Critical thickness for the emergence of Weyl features in Co₃Sn₂S₂ thin films

Abstract

Magnetic Weyl semimetals are quantum phases of matter arising from the interplay of linearly dispersive bands, spin-orbit coupling, and time reversal symmetry breaking. This can be realised, for example, in Co₃Sn₂S₂, based on a cobalt kagome lattice and characterised by intriguing phenomena such as large anomalous Hall effect, Nernst effect, and water oxidation. Here, we attempt to determine the robustness of the twofold necessary conditions for the emergence of the magnetic Weyl semimetal phase in Co₃Sn₂S₂ ultrathin films. Except for two-dimensional layered materials, a reduction of thickness generally makes it difficult to develop topological character and ferromagnetic long-range order. In Co₃Sn₂S₂ films, while ferromagnetic ordering appears robustly even in average thicknesses of one or two unit cells with island-like polycrystalline domains, the anomalous Hall conductivity appears only above a critical thickness of approximately 10 nm. The emergence of surface conduction and large anomalous Hall effect implies the distinct contribution of Weyl nodes and their Berry curvature. These findings reveal an exotic feature of Weyl physics in thin-film based superstructures as well as a potential for future applications in electronic devices.

Introduction

Of proposed magnetic Weyl semimetals (mWSMs)^1,2,3,4, particular interest has been focused on Co₃Sn₂S₂ with a kagome lattice of Co^5,6,7,8,9,10, three layers of which are stacked in one unit cell of the crystal structure (Fig. 1a). The electronic structure of Co₃Sn₂S₂ is schematically drawn in Fig. 1b. Finite contribution of spin-orbit coupling (SOC) produces a gap at the band crossing points except for the protected spatial symmetry positions (from left to centre of Fig. 1b). This is defined as Dirac semimetal (DSM) with possessing helical Fermi arcs (FAs). With broken time-reversal symmetry, the mWSM phase emerges with chiral FAs owing to ferromagnetic exchange splitting (right of Fig. 1b). On the projected surface normal to the plane of Co₃Sn₂S₂ films (Fig. 1c), the surface FAs contribute to provide electrical conduction because the pairs of Weyl nodes are tilted from the magnetisation direction along z axis⁹. The Weyl nodes in the electronic bands enlarge the summation of Berry curvature under the well-regulated Fermi energy (E_F)¹⁰, inducing the large anomalous phenomena^5,6,7. Ultimately, the emergence of the quantum anomalous Hall effect has been theoretically proposed in the monolayer of the kagome lattice¹¹ in Co₃Sn₂S₂¹².

Fig. 1: Thin films of kagome-lattice ferromagnet Co₃Sn₂S₂.

a Crystal structure of Co₃Sn₂S₂ and the ferromagnetic spin ordering below T_C drawn with VESTA²⁸. b Schematic band structures of nodal line semimetal, DSM, mWSM (FM: ferromagnetic coupling). Band crossing points, that is, Dirac and Weyl points, are represented by black and grey ellipsoids. c Distribution of Weyl points in energy–wave number (E–k) space and electrial conduction via chiral FA states in real space. Weyl points with opposite spin chiralities are represented by red and blue circles. d Typical out-of-plane XRD patterns of Co₃Sn₂S₂ films with varied t. Three different targets (A, B and C) were used to check the reproducibility of the film composition and quality. For t ≥ 40 nm, the film compositions determined by EDX are shown. e M versus T curves measured for t = 41, 10, 2.7 and 1.3 nm (fabricated with the target A) at μ₀H = 10 mT. The inset shows the t dependence of T_C.

While the benefit of the SOC is maintained in the ultrathin films, the robustness of the mWSM phase against the thickness reduction is independently influenced by the twofold stability of linear dispersive band and ferromagnetism. On the one hand, for topological materials such as three-dimensional topological insulators and DSMs, the topological phase disappears in ultrathin films owing to topological phase transition driven by hybridisation of surface states^13,14 and crossover by quantum size effect¹⁵, respectively. On the other hand, the stability of ferromagnetism in the thin-limit is an unresolved fundamental problem in Co₃Sn₂S₂. The itinerant ferromagnetism in the Co-kagome lattice of Co₃Sn₂S₂ is generally considered with the Stoner mechanism^16,17. Except for two-dimensional layered compounds such as CrI₃¹⁸ and Cr₂Ge₂Te₆¹⁹, however, it has been well known that the ferromagnetic order becomes drastically weakened in the thin-limit of conventional ferromagnetic metals^20,21.

