  We perform Monte Carlo simulations to study the interplay of structural and
magnetic order in single layer graphene covered with magnetic adatoms. We
propose that the presence of ripples in the graphene structure can lead to
clustering of the adatoms and to a variety of magnetic states such as
super-paramagnetism, antiferromagnetism, ferromagnetism and spin glass
behavior. We derive the magnetization hysteresis and also the magnetoresistance
curves in the variable range hopping regime, which can provide experimental
signatures for ripple induced clustering and magnetism. We propose that the
magnetic states in graphene can be controlled by gate voltage and coverage
fraction.
