Magnetoelectric torque and edge currents in spin-orbit coupled graphene nanoribbons

TL;DR

This paper investigates the magnetic and spin transport properties of graphene nanoribbons with Rashba spin-orbit coupling, revealing gate-controlled magnetoelectric effects, edge spin currents, and chiral charge flows influenced by magnetization orientation.

Contribution

It introduces a detailed analysis of magnetoelectric torque and edge currents in spin-orbit coupled graphene nanoribbons, highlighting novel gate-tunable effects and edge spin phenomena.

Findings

Gate voltage induces a sizable transverse susceptibility.

Non-collinear edge spin polarization occurs due to local torque.

Out-of-plane magnetization produces chiral edge charge currents.

Abstract

For graphene nanoribbons with Rashba spin-orbit coupling, the peculiar magnetic response due to the presence of a magnetization and geometric confinement are analyzed within a tight-binding model. We observe a sizable transverse susceptibility that can be considered as a gate voltage-induced magnetoelectric torque without the need of a bias voltage, with different directions for zigzag and armchair ribbons. The local torque generates non-collinear spin polarization between the two edges and/or along the ribbon, and the net torque averages to zero if the magnetization is homogeneous. Nevertheless, a nonzero net torque can appear in partially magnetized nanoribbons or in nanoflakes of irregular shapes. The equilibrium spin current produced by the spin-orbit coupling also appears in nanoribbons, but the component flowing in the direction of confinement is strongly suppressed. Even without the magnetization, an out-of-plane polarized chiral edge spin current is produced, resembling that in the quantum spin Hall effect. Moreover, a magnetization pointing perpendicular to the edge produces a laminar flow of edge charge currents, whose flow direction is symmetric (non chiral) or antisymmetric (chiral) between the two edges depends on whether the magnetization points in-plane or out-of-plane.