Revealing the origin of the intrinsic anomalous Hall effect in the itinerant ferromagnet Fe$_3$Sn$_2$ by magneto-optical spectroscopy

A single ferromagnetic kagome layer is predicted to realize a Chern insulator with accompanying quantized Hall conductance, which upon stacking can become a Weyl-semimetal possessing large anomalous Hall effect (AHE) and magneto-optical activity. Indeed, in the kagome bilayer material Fe$_3$Sn$_2$, a large AHE was detected, however, it still awaits the direct probing of the responsible band structure features by bulk sensitive methods. By measuring the optical diagonal and Hall conductivity spectra, we identified their origin and determine the intrinsic contribution to the AHE. Facilitated by momentum and band decomposed first-principles calculations, we found that transitions around the K-point are responsible for a step edge at 0.25\,eV in $\sigma_{xx}$, while they strongly modify $\sigma_{xy}$ even towards the DC limit. Together with a broad hump detected around 0.9\,eV originating from multiple transitions, these excitations produce the static AHE.