Beyond germanides: anomalous Hall effect in the silicide LaMn$_2$Si$_2$

By combining symmetry analysis and direct density functional calculations including the spin-orbit coupling, we demonstrate that anomalous Hall effect can be observed in not only germanides with general formula RMn$_2$Ge$_2$, where R is a rare-earth ion or Y. Our calculations predict a large anomalous Hall conductivity in LaMn$_2$Si$_2$, with a non-zero $\sigma_{xy}^{\mathrm{AH}}$ component of $-360~\text{S/cm}$, accompanied by a pronounced magneto-optical response. Remarkably, electron doping of LaMn$_2$Si$_2$ is expected to substantially enhance the Hall conductivity, with values reaching up to $-650$ S/cm. These results suggest that silicides with general formula RM$_2$Si$_2$ can be an interesting platform for studying anomalous Hall effect.