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

To understand the main spin relaxation mechanism in graphene, we investigate the spin relaxation with random Rashba field (RRF) induced by both adatoms and a substrate using the kinetic spin Bloch equation approach. The charged adatoms, on the one hand, enhance the Rashba spin-orbit coupling locally and, on the other hand, serve as Coulomb potential scatterers. Both effects contribute to spin relaxation limited by the D'yakonov-Perel' (DP) mechanism. In addition, the RRF also causes spin relaxation by spin-flip scattering, manifesting itself as an Elliott-Yafet (EY)-like mechanism. Both mechanisms are sensitive to the correlation length of the RRF, which may be affected by environmental parameters such as electron density and temperature. Fitting and comparing the experiments of the Groningen group (Jozsa et al 2009 Phys. Rev. B 80 241403(R)) and the Riverside group (Pi et al 2010 Phys. Rev. Lett. 104 187201; Han and Kawakami 2011 Phys. Rev. Lett. 107 047207), which show either DP (with the spin relaxation rate being inversely proportional to the momentum scattering rate) or EY-like (with the spin relaxation rate being proportional to the momentum scattering rate) properties, we suggest that the DP mechanism dominates the spin relaxation in graphene. The latest experimental finding of a nonmonotonic dependence of spin relaxation time on diffusion coefficient by Jo et al 2011 (Phys. Rev. B 84 075453) is also well reproduced by our model.