Spintronic properties of one-dimensional electron gas in graphene armchair ribbons

We have investigated, using effective mass approach (EMA), magnetic properties of a one-dimensional electron gas in graphene armchair ribbons when the electrons of occupy only the lowest conduction subband. We find that magnetic properties of the one-dimensional electron gas may depend sensitively on the width of the ribbon. For ribbon widths $L_x=3M{a}_0$, a critical point separates ferromagnetic and paramagnetic states while for $L_x=(3M+1)a_0$ paramagnetic state is stable ($M$ is an integer and $a_0$ is the length of the unit cell). These width-dependent properties are a consequence of eigenstates that have a subtle width-dependent mixture of $\mathbf{K}$ and ${\mathbf{K}}^{\mathbf{\prime }}$ states, and can be understood by examining the wavefunction overlap that appears in the expression for the many-body exchange self-energy. Ferromagnetic and paramagnetic states may be used for spintronic purposes.