Co3Sn2S2: Kagome Ferromagnetic Weyl Semimetal
- Co3Sn2S2 is a layered kagome-lattice quantum material featuring intrinsic ferromagnetism, strong spin–orbit coupling, and topological Weyl semimetal behavior.
- Its unique crystal structure with interleaved Co, Sn, and S layers enables band inversion and nodal-line formation that partially gaps into isolated Weyl points.
- The material exhibits anomalous transport phenomena and tunable electronic responses influenced by defects, surface terminations, and chemical substitutions.
CoSnS is a layered kagome-lattice quantum material built from ferromagnetic Co kagome planes sandwiched between S and Sn layers. In the contemporary literature it is described, depending on emphasis, as a shandite-type half-metal ferromagnet, a prototypical magnetic Weyl semimetal, and a prototypical kagome metal. Its importance derives from the coexistence of intrinsic ferromagnetism, strong spin-orbit coupling, kagome-lattice electronic structure, topological Weyl bands and surface Fermi arcs, and nearly flat bands near , which together generate anomalous Hall and Nernst responses, orbital-magnetism-related phenomena, and pronounced sensitivity to defects, surface termination, and magnetic texture (Xing et al., 14 Sep 2025, Liu et al., 2021, Yan et al., 2018).
1. Crystal architecture and topological band framework
CoSnS is consistently treated as a layered shandite compound in which Co atoms form a two-dimensional kagome sublattice in each layer, with metallic Co–Sn layers stacked along the -axis and separated by sulfur-containing layers (Kassem et al., 2017). One structural description presents the crystal as built from CoSnS octahedra connected within the 0 plane by face sharing and along the 1 axis by corner sharing, while additional Sn1 atoms occupy interslab positions; another describes stacked 2-Sn-3-4 layers in a trigonal rhombohedral setting (Yan et al., 2018, Liu et al., 2021). Within this literature set, the crystal symmetry is usually given as rhombohedral 5, whereas one symmetry-based treatment of proposed magnetic structures discusses 6 (Ekahana et al., 2024, Shin et al., 2021).
The topological electronic structure is tied directly to this lattice geometry. In the ferromagnetic state, the combination of inversion symmetry, threefold rotation symmetry, and three mirror planes enables a band inversion near the Fermi level; without spin-orbit coupling, this produces a nodal-line semimetal with six nodal lines located in the three mirror planes (Liu et al., 2021). Spin-orbit coupling partially gaps the nodal line and leaves isolated Weyl-point pairs, so the experimentally relevant state is neither a fully gapped topological insulator nor an ungapped nodal-line semimetal, but a partially gapped nodal-line system with isolated Weyl points (Liu et al., 2021).
A complementary tight-binding analysis for cobalt-based shandites attributes the nodal-line semimetallic state to interlayer Co–Co coupling between different kagome layers and identifies the interaction between Co and the interlayer metal atoms as the main control parameter for the number and type of Weyl points (Luo et al., 2022). For Co7Sn8S9 specifically, that framework places the nodal line in the mirror plane 0 and, after inclusion of spin-orbit coupling, yields three pairs of type-I Weyl points (Luo et al., 2022). This makes the compound a benchmark system for chemically related Co-based shandites and alloys.
2. Ferromagnetism, anisotropy, and critical behavior
Magnetically, Co1Sn2S3 is a strongly anisotropic ferromagnet with the easy axis along 4 and a small ordered moment, commonly reported as about 5 at low temperature (Kassem et al., 2017, Menil et al., 2024). The Curie temperature is generally reported near 6–7 K, with one critical-behavior study giving 8 K from critical isotherm analysis, 9 K from the Kouvel–Fisher analysis of 0, and 1 K from the Kouvel–Fisher analysis of 2 (Yan et al., 2018). Other studies report 3 K, 4 K, or 5 K depending on method and sample set (Menil et al., 2024, Ekahana et al., 2024, Shin et al., 2021).
The critical behavior near the paramagnetic–ferromagnetic transition deviates from standard short-range three-dimensional universality classes. Modified Arrott-plot analysis yields 6 and 7, the Kouvel–Fisher method gives 8 and 9, and the critical isotherm analysis yields 0 (Yan et al., 2018). The data collapse under the scaling form
1
and the exchange is interpreted as long ranged,
2
with 3, consistent with a quasi-two-dimensional, Ising-like description with 4 and 5 (Yan et al., 2018).
