Ferromagnetic topological Weyl semimetals of Co3Sn2S2 with a kagome lattice, have attracted great attention because they host frustrated spin configurations, correlated electron interactions, and topological quantum states of matter8,9. Such a material with its fully polarized spin and topological properties can give rise to rich physical phenomena, such as a Berry curvature-induced anomalous Hall effect (AHE), negative orbital magnetism and Chern gapped topological fermions10,11. Experimental evidence for the bulk Weyl nodes near the Fermi energy and the magnetic topological state was provided by angle-resolved photoemission spectroscopy (ARPES) and magnetotransport measurements12,13. Chiral-anomaly-induced MR, a much high anomalous Nernst signal, and a quantum AHE predicted in the two-dimensional (2D) limit have also been reported8,14−16. However, direct visualization for the flat band related to the exotic correlated electron phenomena has not been detected in Co3Sn2S2 crystals and there has still been a controversial issue of physical properties on the S-terminated and Sn-terminated surfaces15,17. Moreover, the very high mobilities and magnetoresistance usually exhibited in topological Weyl semimetals, attributed to the high Fermi velocity of massless Dirac states and uncompensated electron and hole carriers, still need to be achieved in the Co3Sn2S2 crystals. Therefore, a significant improvement of the crystal quality is strongly desired.
High-quality kagome lattice materials are indeed difficult to prepare due to the requirement of the well-controlled 2D ideal kagome lattice formed by transition metal atoms as well as the elimination of vacancies and impurities18,19. The typical Co3Sn2S2 single-crystals prepared by the self-flux method reported by Liu et al. have an anomalous Hall conductivity (AHC), anomalous Hall angle (AHA), electron mobility, and MR of 1130 Ω−1cm−1 at 2 K, 20%, 730 cm2V− 1s− 1, and ~ 55%, respectively8,20. Thin films of Co3Sn2S2 have been prepared by molecular beam epitaxy, but showing a much lower AHC of 649 Ω−1cm−1 at 2 K and an AHA of 11.4% due to the poor compositional uniformity21. Recently, the chemical vapor transfer (CVT) method6,22 has been applied to grow crystalline Co3Sn2S2 nanoflakes with enhanced AHC of ∼1400 Ω−1cm−1, AHA of ∼32%, MR of ~ 180, and an electron mobility of ∼2600 cm2 V− 1s− 1. Numerical calculations have suggested that residual impurities are the limiting factor for mobility in ultra-high-quality materials23. These results suggest that the transport properties of Co3Sn2S2 crystals could be improved by a CVT method which results in a lower residual impurity and a corresponding lower concentration of carrier scattering centers.
In this article, we report the synthesis of high-quality Co3Sn2S2 crystals with the highest carrier mobility and AHA reported so far by an innovative CVT approach using single-crystal granules as source materials (named crystal-sourced CVT method, CS-CVT). Low-temperature magnetotransport measurements show that the carrier mobility, AHA, and MR of our high-quality Co3Sn2S2 crystals are remarkably enhanced to over 104 cm2V− 1s− 1, 40% and 2500%, respectively. Moreover, an ultranarrow flat band and topological surface states near the Fermi level are observed, which provide good microscopic understanding of the gigantic anomalous Hall effect. The significant enhancement in transport properties and the observation of the topological bands are attributed to our ultra-high-quality sample, as demonstrated by a combination of x-ray diffraction (XRD), scanning transmission electron microscopy (STEM) and STM measurements. Our study provides a feasible way to improve the quality of magnetic topological semimetal materials, showing promise for pursuing new topological properties such as a high-temperature quantum AHE in the 2D limit, as well as possible quantum devices based on topological physics.
