Hot-electron effect in spin dephasing in $n$-type GaAs quantum wells

We perform a study of the effect of the high in-plane electric field on spin precession and spin dephasing due to the D’yakonov–Perel’ mechanism in $n$-type GaAs (100) quantum wells by constructing and numerically solving kinetic Bloch equations. We self-consistently include all scattering such as electron$∕$phonon,electron $∕$nonmagnetic impurity as well as electron–electron Coulomb scattering in our theory and systematically investigate how the spin precession and spin dephasing are affected by the high electric field under various conditions. The hot-electron distribution functions and spin correlations are calculated rigorously in our theory. It is found that the D’yakonov–Perel’ term in the electric field provides a nonvanishing effective magnetic field that alters the period of spin precession. Moreover, spin dephasing is markedly affected by the electric field. The important contribution of the electron–electron scattering to spin dephasing is also discussed.

Figure 1

Electron densities of spin up and down and the incoherently summed spin coherence $\rho$ vs time $t$ for a GaAs QW with initial spin polarization $P=2.5\%$ under different electric fields, $E=0.5$ (solid lines) and $-0.5\text{kV}∕\text{cm}$ (dashed lines). Top panel: $B=0\mathrm{T}$; bottom panel: $B=4\mathrm{T}$. Note the scale of the spin coherence is on the right side and the scale of the top panel is different from that of the bottom one.

Figure 2

Net effective magnetic field $B^{*}$ from the DP term vs drift velocity $V_d$ at $T=120\mathrm{K}$ with impurity density $N_i=0$. The solid curve is the corresponding result from Eq. (7).

Figure 3

SDT ${\tau }_s$ vs the electric field $E$ applied at $T=$ (a) 120 and (b) $200\mathrm{K}$ for initial spin polarization $P=2.5\%$ with different impurity densities: $●$ $N_i=0$; $◆$ $N_i=0.6N_e$; and $▴$ $N_i=1.2N_e$.

Figure 4

SDT ${\tau }_s$ vs electron temperature $T_e$ at lattice temperature $T=120\mathrm{K}$ with initial spin polarization $P=2.5\%$ for $N_i=0$ $(●)$ and $N_i=0.6N_e$ $(◆)$. The curves are plotted as a guide to the eye.

Figure 5

Spin dephasing time ${\tau }_s$ $(•)$ vs the initial spin polarization for $T=120\mathrm{K}$ and $N_i=0$ (a) and $N_i=0.6N_e$ (b) under different electric fields: $●$ $E=0$; $엯$ $E=0.25\text{kV}∕\text{cm}$; $◆$ $E=0.5\text{kV}∕\text{cm}$; $▴$ $E=0.75\text{kV}∕\text{cm}$.

Figure 6

Typical distribution function of spin-up electrons in the steady state with electric field $E=-0.75\text{kV}∕\text{cm}$ and $P=2.5\%$.

Figure 7

Spin dephasing time in GaAs QWs with (closed circles) and without (open circles) Coulomb scattering under different spin polarizations: $P=$ (a) $2.5\%$ and (b) $97.5\%$.

Figure 8

Discrete momentum space.