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Critical temperature of two-dimensional hydrogenated multilayer graphene-based diluted ferromagnet

In the paper a theoretical study of critical (Curie) temperature of diluted ferromagnet based on multilayer graphene (or graphite) with hydrogen adatoms deposited over carbon atoms belonging to single sublattice is presented. The calculations are performed within Pair Approximation (PA) for diluted ferromagnetic system with long-range interactions. The method is able to take into account the spin-space anisotropy of coupling. The results obtained within Mean Field Approximation (MFA) are also presented for comparison. The assumed interaction between hydrogen adatom spins is inversely proportional to their mutual distance, with the additional exponential attenuation reflecting the presence of disorder in the system. The results obtained for a wide range of impurity concentrations and interaction decay length are discussed. The strongly non-linear behaviour of critical temperature as a function of dilution is predicted, at variance with MFA predictions. Moreover, MFA tends to overestimate heavily the critical temperature values compared to PA. An universal dependence of critical temperature on impurity concentration and interaction decay length is found for strong dilution regime.