Structural and magnetic instability of bilayer and trilayer zigzag graphene nanoribbons

Edge states at Fermi energy in layered zigzag graphene nanoribbons are unstable and may lead to structural deformation or magnetization of edges or both. We report first-principle study on structural and magnetic instability of bilayer and trilayer zigzag graphene nanoribbons with two different edge alignments. For layered nanoribbons with β-alignment edges, their edges undergo a structural instability and tend to bend inward; the structural deformation moves edge states away from Fermi energy to lower the total energy of the system and no further magnetization is needed in the bilayer nanoribbon, which leads to a nonmagnetic ground state; while structural deformation alone is not enough to stabilize the electronic structures of the trilayer nanoribbon and thus a further magnetization is needed, which leads to an antiferromagnetic ground state. For layered nanoribbons with β-alignment edges, no structural deformation happens and all layers keep flat; their edges undergo a magnetic instability to move edge states away from Fermi energy, which leads a magnetic ground state; the ground state of the bilayer nanoribbon has an antiferromagnetic intra-layer and ferromagnetic inter-layer magnetic order; the trilayer nanoribbon has a ground state with non-collinear but coplanar inter-layer magnetic moments. Our results reveal the relation between the stabilization mechanism of layered zigzag graphene nanoribbons and their spatial symmetry (determined by number of layers) and their edge interactions (determined by edge alignments).