  It is argued that the subtle crossover from decoherence-dominated classical
magnetism to fluctuation-dominated quantum magnetism is experimentally
accessible in graphene nanoribbons. We show that the width of a nanoribbon
determines whether the edge magnetism is on the classical side, on the quantum
side, or in between. In the classical regime, decoherence is dominant and leads
to static spin polarizations at the ribbon edges, which are well described by
mean-field theories. The quantum Zeno effect is identified as the basic
mechanism which is responsible for the spin polarization and thereby enables
the application of graphene in spintronics. On the quantum side, however, the
spin polarization is destroyed by dynamical processes. The great tunability of
graphene magnetism thus offers a viable route for the study of the
quantum-classical crossover.