Because of the difficulty in the exfoliation from bulk Co₃Sn₂S₂ crystals, we investigate the magnetisation and electrical transport properties in the films approaching the thin-limit by careful synthesis of Co₃Sn₂S₂ thin films with the varied film thickness t using vacuum deposition technique. We here disclose the robustness of mWSM phase in Co₃Sn₂S₂ via characterisation of ferromagnetism and Weyl transport features in Co₃Sn₂S₂ thin films. While the ferromagnetism with perpendicular magnetic anisotropy persists down to a few unit cell thicknesses with island-like polycrystalline domains, the mWSM phase with large anomalous Hall effect (AHE) emerges above a critical thickness of ~10 nm.

Results

Film growth and magnetisation measurements

We fabricated c axis oriented Co₃Sn₂S₂ films on Al₂O₃(0001) substrates by co-sputtering technique²² (Method). The t was controlled from nominal 1.3 nm (roughly one unit cell) to 61 nm. Figure 1d shows typical X-ray diffraction (XRD) patterns of nearly stoichiometric Co₃Sn₂S₂ films capped with SiO_x (a thickness of ~50 nm), where the systematic variation of thickness fringes indicates the uniform film quality and tunable manner of our t control at least down to t~10 nm (Supplementary Figs. 1 and 2). Although the diffraction intensity for t < 4 nm was very weak, the deposition rate for these films was reliably reproducible by the sputtering method. The surface morphology of thin films for t = 4 and 11 nm was fairly flat (Supplementary Fig. 3). Based on these observations, we apply the nominal value of t estimated from the deposition rate in the following discussions.

Figure 1e shows magnetisation M versus temperature T curves measured for films with nominal t values of 41, 10, 2.7 and 1.3 nm. A sharp rise in M occurs, respectively, at T = 181, 177, 143 and 130 K, which correspond to Curie temperature T_C. For t = 41 nm, the saturated value of M (M_s) of 0.29 μ_B per Co (where μ_B is Bohr magneton) at T = 10 K is comparable to the reported bulk value of 0.29–0.33 μ_B per Co^5,6,7,16,17. With decreasing t, both the M_s and the T_C (inset) decrease monotonically. Considering the Stoner mechanism^16,17, these decreases are induced by the reduction of the density of states (DOS) at E_F in the ultrathin films. In fact, the Hall coefficient R_H in the paramagnetic state is systematically decreased²³ (see Supplementary Fig. 4). Given that Co₃Sn₂S₂ thin films have semimetallic bands as in the bulk, the decrease in R_H should correspond to the decrease of carriers that contribute to the ordinary Hall effect, that is, the decrease in the DOS at E_F. However, the monotonous systematic trend of M, T_C and R_H at t > 4 nm in Supplementary Fig. 4 allows us to extrapolate the finite value of R_H in the ultrathin region, indicating that the ferromagnetic order is maintained with finite DOS even in the ultrathin films.

Structure-property relationship in Co₃Sn₂S₂ films

In contrast to these monotonous changes in magnetism, electrical resistivity ρ_xx (=R_s × t, where R_s is the measured sheet resistance) dramatically increases with the t reduction. In Fig. 2a, b, the t dependences of ρ_xx at (a) T = 200 K > T_C and (b) 2 K < T_C are shown, respectively. Here, ρ_xx is estimated based on the assumption that electrical conduction is uniform over the whole region of a film without surface conduction. Above approximately t = 15 nm, both ρ_xx values at T = 200 K and 2 K are virtually constant; the bulk component of electrical conduction is comparable in these thick films. In the intermediate range of ~3 nm < t < ~15 nm, ρ_xx at T = 200 K increases as t decreases, whereas ρ_xx at T = 2 K increases more significantly with a rough relation of $\rho _{xx} \propto t^{ - 1}$. Below t~3 nm, the electrical resistance exceeds the measurement limit. To comprehensively understand the impact of t on ρ_xx and also magnetism, we performed cross-sectional transmission electron microscopy (TEM) experiments for typical samples in these three t regions (nominal t = 45, 10 and 2.7 nm), as displayed in Fig. 2c–e. The 45-nm-thick sample is flat and the nominal t value estimated from the deposition rate is in excellent agreement with the t (t_obs) value observed by TEM. In the 10-nm-thick sample, crystalline domains form a continuous network albeit with t_obs fluctuating between 8 and 12 nm. Island-like polycrystalline domains eventually appear in the nominal 2.7-nm-thick sample (t_obs = 0–6 nm). Overall, the averaged t_obs matches well with the nominal t value, guaranteeing that our calculation of M using the film volume is reasonable (Fig. 1e). Figure 2f–h show the magnetic field μ₀H dependences of M, where μ₀ is the vacuum permeability and H is magnetic field strength (also see Supplementary Fig. 5 for Hall resistivity ρ_yx data). A clear hysteresis of M is observed for nominal t values of 41, 10 and 2.7 nm at T = 100 K. Please note that the coercive field is too large to measure hysteresis loops for t > 10 nm at T < 100 K in our apparatus with an upper limit of 7 T²². The ferromagnetic hysteresis with comparably large M is also obtained for nominal t = 2.7 nm while the coercive field becomes small with decreasing t. As shown in Supplementary Fig. 5d–f, ρ_yx of all films with t = 41, 10 and 4 nm show hysteresis behaviour at T = 100 K. Judging from the consistent hysteresis character of M and ρ_yx in Fig. 2f–h and Supplementary Fig. 5d–f, we confirmed the AHE origin of the observed ρ_yx as being consistent to the bulk^5,6 based on the intrinsic mechanism²⁴. The systematic comparison of these data shows that the high resistance exceeding the measurement limit in the ultrathin films with nominal t < ~3 nm arises from the formation of island-like polycrystalline domains, while the ferromagnetism persists with perpendicular magnetic anisotropy (Fig. 2h). More importantly, the samples with t = 45 and 10 nm exhibit the distinct ρ_xx behaviour (Fig. 2a, b) despite insignificant differences in their film qualities (Figs. 1d, 2c, d, and Supplementary Figs. 1 and 2), which signals a qualitative change in the conduction mechanism between these samples.

