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Aiming to understand the main spin relaxation mechanism in graphene, weinvestigate the spin relaxation with random Rashba field induced by bothadatoms and substrate, by means of the kinetic spin Bloch equation approach.The charged adatoms on one hand enhance the Rashba spin-orbit coupling locallyand on the other hand serve as Coulomb potential scatterers. Both effectscontribute to spin relaxation limited by the D'yakonov-Perel' mechanism. Inaddition, the random Rashba field also causes spin relaxation by spin-flipscattering, manifesting itself as an Elliott-Yafet--like mechanism. Bothmechanisms are sensitive to the correlation length of the random Rashba field,which may be affected by the environmental parameters such as electron densityand temperature. By fitting and comparing the experiments from the Groningengroup [J\'ozsa {\it et al.}, Phys. Rev. B {\bf 80}, 241403(R) (2009)] andRiverside group [Pi {\it et al.}, Phys. Rev. Lett. {\bf 104}, 187201 (2010);Han and Kawakami, {\it ibid.} {\bf 107}, 047207 (2011)] which show eitherD'yakonov-Perel'-- (with the spin relaxation rate being inversely proportionalto the momentum scattering rate) or Elliott-Yafet--like (with the spinrelaxation rate being proportional to the momentum scattering rate) properties,we suggest that the D'yakonov-Perel' mechanism dominates the spin relaxation ingraphene. The latest experimental finding of a nonmonotonic dependence of spinrelaxation time on diffusion coefficient by Jo {\it et al.} [Phys. Rev. B {\bf84}, 075453 (2011)] is also well reproduced by our model.

Electron spin relaxation in graphene with random Rashba field: Comparison of D'yakonov-Perel' and Elliott-Yafet--like mechanisms