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Recent experiments reporting unexpectedly large spin Hall effect (SHE) ingraphene decorated with adatoms have raised a fierce controversy. We applynumerically exact Kubo and Landauer- Buttiker formulas to realistic models ofgold-decorated disordered graphene (including adatom clustering) to obtain thespin Hall conductivity and spin Hall angle, as well as the nonlocal resistanceas a quantity accessible to experiments. Large spin Hall angles of 0.1 areobtained at zero-temperature, but their dependence on adatom clustering differsfrom the predictions of semiclassical transport theories. Furthermore, we findmultiple background contributions to the nonlocal resistance, some of which areunrelated to SHE or any other spin-dependent origin, as well as a strongsuppression of SHE at room temperature. This motivates us to design amultiterminal graphene geometry which suppresses these background contributionsand could, therefore, quantify the upper limit for spin current generation intwo-dimensional materials.

Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene