Spin states of zigzag-edged Möbius graphene nanoribbons from first principles

Mobius graphene nanoribbons have only one edge topologically. How the magnetic structures, previously associated with the two edges of zigzag-edged flat nanoribbons or cyclic nanorings, would change for their Möbius counterparts is an intriguing question. Using spin-polarized density functional theory, we shed light on this question. We examine spin states of zigzag-edged Möbius graphene nanoribbons with different widths and lengths. We find a triplet ground state for a Möbius cyclacene, while the corresponding two-edged cyclacene has an open-shell singlet ground state. For wider zigzag-edged Möbius graphene nanoribbons, the total magnetization of the ground state is found to increase with the ribbon length. For example, a quintet ground state is found for a zigzag-edged Möbius graphene nanoribbon. Local magnetic moments on the edge carbon atoms form domains of majority and minor spins along the edge. Spins at the domain boundaries are found to be frustrated. Our findings show that the Möbius topology (that is, only one edge) causes zigzag-edged Möbius graphene nanoribbons to favor one spin over the other, leading to a ground state with nonzero total magnetization.