  Two magnetic impurities on the edge of a zigzag graphene nanoribbon strongly
interact with each other via indirect coupling, which can be mediated by
conducting carriers. By means of Quantum Monte Carlo (QMC) simulations, we find
that the spin-orbit coupling $\lambda$ and the chemical potential $\mu$ in
system can be used to drive the transition of local-spin exchange from
ferromagnetism to anti-ferromagnetism. Since the tunable ranges for $\lambda$
and $\mu$ in graphene are experimentally reachable, we thus open the
possibilities for its device application. The symmetry in spatial distribution
is broken by the vertical and the transversal spin-spin correlations due to the
effect of spin-orbit coupling, leading to the spatial anisotropy of spin
exchange, which distinguish our findings from the case in normal Fermi liquid.
