  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.
