Electric control of spin transport in GaAs (111) quantum wells

We show by spatially and time-resolved photoluminescence that the application of an electric field transverse to the plane of an intrinsic GaAs (111) quantum well (QW) allows the transport of photogenerated electron spins polarized along the direction perpendicular to the QW plane over distances exceeding 10 $\mu \mathrm{m}$. We attribute the long spin transport lengths to the compensation of the in-plane effective magnetic field related to the intrinsic spin-orbit (SO) interaction by means of the electrically generated SO field. Away from SO compensation, the precession of the spin vector around the SO field decreases the out-of-plane polarization of the spin ensemble as the electrons move away from the laser generation spot. The results are reproduced by a model for two-dimensional drift diffusion of spin polarized charge carriers under weak SO interaction.

Figure 1

(a) GaAs single quantum well (SQW) embedded in a n-i-p structure grown along [111]B. The bias voltage $V_b$ applied between the top $n$ region and the $p$-doped substrate generates the electric field $E_z$ for the control of the SO interaction. Spin polarized carriers are optically generated by a tightly focused pulsed laser. The carriers spread and recombine emitting photoluminescence (PL) away from the excitation spot. Panels (b) and (c) show the images of the time-integrated right ($I_R$) and left ($I_L$) circular PL components with wavelength (vertical scale) and position sensitivity along $y\parallel \left[1\overline{1}0\right]$ (horizontal scale) with respect to the generation point, $y=0$. The dashed boxes mark the PL of the e-hh transition. (d) Intensity profiles of $I_R$ and $I_L$ emitted by the e-hh transition along $y$. The dotted line shows the spatial distribution of the tightly focused laser beam, with a full width at half maximum, ${\varphi }_L=1\mu \mathrm{m}$. The experiment was done at 30 K and $V_b=-1.5$ V.

Figure 2

Time and spatially resolved carrier density $n$ along the $y$ direction after the laser pulse injects electron-hole pairs at $t=0$. Panel (a) shows the two-dimensional color profile for $V_b=1$ V, while panel (b) shows the spatial profiles of panel (a) for $t=0.5,1.0,1.5,2.0,2.5$ and 3.0 ns (squares, circles, up triangles, down triangles, diamonds, and left triangles). The solid lines are fittings to the data according to Eq. (6). Panels (c) and (d) show the corresponding results for $V_b=-1.5$ V. The experiment was performed at 30 K and a laser power of 20 $\mu \mathrm{W}$. The curves are normalized to the maximum value at each panel.

Figure 3

Square of the full width at half maximum of $n$, $w_a$, as a function of time, obtained from the fitting of the curves of Fig. 2 to Eq. (6). The dashed lines are a guide to the eye.

Figure 4

Results of the fitting parameters of Eq. (6) as a function of the applied bias for laser powers 40 $\mu \mathrm{W}$ (squares) and 80 $\mu \mathrm{W}$ (circles), measured at 40 K. (a) Carrier recombination time, ${\tau }_r$. (b) Ambipolar diffusion coefficient $D_a$. The dashed lines in both panels are a guide to the eye.

Figure 5

(a) Time-integrated, out-of-plane spin polarization ${\rho }_z$ as a function of radial distance from the generation spot $r$ under different voltage biases $V_b$. Measured at 30 K and a laser power 125 $\mu \mathrm{W}$. (b) Radial profiles of ${\rho }_z$ for selected bias voltages of panel (a). (c) ${\rho }_z$ at $r=0$ (open symbols) and at $r_t=10\mu \mathrm{m}$ (solid symbols) as a function of $V_b$ and its respective electric field $E_z$. The different symbols correspond to laser powers of 20 $\mu \mathrm{W}$ (squares), 40 $\mu \mathrm{W}$ (circles), 80 $\mu \mathrm{W}$ (triangles), and 125 $\mu \mathrm{W}$ (diamonds). The lines are a guide to the eye.

Figure 6

Time and spatially resolved out-of-plane spin density $s_z$ along the $y$ direction after the laser pulse injects electron-hole pairs at $t=0$. Panel (a) shows the two-dimensional color profiles for $V_b=1$ V, while panel (b) shows the spatial profiles for $t=0.5,1.0,1.5,2.0,2.5,3.0$ ns (squares, circles, up triangles, down triangles, diamonds, and left triangles). The solid lines are simulations according to Eq. (8). Panels (c) and (d) show the same as (a) and (b) for $V_b=-1.5$. The experiment was performed at 30 K and a laser power of 20 $\mu \mathrm{W}$. The curves are normalized to the maximum value at each panel.

Figure 7

Comparison of spatial profiles of $n$ (squares) and $s_z$ (circles) from Figs. 2 and 6 for (a) $V_b=1$ V, and (b) $V_b=-1.5$ V, at a time delay of 2 ns. All curves are normalized to their maximum. The solid lines are simulations according to Eqs. (6), (8), and (15).

Figure 8

Spin decoherence time ${\tau }_s$ estimated from the fitting of $s_z$ by Eq. (8), as a function of the applied bias $V_b$ for laser powers 40 $\mu \mathrm{W}$ (squares) and 80 $\mu \mathrm{W}$ (circles), measured at 40 K. The curves show, for comparison, the spin decoherence time in an homogeneous electron distribution for out-of-plane spins (dashed lines) and precessing spins (dotted line), estimated according to Ref. [15].