Electrical current can be completely spin polarized in a class of materials known as half-metals, as a result of the coexistence of metallic nature for electrons with one spin orientation and insulating for electrons with the other. Such asymmetric electronic states for the different spins have been predicted for some ferromagnetic metals−for example, the Heusler compounds 1 −and were first observed in a manganese perovskite 2 . In view of the potential for use of this property in realizing spin-based electronics, substantial efforts have been made to search for half-metallic materials 3,4 . However, organic materials have hardly been investigated in this context even though carbonbased nanostructures hold significant promise for future electronic device 5 . Here we predict halfmetallicity in nanometre-scale graphene ribbons by using first-principles calculations. We show that this phenomenon is realizable if in-plane homogeneous electric fields are applied across the zigzag-shaped edges of the graphene nanoribbons, and that their magnetic property can be controlled by the external electric fields. The results are not only of scientific interests in the interplay between electric fields and electronic spin degree of freedom in solids 6,7 but may also open a new path to explore spintronics 3 at nanometre scale, based on graphene 8,9,10,11

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our ab initio calculation results very well.