Synthesis and structural characterizations of the ultra pure Co3Sn2S2 single crystals
The high-quality ultra pure Co3Sn2S2 single crystals were synthesized by the CS-CVT method, where single-crystal granules of Co3Sn2S2 were used as the source material and NH4Cl as the transport agent (Fig. 1a). The Co3Sn2S2 crystal has a rhombohedral structure with the space group, R-3m (No. 166), where Co atoms are arranged into a kagome lattice in the ab plane with a Sn atom at the center of each hexagon (Fig. 1b). All as-grown single crystals show a hexagonal shape with a lateral size ranging from 1–8 mm and a thickness of about 0.01mm (Supplementary Fig. 1). A typical optical photograph in Fig. 1c presents a Co3Sn2S2 hexagonal single crystal of 5.5 mm in lateral size, indicating the prior growth of ab plane with the CoSn kagome lattice. Energy dispersive X-ray spectroscopy (EDS) measurement on the as-grown crystals reveals an atomic ratio of Co:Sn:S very close to 3:2:2 (Supplementary Fig. 2). The x-ray diffraction (XRD) pattern of the Co3Sn2S2 single crystal only shows the (00l) diffraction peaks, confirming the pure phase of the as-grown single crystal with a preferred [001] orientation (Fig. 1d). The lattice parameters a, b, and c are measured by single crystal diffraction to be 5.3657 Å, 5.3657 Å and 13.1710 Å, respectively. The double-crystal x-ray rocking curve for the (003) Bragg reflection (Fig. 1e) demonstrates a much smaller crystal mosaic of 0.058°, as compared to 0.105° in typical crystals obtained by the self-flux method, indicating a high crystallinity with a low density of lattice defects. The h0l plane diffraction pattern of the Co3Sn2S2 (Supplementary Fig. 3) shows sharp diffraction spots practically without any split diffraction spots, which confirms the excellent single crystal nature of the material.
To further confirm the high quality of our Co3Sn2S2 crystals, we carried out atomic-scale structural and chemical analysis on cross-sectional samples using aberration corrected scanning transmission electron microscopy (STEM). Figures 1f,g show the simultaneously acquired STEM high-angle annular dark-field (HAADF) Z-contrast image and annular bright-field (ABF) image of the Co3Sn2S2 sample along the [100] zone axis, with the structural models overlaid and main crystallographic planes indexed. The distinct spatial distributions of Co, Sn and S atoms were further confirmed by the atomic-resolution chemical mapping shown in Supplementary Fig. 4e. All the images clearly reveal the perfect crystalline structure of the Co3Sn2S2 without noticeable structural defects. STM images were further used to measure the point-defect density. We identified two kinds of cleaved surfaces, Sn surface and S surface. From the typical 60 nm × 60 nm STM images on the S surface of Co3Sn2S2 obtained by the self-flux and CS-CVT method in Supplementary Fig. 5a,b, the average density of impurities in the Co3Sn2S2 crystal obtained by the self-flux method is 1.2×10− 2 atoms/nm2, which is 6.7 times higher than that of the Co3Sn2S2 crystal obtained by the CS-CVT method (1.8×10− 3 atoms/nm2) (Supplementary Fig. 5e). Similarly, for Sn surface, the average density of impurities in the Co3Sn2S2 crystal obtained by the self-flux method (2.8×10− 2 atoms/nm2) is 25.5 times higher than that of the Co3Sn2S2 crystal obtained by the CS-CVT method (1.1×10− 3 atoms/nm2) (Supplementary Fig. 5c-d,f). It implies only 1 residual impurity for every 1500 S atoms or every 2400 Sn atoms in the Co3Sn2S2 crystal obtained by the CS-CVT method. These results demonstrate that the use of high purity source materials with exact stoichiometry and clean vapor transportation process in the CS-CVT growth, can indeed significantly improve the crystal quality of Co3Sn2S2, without introducing residual atoms of flux agents.
The following question is why the crystal quality using CS-CVT is better than other growth methods previously reported. Compared to the self-flux method, the CS-CVT method can avoid contamination from flux agents, and provide stable thermal dynamics under a suitable constant growth temperature, preferring a growth in (00l) plane of Co3Sn2S2, resulting in the formation of perfect kagome plane. Furthermore, using Co3Sn2S2 single-crystal granules as the precursor ensures the purity of source materials and the initial stoichiometric ratio of Co, Sn, S elements. Compared to CVT method previously reported 6,22, what we used is the NH4Cl as transport agent, which is decomposed to NH3 and HCl gas at about 300 ℃, providing a clean crystallization process. The Cl ions have a strong transport ability for Co and Sn ions, leading to a growth of Co3Sn2S2 with the stoichiometric ratio at a cleaner condition and single-atom process.
