We investigate the magnetic ordering in zigzag edged graphene nanoribbons under cross-ribbon electric fields by using the Hubbard model within the unrestricted Hatree-Fock approximation. In the absence of applied electric field, the ground state is an "edge-magnetized state" with magnetic moments mainly localized on the edges, where the moments on the two edges are mutually antiparallel. Under electric fields, we find that the band gap near the Fermi level becomes spin dependent. On increasing the strength of the electric field, the biased charge distribution decreases or increases the band gap with respect to the majority spin on each edge. Increasing the strength further, the system becomes half-metalic, and finally the magnetization completely disappears.
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