  In the paper we consider the system composed of two magnetic planes attached
to zigzag terminations of the graphene nanostructure being an ultrashort
fragment of the armchair nanoribbon. We investigate theoretically an indirect
coupling between these magnetic planes mediated by charge carriers as a
function of external in-plane electric field. The calculations are based on a
tight-binding model supplemented with Hubbard term to account for coulombic
interactions. For selected sizes of the graphene nanostructure, particularly
high sensitivity of the coupling to the electric field is found. This leads to
the possibility of control over coupling magnitude and continuous switching of
its sign between antiferromagnetic and ferromagnetic one. Such a phenomenon is
demonstrated in the numerical results and its origin is analysed. The
robustness of this effect against armchair edge deformation and variation of
exchange energy between magnetic planes and spins of charge carriers is
discussed in detailed way.
