Gate-dependent spin Hall induced nonlocal resistance and the symmetry of spin-orbit scattering in Au-clustered graphene

Engineering the electron dispersion of graphene to be spin-dependent is crucial for the realization of spin-based logic devices. Enhancing spin-orbit coupling in graphene can induce spin Hall effect, which can be adapted to generate or detect a spin current without a ferromagnet. Recently, both chemically and physically decorated graphenes have shown to exhibit large nonlocal resistance via the spin Hall and its inverse effects. However, these nonlocal transport results have raised critical debates due to the absence of field dependent Hanle curve in subsequent studies. Here, we introduce Au clusters on graphene to enhance spin-orbit coupling and employ a nonlocal geometry to study the spin Hall induced nonlocal resistance. Our results show that the nonlocal resistance highly depends on the applied gate voltage due to various current channels. However, the spin Hall induced nonlocal resistance becomes dominant at a particular carrier concentration, which is further confirmed through Hanle curves. The obtained spin Hall angle is as high as $\ensuremath{\sim}0.09$ at 2 K. Temperature dependence of spin relaxation time is governed by the symmetry of spin-orbit coupling, which also depends on the gate voltage: asymmetric near the charge neutral point and symmetric at high carrier concentration. These results inspire an effective method for generating spin currents in graphene and provide important insights for the spin Hall effect as well as the symmetry of spin scattering in physically decorated graphene.