Introduction

The frustrated kagome lattice, made up of the geometry of corner-sharing triangles, has been studied intensively due to the magnetic frustration-induced quantum spin liquid state1,2. Meanwhile, the construction of topological band theory in recent years has greatly enriched in the electronic band structure of kagome lattice3,4,5. Theoretical studies show the kagome lattice systems as an ideal platform for understanding the topological states with novel topological excitations6,7,8. For example, a flat band (FB) can be constructed by completely destructive interference of Bloch wave functions in two-dimensional (2D) kagome lattice with nearest-neighbor (NN) interaction. Such FBs, just like a counterpart of the Landau level, can be characterized by a Chern number3,7. Representing a highly degenerate and quenched kinetic energy of electron state may give rise to the abundant exotic emergent effects, such as ferromagnetism, high-temperature superconductivity, Wigner crystal, and fractional quantum Hall effects9,10,11,12,13,14,15,16. Besides, the kagome lattice system shares similar topological physics with honeycomb, Dirac cone-type dispersions in the momentum-space K point. Once a net magnetization and intrinsic spin–orbit coupling (SOC) are present, a well-separated non-trivial Chern bands, Chern gap and intrinsic quantum anomalous Hall effect could present when the Fermi energy is tuned properly17,18.

The band structure studies of 3d transition-metal kagome compounds, which are usually strong correlated and exhibit magnetism, remain challenging albeit theoretical predictions19,20,21,22,23,24,25,26,27,28,29,30,31,32. A typical electronic structure of the kagome lattice is the existence of Dirac point (DP) at the Brillouin zone (BZ) corner, a saddle point (SP) at BZ boundary, and a FB over the whole BZ (Fig. 1b). Topological non-trivial electronic properties were observed in kagome lattices constituted of 3d-transition metallic element, i.e., large intrinsic anomalous Hall effect originating from the Berry curvature of Dirac cone-type dispersion of K point both in ferromagnetic (FM) and antiferromagnetic (AFM) materials18,20,21,22,23,24. Another important feature is the dispersionless electronic structure in magnetic kagome materials25,30,31,32 and in paramagnetic (PM) kagome materials27,28,29. In PM kagome materials, extremely flat bands close to EF have been reported in CoSn28,29 and YCr6Ge627. However, in magnetic systems, the direct evidence of the FBs is either unobserved (Fe3Sn2, Co3Sn2S222,30), or far away from EF (FeSn25), due to the strong correlation of 3d electrons, the complexity with magnetic structure, and the interplay between electron correlation and topological properties. Thus, searching for the flat band, and saddle point, in addition to the Dirac fermion near EF in magnetic kagome systems serves as the main objective to manipulate the topological properties in magnetic materials.

Fig. 1: Crystal and electronic structures of YMn6Sn6.
figure 1

a Confinement of electron eigenstate induced by destructive interference in kagome lattice with NN hopping. b Tight-binding calculation of band structure of kagome lattice with NN in-plane hopping without SOC, featuring the Dirac cone at the BZ corner K point, a saddle point at BZ boundary M point, and a FB over the whole BZ. c Crystal structure of YMn6Sn6 with space group P6/mmm (No. 191). d 3D and projected BZs of YMn6Sn6 with marked high-symmetry points. e Photoemission intensity plot measured with 138-eV photons at EF ± 10 meV in the kz ~ 0 plane. Hexagonal BZs are marked with red lines. f Magnetization as a function of temperature with zero field-cooling and field-cooling at B = 0.5 T along the [100] direction. Temperature dependence of longitudinal resistivity ρxx and ρzz with zero-field.

