Magnetic Weyl semimetals with broken time-reversal symmetry are expected to generate strong intrinsic anomalous Hall effects, due to their large Berry curvature. Here, we report a magnetic Weyl semimetal candidate, Co3Sn2S2, with a quasi-two-dimensional crystal structure consisting of stacked Kagome lattices. This lattice provides an excellent platform for hosting exotic topological quantum states. We observe a negative magnetoresistance that is consistent with the chiral anomaly expected from the presence of Weyl nodes close to the Fermi level. The anomalous Hall conductivity is robust against both increased temperature and charge conductivity, which corroborates the intrinsic Berry-curvature mechanism in momentum space. Owing to the low carrier density in this material and the significantly enhanced Berry curvature from its band structure, the anomalous Hall conductivity and the anomalous Hall angle simultaneously reach 1130 Ω-1 cm-1 and 20%, respectively, an order of magnitude larger than typical magnetic systems. Combining the Kagome-lattice structure and the out-of-plane ferromagnetic order of Co3Sn2S2, we expect that this material is an excellent candidate for observation of the quantum anomalous Hall state in the two-dimensional limit.

Giant anomalous Hall effect in a ferromagnetic Kagomé-lattice semimetal.

The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing aspects in condensed matter physics and has been a controversial topic for a long time. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states. In a magnetic Weyl semimetal with broken time-reversal symmetry, there are significant contributions to Berry curvature around Weyl nodes, possibly leading to a large intrinsic AHE. Here, we report the quite large AHE in the half-metallic ferromagnet Co3Sn2S2 single crystal. By systematically mapping out the electronic structure of Co3Sn2S2 both theoretically and experimentally, we demonstrate that the intrinsic AHE from the Weyl fermions near the Fermi energy is dominating. The intrinsic anomalous Hall conductivity depends linearly on the magnetization and can be reproduced by theoretical simulation, in which the Weyl nodes monotonically move with the constrained magnetic moment on Co atom.

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Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co 3 Sn 2 S 2 with magnetic Weyl fermions.

Electronic systems with flat bands are predicted to be a fertile ground for hosting emergent phenomena including unconventional magnetism and superconductivity1–15, but materials that manifest this feature are rare. Here, we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2 (refs. 16–20). We observe a pronounced peak at the Fermi level, which we identify as arising from the kinetically frustrated kagome flat band. On increasing the magnetic field up to ±8 T, this state exhibits an anomalous magnetization-polarized many-body Zeeman shift, dominated by an orbital moment that is opposite to the field direction. Such negative magnetism is induced by spin–orbit-coupling quantum phase effects21–25 tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of a kagome magnet where the low-energy physics can be dominated by the spin–orbit-coupled flat band. The authors show that a magnetic material with kagome lattice planes hosts a flat band near the Fermi level. Electrons in this band exhibit ‘negative magnetism’ due to the Berry curvature.

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Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet

The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing aspect in condensed matter physics and has been controversial for a long time. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states. In a magnetic Weyl semimetal with broken time-reversal symmetry, there are significant contributions on Berry curvature around Weyl nodes, which would lead to a large intrinsic AHE. Here, we report the large intrinsic AHE in the half-metallic ferromagnet Co3Sn2S2 single crystal. By systematically mapping out the electronic structure of Co3Sn2S2 theoretically and experimentally, the large intrinsic AHE should originate from the Weyl fermions near the Fermi energy. Furthermore, the intrinsic anomalous Hall conductivity depends linearly on the magnetization and this can be attributed to the sharp decrease of magnetization and the change of topological characteristics.

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Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions

Magnetic Weyl semimetals (WSMs) with time reversal symmetry breaking exhibit Weyl nodes that act as monopoles of Berry curvature and are thus expected to generate a large intrinsic anomalous Hall effect (AHE). However, in most magnetic WSMs, the Weyl nodes are located far from the Fermi energy, making it difficult to observe the Weyl-node dominated intrinsic AHE in experiments. Here we report a novel half-metallic magnetic WSM in the Kagome-lattice Shandite compound Co3Sn2S2. The Weyl nodes, linked by gapped nodal rings, are crucially located just 60 meV above the Fermi energy. Owing to both the significantly enhanced Berry curvature arising from the Weyl bands and the low charge conductivity, the anomalous Hall conductivity (AHC) and anomalous Hall angle (AHA) experimentally reach up to 1130 ohms-1 cm-1 and 20% respectively, which allows the material to simultaneously host a large AHC and giant AHA. Interpreting WSMs as coupled quantum AHE layers, the present results suggest that thin films of this quasi-two-dimensional WSM present a promising candidate for the bulk-insulating quantum AHE. Co3Sn2S2 as an easy-to-grow magnetic WSM thus represents an ideal platform to study Weyl physics. Our findings further suggest half-metallic Weyl semimetals - combining a topological Weyl phase for one spin channel with a band gap for the other - as a new paradigm for materials with a large Berry-in-origin AHE.

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Giant anomalous Hall angle in a half-metallic magnetic Weyl semimetal

Single crystalline Sn${}_{2}$Co${}_{3}$S${}_{2}$ with the shandite-type structure was investigated by magnetization, magnetoresistance, Hall effect, and heat capacity measurements and by ${}^{119}$Sn M\"o\ss{}bauer spectroscopy. Sn${}_{2}$Co${}_{3}$S${}_{2}$ orders ferromagnetically at 172 K with an easy-axis magnetization of $\ensuremath{\approx}$1 ${\ensuremath{\mu}}_{B}$ along the hexagonal $c$ axis. The half-metallic ferromagnetic state is investigated by detailed band-structure calculations by density functional theory (DFT) methods. The magnetoresistance and the Hall effect as well as the DFT results show that ferromagnetic Sn${}_{2}$Co${}_{3}$S${}_{2}$ is a compensated metal. The ${}^{119}$Sn M\"o\ss{}bauer spectroscopic data confirm these findings. Large transferred hyperfine fields ${B}_{\mathrm{hf}}$ up to 34.2 T are observed.

