Antiferromagnetic spin motion at terahertz (THz) frequencies attracts growing interests for fast spintronics, however their smaller responses to external field inhibit device application. Recently the noncollinear antiferromagnet Mn$_3$Sn, a Weyl semimetal candidate, was reported to show large anomalous Hall effect (AHE) at room temperature comparable to ferromagnets. Dynamical aspect of such large responses is an important issue to be clarified for future THz data processing. Here the THz anomalous Hall conductivity in Mn$_3$Sn thin films is investigated by polarization-resolved spectroscopy. Large anomalous Hall conductivity Re $sigma_{xy} (omega) sim$ 20 $rm{Omega^{-1} cm^{-1}}$ at THz frequencies is clearly observed as polarization rotation. In contrast, Im $sigma_{xy} (omega)$ is small up to a few THz, showing that the AHE remains dissipationless over a large frequency range. A peculiar temperature dependence corresponding to the breaking/recovery of symmetry in the spin texture is also discussed. Observation of the THz AHE at room temperature demonstrates the ultrafast readout for the antiferromagnetic spintronics using Mn$_3$Sn and will also open new avenue for studying nonequilibrium dynamics in Weyl antiferromagnets.
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