Effect of Initial Spin Polarization on Spin Dephasing and the Electron $g$ Factor in a High-Mobility Two-Dimensional Electron System

We have investigated the spin dynamics of a high-mobility two-dimensional electron system (2DES) in a $\mathrm{GaAs}\mathrm{\text{−}}{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single quantum well by time-resolved Faraday rotation in dependence on the initial degree of spin polarization, $P$, of the 2DES. From $P\sim 0$ to $P\sim 30\%$, we observe an increase of the spin dephasing time, $T_2^{*}$, by an order of magnitude, from about 20 ps to 200 ps, in good agreement with theoretical predictions by Weng and Wu [Phys. Rev. B 68, 075312 (2003)]. Furthermore, also the electron $g$ factor is found to decrease for increasing $P$. Fully microscopic calculations reproduce the most salient features of the experiments, i.e., a dramatic decrease of spin dephasing and a moderate decrease of the electron $g$ factor with increasing $P$. We show that both results are determined dominantly by the Hartree-Fock contribution of the Coulomb interaction.

Figure 1

(a) Normalized TRFR traces for different degrees of initial electron spin polarization, $P$. The total densities of electrons, $n_{\mathrm{tot}}=n_e+n_{\mathrm{ph}}^{\mathrm{tot}}$, are 2.19, 2.66, 3.83, 8.39 (in units of ${10}^{11}{\mathrm{cm}}^{-2}$) for $P=1.6\%$, 8%, 18%, 30%, respectively. (b) Comparison of two traces with $P=1.6\%$ at two different temperatures. For the lowest temperature, a coherent electron spin oscillation due to the Dresselhaus-Rashba spin-orbit field is clearly seen. The inset shows a semilogarithmic plot of the data displayed in (a). Note that at low $P$ the zero-field oscillation is superimposed to the decay.

Figure 2

(a) Calculated spin decay curves for the experimental parameters, like initial spin polarization, total electron densities, electron mobility, and temperature $T=4.5\mathrm{K}$ (solid lines). In the calculation, a phenomenological decay time is incorporated as a single fitting parameter $\tau$ (see text). The dashed curve for $P=30\%$ is calculated for a hot electron temperature of $T_e=120\mathrm{K}$. (b) Same as (a) but calculated without the HF term. In particular, for large $P$ the decay is much faster than in the experiments [cf. Fig. 1a]. The inset shows the data, displayed in (a), in a semilogarithmic plot. At low $P$ the zero-field oscillations are superimposed.

Figure 3

Comparison of spin dephasing times, as extracted from the experimental curves in Fig. 1a (■), and from the calculated curves in Fig. 2a with (●) and Fig. 2b without (○) the HF term. In both calculations, phenomenological decay times, $\tau$, as indicated in Fig. 2, were included.

Figure 4

(a) TRFR measurements at $B=4\mathrm{T}$ for different $P$. An increase of the electron precession period with increasing $P$ is clearly observed (arrow). (b) Comparison of electron $g$ factors for different polarization degrees $P$, as extracted from the experiments (■) and the calculations with (●) and without (○) HF term.