Edge magnetism of finite graphene-like nanoribbons in the presence of intrinsic spin–orbit interaction and perpendicular electric field

This paper elucidates the combined effect of intrinsic spin–orbit interaction (ISOI) and perpendicular electric field $\left(E_z\right)$ on edge states in finite graphene-like nanoribbons. It is shown that the ISOI generates magnetic anisotropy which makes the in-plane edge magnetization configuration more energetically stable than the commonly studied out-of-plane one. The anisotropy less severely suppresses the former configuration than the latter. As concerns the E _z effect, the following evolution of electric transport properties is predicted: magnetic insulator, non-magnetic narrow-band semiconductor, and finally non-magnetic band insulator. (paper)