Giant anomalous Hall effect in a ferromagnetic Kagomé-lattice semimetal

Abstract

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 Kagomé 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 Kagomé-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.

Figure 1. Crystal and electronic structures of Co₃Sn₂S₂ and the measured electric resistivity.

a, Unit cell in a hexagonal setting. The cobalt atoms form a ferromagnetic Kagomé lattice with a C_3z-rotation. The magnetic moments are shown along the c-axis. b, Energy dispersion of electronic bands along high-symmetry paths without and with spin-orbit coupling, respectively. "SOC" denotes "Spin-orbit coupling". c, Fermi surfaces of two bands (upper: electron; lower: hole) under spin-orbit coupling calculations. Different colors indicate different parts of the Fermi surface in the Brillouin zone. d, Temperature dependences of the longitudinal electric resistivity (ρ) in zero and 9-T fields. In zero field, a residual resistance ratio (RRR, ρ_300K/ρ_2K) value of 8.8 and a residual resistivity of ρ_2K ~ 50 μΩ cm is observed. e, Magnetoresistance measured in fields up to 14 T at 2 K, showing a non-saturated positive magnetoresistance. f, Hall data with a non-linear behaviour at high fields, indicating the coexistence of electron and hole carriers at 2 K. All transport measurements depicted here were performed in out−of−plane configuration with I // x // [21̄1̄0] and B // z // [0001]. The x and z axes, respectively, are thus parallel to the a and c ones shown in a.

Figure 2. Theoretical calculations of the Berry curvature and anomalous Hall conductivity.

a, Linear band crossings form a nodal ring in the mirror plane. b, The nodal rings and distribution of the Weyl points in the Brillouin zone. c, Spin-orbit coupling breaks the nodal ring band structure into opened gaps and Weyl nodes. The Weyl nodes are located just 60 meV above the Fermi level, and the gapped nodal lines are distributed around the Fermi level. d, Berry curvature distribution projected to the k_x–k_y plane. e, Berry curvature distribution in the k_y = 0 plane. The color bar for d and e are in arbitrary units. f, Energy dependence of the anomalous Hall conductivity in terms of the components of ${\Omega }_{yx}^z(k).$

Figure 3. Chiral anomaly induced negative magnetoresistance.

a, Schematic of chiral anomaly. When electron current I and magnetic field B are not perpendicular, the charge carriers pump from one Weyl point to the other one with opposite chirality, which leads to an additional contribution to the conductivity and negative magnetoresistance. b, Angle dependence of magnetoresistance at 2 K. For B ⊥ I // x // [21̄1̄0] (θ = 90°), the magnetoresistance curve shows a positive, non-saturated behaviour up to 14 T. The MR decreases rapidly with decreasing angle. A negative magnetoresistance appears when B // I // x // [21̄1̄0] (θ = 0°). c, Magnetoconductance at 2 K in both cases of B ⊥ I and B // I. The magnetoconductance is an equivalent description for the magnetoresistance. The positive magnetoconductance is observed in Co₃Sn₂S₂ when B // I. The fitting of the positive magnetoconductance in Inset shows a ~B^1.9 dependence, which is very close to the parabolic (~B²) field dependence.

Figure 4. Transport measurements of the AHE.

a, Temperature dependence of the anomalous Hall conductivity (σ_H^A) at zero magnetic field. The inset shows the logarithmic temperature dependence of σ_H^A. b, Field dependence of the Hall conductivity σ_H at 100, 50, and 2 K with I // x // [21̄1̄0] and B // z // [0001]. Hysteretic behaviour and the sharp switching appears at temperatures below 100 K. c, Temperature dependence of the anomalous Hall resistivity (ρ_H^A). A peak appears around 150 K. Since ρ_H^A was derived by extrapolating the high-field part of ρ_H to zero field, non-zero values can be observed just above T_C due to the short-range magnetic exchange interactions enhanced by high fields. d, σ dependence of σ_H^A. The σ-independent σ_H^A (i.e., σ_H^A ~ (σ)⁰ = constant), below 100 K, puts this system into the intrinsic regime according to the unified model of AHE physics (for more details see Supplementary Information),.

Figure 5. Transport measurements of the anomalous Hall angle.

a, Temperature dependences of the anomalous Hall conductivity (σ_H^A), the charge conductivity (σ), and the anomalous Hall angle (σ_H^A/σ) at zero magnetic field. Since the ordinary Hall effect vanishes at zero field, only the anomalous Hall contribution prevails (see Supplementary Information). b, Contour plots of the Hall angle in the B–T space. c, Comparison of our σ_H^A-dependent anomalous Hall angle results and previously reported data for other AHE materials. "(f)" denotes thin-film materials. The dashed line is a guide to the eye. The reported data were taken from references that can be found in the Supplementary Information.