  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 Mobius
counterparts is an intriguing question. Using spin-polarized density functional
theory, we shed light on this question. We examine spin states of zigzag-edged
Mobius graphene nanoribbons (ZMGNRs) with different widths and lengths. We find
a triplet ground state for a Mobius cyclacene, while the corresponding
two-edged cyclacene has an open-shell singlet ground state. For wider ZMGNRs,
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 ZMGNR. 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 Mobius topology (i.e., only one edge)
causes ZMGNRs to favor one spin over the other, leading to a ground state with
non-zero total magnetization.
