Giant magneto-optical responses in magnetic Weyl semimetal Co3Sn2S2

Topological electronic band structures can generate enhanced electromagnetic responses. A key example is the intrinsic anomalous Hall effect (AHE), where Berry curvature from nontrivial band topology governs the Hall conductivity and can be maximized when the Fermi level is tuned near (anti-)crossings. Magnetic Weyl semimetals (WSMs), which host pairs of Weyl points acting as monopole/antimonopole sources of Berry curvature, have exhibited very large anomalous Hall conductivities and angles. However, direct, conclusive linkage between such large AHE and topological band features has been lacking. Theory predicts that intrinsic AHE leaves a fingerprint in the frequency-dependent optical Hall conductivity σxy(ω): interband transitions near topological crossings produce resonances, with Re σxy(ω) extrapolating to the dc Hall conductivity and Im σxy(ω) exhibiting onset above the interband threshold. Additionally, large magneto-optical (MO) Faraday and Kerr rotations are anticipated because they scale with the Hall angle. This study investigates whether the magnetic WSM Co3Sn2S2 exhibits these predicted low-energy optical signatures of intrinsic AHE and topological band structure, using terahertz Faraday and infrared Kerr spectroscopy together with first-principles calculations.

The work builds on extensive literature on topological semimetals and related responses: discovery and characterization of Weyl and Dirac semimetals and their Fermi-arc surface states; observations of large intrinsic AHE in various materials, including kagome-lattice ferromagnets; and theoretical proposals that optical Hall conductivity carries resonant features tied to Berry curvature near band crossings. Prior optical studies have identified large nonlinear responses in WSMs and explored MO effects in itinerant ferromagnets, as well as Faraday/Kerr phenomena in topological insulators. For Co3Sn2S2 specifically, prior ARPES has established Weyl points and Fermi arcs, and transport has shown giant AHE. These set the stage to test the predicted intrinsic AHE optical fingerprints and potential MO enhancement in a magnetic WSM.

Samples: Single crystals of Co3Sn2S2 were grown by a Bridgman method from stoichiometric Co, Sn, S sealed in quartz, heated to 1323 K and cooled to 973 K at 4 mm/h. Phase purity and structure were confirmed by powder X-ray analysis. A 42-nm-thick c-axis-oriented Co3Sn2S2 thin film with a 50-nm SiO2 cap was grown by RF magnetron sputtering on Al2O3(0001). Structure/composition were verified by XRD and EDX. Transport: Magnetoresistivity and Hall resistivity were measured using a PPMS. Magneto-optical measurements: Infrared Kerr rotation/ellipticity spectra (0.08–1 eV) on bulk crystals were measured with a photoelastic modulator. Samples were field-cooled from 200 K in −70 mT to set a single ferromagnetic domain; measurements were taken at zero field, and spectra were antisymmetrized for opposite magnetizations. Terahertz Faraday rotation/ellipticity (1–8 meV) on thin films were obtained via THz time-domain spectroscopy (THz-TDS) with crossed-Nicol polarizers. Samples were field-cooled from 200 K in ±1 T; measurements were done at zero field. The complex Faraday rotation θ(ω)+iη(ω) was computed from Fourier transforms of orthogonal THz field components: θ(ω)+iη(ω)=tan−1(Ey(ω)/Ex(ω)). Optical conductivity extraction: For bulk crystals, reflectivity (0.01–5 eV) was Kramers–Kronig transformed to obtain σxx(ω). Low-energy extrapolation used Hagen–Rubens; high-energy extrapolation assumed reflectivity ∝ ω. For thin films in THz, complex conductivity σ(ω)=σ1+iσ2 was obtained from the complex transmittance t(ω) using standard thin-film formulas on a sapphire substrate with thickness d and vacuum impedance Z0=377 Ω. The SiO2 cap’s THz conductivity is negligible. Hall conductivity from MO: In infrared, σxy(ω)=−σxx(ω)ε1/2(ω)[θK(ω)+iηK(ω)], where ε is the complex dielectric function. In THz, σxy(ω)=σxx(ω)[θ(ω)+iη(ω)]/2. For thin films, Faraday rotation relates to Hall angle via θF+iηF≈Z0σxy d/(1+ns+Z0σxx d). First-principles calculations: Electronic structure was computed with OpenMX using LSDA, norm-conserving pseudopotentials with spin–orbit coupling via total-angular-momentum-dependent pseudopotentials. Basis: Co 6.0-s3p3d3, Sn 7.0-s4p3d1; charge-density cutoff 350 Ry; k-mesh 31×31×31; lattice constants a=5.36 Å, c=13.17 Å; calculated magnetic moment 0.9 μB/f.u. Wannierization used Wannier90 to build a basis of (s,p,d) orbitals on Co and Sn and (s,p) on S, totaling 106 orbitals/f.u. including spin, extracted from 194 bands spanning −20 to +50 eV. Optical conductivities were computed via the Kubo–Greenwood formula on a 100×100×100 k-grid with 20 meV smearing. To include correlation effects, all calculated energies were rescaled by a renormalization factor of 1.52 (energies divided by 1.52). Intraband (Drude) contributions were omitted in theoretical σxx and σxy.

