Frequency-independent terahertz anomalous Hall effect in DyCo$_{5}$, Co$_{32}$Fe$_{68}$ and Gd$_{27}$Fe$_{73}$ thin films from DC to 40 THz

The anomalous Hall effect (AHE) is a fundamental spintronic charge-to-charge-current conversion phenomenon and closely related to spin-to-charge-current conversion by the spin Hall effect. Future high-speed spintronic devices will crucially rely on such conversion effects at terahertz (THz) frequencies. Here, we reveal that the AHE remains operative from DC up to 40 THz with a flat frequency response in thin films of three technologically relevant magnetic materials: DyCo$_{5}$, Co$_{32}$Fe$_{68}$ and Gd$_{27}$Fe$_{73}$. We measure the frequency-dependent conductivity-tensor elements ${\sigma}_{xx}$ and ${\sigma}_{yx}$ and find good agreement with DC measurements. Our experimental findings are fully consistent with ab-initio calculations of ${\sigma}_{yx}$ for CoFe and highlight the role of the large Drude scattering rate (~100 THz) of metal thin films, which smears out any sharp spectral features of the THz AHE. Finally, we find that the intrinsic contribution to the THz AHE dominates over the extrinsic mechanisms for the Co$_{32}$Fe$_{68}$ sample. The results imply that the AHE and related effects such as the spin Hall effect are highly promising ingredients of future THz spintronic devices reliably operating from DC to 40 THz and beyond.