Dependence of spin dephasing on initial spin polarization in a high-mobility two-dimensional electron system

We have studied the spin dynamics of a high-mobility two-dimensional electron system in a $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single quantum well by time-resolved Faraday rotation and time-resolved Kerr rotation in dependence on the initial degree of spin polarization, $P$, of the electrons. By increasing the initial spin polarization from the low-$P$ regime to a significant $P$ of several percent, we find that the spin dephasing time, $T_2^{*}$, increases from about $20\text{to}200\mathrm{ps}$. Moreover, $T_2^{*}$ increases with temperature at small spin polarization but decreases with temperature at large spin polarization. All these features are in good agreement with theoretical predictions by Weng and Wu [Phys. Rev. B 68, 075312 (2003)]. Measurements as a function of spin polarization at fixed electron density are performed to further confirm the theory. A fully microscopic calculation is performed by setting up and numerically solving the kinetic spin Bloch equations, including the D’yakonov-Perel’ and the Bir-Aronov-Pikus mechanisms, with all the scattering explicitly included. We reproduce all principal features of the experiments, i.e., a dramatic decrease of spin dephasing with increasing $P$ and the temperature dependences at different spin polarizations.

Figure 1

(Color online) (Open circles) Power-dependent PL spectra measured with a grating spectrometer. The local temperature at the laser focus spot was determined by fitting the Fermi-Dirac distribution function to the high-energy tail of the PL (red line). (a) PL spectrum and fit for low pump fluence of $0.08\mathrm{mW}$. The corresponding local temperature is $6.7\pm 1\mathrm{K}$. (b) PL spectrum and fit for high pump fluence of $5.7\mathrm{mW}$. The corresponding local temperature is $16\pm 2\mathrm{K}$.

Figure 2

(Color online) (a) Schematic of the geometry of the Rashba spin-orbit field for the [001]-grown QW. For electrons at the Fermi energy, while the direction of the Rashba field varies within the $x-y$ plane, its magnitude is constant. Thus the $z$ component of the electron spins performs a coherent oscillation. (b) TRFR traces at low excitation density taken at two different temperatures. For the lower temperature, a coherent oscillation at zero magnetic field is clearly observed. (c) Calculated spin decay curves for these two temperatures.

Figure 3

(Color online) (a) TRFR traces for different pump beam fluences and therefore different initial spin polarizations. $P_m$ is the maximum initial spin polarization calculated from Eq. (2). (b) Calculated spin polarization decay curves for different initial spin polarizations $P$ with (solid curve) and without (dashed curve) HF term. The free parameters in the calculations are the initial spin polarization, and we present the optimal fitting parameters. (c) Calculated spin polarization decay curves with (solid curve) and without (dashed curve) the electron-hole Coulomb scattering. (d) Calculated spin polarization decay curves with (solid curve) and without (dashed curve) the screening from holes.

Figure 4

(Color online) Two TRFR traces for different initial spin polarizations, which were created by varying the circular polarization degree of the pump beam.

Figure 5

(Color online) (a) SDTs as a function of initial spin polarization for constant, low excitation density and variable polarization degree of the pump beam. The measured spin dephasing times are compared to calculations with and without the HF term, showing its importance. (b) The SDTs measured and calculated for constant, high excitation density and variable polarization degree. The values for lowest and highest initial spin polarization correspond to the TRFR traces shown in Fig. 4.

Figure 6

(Color online) (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 (solid squares), and the calculations with (solid dots) and without (open dots) HF term.

Figure 7

(Color online) Spin dephasing time as a function of sample temperature, for different initial spin polarizations. The measured data points are represented by solid points, while the calculated data are represented by lines of the same color.

Figure 8

(Color online) Electron temperature determined from intensity-dependent PL measurements as a function of the nominal sample temperature, for different pump beam fluence and initial spin polarization, under experimental conditions corresponding to the measurements shown in Fig. 7. The measured data points are represented by solid points, while the lines serve as guides to the eye.