Fig. 2: Structure-property relationship.

a, b t dependence of ρ_xx at T = 200 K and 2 K, respectively. The symbols in a and b correspond to the used sputtering targets: A (circles), B (triangles) and C (squares). The red solid line in a is a guide to the eye, corresponding to the value of ρ_xx^bulk = 2.9 × 10⁻⁴ Ω cm. The blue solid line in b represents a rough relation of $\rho _{xx} \propto t^{ - 1}$. These data suggest three t regions with distinct conduction mechanisms: mWSM for t > ~15 nm, bad metal without surface conduction for ~3 nm < t < ~15 nm, and structurally disordered islands without electrical connection for t < ~3 nm. c–e Cross-sectional TEM images for t = 45, 10 and 2.7 (nominal) nm, respectively. The t_obs values represent rough thicknesses of Co₃Sn₂S₂ estimated from the TEM images. f–h M versus μ₀H curves for t = 41, 10 and 2.7 (nominal) nm, respectively. The used sputtering targets were A for e–h, B for d, and C for c.

Thickness dependence of electrical and AHE properties

The anomalous electrical transport properties are pronounced on the t dependent systematic variation in Fig. 3. As shown in Fig. 3a, thick films with t ≥ 20 nm exhibit metallic behaviour down to the lowest T of 2 K. The ρ_xx shows an inflection near T = 180 K, which agrees well with T_C detected by magnetisation measurements (Fig. 1e). In addition, two samples for t = 41 and 59 nm (broken lines) represent superior conductive behaviour in low T region with a comparable residual resistivity ratio to that for bulk single crystals^5,6,7,10. A decrease in t to <10 nm substantially increases the ρ_xx without an inflection around T_C (t = 5 and 4 nm) although M develops ferromagnetically. The ρ_xx for the films with nominal t = 2.7 and 1.3 nm was undetectable above the measurement limit (Fig. 2a, b) because of the disconnection of film domains (Fig. 2e). In Hall conductivity, $\sigma _{xy} = \frac{{\rho _{yx}}}{{\rho _{xx}^2 + \rho _{yx}^2}}$ (Supplementary Fig. 6a for the T dependence of ρ_yx) in Fig. 3b, the σ_xy dramatically increases at T comparable with T_C for M (Fig. 1e) and saturates at low T. Although many of the thick films (t > 10 nm) show σ_xy exceeding 1000 Ω⁻¹ cm⁻¹ at T = 2 K, which is comparable or even higher than the bulk values^5,6 and theoretically calculated values^5,12, the σ_xy for t = 5 and 4 nm is much suppressed. These bulk-comparable T-dependent ρ_xx and σ_xy strongly support that the AHE character in thick films t > 10 nm reflects the Weyl features of electronic bands. In addition to the high σ_xy, we observed a negative magnetoresistance in an in-plane H configuration, called the chiral anomaly^2,3,4,25, which has been discussed as a hallmark of the mWSM state⁵ (Supplementary Fig. 7).

