Abstract
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 (Józsa 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.
Highlights
While a decrease of spin relaxation rate with increasing momentum scattering rate has been observed by Riverside group by surface chemical doping at 18 K,24 a linear scaling between the momentum and spin scattering has been observed by both Groningen group[20,22,23] at room temperature and very recently Riverside group[26] at low temperature (≤ 100 K) via varying the electron density in graphene
At a temperature as low as 4.2 K, a nonmonotonic dependence of spin relaxation time on diffusion coefficient with the increase of electron density was reported by Jo et al very recently.[27]
We investigate spin relaxation in graphene with random Rashba field (RRF) induced by adatoms and substrate by means of the kinetic spin Bloch equation (KSBE) approach.[40]
Summary
A two-dimensional allotrope of carbon with a honeycomb lattice, has attracted much attention due to its two dimensionality, Dirac-like energy spectrum and potential for the all-carbon based electronics and spintronics in recent years.[1,2,3,4,5,6,7,8] With the breaking of inversion symmetry, possibly caused by ripples,[9] perpendicular electric fields,[9,10,11,12,13] adsorbed adatoms,[13,14,15] the substrate,[16,17,18] etc., the Rashba spinorbit coupling[10,11,19] arises and results in spin relaxation in the presence of scattering in graphene. As proposed by Sherman in semiconductors,[36,37,38] the randomness of spin-orbit coupling contributes to or even dominates spin relaxation by spin-flip scattering under certain conditions.[32,36,37,38,39] For graphene, the Rashba field induced by a fluctuating electric field from ionized impurities in the substrate or ripples is random in the real space The former case, with the average Rashba field being nonzero, has been investigated by Ertler et al via Monte Carlo simulation,[18] while the latter one, with the average Rashba field being zero, has been studied by Dugaev et al.[32] via the kinetic equations.
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