We investigate the spin diffusion and transport in a graphene monolayer on SiO$_2$ substrate by means of the microscopic kinetic spin Bloch equation approach. The substrate causes a strong Rashba spin-orbit coupling field $\sim 0.15$ meV, which might be accounted for by the impurities initially present in the substrate or even the substrate-induced structure distortion. By surface chemical doping with Au atoms, this Rashba spin-orbit coupling is further strengthened as the adatoms can distort the graphene lattice from $sp^2$ to $sp^3$ bonding structure. By fitting the Au doping dependence of spin relaxation from Pi {\sl et al.} [Phys. Rev. Lett. {\bf 104}, 187201 (2010)], the Rashba spin-orbit coupling coefficient is found to increase approximately linearly from 0.15 to 0.23 meV with the increase of Au density. With this strong spin-orbit coupling, the spin diffusion or transport length is comparable with the experimental values. In the strong scattering limit (dominated by the electron-impurity scattering in our study), the spin diffusion is uniquely determined by the Rashba spin-orbit coupling strength and insensitive to the temperature, electron density as well as scattering. With the presence of an electric field along the spin injection direction, the spin transport length can be modulated by either the electric field or the electron density. (The remaining is omitted due to the limit of space)Comment: 14 pages, 7 figures, to be published in PR
Multi-valley spin relaxation in n-type GaAs quantum wells with in-plane electric field is investigated at high temperature by means of kinetic spin Bloch equation approach. The spin relaxation time first increases and then decreases with electric field, especially when the temperature is relatively low. We show that L valleys play the role of a "drain" of the total spin polarization due to the large spin-orbit coupling in L valleys and the strong Γ-L inter-valley scattering, and thus can enhance spin relaxation of the total system effectively when the in-plane electric field is high. Under electric field, spin precession resulting from the electric-field-induced magnetic field is observed. Meanwhile, due to the strong Γ-L inter-valley scattering as well as the strong inhomogeneous broadening in L valleys, electron spins in L valleys possess almost the same damping rate and precession frequency as those in Γ valley. This feature still holds when a finite static magnetic field is applied in Voigt configuration, despite that the g-factor of L valleys is much larger than that of Γ valley. Moreover, it is shown that the property of spin precession of the whole system is dominated by electrons in Γ valley. Temperature, magnetic field, and impurity can affect spin relaxation in low electric field regime. However, they are shown to have marginal influence in high electric field regime.
Carrier density dependence of electron spin relaxation in an intrinsic GaAs quantum well is investigated at room temperature using time-resolved circularly polarized pump-probe spectroscopy. It is revealed that the spin relaxation time first increases with density in the relatively low density regime where the linear D'yakonov-Perel' spin-orbit coupling terms are dominant, and then tends to decrease when the density is large and the cubic D'yakonov-Perel' spin-orbit coupling terms become important. These features are in good agreement with theoretical predictions on density dependence of spin relaxation by Lü et al. [Phys. Rev. B 73, 125314 (2006)]. A fully microscopic calculation based on numerically solving the kinetic spin Bloch equations with both the D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms included, reproduces the density dependence of spin relaxation very well.
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