Fig. 3: Critical t for the emergence of Weyl features in electrical transport properties.

a, b T dependence of ρ_xx and σ_xy measured at zero field after field-cooled at μ₀H = 1 T, respectively. The used sputtering targets were A for t = 41 nm, B for t = 40, 20, 10, 5 and 4 nm, and C for t = 59 nm. c t dependence of R_s⁻¹ at T = 2 K (blue symbols) and 200 K (red symbols). The red solid line is a linear fit to the data at T = 200 K. The blue solid and dashed lines for the data at T = 2 K represent two sample groups with different σ_s values. The blue solid curve is a guide to the eye. d t dependence of σ_xy at T = 2 K. The blue solid curve is a guide to the eye. Symbols in c and d correspond to the used sputtering targets: A (circles), B (triangles) and C (squares).

To find the surface-specific conductance contributions by surface FAs (Fig. 1c), we plot sheet conductance $\frac{1}{{R_{\mathrm{s}}}} = \frac{t}{{\rho _{xx}^{{\mathrm{bulk}}}}} + \sigma _{\mathrm{s}}$ as a function of t in Fig. 3c, where ρ_xx^bulk is the bulk resistivity of Co₃Sn₂S₂ film and σ_s is the t-independent surface conductance. We here summarise all data acquired for films fabricated with the three sputtering targets A (circles), B (triangles) and C (squares) to see the overall tendency and reproducibility. In the paramagnetic state at T = 200 K, a reliable linear fit to the data yields ρ_xx^bulk = 2.9 × 10⁻⁴ Ω cm (Fig. 2a) and a t offset of 1.1 nm. This linear relation indicates that the electrical conduction in the paramagnetic state for t = 5–61 nm is well dominated and reproduced by ρ_xx^bulk. In contrast, a finite R_s⁻¹ offset, which corresponds to the surface conductance σ_s, is extracted from the data for t > 20 nm at T = 2 K (indicated by the black arrow). There seem two sample groups with different σ_s (the blue solid and dashed lines); the detailed analysis will be reported elsewhere. The σ_xy in Fig. 3d initiates to increase above 10 nm with saturation in the thicker region. The σ_xy in the mWSM is discussed to be proportional to the distance between two Weyl points with opposite chiralities in k-sapce^1,26. Under the overall ferromagnetic condition against t variation, the gradual increase of σ_xy with increasing t reflects the development of pairs of Weyl nodes in the electronic bands, resulting in the simultaneous emergence of conductance contribution by the projected surface FAs at t > 20 nm. These significant variations reveal the presence of a critical thickness of Co₃Sn₂S₂ films hindering a feature of mWSM.

Stability of mWSM phase in Co₃Sn₂S₂ films

Using σ_xy and electrical conductivity $\sigma _{xx} = \frac{{\rho _{xx}}}{{\rho _{xx}^2 + \rho _{yx}^2}}$, we calculated a tangent of the Hall angle for AHE, σ_xy/σ_xx, which is directly linked to the Berry curvature of electronic bands in the intrinsic mechanism²⁴. As shown in Fig. 4a, the 40-nm-thick film exhibits σ_xy/σ_xx as large as 0.24 at T = 130 K. With a decrease in t, the T at which σ_xy/σ_xx becomes the largest shifts to low T. The T-dependent σ_xy/σ_xx can be apparently classified to two trends with/without peak at finite T (Supplementary Fig. 6b), which indicates that the AHE in all films is governed by the intrinsic mechanism identical to that for the bulk with different T-dependent σ_xx (Supplementary Fig. 8). To emphasise this trend, we made a contour plot of the σ_xy/σ_xx as functions of T and the sample thickness in Fig. 4b, where the nominal number of Co-kagome layers (three Co-kagome layers ~1.3 nm) is used as the sample thickness instead of t. The T_C values (black circles) determined by magnetisation measurements (Fig. 1e) define the ferromagnetic/paramagnetic regions in the diagram. As discussed in Figs. 1e and 2, the average one- and two-unit-cells-thick samples with island-like polycrystalline domains maintain the ferromagnetic ordering, securing that the time reversal symmetry is broken in overall t regions. It is now more obvious that a large-σ_xy/σ_xx region vanishes below a few tens Co-kagome layers, unveiling a mWSM phase emerges in the thicker region. The linear dispersive electronic bands would be intrinsically diminished in the thinner t region similarly to band renormalisation in DSM of Cd₃As₂ thin film^15,27. Though it is difficult to fully understand the additional role of disorder by lattice distortion and roughness in the disappearance of AHE in the ultrathin films, the intrinsic band modification in ultrathin films may be examined in future study by spectroscopy after overcoming the difficulty of surface treatment or exfoliation.

