  Recent experiments reporting unexpectedly large spin Hall effect (SHE) in
graphene decorated with adatoms have raised a fierce controversy. We apply
numerically exact Kubo and Landauer- Buttiker formulas to realistic models of
gold-decorated disordered graphene (including adatom clustering) to obtain the
spin Hall conductivity and spin Hall angle, as well as the nonlocal resistance
as a quantity accessible to experiments. Large spin Hall angles of 0.1 are
obtained at zero-temperature, but their dependence on adatom clustering differs
from the predictions of semiclassical transport theories. Furthermore, we find
multiple background contributions to the nonlocal resistance, some of which are
unrelated to SHE or any other spin-dependent origin, as well as a strong
suppression of SHE at room temperature. This motivates us to design a
multiterminal graphene geometry which suppresses these background contributions
and could, therefore, quantify the upper limit for spin current generation in
two-dimensional materials.