The magnetic anisotropy is exceptionally large. High-field measurements report an out-of-plane saturation field 6 kOe and an in-plane saturation field 7 kOe at 2 K, together with a magnetocrystalline anisotropy coefficient 8 (2002.03940). The same work emphasizes that it is extremely difficult to align the small moment of 9 from the 0 axis into the kagome plane (2002.03940). In parallel, XMCD establishes that the Co magnetic moment is spin dominated with negligible orbital moment at all measured temperatures, and that the effective spin moment vanishes near 1 K (Ekahana et al., 2024).
3. Spin–orbit coupling, correlations, and flat-band physics
Spin–orbit coupling is not a perturbative detail in Co2Sn3S4; it is a defining mechanism of the Weyl state. High-resolution ARPES directly resolves the spin–orbit-coupling-induced reconstruction of the nodal line, showing that the gap varies strongly along the nodal line, from 0 up to about 50 meV in calculation, with an experimentally extracted gap size of about 55 meV in the occupied part of the gapped nodal line (Liu et al., 2021). This observation gives an electronic-structure basis for the material’s giant anomalous Hall conductivity, anomalous Hall angle, and anomalous Nernst effect (Liu et al., 2021).
Electronic correlations further renormalize the low-energy structure without destroying the Weyl phase. Optical spectroscopy combined with DFT+DMFT finds that the experimental electronic kinetic energy is about half of the noninteracting theoretical value, with 5 from Drude weight and 6 from plasma frequencies (Xu et al., 2019). The same work estimates a Coulomb interaction strength of 7 eV and concludes that the Weyl semimetal state, including bulk Weyl cones and surface Fermi arcs, survives in this correlated regime (Xu et al., 2019). A characteristic consequence is a correlation-induced flattened band connecting the two Weyl cones, associated experimentally with an asymmetric optical conductivity peak around 36 meV (Xu et al., 2019).
Flat-band physics near 8 is a recurrent theme. A scanning-tunneling perspective describes a sharp STS peak at about 9 meV below 0 on the S-terminated surface as a kagome-derived flat band and interprets its field dependence in terms of Berry-curvature-induced orbital magnetism and a magnetization-polarized Zeeman effect, with an extracted moment of about 1 (Liu et al., 15 Aug 2025). That interpretation is not uncontested: XMCD reports that the Co moment is overwhelmingly spin dominated with negligible orbital moment and explicitly notes that this conflicts with earlier STS-based interpretations that inferred a very large negative orbital moment from a flat-band peak near 2 (Ekahana et al., 2024). The literature therefore supports the existence of flat-band-related low-energy structure, while the partition between Co spin moment and orbital-magnetism-based spectroscopic response remains an active interpretive issue.
4. Surface terminations, Fermi arcs, edge modes, and thin films
Cleavage of Co3Sn4S5 produces two principal terminations, conventionally described as Sn terminated and S terminated, and the termination dependence is central to surface spectroscopy (Liu et al., 15 Aug 2025). The same perspective argues that the weakly bonded Sn interlayer governs cleavage, yielding atomically flat and generally unreconstructed surfaces that are unusually well suited to STM/STS (Liu et al., 15 Aug 2025). On the Sn-terminated surface, Fermi-arc-related states are described as lying in an energy window from the Weyl-point energy toward 6, whereas on the S-terminated surface their energy placement and scattering behavior differ (Liu et al., 15 Aug 2025).
Transport in thin films provides an independent surface-sensitive signature. Thickness-dependent sheet-conductance measurements on films in the 23–61 nm range show that above 7, in the paramagnetic Dirac semimetal phase, the conductance scales as an ordinary 3D conductor, but below 8, in the ferromagnetic Weyl semimetal phase, the sheet conductance acquires a finite thickness-independent intercept (Ikeda et al., 2021). The analysis uses
9
and interprets the nonzero intercept as a 2D surface conduction channel consistent with Fermi-arc surface states (Ikeda et al., 2021). The effective thickness of the surface conducting region is estimated as 0 nm, substantially larger than the 1 nm scale quoted for Bi2Se3 (Ikeda et al., 2021).
