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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 $L_x=3Ma_0$, 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 $\mathbf{K'}$ 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.