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In this paper, we study the electronic structure of kagome lattice YMn6Sn6 with in-plane ferromagnetism and helical antiferromagnetism along c-axis by combining angle-resolved photoemission spectroscopy (ARPES) and density functional theory plus dynamical mean-field theory (DFT + DMFT) calculations. We report the first experimental observation of the complete characters of kagome electronic structure: Dirac cone, flat band, and saddle point, in such a magnetic system. One complete set of the characteristic of kagome lattice includes a Dirac point (DP1) above EF, a saddle point (SP1) near EF and a flat band (FB1) locates at ~0.4 eV below EF across the whole BZ. They show negligible kz dispersion, suggesting the major 2D characters of the kagome structure in YMn6Sn6. The DFT + DMFT calculations with orbital-resolved electronic structures further confirm the 2D features with the in-plane orbital composition of dxy/\({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\). Moreover, we detected the existence of extra kagome characters, including a Dirac point (DP2) and a flat band (FB2) in the vicinity of EF. The DP2 has a dxy/\({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) with mixture of \({d}_{{{\rm{z}}}^{2}}\) orbital character, and presents a weak dispersion along kz, while the FB2 is mainly dominated by dxz/dyz orbitals. In the presence of SOC, the flat band and Dirac point have Chern numbers arising from the non-trivial Berry phase and supporting the orbital magnetism32. Altogether, these topological non-trivial bands in the kagome material will help understand the relationship between electronic/magnetic correlation and peculiar lattice geometry, and open an opportunity in manipulating the topological properties in magnetic materials.

Results

The crystal structure and transport property of YMn6Sn6

Kagome compound YMn6Sn6 has a hexagonal structure with space group P6/mmm (No. 191). It contains three kinds of Sn sites, stacking of Y-Sn3 layer and Mn–Sn1–Sn2–Sn1–Mn slab, with double Mn kagome lattice layers as shown in Fig. 1c. The Sn2 atoms form the honeycomb lattice located at the center of Mn–Sn1–Sn2–Sn1–Mn slab. As for the Mn kagome layers, neutron diffraction experiments reported FM coupling in each kagome bilayer, along with c-axis AFM coupling between the bilayer to the next bilayer below room temperature33,34,35.

Figure 1d shows the 3D BZ with high-symmetry points and projected BZ along c-axis. In Fig. 1e, the integrated intensity at EF ± 10 meV obtained from ARPES measurement at kz ~ 0 plane is shown to represent the Fermi surface (FS). There exist two pockets centered at \(\bar{K}\) point as marked, both with strong matrix element effects to modulate the intensity in different BZs36,37. The large one (β) is clearly identified in the 1st BZ but weaker in the 2nd BZ. It looks like an “arc-like” band in the 1st BZ and crosses the zone boundary near M, forming a closed “triangle”-like Fermi pocket. The small one (α) is more clearly visible in the 2nd BZ than in the 1st BZ, and forms a smaller pocket around \(\bar{K}\). Figure 1f shows the magnetization as a function of temperature with zero field-cooling and field-cooling at B = 0.5 T along the [100] direction. Two transformative peaks at TN = 359 K and Thel = 326 K are observed. The former temperature corresponds to the paramagnetism–antiferromagnetism phase transition. The latter corresponds to a transition from an AFM order along the c-axis above Thel to a c-axis helical order with in-plane FM order at low temperature, consistent with the previous results33,34,35,38,39. Moreover, the temperature dependence of longitudinal resistivity ρxx and ρzz with zero-field shows a metallic behavior with weak anisotropy, similar to GdMn6Sn640.

The complete characteristics of kagome structure

In order to investigate the kagome lattice related topological electronic structure, we measured the band structures in the 1st BZ at kz ~ 0 plane along with the high-symmetry lines. The intensity plots along the Γ–M–K–Γ line and the corresponding second derivative plots are shown in Fig. 2a, b, respectively. Along Γ–M, one can clearly see a quadratic band (QB) with its bottom at about 0.4 eV below EF at Γ dispersing upward towards M, and gradually becoming flat at the M point. Along M–K, an electron-like band disperses linearly upward towards EF and acrosses EF about one third between M and K, forming the β FS in Fig. 1e. At M point, it conforms to the dispersion of SP1 at EB ~ 40 meV, as marked in Fig. 2b. From intensity plot along Γ–K, the β band passes through the EF, forming a large holelike FS around K point, which can be more clearly seen in second derivative plots (Fig. 2b). This β band forms a Dirac point (DP1) at about 0.3 eV above EF by linear extrapolation, as indicated by the blue circle in Fig. 2c. Another feature is a flat band at about 0.4 eV below EF, FB1, which exists through the whole BZ. It can be regarded as a direct consequence of quantum phase interference effects in the kagome lattice, as shown in Fig. 1a. This flat band feature has a narrow bandwidth and the intensity is more visualized along Γ–K due to the matrix element effect. The band dispersion closely follows the DFT + DMFT calculations shown in Fig. 2c. In particular, it exhibits the complete characteristics of kagome electronic structure, a flat band (FB1) over the whole BZ touching a quadratic band at Γ point that emerges from the Dirac band (DP1) at K point and forms a saddle point (SP1) at M.