- Co3Sn2S2 is a ferromagnetic metal (Tc ≈ 175 K) with a kagome Co network. DFT without SOC shows spin-polarized nodal rings; with SOC, nodal rings gap out leaving anti-crossing lines and Weyl points, consistent with ARPES literature. - Transport: Giant anomalous Hall conductivity σxy ≈ 1300 Ω−1 cm−1 at low T with field along c, among the largest known. Thin-film transport shows similar behavior. - Terahertz and infrared MO: Upon zero-field measurements after field cooling, both terahertz Faraday and infrared Kerr signals grow below Tc. • Faraday rotation θF up to ≈ 160 mrad (~9.4°) with Faraday ellipticity showing a negative slope versus energy; low-energy (1.38 meV) temperature dependence follows the dc Hall angle. • Infrared Kerr rotation θK exhibits a pronounced negative peak near 0.1 eV, reaching ≈ 57 mrad (~3.2°); Kerr ellipticity ηK shows two negative peaks at ≈ 0.15 eV and ≈ 0.3 eV. - Longitudinal optical conductivity σxx(ω): Drude response dominates below ≈ 0.02 eV; interband features include broad peaks at ≈ 0.2 eV and ≈ 0.6 eV, reproduced by DFT (after energy renormalization 1.52). Prior work associates ~0.2 eV with Co 3d–3d same-spin transitions and ~0.6 eV with Co 3d t2g → eg. - Optical Hall conductivity σxy(ω): • Experimental Re σxy(ω) increases toward zero energy below ~0.3–0.4 eV, changes sign around ~0.2 eV, and approaches the dc value in the THz limit; Im σxy(ω) forms a broad peak centered around ~0.1 eV and vanishes as ω→0, consistent with causality. • Theoretical σxy(ω) including interband transitions reproduces these features, with low-energy weight predominantly arising from interband transitions between the two bands forming the Weyl points and anti-crossing lines. • The spectral weight is distributed over a broad range (<0.4 eV), well beyond the Drude scattering rate (~3 meV), excluding extrinsic (intraband-scattering) AHE as the dominant mechanism. • The integration over dispersive anti-crossing lines crossing EF yields a continuum of resonance energies, producing a broad low-energy resonance band in σxy(ω) and a large dc AHE. - Hall angle and MO enhancement: • Hall angle tan θH = σxy/σxx reaches ≈ 0.5 near ~0.1 eV due to topological interband transitions. • Faraday rotation per thickness exceeds that of archetypal MO materials (e.g., Bi:YIG); quantitative metrics at 7.5 meV include Δn ≈ 10.6 and figure of merit ω0 λ n d / (2c) ≈ 451 mrad. • Kerr rotation is strongly enhanced even in far-infrared, surpassing typical ferromagnetic metals where Kerr is suppressed by large |εxx|1/2 from Drude response. Enhancement here originates from large Hall angle of topological bands rather than plasma-edge effects.

The observations directly link the giant dc AHE in Co3Sn2S2 to interband transitions involving topological band features (Weyl points and anti-crossing lines). The frequency dependence of σxy(ω)—a broad low-energy resonance band with Im σxy peaking near ~0.1 eV and Re σxy rising to the dc limit—matches theoretical expectations for intrinsic AHE driven by Berry curvature near gapped/barely gapped crossings, and differs qualitatively from extrinsic, intraband-driven responses. The dispersive anti-crossing lines that traverse EF naturally produce a continuum of transition energies, yielding the observed broad resonance and large zero-frequency extrapolation. Consequently, the MO responses, which scale with the Hall angle, are dramatically enhanced: Faraday and Kerr rotations reach unusually large values in the THz and infrared ranges, respectively, exceeding those of conventional (ferro)magnetic metals. This enhancement stems from Berry-curvature physics in the magnetic Weyl semimetal and is distinct from plasma-edge-related MO amplification. The results establish σxy(ω) as a spectroscopic fingerprint of intrinsic, topological AHE and demonstrate a pathway to strong low-energy MO functionalities in topological materials.

Magneto-optical spectroscopy combined with first-principles calculations reveals that Co3Sn2S2 hosts broad, low-energy resonances in the optical Hall conductivity arising from interband transitions across Weyl points and anti-crossing lines. These resonances account for the giant intrinsic dc anomalous Hall conductivity and produce exceptionally large terahertz Faraday and infrared Kerr rotations. The work provides conclusive spectroscopic evidence for the topological origin of the AHE in a magnetic WSM and demonstrates a MO enhancement mechanism rooted in Berry curvature, distinct from conventional plasma-edge effects. The mechanism is general and should apply to other topological materials, including nonmagnetic Dirac and Weyl semimetals, suggesting opportunities for low-energy MO and optoelectronic applications. Future research could extend measurements over remaining spectral gaps, explore gating or doping to tune EF relative to crossings, and survey broader material families to optimize MO figures of merit.

- Spectral gap: Direct MO measurements were not performed between 8 and 80 meV; connections in σxy(ω) across this window are inferred assuming no sharp resonances. - Theoretical modeling: Calculated σxx(ω) and σxy(ω) include only interband transitions; intraband (Drude) contributions are omitted. A phenomenological energy renormalization factor (1.52) is applied to match experiment. - Optical data processing relies on reflectivity extrapolations (Hagen–Rubens at low energy, linear-in-ω at high energy), which can introduce systematic uncertainties. - Measurements were performed in zero field after field cooling to select single-domain states; domain effects and hysteresis outside this protocol are not explored. - Results are shown for one compound (bulk and thin film); generality to other materials is argued but not experimentally verified here.