Carrier density and magnetism in graphene zigzag nanoribbons

The influence of carrier density on magnetism in a zigzag graphene nanoribbon is studied in a $\ensuremath{\pi}$-orbital Hubbard-model mean-field approximation. Departures from half filling alter the magnetism, leading to states with charge-density variation across the ribbon and parallel spin alignment on opposite edges. Finite carrier densities cause the spin density near the edges to decrease steadily, leading eventually to the absence of magnetism. At low doping densities the system shows a tendency to multiferroic order in which edge charges and spins are simultaneously polarized.