All-optical measurement of Rashba coefficient in quantum wells

We perform an all-optical spin-dynamic measurement of the Rashba spin-orbit interaction in (110)-oriented $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wells under applied electric field. This crystallographic orientation allows us to isolate the Rashba from other contributions, giving precise values of the Rashba coefficient. At low temperature, we find good agreement between our measurements and the $k\cdot p$ theory. Unexpectedly, we observe a temperature dependence of the Rashba coefficient that may signify the importance of higher-order terms of the Rashba coupling.

Figure 1

Experimental configurations for measurements of (a) spin relaxation and (b) spin diffusion. Upper diagrams: incident pump and probe beams and their polarizations; lower diagrams: profile of focused pump spot with a (a) spin polarized population and (b) spin grating with spacing $\Lambda$.

Figure 2

Electric field dependence of spin-relaxation rate at three temperatures. The high field linear regions of the graphs extrapolate to the origin and the slopes are used to determine the Rashba coefficient.

Figure 3

Logarithmic plot of the electron mobility in a sample from the same wafer as data of Fig. 2, determined by the spin-grating method. The electric field is the built-in field of the $p\text{−}i\text{−}n$ structure, $2.80\times {10}^6\mathrm{V}{\mathrm{m}}^{-1}$. The $T^{-1}$ temperature dependence is as expected for a nondegenerate two-dimensional electron system with dominant phonon scattering. The inset is a typical grating decay signal at $221\mathrm{K}$.

Figure 4

Rashba coefficient obtained from combination of spin relaxation and mobility measurements. The solid curve is eight-band $k\cdot p$ calculation including temperature dependence of band edges and of interband momentum matrix element. The dotted curve is the $k\cdot p$ theory plus an empirical linear-in-$T$ term.