  We study graphene nanoribbons (GNRs) with armchair edges in the presence of
Rashba spin-orbit interaction (RSOI). We impose the boundary conditions on the
tight binding Hamiltonians for bulk graphene with RSOI by means of a sine
transform and study in detail the influence of RSOI on the spectra and the spin
polarization. We show that the spin polarization perpendicular to the GNR
changes sign when reversing the momentum along the GNR if the bands are coupled
by strong RSOI. Furthermore, we derive a linearized approximation to the RSOI
Hamiltonian and find that only the neighboring modes of an energy band have to
be taken into account in order to achieve a good approximation for the same
band. Due to their experimental availability and various proposals for
engineering appropriate RSOI, GNRs with armchair edges are a promising
candidate for possible spintronics applications.
