▎ 摘　　要

Graphene on a substrate will suffer an inversion-symmetry-breaking (ISB) lattice potential. Taking electron-electron interaction into account, we study in this paper the possibility of half-metallicity and a noncollinear (NC) magnetic phase for graphene zigzag nanoribbons without inversion symmetry. At half-filling it is found that the half-metallic (HM) state can be achieved at an intermediate value of the ISB potential due to its competition with the electron-electron interaction. Away from half-filling, the phase diagrams of doping versus ISB potential for different ribbon width are given, where the regimes for the HM states and NC magnetic state are clearly indicated and discussed. For ribbons with perfect edges, we predict a topological transition between two HM states with different magnetic structures, which is accompanied by an abrupt transition of electrical conductance along the ribbon from 2e(2)/h to e(2)/h.