  We present a theoretical study of the optical conductivity of graphene with
magnetic and nonmagnetic adatoms. First, by introducing alternating potential
in a pure graphene, we demonstrate a gap formation in the density of states and
the corresponding optical conductivity. We highlight the distinction between
such a gap formation and the so-called Pauli blocking effect. Next, we apply
this idea to graphene with adatoms by introducing magnetic interactions between
the carrier spins and the spins of the adatoms. Exploring various possible
ground-state spin configurations of the adatoms, we find that antiferromagnetic
configuration yields the lowest total electronic energy, and is the only
configuration that forms a gap. Furthermore, we analyze four different
circumstances leading to similar gaplike structures and propose a means to
interpret the magneticity and the possible orderings of the adatoms on graphene
solely from the optical conductivity data. We apply this analysis to the
recently reported experimental data of oxygenated graphene.
