Fluorine adatoms on graphene induce local changes in electronic and magnetic properties, and subtle correlation effects. We investigate the GGA and GGA+U approaches as possible solutions to describe the magnetic moment and electronic band structure of graphene sheets with fluorine adatoms, and compare to experiments. We show that, due to a lack of strong electronic correlations, GGA fails to reproduce the measured magnetic moment in this structure. In particular, the GGA incorrectly predicts a nonmagnetic ground state with a zero band gap. On the other hand, GGA+U is a computationally efficient tool which provides physically reasonable properties. Using Hubbard U and exchange J parameters of 5 eV and 0.1 eV provides a magnetic moment and optical gap in agreement with experiments. Our results imply that the magnetic moment observed in the experiment is injected by fluorine in carbon pz orbitals throughout the graphene sheet. The spin- orbit coupling (SOC) has almost no influence (ca. 2%) on the magnetism. No Rashba effect is detected and the magnetic moment induced by fluorine strongly dominates the electronic properties. Our findings explain the anisotropic magnetic behavior observed experimentally.
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