▎ 摘　　要

In this paper we study the edge polarizations and their consequences for a biased Bernal stacked bilayer graphene nanoribbon with zigzag termination. The magnetic states are classified according to the interlayer and intralayer couplings between the edge polarizations, and the magnetic phase diagram of doping versus bias voltage is given. A coplanar magnetic phase is found and the variation of its magnetic structure with bias voltage is investigated. For all the magnetic states, we also discuss the possibility of half-metallicity, and for a ribbon with perfect zigzag edges, we predict seven kinds of half-metallic states, which are characterized by their distinct magnetic structures and quantized electrical conductances along the ribbon.