Topological materials, possessing unique electronic band structures, are predicted to exhibit exotic electromagnetic responses. The intrinsic anomalous Hall effect (AHE), unlike its extrinsic counterpart, arises from Berry curvature associated with the electronic band topology. Materials with non-trivial band crossings near the Fermi level are prime candidates for large AHE, with Weyl semimetals (WSMs) – hosting pairs of Weyl points with opposite chirality – being of particular interest. While some WSMs have shown exceptionally large AHE, conclusive evidence linking this to their topological structure has been lacking. The intrinsic AHE is expected to manifest as a resonant structure in the optical Hall conductivity spectra, arising from interband transitions influenced by Berry curvature. This resonant behavior differs from extrinsic mechanisms, providing a distinct experimental signature. Furthermore, the enhanced Hall conductivity near Weyl points should lead to a giant magneto-optical (MO) Faraday/Kerr effect – rotation of light polarization in magnetic media. This study investigates the intrinsic AHE and giant MO effect in the recently discovered magnetic WSM Co3Sn2S2 using terahertz Faraday/infrared Kerr spectroscopy on thin films and bulk single crystals, alongside first-principles calculations. The thin film allows precise measurement of the low-energy optical response, probing the conduction electron dynamics.

Previous research has demonstrated large AHE in various materials, including some WSMs exceeding 1000 Ω⁻¹cm⁻¹ and 10% Hall angle. However, direct experimental proof linking the large AHE to topological electronic structure has been lacking. Theoretical studies have predicted a resonant structure in optical Hall conductivity as a fingerprint of the intrinsic AHE, arising from interband transitions near Weyl points. The potential for a giant magneto-optical effect, stemming from enhanced Hall conductivity, in magnetic WSMs has also been suggested but remained unexplored experimentally. Several studies reported on the synthesis and characterization of Co3Sn2S2 as a magnetic Weyl semimetal, noting its large anomalous Hall effect. However, a detailed investigation linking this effect to optical properties was missing. This study directly addresses this gap.

Single crystals of Co3Sn2S2 were grown using the Bridgman method, and a 42-nm-thick c-axis-oriented thin film with a 50-nm SiO2 cap layer was fabricated by radio-frequency magnetron sputtering. Magneto-transport measurements were performed using a Physical Property Measurement System. Terahertz Faraday rotation was measured using terahertz time-domain spectroscopy (THz-TDS) in a crossed-Nicol configuration after field cooling. Infrared Kerr rotation and ellipticity were measured using a photoelastic modulator. Optical conductivity (σxx(ω)) was obtained from reflectivity measurements via Kramers-Kronig transformation. Optical Hall conductivity (σxy(ω)) was calculated from σxx(ω) and the MO Faraday/Kerr effects. First-principles calculations using density functional theory (DFT) within the local spin density approximation, including spin-orbit coupling, were performed to obtain the electronic band structure and optical conductivities using the OpenMX and Wannier90 codes. A renormalization factor of 1.52 was applied to the calculated energies to account for electron correlation effects.

Co3Sn2S2 exhibited a giant AHE, reaching 1300 Ω⁻¹cm⁻¹ at low temperatures. Terahertz Faraday rotation and infrared Kerr rotation showed significant enhancement below the Curie temperature (Tc ~ 175 K). The low-energy limit of terahertz Faraday rotation exhibited a similar temperature dependence to the DC Hall angle. Infrared Kerr rotation spectra showed a pronounced negative peak at 0.1 eV, and the Kerr rotation angle reached 57 mrad (~3.2°). Longitudinal optical conductivity (σxx(ω)) spectra revealed interband transitions at 0.2 and 0.6 eV, consistent with DFT calculations. Optical Hall conductivity (σxy(ω)) spectra were distinctly different from σxx(ω), showing a gradual increase in Re(σxy(ω)) toward zero frequency, consistent with the DC AHE value. Im(σxy(ω)) showed a broad peak structure around 0.1 eV. These spectral characteristics, both experimental and theoretical, strongly suggest the intrinsic origin of the AHE, attributed to interband transitions near Weyl points and anti-crossing lines. The observed Faraday rotation (~160 mrad, 3.8 mrad/nm), significantly larger than in conventional ferromagnets, and the enhanced infrared Kerr rotation, were attributed to the large Hall angle caused by the topological electronic structure. The broad spectral width of resonances in σxy(ω) was explained by the presence of dispersive anti-crossing lines near the Fermi level. The observed Faraday and Kerr rotations were shown to be proportional to the Hall angle, σxy/σxx = tan(θH).

The observed giant MO responses in Co3Sn2S2 are directly linked to the Berry curvature of its topological electronic structure. The resonance in the optical Hall conductivity, arising from interband transitions near Weyl points and anti-crossing lines, accounts for both the large AHE and the enhanced MO effects. This mechanism differs from the conventional plasma-edge enhancement and is expected to apply to a broader range of topological materials, including non-magnetic Dirac and WSMs. The large Faraday and Kerr rotations observed represent a significant enhancement compared to typical ferromagnetic materials and demonstrate the potential for novel optical and electronic applications based on topological materials.

This study demonstrates a strong correlation between the topological electronic structure of Co3Sn2S2 and its giant magneto-optical responses. The observed giant AHE and significantly enhanced Faraday and Kerr rotations are directly linked to the optical Hall conductivity arising from interband transitions near Weyl points and anti-crossing lines. This highlights the potential of topological materials for developing novel optical and electronic devices. Future research should explore the application of this effect in diverse topological materials and investigate the potential for tailoring these responses through material engineering.

The study primarily focuses on the optical properties of Co3Sn2S2 at low temperatures. Further investigation is needed to explore the temperature and frequency dependence across a wider range, and to study potential influence of defects and impurities. Moreover, the determination of optical Hall conductivity relied on the assumption of a relationship between the magneto-optical effects and the Hall angle. Additional experimental techniques could further validate this relationship.