  We theoretically study graphene nanoribbons in the presence of spatially
varying magnetic fields produced e.g. by nanomagnets. We show both analytically
and numerically that an exceptionally large Rashba spin orbit interaction (SOI)
of the order of 10 meV can be produced by the non-uniform magnetic field. As a
consequence, helical modes exist in armchair nanoribbons that exhibit nearly
perfect spin polarization and are robust against boundary defects. This paves
the way to realizing spin filter devices in graphene nanoribbons in the
temperature regime of a few Kelvins. If a nanoribbon in the helical regime is
in proximity contact to an s-wave superconductor, the nanoribbon can be tuned
into a topological phase sustaining Majorana fermions.
