Nodal line resonance generating the giant anomalous Hall effect of Co$_3$Sn$_2$S$_2$

TL;DR

This study reveals that tilted nodal line segments near the Fermi energy in Co$_3$Sn$_2$S$_2$ are responsible for its giant anomalous Hall effect, identified through broadband spectroscopy and theoretical modeling.

Contribution

It demonstrates that nodal line segments, rather than Weyl points, dominate the low-energy optical response and anomalous Hall effect in Co$_3$Sn$_2$S$_2$, supported by experimental and theoretical analysis.

Findings

Strong resonance at 40 meV linked to nodal line segments

Weyl points contribute negligibly to the AHE

Theoretical model matches experimental spectra well

Abstract

Giant anomalous Hall effect (AHE) and magneto-optical activity can emerge in magnets with topologically non-trivial degeneracies. However, identifying the specific band structure features like Weyl points, nodal lines or planes which generate the anomalous response is a challenging issue. Since the low-energy interband transitions can govern the static AHE, we addressed this question in the prototypical magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ also hosting nodal lines by broadband polarized reflectivity and magneto-optical Kerr effect spectroscopy with a focus on the far-infrared range. In the linear dichroism spectrum we observe a strong resonance at 40\,meV, which also shows up in the optical Hall conductivity spectrum and primarily determines the static AHE, thus, confirms its intrinsic origin. Our material-specific theory reproduces the experimental data remarkably well and shows that strongly tilted nodal line segments around the Fermi energy generate the resonance. While the Weyl points only give vanishing contributions, these segments of the nodal lines gapped by the spin-orbit coupling dominate the low-energy optical response.