Interplay of spin-orbit coupling and magnetic chirality: Multidirectional spin polarization in a helical antiferromagnet

Abstract

We investigate spin-dependent transport in a non-collinear helical antiferromagnet in the presence of spin-orbit coupling within a tight-binding framework. Using the Landauer-B\"{u}ttiker formalism, we analyze the generation of spin polarization arising from the combined effects of the helical magnetic texture and spin-orbit interaction. We find that finite spin polarization can be generated simultaneously along the $\hat{x}$, $\hat{y}$, and $\hat{z}$-directions, in contrast to the predominantly single-axis spin polarization commonly observed in conventional spin-filtering systems. The multidirectional spin polarization originates from the symmetry breaking introduced by the non-collinear magnetic order. We further show that the spin polarization is modified significantly in the presence of spin-orbit coupling and it has strong dependence on the parameters associated with the helical system. In particular, long-range hopping significantly enhances the spin-filtering effect, leading to large spin polarization components along all three spatial directions.