  We perform density functional calculations on one-dimensional zigzag edge
graphene nano-ribbons (ZGNRs) of different widths, with and without edge doping
including semi-local exchange-correlations. Our study reveals that, although
the ground state of edge passivated (with hydrogen) ZGNRs prefers to be
anti-ferromagnetic, the doping of both the edges with Boron atoms stabilizes
the system in a ferromagnetic ground state. Both the local and semi-local
exchange-correlations result in half-metallicity in edge passivated ZGNRs at a
finite cross-ribbon electric field. However, the ZGNR with Boron edges shows
half-metallic behavior irrespective of the ribbon-width even in absence of
electric field and this property sustains for any field strength, opening a
huge possibility of applications in spintronics.
