Ab initio modelling of spin relaxation lengths in disordered graphene nanoribbons{\dag}

The spin-dependent transport properties of armchair graphene nanoribbons in the presence of extrinsic spin-orbit coupling induced by a random distribution of Nickel adatoms is studied. By combining a recursive Green's function formalism with density functional theory, we explore the influence of ribbon length and metal adatom concentration on the conductance. At a given length, we observed a significant enhancement of the spin-flip channel around resonances and at energies right above the Fermi level. We also estimate the spin-relaxation length, finding values on the order of tens of micrometers at low Ni adatom concentrations. This study is conducted at singular ribbon lengths entirely from fully ab-initio methods, providing indirectly evidence that the Dyakonov-Perel spin relaxation mechanism might be the dominant at low concentrations as well as the observation of oscillations in the spin-polarization.