Giant magneto-optical responses in magnetic Weyl semimetal Co3Sn2S2

Abstract

The Weyl semimetal (WSM), which hosts pairs of Weyl points and accompanying Berry curvature in momentum space near Fermi level, is expected to exhibit novel electromagnetic phenomena. Although the large optical/electronic responses such as nonlinear optical effects and intrinsic anomalous Hall effect (AHE) have recently been demonstrated indeed, the conclusive evidence for their topological origins has remained elusive. Here, we report the gigantic magneto-optical (MO) response arising from the topological electronic structure with intense Berry curvature in magnetic WSM Co₃Sn₂S₂. The low-energy MO spectroscopy and the first-principles calculation reveal that the interband transitions on the nodal rings connected to the Weyl points show the resonance of the optical Hall conductivity and give rise to the giant intrinsic AHE in dc limit. The terahertz Faraday and infrared Kerr rotations are found to be remarkably enhanced by these resonances with topological electronic structures, demonstrating the novel low-energy optical response inherent to the magnetic WSM.

Fig. 1. Electronic structure and anomalous Hall effect (AHE) of magnetic Weyl semimetal Co₃Sn₂S₂.

a Optical Hall conductivity σ_xy(ω) calculated for a single anti-crossing point in the two-dimensional electronic structure with mass gap m = 0.03 eV and chemical potential μ = 0.05 eV. The red and blue curves are the real and imaginary parts of σ_xy(ω), respectively. The inset shows the schematics of the band structure assumed in this calculation. b The crystal structure of Co₃Sn₂S₂ and kagome network within Co₃Sn layer. c Band structure obtained from the first-principles calculation. The red and blue lines represent the spin-up and spin-down bands, respectively, without spin–orbit coupling. The dotted line represents the band structure with the spin–orbit coupling. d Schematic illustrations of the simplified band structures: nodal ring structure (left) open the gaps with the anti-crossing nodal line connected to the Weyl points (right) due to the spin–orbit coupling. e Magnetic-field dependence of the Hall conductivity for each temperature when the magnetic field is applied parallel to the c axis for the bulk single crystal. f Temperature dependence of Hall conductivity at 0 T (red open circles) and at 0.1 T (red filled circles), and resistivity at 0 T (blue line) for the bulk single crystal.

Fig. 2. Terahertz Faraday and infrared Kerr rotations.

a Terahertz Faraday rotation (θ_F) spectra. Inset: the schematic illustration of the Faraday rotation measurement. b Faraday ellipticity (η_F) spectra. c Infrared Kerr rotation (θ_K) spectra. d Infrared Kerr ellipticity (η_K) spectra. Inset: the schematic illustration of the Kerr rotation measurement. The measurements were done after the field cooling from 200 K.

Fig. 3. Longitudinal optical conductivity and optical Hall conductivity spectra obtained from the experiment and first-principles calculation.

Experimental (a) longitudinal optical conductivity spectra σ_xx(ω) and (c) optical Hall conductivity spectra σ_xy(ω). The red circle at zero energy in c represents the DC value of the σ_xy of the bulk single crystal. The inset of c shows the optical Hall conductivity spectra including the terahertz spectra on the logarithmic energy scale. The red square at zero energy in the inset of c represents the DC value of the σ_xy of the thin film. The dashed lines in c for a photon energy region of 8–80 meV, where the MO measurements could not be done, represent the anticipated connections between the experimental σ_xy(ω) values in THz/DC and infrared regions, assuming that no sharp resonance structure is present in this narrow energy window. Theoretical (b) longitudinal optical conductivity spectra σ_xx(ω) and (d) Hall conductivity spectra σ_xy(ω) (see Method). In d, the red and blue curves represent the σ_xy(ω) spectra which take into account all band structures, while the pink and light blue ones show the σ_xy(ω) arising from the topological bands indicated by bold lines in e. These theoretical calculations include only the interband transition, so that the response from the intraband transition or Drude response of conduction electrons is omitted. e The band structure obtained from the calculation considering the renormalization factor. The two bands indicated by bold curves compose the anti-crossing lines and Weyl points. f Optical Hall conductivity σ_xy(ω) calculated for a single anti-crossing point in the two-dimensional electronic structure with mass gap m = 0.02 eV and chemical potential μ = 0.03 eV (red), 0.05 eV (orange), 0.07 eV (green), 0.09 eV (blue). The dotted line illustrates the schematic curve of the integrated sum of these resonances arising from the dispersive nodal ring. (Inset) Schematic illustration of the optical transitions on the cross-sections of the dispersive anti-crossing lines.

Fig. 4. Large magneto-optical responses due to Berry curvatures.

a Hall angle spectra, tanΘ_H = σ_xy/σ_xx. The red circle at zero frequency represents the DC value of the Hall angle of the bulk single crystal. The inset shows the Hall angle spectra including the terahertz spectra on the logarithmic energy scale. The red square at zero frequency represents the DC value of the Hall angle of the thin film. b The peak magnitudes of the Faraday rotation angle divided by the sample thickness, d, for several ferromagnets. c Spectra of square root of the complex dielectric constant, ε_xx^1/2(ω). d The peak magnitudes of the Kerr rotation angle for several ferromagnetic metals.