Enhanced spin-relaxation time due to electron-electron scattering in semiconductor quantum wells

We present a detailed experimental and theoretical analysis of the spin dynamics of two-dimensional electron gases (2DEGs) in a series of $n$-doped $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells. Picosecond-resolution polarized pump-probe reflection techniques were applied in order to study in detail the temperature, concentration, and quantum-well-width dependencies of the spin relaxation rate of a small photoexcited electron population. A rapid enhancement of the spin lifetime with temperature up to a maximum near the Fermi temperature of the 2DEG was demonstrated experimentally. These observations are consistent with the D’yakonov-Perel’ spin-relaxation mechanism controlled by electron-electron collisions. The experimental results and theoretical predictions for the spin relaxation times are in good quantitative agreement.

Figure 1

Temperature dependence of the electron momentum-relaxation time (from mobility) for different samples. The mobility in the NU535 sample is essentially the same as in the NU211 sample and is not shown here.

Figure 2

Photoluminescence (PL) and photoluminescence excitation (PLE) spectra of the different samples at $5\mathrm{K}$. The measurements were taken at the maximum value of $N_S$ permitted by the sample design. The electron concentrations in the 2DEGs were determined from the energy difference between PL peak and PLE onset, which involve interband transitions as indicated in the inset. Time-resolved pump-probe measurements of spin dynamics were carried out with the laser tuned to the PLE onset.

Figure 3

Time evolution of the $\Delta \theta$ signal and hence the spin polarization for NU211 sample for a range of temperatures. At $20\mathrm{K}$ and above the evolution is exponential with rapidly increasing decay time. At $5\mathrm{K}$, oscillatory behavior was observed (inset) and was analyzed by Monte Carlo techniques (solid) (Ref. 5) to give directly $\Omega \left(k_F\right)$ and ${\tau }_p^{*}$.

Figure 4

(Color online) Spin-relaxation times vs temperature. The points present the experimental results; solid squares are directly measured exponential decay times, whereas open squares are values of ${\left[\Omega {\left({\mathrm{k}}_F\right)}^2{\tau }_p^{*}\right]}^{-1}$ for cases of oscillatory spin evolution. Lines are the theoretical results calculated using the experimental values of the ensemble momentum-relaxation times including (solid, dashed) and not including (dotted) electron-electron collisions.

Figure 5

Qualitative picture of the temperature dependence of the spin-relaxation time. Dashed curve presents the contribution of the ensemble momentum-scattering processes. Dotted curve is the prediction for electron-electron collisions only. The solid curve is the combined total spin-relaxation time.