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We have investigated, using effective mass approach (EMA), magneticproperties of a one-dimensional electron gas in graphene armchair ribbons whenthe electrons of occupy only the lowest conduction subband. We find thatmagnetic properties of the one-dimensional electron gas may depend sensitivelyon the width of the ribbon. For ribbon widths $L_x=3Ma_0$, a critical pointseparates 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 ofthe unit cell). These width-dependent properties are a consequence ofeigenstates that have a subtle width-dependent mixture of $\mathbf{K}$ and$\mathbf{K'}$ states, and can be understood by examining the wavefunctionoverlap that appears in the expression for the many-body exchange self-energy.Ferromagnetic and paramagnetic states may be used for spintronic purposes.

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