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 varies periodically 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 decays double exponentially with two decay rates 1/τ+ and 1/τ−. In high temperature regime, the average of these two rates varies with the grating wave-vector q quadratically, i.e., (1/τ+ + 1/τ−)/2 = Dsq 2 + 1/τs, with Ds andτs 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.

Microscopic theory for Doppler velocimetry of spin propagation in semiconductor quantum wells

“…q 0 = m * (β + α) and q ′ 0 = m * (β ′ + α) with m * representing the effective mass, α being the Rashba coefficient 12 andβ,β ′ both standing for the coefficients of the linear Dresselhaus term 25 with corrections from the cubic Dresselhaus terms. 21 Without the applied electric field, v d = 0 and the amplitude of the SDW decays biexponentially with fast and slow rates Dq 2 +1/τ s ±2Dqq 0 . 17,21 When there is an applied electric field but without the CSP (q 0 = q ′ 0 = 0), the SDW decays exponentially and gains a phase shift which changes linearly with time with a slope qv d , which is equivalent to a normal Doppler shift in experiments.…”

“…21 Without the applied electric field, v d = 0 and the amplitude of the SDW decays biexponentially with fast and slow rates Dq 2 +1/τ s ±2Dqq 0 . 17,21 When there is an applied electric field but without the CSP (q 0 = q ′ 0 = 0), the SDW decays exponentially and gains a phase shift which changes linearly with time with a slope qv d , which is equivalent to a normal Doppler shift in experiments. With the CSP, the situation is more complex.…”

“…Without the electric field, the amplitude S 0 z (q, t) decays biexponentially when the SDW diffuses along the [110] crystal axis in (001) GaAs quantum wells (QWs) as spin rotates along the net effective magnetic field due to the SOC and diffusion. 17,21,23 Based on the kinetic spin Bloch equation (KSBE) approach, 5,24 it is shown that the information about spin diffusion coefficient, CSP and spin relaxation can be extracted from the wave-vector dependence of the two decay rates. 21 In this paper we will further extend the theory to include the electric field and show, both analytically and numerically, that the theoretical and experimental results agree well with each other.…”

“…17,21,23 Based on the kinetic spin Bloch equation (KSBE) approach, 5,24 it is shown that the information about spin diffusion coefficient, CSP and spin relaxation can be extracted from the wave-vector dependence of the two decay rates. 21 In this paper we will further extend the theory to include the electric field and show, both analytically and numerically, that the theoretical and experimental results agree well with each other. We will demonstrate that the CSP is robust even in high temperature regime for narrow QWs and point out that to observe the effect of the CSP at high temperature, one has to carry out the observation for a longer time than the case at low temperature.…”

“…By optically monitoring the temporal evolution of the amplitude S 0 z (q, t), one obtains the spin diffusion coefficient and relaxation rate. [15][16][17][18][19][20][21] Very recently, the spin drifting and CSP were studied by the Doppler velocimetry which monitors the phase shift φ(t). 15,22 For pure spin drift without spin precession, the phase shift is simply φ(t) = qv d t, where v d stands for the drift velocity.…”