a shows an STM topography image and corresponding dI/dV maps taken at the energies specified without a magnetic field, where a close-packed structure is observed. While the close-packed structure is further confirmed by the FFT patterns shown in Fig. 5b, slight variations are present in the FFT peak intensities, indicative of a stripe modulation. This is not simply due to an asymmetrical tip, as confirmed by additional energy-dependent STM imaging (Supplementary Fig. S13).

Fig. 5: Stripe modulations tunable by an in-plane magnetic field.
figure 5

a Topographic STM image and dI/dV maps at −144, −98.7, and −50.7 meV under B = 0 T. Setpoint: V = 0.2 V, I = 0.7 nA. b Patterns generated by Fast Fourier transformation (FFT) of the image and maps in (a). c Topographic STM image and dI/dV maps at the same energies as (a) with an in-plane magnetic field B// = 2 T along the direction marked by the red arrow. Setpoint: V = 0.2 V, I = 0.7 nA. d FFT patterns generated from the image and maps in (c). e Topographic STM image and dI/dV maps at the same energies as (a) & (c) after removing the in-plane magnetic field. Setpoint: V = 0.2 V, I = 0.7 nA. f FFT patterns generated from the image and maps in (e). g Left panel: line profile along the white dotted line in (d), with the FFT peak intensity marked by a black circle; and right panel: the energy-dependent FFT peak intensity for all the dI/dV maps at zero, 2 T applied field, and after the field is removed. The curves are shifted vertically for clarity. The FFT peak intensity is normalized to their corresponding averaged background intensity.

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With an applied 2 T in-plane magnetic field along the direction shown by the red arrow (Fig. 5c), the topography image is more symmetrical. However, the energy-dependent stripe modulations become more pronounced in the dI/dV maps. At −144 meV, the close-packed structure is modulated along one of the crystallographic directions, leading to substantially enhanced intensity at two of the peaks in the FFT pattern (second panel in Fig. 5d). Interestingly, a honeycomb structure appears at −98.7 meV, leading to a symmetrical FFT pattern. Then, the structure reverts to be close-packed at −50.7 meV (right panel in Fig. 5c), but with a stripe modulation rotated 60° from that at −144 meV. This stripe formation is again evident in the asymmetrical FFT patterns (Fig. 5d, right panel). Additional dI/dV maps in the energy window of −144 to 144 meV are provided in the Supplementary Information Figs. S14–16 to support this observation. While stripe modulations are also seen for a 9 T out-of-plane magnetic field, no clear energy dependence is detected.

To quantify the evolution of the stripe modulation, the energy-dependent FFT peak intensity is plotted in Fig. 5g and Supplementary Fig. S17. Along the direction marked by a white dotted line in Fig. 5d second panel, the maximum peak intensity shifts from ∼50 meV below Fermi level at zero field to ∼−100 meV at 2 T in-plane field. Interestingly, this shift is also remanent after removing the magnetic field. However, such behavior is not observed in the other two directions (Supplementary Fig. S17). These results clearly show a stripe modulation highly tunable by the magnetic field, indicating the coupling of magnetism with the charge order of the Kagome layer. However, the mechanism is likely complex, similar to other materials such as YBCO29, Fe5-xGeTe230, UTe231, and NdSbxTe2-x-δ32, where coupling between spatial charge modulation and magnetic order has also been reported.

Discussion

Our experimental findings reveal an intriguing trimerization of the Fe3Sn Kagome layer in epitaxial FeSn films that breaks the six-fold rotational symmetry but not the translational symmetry. This is in contrast to the (2 × 2) or (4 × 1) CDWs reported in AV3Sb5 compounds16,17 and FeGe18,19,20 that all resulted in breaking the translational symmetry. One may attribute this trimerization to a breathing Kagome lattice characterized by anisotropic bond strengths with hop** parameters JA/JB between nearest neighbors. Such a structure is suggested for the Fe3Sn bilayer in Fe3Sn2, where the two corner-sharing triangles have different bond lengths33. However, the films studied here are the FeSn phase with alternatingly stacked single Sn and Fe3Sn layers, as confirmed by the XRD data (Supplementary Fig. S2), and the observation of a perfect honeycomb without buckling on the Sn termination (Figs. 1d and 2a), in direct contrast to that observed on Sn-terminated bulk Fe3Sn23,26. Thus, a breathing Kagome lattice in the FeSn films is unlikely.