Fig. 2: Band structure evolution in the 1st BZ.
figure 2

a Photoemission intensity plots of YMn6Sn6 along Γ–M–K–Γ in the kz ~ 0 plane. b Corresponding second derivative plots of a. The appended colored lines serve as guides to the bands, which are extracted from DFT + DMFT calculations. c DFT + DMFT calculated ARPES in the FM state with SOC and with the experimentally determined EF shifted downwards about 76 meV. Dirac point (DP1 and DP2), saddle point (SP1) and flat band (FB1) are indicated by the blue circles and blue-colored region, respectively. d, e EDC plots along K–M and M–Γ–M, respectively. f, g MDC and EDC plots along the \(\bar{K}\)–\(\bar{K}\)–\(\bar{K}\) direction, with the momentum path indicated as inset. h Constant energy maps at different binding energies.

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At the K point, a linearly dispersing Dirac point (DP2) is found at around 45 meV below EF, which is also characteristic of the band structure as a result of kagome lattice similar as previously observed in FeSn and CoSn25,28,29. According to our DFT + DMFT calculated orbital-resolved electronic structures in FM configuration, the DP2 belongs to the spin-polarized band with minority-spin state, as shown in the Supplementary Fig. 5. The DP2 can be also clearly seen from the momentum distribution curves (MDCs) and energy distribution curves (EDCs) in Fig. 2f, g, respectively. With consideration of SOC, a small bandgap <10 meV will open at DP2, adding a mass term to the linearly dispersive band, and a massive Dirac fermion thus can be formed. In consideration of in-plane FM configuration, it could realize a spin-polarized Dirac fermion with a non-trivial Chern gap in YMn6Sn6 as previously observed in TbMn6Sn6 by scanning tunneling microscopy/spectroscopy (STM/S) measurement18. In our result, this non-trivial Dirac fermion is in the occupied state and closer to EF than in TbMn6Sn6, and contributes to the intrinsic anomalous Hall effect at high magnetic field in transport measurement34.

Figure 2 h shows a series of constant energy evolution maps in the kz ~ 0. We notice that the β band constitutes a hole pocket and the α band holds an electron pocket around K point. Along with the energy going from EF to higher binding energy, the hole pockets gradually expand and the branches of β band get closer to each other along K–M–K, finally touching at SP1 with the binding energy ~40 meV. Further away from the energy, the band forms a hole band along Γ–M. At M point, the band dispersion conforms a saddle point at ~40 meV below EF. The α pocket firstly shrinks into a single point at K and then expands forming a Dirac point at about EB = 45 ± 10 meV.

In Fig. 3a, b, we show the ARPES data along Γ–K–M–K with photon energies from 70 to 180 eV, which covers near four BZs along kz. In Figure 3a, one can see that the band dispersions show no qualitative change at various photon energies. Especially, the β band shows no noticeable kz dependence, which is also identified by the constant crossing point of kF,∥ in Fig. 3b. The FB1 at about 0.4 eV below EF is also presented in every photon energy, with a limited bandwidth (does not exceed 150 meV) along Γ–A as shown in Fig. 3d, indicating a near 2D character of the band. Figure 3b shows the integrated intensity at EF ± 10 meV in ΓK–AH plane which covers part of K–M–K at extended in-plane BZs. The β band shows a little variation, further confirms the 2D-like character and ensures the 2D Dirac cone of DP1. The Dirac-related α band around \(\bar{K}\) also displays a negligible dispersion along kz, which has intensity modulation associated with matrix element effect, similar to FeSn and CoSn25,29. The kz dependence supports the quasi-2D characters of the DP1, DP2, and FB1 bands. An explanation to the 2D-like band structure is that the bands mainly originate from the orbitals confined by the kagome lattice.