Magnetization, resistivity, and large magnetoresistance
In the temperature dependence of magnetization of the Co3Sn2S2 crystal obtained by the CS-CVT method, a sharp magnetic transition was observed with a Curie Temperature (Tc) of 177 K (Fig. 2a and Supplementary Fig. 6). A non-collinear magnetic transition around 150 K is unnoticeable due to the high quality of the Co3Sn kagome lattice in our sample. The field dependence of out-of-plane magnetization reveals a large coercivity (Hc~5000 Oe), while the in-plane magnetization displays no sign of saturation in magnetic fields up to 2 T, suggesting that the Co3Sn2S2 crystal has strong magnetic crystalline anisotropy (Supplementary Fig. 6e,f). From the temperature-dependent resistivity curves (Fig. 2b), a kink at Tc = 181 K is clearly observed, which is slightly higher than the 177 K observed in magnetization measurements. The residual resistivity ratio (RRR) \({\rho }_{300K}/{\rho }_{2K}\) is over 128, which is about one order of magnitude higher than the values of 5–20 reported in previous works7,8,22, indicating the high quality of the present Co3Sn2S2 crystals. Importantly, we firstly observed a magnetic-field-induced metal-insulator-like transition, suggesting a high carrier mobility in the present Co3Sn2S2 crystal, which is similar to other topological semimetals such as LaSb, TaP and NbP24,25. The inset in Fig. 2b shows the conductivity reaches 2.3 × 105 Ω−1cm−1 at 2 K, which is one order magnitude higher than the reported values8,22, indicating that our Co3Sn2S2 single crystal is close to clean-limit regime26.
Figure 2c manifests the magnetic field dependence of transverse magnetoresistance under out-of-plane and in-plane magnetic fields at different temperatures. Notably, the non-saturated positive MR reached 2500% under a magnetic field of 15 T at 2 K at B⊥I, which is one order of magnitude larger than the previously reported results ranging from 55 to 250% in Co3Sn2S2 crystals6,8,27−31. The large MR in the present Co3Sn2S2 crystals is ascribed to a high carrier mobility and a low scattering rate of the carriers. Besides, a negative MR due to the chiral anomaly was observed at high temperature regime. The chiral-anomaly-induced MR is attributed to the Dirac band of the kagome lattice32. Longitudinal magnetoresistances measured with B parallel to the current at various temperatures in Fig. 2d show a net weakly positive MR below 40 K and a negative MR above 40 K due to the chiral anomaly, which represents a crucial peculiarity of Weyl fermions for Co3Sn2S2 crystals22,33. The different behavior of the longitudinal and the transverse magnetoresistance is on account of the strong out-of-plane anisotropy.
Gigantic AHE and underlying mechanism
The field-dependent \({\rho }_{yx}\) measured at different temperatures from 2 K to 180 K, in an out-of-plane configuration with B⊥I, shows the coexistence of AHE with hysteretic behavior and the normal Hall effect (NHE) with nonlinear profile (Supplementary Fig. 8). The \({\rho }_{yx}\) versus temperature shows a remarkable nonlinear change from 2 K to 20 K, which is attributed to the dual-carrier conduction mechanism. The field-dependence of the Hall conductivity (\({\sigma }_{yx}\)) from 2 K and 160 K calculated according to the formula \({\sigma }_{yx}=\frac{-{\rho }_{yx}}{{\rho }_{yx}^{2}+{\rho }_{xx}^{2}}\) (Fig. 3a and Supplementary Fig. 9), exhibits significant nonlinear behavior as the temperature decreases, indicating the enhancement of the dual-carrier conduction mechanism. The shaded areas in Fig. 3a represent the contribution of AHE. After subtracting the AHE signals, we thus extract the carrier densities and carrier mobilities by using the semiclassical Drude model (Supplementary Fig. 10a,b). The extracted carrier densities of electrons and holes (2 K) are about 7.9 × 1019 cm− 3 and 2.2 × 1020 cm− 3, respectively, and the corresponding mobilities of electrons and holes at 2 K are 10490 cm2V− 1s− 1 and 2480 cm2V− 1s− 1, respectively (Supplementary Fig. 10c). The electron mobility observed in our Co3Sn2S2 crystals is the largest among all reported magnetic topological semimetals, (e.g., Co3Sn2S2 ~ 2600 cm2V− 1s− 1, MnBi2Te4 ~ 3110 cm2V− 1s− 1, GaPtBi ~ 1500 cm2V− 1s− 1, Co2MnGa ~ 35 cm2V− 1s− 1)6,34−36. The carrier mobility and MR are useful metrics to quantify the quality of a semimetal crystal. The electron mobility is straightforward to measure and is inversely proportional to the average electron scattering rate in semimetal crystals. High mobility values in crystals imply that electrons are less likely to scatter over prolonged trajectories. The electrical transport in a semimetal usually consists of two types of carriers (electrons and holes) and an extremely high MR is usually attributed to a perfectly balanced hole-electron resonance condition that is much stronger than that in normal metals and semiconductors. Thus, it is crucial to obtain high-purity Co3Sn2S2 samples to realize a balance between electrons and holes and a high carrier mobility (µ), both of which will enhance the MR effect.
