  We study graphene with an adsorbed spin texture, where the localized spins
create a periodic magnetic flux. The latter produces gaps in the graphene
spectrum and breaks the valley symmetry. The resulting effective electronic
model, which is similar to Haldane's periodic flux model, allows us to tune the
gap of one valley independently from that of the other valley. This leads to
the formation of two Hall plateaux and a quantum Hall transition. We discuss
the density of states, optical longitudinal and Hall conductivities for nonzero
frequencies and nonzero temperatures. A robust logarithmic singularity appears
in the Hall conductivity when the frequency of the external field agrees with
the width of the gap.
