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Exchange interactions and Tc in rhenium doped silicon: DFT, DFT+U and Monte Carlo calculations

Interactions between rhenium impurities in silicon are investigated by means of the density functional theory (DFT) and the DFT+U scheme. All couplings between impurities are ferromagnetic except the Re-Re dimers which in the DFT method are nonmagnetic, due to formation of the chemical bond supported by substantial relaxation of the geometry. The critical temperature is calculated by means of classical Monte Carlo (MC) simulations with the Heisenberg hamiltonian. The uniform ferromagnetic phase is obtained with the DFT exchange interactions at room temperature for the impurities concentration of 7%. With the DFT+U exchange interactions, the ferromagnetic clusters form above room temperature in MC samples containing only 3% Re.