To study the large AHE of the high-quality Co3Sn2S2 crystals, we subtract the NHE contributions according to the dual-carrier Drude model (Supplementary Fig. 11, 12). The AHC \({\sigma }_{yx}^{A}\) shows a strong dependence on temperature and reaches a maximum of 1600 Ω−1cm−1 around 50 K (Fig. 3b), which is the largest value among all the reported pure Co3Sn2S2 crystals so far. In addition to a large AHC, the Co3Sn2S2 crystals show a gigantic AHA of \({\sigma }_{yx}^{A}/{\sigma }_{xx}\). The temperature dependence of \({\sigma }_{yx}^{A}/{\sigma }_{xx}\) (Fig. 3c) shows that AHA firstly increases and then decreases with increasing temperature. The \({\sigma }_{yx}^{A}/{\sigma }_{xx}\) exceeds 30% within a broad temperature range of 100 K to 160 K, and has a maximum of approximately 40% around 140 K. It is well established that a large intrinsic AHE is present in the magnetic Weyl semimetal Co3Sn2S2 due to the topologically enhanced Berry curvature, resulting in a giant intrinsic AHC. The theoretical AHC obtained from the integral of Berry curvature is about 1310 Ω−1cm−1 at 0 K7. However, the maximum AHC measured in our Co3Sn2S2 crystals reaches 1600 Ω−1cm−1 (Fig. 3d), suggesting that other mechanisms exist in the high-quality Co3Sn2S2 crystal. Smit and Berger proposed the skew scattering and side-jump effects that are affected by the spin-orbit interaction37,38. However, such mechanisms are usually observed in materials with a high conductivity, larger than 104 Ω−1cm−1, since the skew scattering can be suppressed by the increasing impurity scattering26. Indeed, the conductivity of our Co3Sn2S2 crystals reaches 104 Ω−1cm−1 around 100 K and rapidly increases to 2.3 × 105 Ω−1cm−1 at 2 K (Supplementary Fig. 13a). We also note that the measured AHC reaches the theoretical maximum for the intrinsic mechanism (1310 Ω−1cm−1) at 100 K. With further decreasing temperature, the AHC first increases to its maximum (1600 Ω−1cm−1) around 50 K then decreases to about 970 Ω−1cm−1 at 2 K with a linear dependence on the longitudinal conductivity \({\sigma }_{xx}\), as shown in Fig. 3d. Our results are very different from the previous results8, where AHC is almost independent to longitudinal conductivity σxx in the relatively low temperature range.
To understand the origin of the large AHC, we study the relationship between the anomalous Hall resistivity \({\rho }_{yx}\) and the longitudinal resistivity \({\rho }_{xx}\) by using the formula \({\rho }_{xy}^{A}=(a{\rho }_{xx}+b{\rho }_{xx}^{2})\bullet M\). The first term represents the skew scattering contribution, while the second term corresponds to the intrinsic or side-jump contributions. Both parts are linearly proportional to magnetization M. As shown in Fig. 3e, we plot the \({\rho }_{yx}\)/(\({\rho }_{xx}\bullet M\)) against \({\rho }_{xx}\), which exhibits a good linear relationship below 80 K. Therefore, we extract the contribution from the skew scattering, and the sum of side-jump and intrinsic contributions. The results are shown in Fig. 3f. We find that the fitted AHC of \({\sigma }_{total}\) is in good agreement with the experimentally observed values. Remarkably, the skew scattering gives a negative contribution to AHC, which is consistent with previous results6,7. Moreover, it becomes more significant with decreasing temperature due to the enhancement of the longitudinal conductivity. Therefore, we conclude that the reduction of AHC below 50 K is ascribed to the large negative contribution from skew scattering.
To distinguish the intrinsic and side-jump contributions to the AHC, we adopt a new scaling relation for the Hall conductivity \({\sigma }_{yx}\) and longitudinal conductivity \({\sigma }_{xx}\) in the limit of \({\rho }_{yx}\) ≪ \({\rho }_{xx}\) range. As shown in Supplementary Fig. 13b, we find that the intrinsic AHC is about 1400 Ω−1cm−1, close to the theoretical value. On the other hand, we also note that the skew scattering is almost negligible when the temperature is between 50 K and 80 K. In this range, therefore, the AHC increases with decreasing temperatures and exceeds the maximum intrinsic value, which is mainly due to the significant contribution from the side-jump effects. The observation of remarkable contributions of skew scattering and side-jump to AHE in our Co3Sn2S2 crystals further indicates that the sample is close to the clean-limit, i.e., ultra-low densities of defects and impurities39. We compare the previously reported key transport parameters of Co3Sn2S2 crystals and other magnetic topological materials in Supplementary Figs. 14 and 15, and the values of the carrier mobility, AHA, and MR observed in our Co3Sn2S2 samples are all the largest40–46.
