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We investigated the emergence of spin spiral ground state induced by theelectric field in the bilayer zigzag graphene nanoribbons for the ferromagneticedge states. To do that, we employed the generalized Bloch theorem to createflat spiral alignments for all the magnetic moments of carbon atoms at theedges within a constraint scheme approach. While the small ribbon width canpreserve the ferromagnetic ground state, the large one shows the spiral groundstate starting from a certain value of the electric field. We also pointed outthat the spiral ground state is caused by the reduction of spin stiffness. Inthis case, the energy scale exhibits a subtle nature that can only beconsidered at the low temperature. For the last discussion, we also revealedthat the spin spiral ground state appears more rapidly when the thicknessincreases. Therefore, we justify that the large ribbon width and largethickness can generate many spiral states induced by the electric field.

Electric-field-induced spin spiral state in bilayer zigzag graphene nanoribbons