  Using a tight-biding model, we elaborate that the previously discovered
out-of-plane polarized helical edge spin current caused by Rashba spin-orbit
coupling can be attributed to the fact that in a strip geometry, a positive
momentum eigenstate does not always have the same spin polarization at the edge
as the corresponding negative momentum eigenstate. In addition, in the presence
of a magnetization pointing perpendicular to the edge, an edge charge current
is produced, which can be chiral or nonchiral depending on whether the
magnetization lies in-plane or out-of-plane. The spin polarization near the
edge develops a transverse component orthogonal to the magnetization, which is
antisymmetric between the two edges and tends to cause a noncollinear magnetic
order between the two edges. If the magnetization only occupies a region near
one edge, or in an irregular shaped quantum dot, this transverse component has
a nonzero average, rendering a gate voltage-induced magnetoelectric torque
without the need of a bias voltage. We also argue that other types of
spin-orbit coupling that can be obtained from the Rashba type through a unitary
transformation, such as the Dresselhaus spin-orbit coupling, will have similar
effects too.
