  In this work spin transport in corrugated armchair graphene nanoribbons (AGNR) is studied. We survey combined effects of spin-orbit interaction and surface roughness, employing the non-equilibrium Green's function formalism and four orbitals tight-binding model. We modify hopping parameters regarding bending and distance of corrugated carbon atoms. The effects of surface roughness parameters, such as roughness amplitude and correlation length, on the spin transport of the graphene nanoribbons are studied. We show that increasing surface roughness amplitude breaks the AGNR symmetry and hybridize $\mathit{\sigma}$ and $\mathit{\pi}$ orbitals, leading to more spin flipping and therefore decrease in polarization. Unlike the roughness amplitude, the longer correlation length makes AGNR surface smoother and increases polarization. Moreover, the Spin diffusion length of carriers is extracted and its dependency on the roughness parameters is investigated. We find the spin diffusion length for various surface corrugation amplitudes in order of 1 to 80 micrometers. 
Spin Relaxation at Graphene Nanoribbons in the presence of Substrate   Surface Roughness