Having ruled out the structural origin for breaking the six-fold rotational symmetry of the Kagome lattice, we discuss electronic orders, including charge and bond orders, as other possible causes. For charge density order in non-magnetic Kagome materials, while most studies focused on the impact of the van Hove singularities at the M points7,18,20, recent work highlighted the interlayer coupling of the Kagome layers where the interactions between modes at M and L points of the BZ lead to multiple CDWs34, including possibly the nematic order observed in CsV3Sb516. Similarly, for magnetic Kagome material FeGe, a recent study suggested that coupling between magnetism and (2 × 2) CDW order can lead to Kekulé-like bond order in the Ge layer35. In the current system of epitaxial FeSn thin film, the coupling between the Sn honeycomb layer and the Fe3Sn Kagome layer could lead to modifying the Kagome lattice. For example, if the Sn layer exhibits (√3 × √3) CDWs, such an order can cause different displacements of the Sn atoms underneath the neighboring triangles of the Kagome lattice, potentially leading to the trimerization. Evidence for such enhanced interlayer coupling can be found in the XRD data, where the (002) and (021) peaks of the FeSn are shifted slightly to larger values (Supplementary Fig. S2), indicating a smaller c-axis lattice constant. Furthermore, we have reported a strain-induced substantial deformation of the Sn honeycomb on the Sn-termination for thin FeSn films36 (Supplementary Figs. S18 and 19).

Another possible cause for breaking the six-fold rotational symmetry is the interaction-driven bond order predicted for Kagome lattices9,10,

Methods

Sample preparation

The FeSn films were prepared by MBE with a Sn/Fe flux ratio >3 on Nb-doped (0.05 wt%) SrTiO3(111) substrates. The SrTiO3(111) substrates were first degassed at 600 °C for 3 h, followed by annealing at 950 °C for 1 h to obtain an atomically flat surface with step-terrace morphology. During the MBE growth, high-purity Fe (99.995%) and Se (99.9999%) were evaporated from Knudson cells on the SrTiO3 substrate with temperatures between 480 and 530 °C.

LT-STM/S characterization

The STM/S measurements were carried out in a low-temperature Unisoku STM system at T = 4.5 K. A polycrystalline PtIr tip was used, which was tested on Ag/Si(111) films before the STM/S measurements. dI/dV tunneling spectra were acquired using a standard lock-in technique with a small bias modulation Vmod at 732 Hz.

X-ray diffraction characterization

The XRD patterns of samples were obtained using a Panalytical X’Pert Pro MPD powder X-ray diffractometer with Cu Kα X-ray source operating at 45 kV and 40 mA in the Bragg-Brentano geometry. The spectra were collected over a 2-theta range of 30° to 50° with a solid-state X-ray detector.

DFT calculations

First-principles calculations were carried out in the framework of generalized gradient approximation with the Perdew-Burke-Ernzerhof functionals43 using the Vienna Ab initio simulation package (VASP). All calculations were performed with a plane-wave cutoff of 500 eV on 7 × 7 × 1 Monkhorst-Pack k-point mesh. In geometric optimization, the atom positions were fully relaxed until the forces less than 0.02 eV/Å. The Fe3Sn-terminated (Sn-terminated) surface was modeled by a slab geometry consisting of seven (five) atomic layers with ∼15 Å of vacuum, in which the upper three layers were relaxed. The theoretical STM images were simulated using the Tersoff-Hamann approximation44 with a larger k-points mesh (21 × 21 × 1). The STM tunneling current is proportional to the local density of states of the sample surface at the position of the tip. Therefore, the simulated STM image is the plot of the charge density distribution in a chosen energy window on one horizontal plane above the sample surface. Here, the theoretical energy window is compared to the STM bias voltage, and the vertical position of the horizontal plane is compared to the height of the STM tip. In the simulations, the orbital of the STM tip is considered an isotropic s-wave, and the density is directly obtained from the DFT calculations.