  The scattering of two-dimensional massless Dirac fermions from local
spin-orbit interactions with an origin in dilute concentrations of physisorbed
atomic species on graphene is theoretically investigated. The hybridization
between graphene and the adatoms' orbitals lifts spin and valley degeneracies
of the pristine host material, giving rise to rich spin-orbit coupling
mechanisms with features determined by the exact adsorption position on the
honeycomb lattice - bridge, hollow or top position - and the adatoms'
outer-shell orbital type. Effective graphene-only Hamiltonians are derived from
symmetry considerations, while a microscopic tight-binding approach connects
effective low-energy couplings and graphene-adatom hybridization parameters.
Within the $T$-matrix formalism, a theory for (spin-dependent) scattering
events involving graphene's charge carriers, and the spin-orbit active adatoms
is developed. Spin currents associated with intravalley and intervalley
scattering are found to tend to oppose each other. We establish that under
certain conditions, hollow-position adatoms give rise to the spin Hall effect,
through skew scattering, while top-position adatoms induce transverse charge
currents via trigonal potential scattering. We also identify the critical Fermi
energy range where the spin Hall effect is dramatically enhanced, and the
associated transverse spin currents can be reversed.