STM/STS studies of partially exposed kagome terraces have been used to probe boundary modes more locally. On narrow Co4Sn terraces, one study reported linearly dispersing quantum-well-like states attributed to hybridized chiral edge modes and estimated a velocity of order 5 (Howard et al., 2019). A later perspective likewise described approximately linear edge-state dispersion but quoted a velocity of about 6 and cautioned that the available data and error bars do not yet fully exclude trivial alternatives such as parabolic quantum-well states (Liu et al., 15 Aug 2025). More generally, the STM literature emphasizes that QPI-based identification of Fermi arcs is intrinsically difficult because trivial-to-trivial, trivial-to-arc, arc-to-arc, and bulk-assisted scattering channels can overlap on the same surface (Liu et al., 15 Aug 2025).
5. Intrinsic defects and oxygen-related quantum clusters
A recent atomic-scale study identifies the dominant intrinsic defects on both cleaved surfaces as native oxygen-related point defects and names them “intrinsic quantum clusters” because they act as tunable local quantum perturbations (Xing et al., 14 Sep 2025). The study combines STM/STS, non-contact AFM, and STEM/EELS; chemically, the oxygen assignment is supported by high-angle annular dark-field and annular bright-field STEM together with an oxygen 7-edge onset at 8 eV in EELS (Xing et al., 14 Sep 2025). The work concludes that oxygen-related defects dominate the intrinsic defect landscape on both cleaved surface terminations.
The defect configuration depends strongly on surface termination. On the Sn-terminated surface, oxygen impurities occupy the threefold hollow site among three surface Sn atoms, and nc-AFM confirms that all Sn sites are occupied rather than vacant (Xing et al., 14 Sep 2025). These defects strongly perturb the flat band near the Fermi level: the defect resonance near 9 shifts by about 5 meV relative to the impurity-free surface, consistent with local hole-doping behavior, and the perturbation extends over about 15 surrounding atoms in dI/dV maps (Xing et al., 14 Sep 2025). Under a perpendicular magnetic field up to 0 T, the near-1 peak shifts linearly to higher energy, interpreted as an orbital-magnetism-induced unconventional Zeeman response (Xing et al., 14 Sep 2025).
On the S-terminated surface, oxygen interstitials lie slightly off center relative to the S lattice, with nc-AFM indicating a displacement of about 80 pm from center and a position slightly lower than neighboring S atoms (Xing et al., 14 Sep 2025). These defects generate occupied in-gap impurity states below roughly 2 mV. Their local spectral pattern has 3 symmetry at higher energy and reduces to 4 symmetry at lower energy; specifically, the reported pattern changes from 5 at 6 mV to 7 at 8 mV (Xing et al., 14 Sep 2025). In contrast to the Sn-terminated case, these impurity states show no measurable magnetic-field response from 9 T to 0 T, indicating a nonmagnetic origin (Xing et al., 14 Sep 2025).
The broader implication is that even nominally unintentional oxygen is not merely disorder. In Co1Sn2S3, oxygen-related intrinsic point defects can tune flat-band structure, generate impurity-bound states, and produce surface-dependent symmetry and magnetic response (Xing et al., 14 Sep 2025). That conclusion aligns with a broader STM-based view that chemically controlled markers such as Fe-for-Co, In-for-Sn, and Se-for-S substitutions, ideally up to about 10%, could provide decisive layer-selective identifiers for future surface studies (Liu et al., 15 Aug 2025).
6. Magnetic phase complexity, metastability, and the low-temperature controversy
Although Co4Sn5S6 is often introduced as a 7-axis ferromagnet, its ordered phase is not universally described as a single simple state. Early low-field magnetization and AC-susceptibility measurements established an anomalous equilibrium “A phase” just below 8, bounded by 9 and 00, characterized by humps and dips in 01 and 02, a sizeable 03 only in the interval 04, and relaxation times of order seconds (Kassem et al., 2017). The same work argued against a conventional spin glass and suggested a nontrivial spin texture, with stripe domains, soft or hard magnetic bubbles, biskyrmions, or skyrmion-like states remaining possibilities (Kassem et al., 2017).
Subsequent studies diverged on the interpretation of the sub-05 anomaly. One angle-dependent magnetization study concluded that many sharp jumps seen for 06 are dominated by demagnetization effects, whereas a genuine second transition exists at 07 K only in the in-plane response; DFT in that work gives a weakly canted umbrella structure with 08 and attributes the 09 anomaly to an additional tiny in-plane canting 10–11 (Zivkovic et al., 2022). Another study argues that the famous 12 scale, reported there as 13 K, is not a thermodynamic phase transition at all but the crossing point between metastability boundaries set by a coercive field 14 and a demagnetization-controlled bow-tie threshold 15 (Menil et al., 2024).
