We calculate the electronic structure and magnetic properties of hydrogenated graphite surfaces using van der Waals density functional theory (DFT) and model Hamiltonians. We find, as previously reported, that the interaction between hydrogen atoms on graphene favors adsorption on different sublattices along with an antiferromagnetic coupling of the induced magnetic moments. On the contrary, when hydrogenation takes place on the surface of graphene multilayers or graphite (Bernal stacking), the interaction between hydrogen atoms competes with the different adsorption energies of the two sublattices. This competition may result in all hydrogen atoms adsorbed on the same sublattice and, thereby, in a ferromagnetic state for low concentrations. Based on the exchange couplings obtained from the DFT calculations, we have also evaluated the Curie temperature by mapping this system onto an Ising-like model with randomly located spins. Remarkably, the long-range nature of the magnetic coupling in these systems makes the Curie temperature size dependent and larger than room temperature for typical concentrations and sizes.
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