Magnetism and magnetotransport in disordered graphene

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 superparamagnetism, 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.