  Noncollinear antiferromagnets (AFMs) in the family of Mn$_3X$ ($X$=Ir, Sn,
Ge, Pt, etc.) have recently attracted attention in the emerging field of
antiferromagnetic spintronics because of their various interesting transport,
magnetic, and optical properties. Due to the noncollinear magnetic order, the
localized electron spins on different magnetic sublattices are not conserved
even when spin-orbit coupling is neglected, making it difficult to understand
the transport of spin angular momentum. Here we study the conserved Noether
current associated with spin-rotation symmetry of the local spins in
noncollinear AFMs. We found that a Hall component of the d.c. spin current can
be created by a longitudinal driving force associated with a propagating spin
wave, and is proportional to a response coefficient that we denote as the Hall
(inverse) mass. Such a Hall spin current can be generated by spin pumping in a
ferromagnet (FM)-noncollinear AFM bilayer structure as we demonstrated
numerically. Finally we showed that the Hall mass is an isotropic quantity,
similar to the isotropic spin Hall conductivity, and should generally exist in
noncollinear AFMs and their polycrystals. Our results shed light on the
potential of noncollinear AFMs in manipulating the polarization and flow of
spin currents in general spintronic devices.
