  We propose a concept of non-collinear spin current, whose spin polarization
varies in space even in non-magnetic crystals. While it is commonly assumed
that the spin polarization of the spin Hall current is uniform, asymmetric
local crystal potential generally allows the spin polarization to be
non-collinear in space. Based on microscopic considerations we demonstrate that
such non-collinear spin Hall currents can be observed for example in layered
Kagome Mn$_3$X (X = Ge, Sn) compounds. Moreover, by referring to atomistic spin
dynamics simulations we show that non-collinear spin currents can be used to
switch the chiral spin texture of Mn$_3$X in a deterministic way even in the
absence of an external magnetic field. Our theoretical prediction can be
readily tested in experiments, which will open a novel route toward electric
control of complex spin structures in non-collinear antiferromagnets.
