Magnetoelectric torque and edge currents caused by spin-orbit coupling

TL;DR

This paper uses a tight-binding model to explain how Rashba spin-orbit coupling induces edge spin currents and charge currents in magnetic systems, revealing new magnetoelectric effects and the role of edge geometry.

Contribution

It demonstrates that Rashba spin-orbit coupling causes edge spin and charge currents, and introduces a mechanism for gate-controlled magnetoelectric torque without bias voltage.

Findings

Edge spin currents are due to momentum-dependent spin polarization.

Magnetization induces chiral or nonchiral edge charge currents.

Transverse spin polarization can cause magnetoelectric torque.

Abstract

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.