Detection of large magnetoanisotropy of electron spin dephasing in a high-mobility two-dimensional electron system in a [001] $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum well

In time-resolved Faraday rotation experiments, we have detected an in-plane anisotropy of the electron spin-dephasing time (SDT) in an $n$-modulation-doped $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single quantum well. The SDT was measured with magnetic fields of $B⩽1\mathrm{T}$, applied in the [110] and $\left[1\overline{1}0\right]$ in-plane crystal directions of the GaAs quantum well. For fields along $\left[1\overline{1}0\right]$, we have found up to a factor of about 2 larger SDT than in the perpendicular direction. The observed SDTs also show strong anisotropic magnetic-field dependence. Fully microscopic calculations, by numerically solving the kinetic spin Bloch equations considering the D’yakonov-Perel’ and the Bir-Aronov-Pikus mechanisms, reproduce the experimental findings quantitatively. This quantitative analysis of the data allowed us to determine the relative strengths of Rashba and Dresselhaus terms in our sample. Moreover, we could predict the SDT for spins aligned in the [110] in-plane direction to be on the order of several nanoseconds, which is up to 2 orders of magnitude larger than that in the perpendicular in-plane direction.

Figure 1

(Color online) (a) Schematic picture of the time-resolved Faraday rotation experiment. In-plane magnetic fields are applied either in the [110] or the $\left[1\overline{1}0\right]$ directions. (b) Sketch of the precession of optically oriented spins about a $\left[1\overline{1}0\right]$ in-plane magnetic field. (c) Same as (b) but for [110] magnetic field.

Figure 2

(Color online) Experimental TRFR traces for different directions of the in-plane magnetic field.

Figure 3

(Color online) (a) Comparison of the experimental (solid symbols) and theoretically calculated (open symbols) spin-dephasing times for different in-plane magnetic-field directions. $\alpha$ and $\beta$ are the Rashba and Dresselhaus spin-orbit coefficients, respectively. [(b) and (c)] Comparison of experimental TRFR traces at $B=0.2\mathrm{T}$ for the two different in-plane directions of the magnetic field.

Figure 4

(Color online) Comparison of spin-dephasing times, calculated with identical parameters for initial spin polarizations parallel to the [001] (open symbols) and the [110] and $\left[1\overline{1}0\right]$ directions (solid symbols), in dependence on magnetic fields parallel to the [110] and $\left[1\overline{1}0\right]$ in-plane directions.