Fig. 3: Photon-energy-dependence measurement of YMn6Sn6.
figure 3

a Photoemission intensity plots of YMn6Sn6 with variable photon energies along Γ(A)–K(H), the flat band (FB1) locates at the binding energy of about 0.4 eV through the whole BZ. The β band appears in every photon energy. b ARPES intensity map at EF in the k∥-kz plane with variable photon energies along Γ(A)–K(H), showing a well defined 2D-like band structure. c Energy-momentum dispersion of YMn6Sn6 measured at hν = 92 eV (kz ~ 0.6 π/c). d Photoemission intensity plot and DFT + DMFT calculated ARPES in the FM state with SOC along the Γ–A direction, respectively. e DFT + DMFT calculated ARPES in the FM state with SOC along Γ–K–H–A–Γ, with the experimentally determined EF shifted downwards about 76 meV. The blue-colored region highlights the manifestation of the kagome flat band.

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To confirm the speculation of the orbital characters in the helical magnetic state along c-axis, we carry out the DFT + DMFT calculations in FM configuration with SOC and show the results in Fig. 3e (and in Supplementary Fig. 4). In the DFT + DMFT calculated spectra, we downshift the chemical potential of 76 meV to match the experiment value Eexp mostly caused by a chemical doping of the sample. The calculations in the FM configurations agreed well with the observation, the orbital-resolved ARPES without SOC shows that the β band mainly originates from the minority-spin branch of dxy/\({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbitals (Supplementary Fig. 5). The DP1 locates at ~0.3 eV above EF and shows negligible dispersion along K–H as shown in Fig. 3e. The FB1 passing through the whole in-plane BZ originates from the minority-spin branch of the in-plane dxy/\({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbitals, and has a limited bandwidth at the entire BZ district.

Signature of phase-destructive flat band near E F

A feature that is faint in the 1st BZ but more clearly visible in the 2nd BZ is the existence of another flat band near EF at the BZ center, labeled as FB2 in Fig. 4. In Fig. 4a, the ARPES intensity plots and the corresponding second derivative plots along the Γ–M–K–Γ lines of the 2nd BZ at kz ~ 0 plane are shown. In the 2nd BZ, a spectral weight close to EF with binding energy ~60 ± 20 meV is clearly seen and extends over a large part of the BZ except around the K points due to the intensity leakage from the Dirac bands. In comparison, the intensity of the β and FB1 bands are stronger in the 1st BZ but become feeble in the extended BZ. We assign the contrasting behaviors between FB2 and FB1+β bands to the Brillouin-Zone-selection effects that show the different signal intensity in the first BZ and extended BZ36,37 due to the different parity, symmetries or spin-polarization of the bands. In Fig. 4b, we present the DFT + DMFT calculations of the band structure in the FM state with SOC, with a downshift adjustment of the chemical potential of 76 meV as in Fig. 3e. Figure 4c, d show EDC plots over more than one BZ along the high-symmetry line as marked in the insets. The contrast of the intensity among different BZs is shown, and the flat bands (FB1 and FB2) and the Dirac point (DP2) can be confirmed unambiguously. For the FB1, it is predicted to degenerate with the QB at the center of the BZ (Γ) without SOC. With the consideration of SOC, the two bands further hybridize and open a gap ~40 ± 10 meV, which is similar to the results in PM CoSn28. The FB2 declines weakly close to M and K points. It is noticed that the peak width becomes broader and the intensity becomes weaker near M and K points, which cause the expected Dirac points feature blurry and nearly indistinguishable, in agreement with the DFT + DMFT calculations in Fig. 4b. In conventional DFT calculations, there should be more band features in magnetic state, and several kagome-related structures are expected. However, in the DFT + DMFT calculations with consideration of the correlation effect which is normally present in the magnetic system, the broadness and the weaker intensity cause the smearing out of the band, the ARPES measurements normally observe fewer bands than DFT predictions, i.e., some band features around M, K, and along M–K.

