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.
The boundary of topological insulators exhibits a pure spin current owing to the topological edge states. To exploit this edge spin current for spintronic purposes, a promising design is to make the topological insulator in contact with a metallic ferromagnetic thin film, such that the edge spin current can be used to manipulate the magnetization or vice versa. We demonstrate that in a 2D version of the topological insulator/ferromagnet junction, the topological edge state percolates into the ferromagnet, and the detail of the percolation depends significantly on the band structure and the magnetization orientation. Moreover, we uncover novel effects such as the existence of a room temperature persistent charge current, and elaborate how the real wave function of the percolated edge state makes the current-induced spin torque entirely field-like. This work is supported by FAPESP grant number 2016/08468-0.
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