Spin Hall effect emerging from a noncollinear magnetic lattice without spin-orbit coupling

The spin Hall effect (SHE), which converts a charge current into a transverse spin current, has long been believed to be a phenomenon induced by the spin--orbit coupling. Here, we propose an alternative mechanism to realize the intrinsic SHE through a chiral magnetic structure that breaks the spin rotation symmetry. No spin--orbit coupling is needed even when the scalar spin chirality vanishes, different from the case of the topological Hall effect. In known chiral antiferromagnetic compounds Mn$_3X$ ($X=$ Ga, Ge, and Sn), for example, we indeed obtain large spin Hall conductivities based on \textit{ab initio} calculations. Apart further developing the conceptual understanding of the SHE, our work suggests an alternative strategy to design spin Hall materials without involving heavy elements, which may be advantageous for technological applications.