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Ferromagnetic ordering and half-metallic state of Sn2Co3S2 with the shandite-type structure

The half metal (HFM) Sn2Co3S2 shows a fascinating S = 1/2 magnetism. Anisotropic coupling of spins in and between Co Kagome layers by Sn sites is now studied from the substitution effects of S by Se by systematic and local experimental and first principles data. Trends in crystal structure changes (c/a ratio) as retrieved from XRD data on the solid solution Sn2Co3S2−xSex are complemented by DFT modelling on Sn2Co3SeS and hitherto unknown Sn2Co3Se2. The relationship of crystal structure effects with changes in Curie temperatures and magnetic hysteresis is shown from susceptibility measurements. An insight into the role of the Sn sites in magnetism and bonding is gained from 119Sn Mossbauer spectroscopic measurements. Isomer shifts, quadrupole splitting, and magnetic hyperfine fields are interpreted by DFT calculations on chemical bonding, electric field gradients (EFG), Fermi contact, and spin polarization.

Tuneable anisotropy and magnetism in Sn2Co3S2−xSex – probed by 119Sn Mößbauer spectroscopy and DFT studies

In the shandite type solid solution InxSn2–xCo3S2 the transition from half metal ferromagnetic Sn2Co3S2 to the new thermoelectric InSnCo3S2 is related to A = In, Sn on different crystallographic sites. Effects and origin of crystal and electronic structure changes induced by A = In are now investigated within the solid solution 0 ≤ x ≤ 2 including In2Co3S2. Effects are studied from X-ray data, 119Sn Mosbauer spectroscopy, and ab initio calculations. Their origin is explored by DFT modeling on site preference of In and Sn in a supercell, electric field gradients (EFG), spin polarization, band structures, and direct space analyses (ELF, AIM). Indium is found to cause the crystal structure distortion on one A site, the electronic structure distortion to the other, as a consequence of inverted anisotropic bonding.

Half Antiperovskites VI: On the Substitution Effects in Shandites InxSn2–xCo3S2 †‡

Ag9FeS4.1Te1.9 was prepared by solid state synthesis from stoichiometric amounts of the elements at 873 K. The compound forms gray crystals which are stable against air and moisture. The crystal structure was determined by X-ray diffraction from selected single crystals. Ag9FeS4.1Te1.9 crystallizes in the space group F43m, a = 11.0415(7) A, V = 1346.1(1) A3, and Z = 4 (powder data at 293 K). The compound shows a reversible phase transition upon cooling to the space group P213, a = 11.0213(1) A, V = 1338.75(2) A3, and Z = 4 (single crystal data at 200 K). The title compound is the first example of an iron containing argyrodite-type material with Fe3+ located in tetrahedral sites. Silver atoms are disordered at room temperature which was taken into account by nonharmonic refinement of the silver positions. The refinement converged to R1 = 3.51% and wR2 = 10.66% for the room temperature measurement and to R1 = 1.55% and wR2= 5.23% for the 200 K data set (all data). Impedance measurements were performed in t...

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Synthesis and Crystal Structure Determination of Ag9FeS4.1Te1.9, the First Example of an Iron Containing Argyrodite

Phase pure Ag2MnSnS4 was synthesized from the elements using standard high-temperature solid-state methods. Its crystal structure was solved from single-crystal X-ray diffraction data collected from a pseudo-merohedrally twinned crystal as well as by Rietveld refinement of X-ray powder diffraction data. Ag2MnSnS4 crystallizes in the monoclinic space group Pc (no. 7) with the unit cell parameters a = 6.651(1), b = 6.943(1), c = 10.536(2) angstrom, beta = 129.15(1)degrees, V = 337.3(1) angstrom(3), and Z = 2. The tetrahedraly compound crystallizes in a superstructure of the wurtzite type and the tetrahedra volumes are in good agreement with the model for diamond-related compounds derived from the wurtzite structure type. The red semiconductor Ag2MnSnS4 has an optical bandgap of E-g = 2.0 eV and is stable up to its peritectic decomposition temperature of approximately 700 degrees C. Ag2MnSnS4 is a Curie-Weiss paramagnet with an experimental magnetic moment of mu(exp) = 5.4(1) mu(B) per manganese atom. Antiferromagnetic ordering is detected at a Neel temperature of T-N = 8.8(1) K. Sn-119 Mo ss bauer spectra at 78 K underline the single tetrahedrally coordinated Sn-IV site (delta = 1.34(1) mm center dot s(-1)). The 6 K spectrum (magnetically ordered state) reveals a small transferred magnetic hyperfine field of 1.02(1) T.

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Rainer Pöttgen

Papers

Ferromagnetic ordering and half-metallic state of Sn2Co3S2 with the shandite-type structure

Tuneable anisotropy and magnetism in Sn2Co3S2−xSex – probed by 119Sn Mößbauer spectroscopy and DFT studies

Half Antiperovskites VI: On the Substitution Effects in Shandites InxSn2–xCo3S2 †‡

Synthesis and Crystal Structure Determination of Ag9FeS4.1Te1.9, the First Example of an Iron Containing Argyrodite

Synthesis and Characterization of Ag2MnSnS4, a New Diamond-like Semiconductor