Fig. 4: Band structure evolution in the 2nd BZ.
figure 4

a Photoemission intensity plots and corresponding second derivative plots of YMn6Sn6 in 2nd BZ along Γ–M–K–Γ in the kz ~ 0 plane. The dashed lines are served as guides to the eyes. Inset: with the zoomed-in plot. b DFT + DMFT calculated ARPES in the FM state with SOC to according to the corresponding path of a and with experimental EF. Dirac point, saddle point and flat band are indicated by the blue circles and blue-colored regions, respectively. c, d EDC plots along the high-symmetry lines, with the momentum paths indicated as inset. The flat bands (FB1 and FB2) and the parabolic band (QB) are indicated by the black dashed lines with thick and thin, respectively.

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We also present the evolution of the FB2 as a function of out-of-plane momentum kz measured in the in-plane-2nd-BZ along \({{{\Gamma }}}^{\prime}\)-\({A}^{\prime}\) as shown in Supplementary Fig. 3. The FB2 displays a weak dispersion over more than one BZ along kz. Combining its in-plane flat dispersion in the kz ~ 0 plane, weak dispersion along kz, and the DFT + DMFT calculated orbital-resolved ARPES as shown in Supplementary Fig. 5, we assign the orbital character of FB2 to dxz/dyz orbitals. It is worth notice that there exists an out-of-plane \({d}_{{{\rm{z}}}^{2}}\) orbital with a steep kz dispersion and crossing EF at certain kz, it thus might contribute to the c-axis conductivity in our transport measurements. Further, the FB1 displays a limited bandwidth (<150 meV) along kz in the 2nd BZ as shown in Supplementary Fig. 3. It is consistent with results in the 1st BZ with the in-plane dxy/\({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbital composition, as discussed earlier. According to the spin-polarized DFT + DMFT calculations, FB2 with a high density of states (DOS) around the EF is from the majority-spin state, indicating its singly spin degenerate origin. FB2 is the first momentum-space evidence of the flat band really close to EF in the magnetic kagome system, which could give interesting phenomena such as orbital magnetism32.

The band calculations

To take into account the strong electronic correlation effect of the Mn 3d electrons, in the DFT + DMFT calculations, we include an onsite Coulomb interaction parametrized with a Hubbard U = 4.0 eV and a Hund’s coupling J = 0.7 eV among the Mn 3d electrons in both the PM and FM states. In the PM state, the mass enhancements of the Mn 3d electrons near the EF are about 5–7, which are similar to the values in some iron chalcogenide superconductors41. The fluctuating local moment of Mn 3d electrons, namely, the average value of g[S(S+1)]1/2, is about 3.9 μB with an effective spin S = 1.5, indicating YMn6Sn6 has a large fluctuating local moment due to the Hund’s rule coupling. Combining with its metallic behavior, we conclude that YMn6Sn6 is a strongly correlated Hund’s metal41.

When the Mn 3d local moments are partially frozen and form long-range static FM order in the hexagonal ab plane, the mass enhancements of the Mn 3d electrons near the EF are substantially reduced to about 2-3. The fluctuating local moment of Mn 3d electrons remains the same value as in the PM state whereas the statically ordered moment is 2.1 μB, which is in excellent agreement with experimental measurement33,34.

Discussion

In the PM state, the YMn6Sn6 has two major characters, including the strong electronic correlation and the kagome related features. The kagome structure has a flat band, while the strong correlation gives extra mass enhancement. These combinations will contribute large DOS around EF and could cause several instabilities, such as charge density waves42, superconductivity12,43, or magnetic instability9,44. In the magnetic state, the spin degeneracies are lifted, and a few spin-polarized branches shift below EF. ARPES data reveal the existence of flat band with large DOS and Dirac point near EF in YMn6Sn6, these bands are thus of singly spin degenerate branches. With consideration of SOC, Chern gaps are opened and Chern numbers are assigned to each band correspondingly.

