Theory of spin-orbit coupling in fluorinated graphene

We performed first-principles calculations of the spin-orbit coupling in graphene with fluorine adatom. The chemisorption of fluorine modifies the structural symmetry of graphene by breaking the pseudospin symmetry and inducing local corrugation towards $sp^3$ hybridization. We show that there are two dominant contributions to the spin-orbit field -- Rashba term and a term due to pseudospin inversion asymmetry (PIA). In addition to the $sp^3$ induced spin-orbit coupling enhancement the spin-orbit split of the fluorine $p$ orbitals is substantially transferred to graphene. Using group theoretical arguments we propose a realistic minimal Hamiltonian that reproduce the relevant spin-orbit effects calculated from first-principles. Our realistic effective Hamiltonian should be useful for spin transport and spin relaxation investigations.