At the same time, several papers report antiferromagnetic components or phase coexistence. A single-crystal study on Co16Sn17S18 and Co19Sn20S21Se22 describes a degenerate ground state in the parent compound consisting of coexisting out-of-plane ferromagnetism and in-plane antiferromagnetism, with 23 K and 24 K for 25, and a metastable state identified semiclassically as weak out-of-plane antiferromagnetism plus in-plane antiferromagnetism below 26 K (Shin et al., 2021). Independently, XMCD plus spatially resolved 27-ARPES and DFT detect an in-plane AFM minority phase embedded in a majority FM background, with the AFM-like “butterfly” dispersion persisting down to 6 K (Ekahana et al., 2024). A Hall-hysteresis study under field rotation further shows that tilting the field from 28 toward the kagome plane drives loop evolution from rectangular to bow-tie-like within a narrow angular window near the plane and introduces exchange bias, which is interpreted as evidence for the contribution of in-plane AFM interactions (Pate et al., 2023).
Taken together, these results indicate that the low-temperature magnetic state of Co29Sn30S31 is best treated as a problem of competing FM, AFM, canting, demagnetization, and metastability effects rather than as a settled single-order-parameter ferromagnet. The disagreement is not over the existence of strong 32-axis ferromagnetism, but over whether the additional structure below 33 is best understood as nontrivial texture, AFM minority phase, tiny symmetry-lowering canting, or metastable domain physics.
7. Anomalous transport, spin Hall physics, and chemical tuning
Co34Sn35S36 is a reference system for Berry-curvature-driven transport. Angular Hall measurements show that Berry curvature and ferromagnetism are both strongly anisotropic and remain parallel as the magnetization direction is varied (2002.03940). For the easy-axis configuration, the reported anomalous Hall conductivity reaches 37 at 10 kOe and 38, while in-plane transport for 39 and 40 is nearly isotropic, with 41 and 42, and maximal anomalous Hall angles of 43 and 44, respectively (2002.03940). A separate doping study describes the intrinsic anomalous Hall conductivity of pristine Co45Sn46S47 as having a plateau of about 48 over an energy window of roughly 100 meV just below 49 (Shen et al., 2020).
Chemical substitution can preserve, enhance, or suppress these responses. Small Fe substitution on Co sites adds an extrinsic skew-scattering contribution to the intrinsic Berry-curvature background and raises the anomalous Hall conductivity up to 50 and the anomalous Hall angle up to 51, with the intrinsic and extrinsic parts separated through the TYJ model (Shen et al., 2020). By contrast, Ni substitution systematically weakens ferromagnetism while preserving an intrinsic, topological anomalous Hall effect over a broad substitution range; the pristine anomalous Hall conductivity is reported as 52, decreasing to about 53 at 54, while the coercive field rises to a maximum of 55 T near 56–0.45 (Thakur et al., 2020). In a more drastic perturbation, replacing Sn in the kagome-layer environment by In in Co57SnInS58 nearly quenches ferromagnetism, shifts Weyl-type crossings far above the Fermi level, and reduces the anomalous Hall angle from roughly 59 in Co60Sn61S62 to about 63 (Singh et al., 3 Mar 2026).
Low-temperature transport also shows quantum-interference signatures associated with surface states. Single crystals display magnetoresistance of around 64 at 2 K, and low-field magnetoconductivity below about 30 K is well fitted by the Hikami–Larkin–Nagaoka form for weak antilocalization, with 65 at 2 K and a phase-coherence length of about 49 nm (Kuma et al., 2022). The same work reports that plotting the conductivity against 66 collapses the low-field curves, supporting a two-dimensional surface-state origin of the weak antilocalization (Kuma et al., 2022).
Theoretical work extends the transport discussion from charge Hall to spin Hall responses. An effective stacked-kagome model finds that the intrinsic spin Hall conductivity depends strongly on the direction of the ferromagnetic moment and distinguishes in-plane from out-of-plane spin Hall currents (Ozawa et al., 2023). In that analysis, out-of-plane spin Hall currents vanish with only Kane–Mele-type SOC but emerge once staggered Rashba SOC is included; the resulting surface spin accumulation is proposed as a route to perpendicular magnetization switching via spin–orbit torque (Ozawa et al., 2023). This suggests that Co67Sn68S69 functions not only as a magnetic Weyl semimetal with a large anomalous Hall effect, but also as a directionally tunable intrinsic spin-current source.