YMn6Sn6 posses a ferromagnetic bilayers which antiferromagnetically couple with neighboring bilayers. At low temperature, it exhibits an incommensate magnetic phase along c-axis33,35. With the breaking of the combined symmetry of inversion and time-reversal symmetry PT, the electron bands become spin-polarized. In order to confirm the spin configuration of individual bands and the corresponding flat band and Dirac point (Weyl point), further spin-polarized ARPES measurements are needed.

These spin-polarized bands carry Berry curvatures and also cause the orbital magnetism. The existence of an orbital magnetic moment has been reported in Co3Sn2S2, and was attributed to the kagome flat band32. However, the ARPES observation of flat band near EF has not been reported in Co3Sn2S2 yet. The orbital magnetism of the flat band of tight-binding model in kagome lattice with Kane–Mele SOC was calculated in Supplementary Fig. 7, which is closely related to the Berry curvature. Both the flat band with non-zero group velocity part and the massive Dirac fermion will contribute to the orbital magnetism. Our ARPES results first reveal FB and Dirac fermion near EF with orbital-selective characters, so multiorbital-magnetisms are expected.

In summary, based on ARPES measurement and in combination with theoretical calculations, we have fully revealed the band structure of magnetic kagome YMn6Sn6, and presented the first experimental observation of the complete characteristics of kagome lattice near EF with spin polarization and non-trivial topological properties. The Dirac point and flat band near EF arise from the spin-polarized band with intrinsic Berry curvature may explain the anomalous Hall effect observed in transport measurements, and the orbital magnetic moment observed in STM/S measurement. As an ideal candidate for magnetic kagome lattice material with the electronic structure near EF, it opens up a new avenue to comprehend the intrinsic properties of magnetic topological electronic material. Furthermore, if the non-trivial band structures–Dirac points, flat band and/or saddle point are further tuned properly, it would possibly realize more versatile quantum phenomena in such material.

Methods

Sample growth and characterizations

Single crystals of YMn6Sn6 were grown by using Sn flux. Y lumps (purity 99.99%), Mn granules (purity 99.9%), and Sn grains (purity 99.99%) with a molar ratio of Y:Mn:Sn = 1:6:30 were put into an alumina crucible and sealed in a quartz ampoule under partial argon atmosphere. The sealed quartz ampoule was heated up to 1273 K and held for 24 h. Then it was cooled down slowly to 873 K at a rate of 5 K/h. Finally, the ampoule was taken out from the furnace and decanted with a centrifuge to separate YMn6Sn6 crystals from excess Sn flux. Magnetization and electrical transport measurements were carried out by using Quantum Design PPMS-14 T.

ARPES measurements

ARPES measurement were performed at the Dreamline and 03U beamline of the Shanghai Synchrotron Radiation Facility (SSRF), and 1-squared ARPES end-station of BESSY. The optimal energy and angular resolutions were set to 20 meV and 0.2°, respectively. Samples were cleaved in situ along (001) surface. During the measurements, the temperature was kept at 25 K and the pressure was maintained less than 5 × 10−11 Torr.

DFT + DMFT calculations

The electronic structures of YMn6Sn6 were computed by using DFT + DMFT45. The DFT part is based on the full-potential linear augmented plane wave method implemented in WIEN2k46. The Perdew–Burke–Ernzerhof generalized gradient approximation47 is used for the exchange correlation functional. DFT + DMFT was implemented on top of WIEN2k and was described in details48. In the DFT + DMFT calculations, the electronic charge was computed self-consistently on DFT + DMFT density matrix. The quantum impurity problem was solved by the continuous time quantum Monte Carlo method49,50 with a Hubbard U = 4.0 eV and Hund’s rule coupling J = 0.7 eV. The experimental crystal structure51 (space group P6/mmm, No. 191) of YMn6Sn6 with lattice constants a = b = 5.512 Å and c = 8.984 Å was used in the calculations.