Spin relaxation in n-type GaAs quantum wells with transient spin grating

Abstract

By solving the kinetic spin Bloch equations, we study the time evolution of the transient spin grating, whose spin polarization periodically varies in real space, confined in (001) GaAs quantum wells. With this study, we can investigate the properties of both the spin transport and the spin relaxation at the same time. The Fourier component of the spin signal double exponentially decays with two decay rates 1∕τ+ and 1∕τ−. In the high temperature regime, the average of these two rates quadratically varies with the grating wave vector q, i.e., (1∕τ++1∕τ−)∕2=Dsq2+1∕τ̃s, with Ds and τ̃s representing the spin diffusion coefficient and the average of the out-of-plane and the in-plane spin relaxation times, respectively. τ± calculated from our theory are in good agreement with the experimental data by Weber et al. [Phys. Rev. Lett. 98, 076604 (2007)]. By comparing Ds with and without the electron-electron Coulomb scattering, we calculate the contribution of Coulomb drag to the spin diffusion coefficient. With the transient spin grating result, we further reveal the relations among different characteristic parameters such as spin diffusion coefficient Ds, spin relaxation time τs, and spin injection length Ls. We show that in the presence of the Dresselhaus and/or Rashba spin-orbit coupling, the widely used relation Ls=Dsτs is generally inaccurate and can even be very wrong in some special cases. We present an accurate way to extract the steady-state transport characteristic parameters from the transient spin grating signals.