|
We elaborate that Rashba spin-orbit coupling causes an out-of-plane polarized helical edge spin current at the boundaries of 2D metals. In the presence of a magnetization pointing perpendicular to the edge, an edge charge current is also produced, which can be either 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 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 renders a gate voltage-induced magnetoelectric torque without the need of a bias voltage. We also argue that these phenomena are generic effects of a variety of spin-orbit couplings irrespective of the detail of the band structure, as also demonstrated for the Dresselhaus spin-orbit coupling and graphene nanoribbons.
|
