Precession and Motional Slowing of Spin Evolution in a High Mobility Two-Dimensional Electron Gas

Optical spin-dynamic measurements in a high-mobility $n$-doped $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum well show oscillatory evolution at 1.8 K consistent with a quasi-collision-free D’yakonov-Perel’-Kachorovskii regime. Above 5 K evolution becomes exponential as expected for collision-dominated spin dynamics. Momentum scattering times extracted from Hall mobility and Monte Carlo simulation of spin polarization agree at 1.8 K but diverge at higher temperatures, indicating the importance of electron-electron scattering and an intrinsic upper limit for the spin-relaxation rate.

Figure 1

(a) Schematic band structure showing electron Fermi sea and main optical transitions, (b) 1.8 K photoluminescence (PL), photoluminescence excitation (PLE), and electroreflectance (ER) spectra, and (c) Hall mobility and corresponding momentum scattering time $({\tau }_p)$ of 10 nm $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ $n$-modulation doped quantum well. Pump/probe indicates energy and spectral width of spin evolution measurement.

Figure 2

(a) Polar plot of calculated precession frequency $|\mathbf{\Omega }({\mathbf{k}}_F)|$ for electrons at the Fermi wave vector, and (b) corresponding predicted evolution of averaged spin $z$-component $⟨S_z⟩$ in the absence of momentum scattering for $E_z^{\mathrm{e}\mathrm{f}\mathrm{f}}=0$ (solid curves) and $15\mathrm{k}\mathrm{V}{\mathrm{c}\mathrm{m}}^{-1}$ (dotted curves).

Figure 3

(a) Polarization rotation signal, $\Delta \Theta$, proportional to $⟨S_z⟩$, at various temperatures showing damped oscillatory behavior at 1.8 K [expanded view in (b)] and monotonic decay at higher temperatures: points are experimental; curves are Monte Carlo simulation (see text). Excitation energy as indicated in Fig. 1b and density $\sim 2\times {10}^9{\mathrm{c}\mathrm{m}}^{-2}$. (c) Momentum scattering times from mobility $({\tau }_p)$ and from Monte Carlo simulation of spin evolution $({\tau }_p^{*})$. Solid curve is derived from the sum of scattering rates represented by an empirical $T^{-1}$ fit to ${\tau }_p^{*}$ at high temperature (dashed line) and ${\tau }_p$ (dotted curve).