Visualization of ultranarrow kagome flat bands using ARPES.
To understand the possible mechanism for the great improvement in the electronic transport properties of Co3Sn2S2 crystals, its Fermi surface and band structures were measured by high-resolution vacuum ultraviolet (VUV) laser ARPES at 20 K47. Figure 4a shows the Fermi surface mapping of Co3Sn2S2 crystals by integrating the spectra weight within ± 10 meV energy window with respect to the Fermi level. The Fermi surface is obtained by symmetrizing the original mapping considering the three-fold and mirror symmetry. Six small pockets are clearly observed firstly surrounding the Brillouin zone center Γ. The experimental Fermi surface in Fig. 4a is in conformity with the projections of the calculated Fermi surface (Fig. 4b). For the sake of understanding the origin of the strong spectral weights around the Brillouin zone corner k(k´), two tangent lines (marked Cut1 and Cut2 in Fig. 4a) are taken along two different momentum directions to display the band structure near point K. The detailed band structures near-EF(Cut1) along Γ-K directions are shown in Fig. 4c. The topological surface state marked by the red circle (labeled TSS) is observed with kF about 0.4 Å−1 away from the K point, which can be more clearly identified in the corresponding second derivative spectrum. The positions of the topological surface states observed in the experiment are consistent with the results reported previously48. The topological surface states across the Fermi level are usually considered to enhance the carrier mobility due to the low effective mass49.
Moreover, around the K point, a nearly dispersionless flat band is captured (obviously presented in its relevant second derivative spectra). The flat band around the K point can expand a larger momentum space along the momentum Cut2 (indicated by red arrow in Fig. 4d). The corresponding EDCs are shown in Fig. 4e. Around the Fermi level, all the EDCs show very sharp peaks and the linewidths are all below 10 meV. Subtracting the temperature broadening of 7 meV at 20 K, the intrinsic line widths are about 6–7 meV. Such an ultranarrow flat band directly visualized by ARPES wass first reported in the kagome materials. In order to understand the origin of the flat bands, the band structure of Co3Sn2S2 is calculated based on relativistic density functional theory (DFT) projected on the Sn plane (Fig. 4f). The red line highlights the manifestation of the kagome flat band, showing quite flat and dispersionless behavior around both the Γ and K points. The calculated results are quite consistent with our ARPES results. In detail, the calculated band bottom around Γ is slightly above the Fermi level and the band bottom around K is just below the Fermi level. This also agrees with our ARPES results that a strong flat spectral weight is measured around the K point and quite weak spectral weight is measured around the Γ point. Combining the ARPES results and the band calculation, we conclude there is a kagome flat band around the Fermi level in Co3Sn2S2 which means the electron kinetic energy is strongly quenched by quantum interference effects, preventing delocalization of the wave function across the lattice. The appearance of flat bands is expected to increase the distance between a pair of Weyl nodes with opposite chirality which is nearly proportional to intrinsic AHE in magnetic Weyl semimetal magnetic50,51.
In summary, using a “crystal-sourced chemical vapor transport” approach, we have successfully synthesized large-size, high-quality, hexagonal Co3Sn2S2 single crystals with an ultra-low impurity density. The improvement of crystal quality enables the first observation of an ultranarrow topological flat band and makes a huge enhancement for nearly all the physical properties of Co3Sn2S2. Our high-quality samples display an ultrahigh AHA of 40%, intrinsic carrier mobility of 10490 cm2V-1s-1, AHC of 1600 Ω-1 cm-1, and MR of 2500%, which are the highest among all reported results for Co3Sn2S2. Besides the contribution to AHE from Berry curvature, the observation of the skew scattering and side-jump effects on AHE suggests that our sample is close to the clean-limit regime. This CS-CVT method can be extended to fabricate other kagome materials with improved crystal quality and physical properties compared with other methods reported in the past. For example, we have successfully synthesized Co3In2S2 and Ni3In2S2 crystals of the best quality and highest carrier mobility (Supplementary Figs. 16 and 17). The present results provide a useful way towards the growth of high-quality magnetic topological materials and suggest a bright future for the investigation of exotic physics in topological materials and kagome lattice materials.