Fig. 4: Phase diagram of Co₃Sn₂S₂ films for magnetic WSM.

a T dependence of σ_xy/σ_xx measured for films with t = 40, 20, 10, 5 and 4 nm (fabricated with the target B) at zero field after field-cooled at μ₀H = 1 T. b Contour plot of σ_xy/σ_xx as a function of T and the nominal number of Co-kagome layers in the Co₃Sn₂S₂ films (PM: paramagnetic). The nominal number of Co-kagome layers was calculated using the c axis length determined by XRD (Supplementary Fig. 1). T_C (Fig. 1e) and T_peak are included for comparison. c Sheet Hall conductance tσ_xy at T = 2 K as a function of the number of Co-kagome layers. The solid line indicates the fitting result using a linear relation of ${\mathrm{log}}\,t\sigma _{xy} = a + {\mathrm{log}}\,N_{{\mathrm{Co}}}$.

Discussion

The final remark in this study is the verification of quantum Hall conductance e²/h (e: elementary charge, h: Planck constant) of one Co-kagome layer in the mWSM by a systematic extrapolation of sheet Hall conductance tσ_xy shown in Fig. 4c, which has been theoretically expected in kagome layer with a flat band feature^5,11,12. The good agreement of a linear relationship in the certain region may exemplify the two-dimensional contribution of each Co-kagome layer to the Hall conductivity with close E_F to the gap. In comparison with the 1.28 e²/h in each kagome layer calculated from the σ_xy value of 1130 Ω⁻¹ cm⁻¹ for bulk crystal⁵, the extrapolated value of 1.3 e²/h by fitting in Fig. 4c using a linear relation of ${\mathrm{log}}\,t\sigma _{xy} = a + {\mathrm{log}}\,N_{{\mathrm{Co}}}$, where a is a fitting parameter and N_Co is the number of Co-kagome layer, is further reasonable (Supplementary Fig. 9). The robust ferromagnetism in the ultrathin films, large AHE, and a verification of quantum conductance experimentally prove the significant feature of mWSM Co₃Sn₂S₂ thin films. Stabilisation of ultimate thin-limit of Co-kagome monolayer is a future interesting challenge to perform direct measurement of magnetic interaction in the layer and quantum conductance. In view of a wide variety of mWSMs and magnets with kagome lattice, heterostructure engineering and E_F tuning will pave a way to find emergent phenomena that relate with Weyl nodes.

Methods

Thin-film growth

The Co₃Sn₂S₂ films were grown on Al₂O₃(0001) substrates by radio-frequency magnetron sputtering²² with Co−SnS_1.35 mosaic targets. The mosaic target was prepared using an SnS_1.35 disc (mixed-phase of SnS and SnS₂) and Co metal chips. The film composition was controlled by the number and location of the Co metal chips. Three Co−SnS_1.35 mosaic targets were used, which are referred to as A, B and C in the text. To suppress possible influences by impurities, e.g., unreacted/segregated ferromagnetic Co, particular attention was paid to the reproducibility of the film composition using the three different targets. Prior to the film growth, the substrates were annealed at 1000 °C in air to obtain atomically smooth surfaces. The films were deposited at 400 °C and then capped with SiO_x, followed by in situ annealing at 800 °C in a vacuum. The crystal structure and composition of the films were analysed by XRD using Cu K_α radiation and energy-dispersive X-ray spectroscopy, respectively.

Electrical and magnetic measurements

Electrical measurements were performed with a Physical Property Measurement System (Quantum Design, Inc.). A Hall-bar shaped channel was patterned by mechanically scratching the film. Electrical contacts were made with indium solder. The measured ρ_yx versus μ₀H curves were anti-symmetrized. The T dependence of ρ_yx was obtained by anti-symmetrizing data taken at zero field after field-cooled at μ₀H = ±1 T. Magnetisation measurements were performed with a Magnetic Property Measurement System (Quantum Design, Inc.). Before the measurements, the bottom surface of Al₂O₃ substrate was polished to remove possible magnetic contaminations from the substrate holder used. For the M versus T measurements in Fig. 1e, the samples were cooled from T = 300 K to 10 K in an out-of-plane magnetic field of μ₀H = 1 T. Subsequently, M at μ₀H = 10 mT was measured in a heating process. The measured M versus μ₀H curves were anti-symmetrized for a comparison with ρ_yx versus μ₀H characteristics.