  Realizing magnetism in graphene/carbon nanostructures is a decade-long
challenge. The magnetic edge state and half metallicity in zigzag graphene
nanoribbons are particularly promising [Y.-W. Son, et al., Nature 444, 347
(2006)]. However, its experimental realization has been hindered by the
stringent requirement of the mono-hydrogenated zigzag edge. Using
first-principle calculations, we predict that free-carrier doping can overcome
this challenge and realize ferromagnetism and half-metallicity in narrow
graphene nanoribbons of general types of edge structures. This magnetism exists
within the density range of gate-doping experiments (~1013 cm-2) and has large
spin polarization energy up to 17 meV per carrier, which induces a Zeeman
splitting equivalent to an external magnetic field of a few hundred Tesla.
Finally, we trace the formation mechanics of this edge-insensitive magnetism to
the quantum confinement of the electronic state near the band edge and reveal
the scaling law of magnetism versus the ribbon width. Our findings suggest that
combining doping with quantum confinement could be a general tool to realize
transition-metal-free magnetism in light-element nanostructures.
