  We perform a comparative study of the spin relaxation by spin-orbit coupling
induced from adatoms (hydrogen and fluorine) in graphene. Two methods are
applied, giving consistent results: a full quantum transport simulation of a
graphene nanoribbon, and a T-matrix calculation using Green's functions for a
single adatom in graphene. For hydrogenated graphene the dominant spin-orbit
term for spin relaxation is PIA, the hitherto neglected interaction due to
pseudospin inversion asymmetry. In contrast, in fluorinated graphene PIA and
Rashba couplings destructively interfere, reducing the total spin relaxation
rate. In this case we also predict a strong deviation from the expected 2:1
spin relaxation anisotropy for out- and in-plane spin orientations. Our
findings should be useful to benchmark spin relaxation and weak localization
experiments of functionalized graphene.
