Energy-dependent electron-electron scattering and spin dynamics in a two-dimensional electron gas

The measurement of spin dynamics of electrons in a degenerate two-dimensional electron gas, wherein the Dyakonov–Perel mechanism is dominant, has been used to investigate the electron scattering time $\left({\tau }_p^{*}\right)$ as a function of energy near the Fermi energy. Close to the Fermi energy, the spin evolution is oscillatory, which indicates a quasicollision-free regime of spin dynamics. As the energy is increased, a transition to an exponential, collision-dominated spin decay occurs. The oscillation frequency and the value of ${\tau }_p^{*}$ are extracted by using a Monte Carlo simulation method. At the Fermi energy, ${\tau }_p^{*}$ is very close to the ensemble momentum relaxation time $\left({\tau }_p\right)$ obtained from the electron mobility. For higher energies, ${\tau }_p^{*}$ falls quadratically, which is consistent with the theoretical expectations for the onset of the electron-electron scattering, which is inhibited by the Pauli principle at the Fermi energy.

Figure 1

Examples of $\Delta \theta$ [i.e., $⟨S_z⟩\left(t\right)$] signals at 1.5 and at 5 K for a range of electron energies relative to the Fermi energy. At 1.5 K, the observed decays were all oscillatory, whereas at 5 K, there is a transition from an oscillatory to a monotonic decay as the energy increases. The sign of the signals inverts near $E_F$, as discussed in the text.

Figure 2

Results of Monte Carlo simulation of Dyakonov–Perel spin decays, as described in the text. The precession frequency ${\Omega }_{\text{ex}}$ was kept fixed at 0.063 rad/ps and the electron momentum scattering time ${\tau }_p^{*}$ was varied to give different values of ${\Omega }_{\text{ex}}{\tau }_p^{*}$. The transition from an oscillatory to a monotonic decay occurs at ${\Omega }_{\text{ex}}{\tau }_p^{*}=1/2$.

Figure 3

(a) Experimental values of ${\tau }_p^{*}$ extracted from data of Fig. 1 at 1.5 and 5 K by using the Monte Carlo simulation method, as described in the text and in Ref. 7. The solid symbols correspond to oscillatory spin decays and the open symbols correspond to monotonic relaxations. The solid and dotted curves are theoretical fits as described in the text. The boundary of the shaded region corresponds to ${\Omega }_{\text{ex}}{\tau }_p^{*}=1/2$ in the simulations. (b) PLE spectrum at 5 K for detection at 1.516 eV. The horizontal bar indicates the resolution set by the spectral width of the mode-locked Ti-sapphire laser. The Fermi energy $E_F$ was taken to be the half-intensity point of the PLE.