  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.
