Hall mass and transverse Noether spin currents in noncollinear antiferromagnets

Noncollinear antiferromagnets (AFMs) have recently attracted attention in the emerging field of antiferromagnetic spintronics because of their various interesting 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 due to spin-rotation symmetry of the local spins in noncollinear AFMs. Interestingly, we find that a Hall component of the spin current can be generically created by a longitudinal driving force associated with a propagating spin wave, inherently distinguishing noncollinear AFMs from collinear ones. We coin the corresponding Hall coefficient, an isotropic rank-4 tensor, as the Hall (inverse) mass, which generally exists in noncollinear AFMs and their polycrystals. The resulting Hall spin current can be realized by spin pumping in a ferromagnet (FM)-noncollinear AFM bilayer structure as we demonstrate numerically, for which we also give the criteria of ideal boundary conditions. Our results shed light on the potential of noncollinear AFMs in manipulating the polarization and flow of spin currents in general spintronic devices.