  We study the interaction energy between two graphene nanoribbons by first
principles calculations, including van der Waals interactions and spin
polarization. For ultranarrow zigzag nanoribbons, the direct stacking is even
more stable than Bernal, competing in energy for wider ribbons. This behavior
is due to the magnetic interaction between edge states. We relate the reduction
of the magnetization in zigzag nanoribbons with increasing ribbon width to the
structural changes produced by the magnetic interaction, and show that when
deposited on a substrate, zigzag bilayer ribbons remain magnetic for larger
widths.
