Observation of the intrinsic spin Hall effect in a two-dimensional electron gas

The experimental demonstration of the spin Hall effect in a high mobility two-dimensional electron system is reported. The spatial dependence is studied by Kerr rotation as a function of the external magnetic field using an applied electric field amplitude and direction as control parameters. We observe that the effect is robust in a bilayer structure with a nonzero Rashba coefficient displayed by an electrically controllable internal magnetic field, a large spin Hall conductivity in the range of the universal intrinsic value, and a mobility-enhanced spin diffusion constant. With the application of an unidirectional electric field, the role of the spin drift was also studied. The data was analyzed following both phenomenological and microscopic approaches and compared with experimental references in a single-layer configuration.

Figure 1

One-dimensional spatial profile of the spin accumulation as a function of $B_{\text{ext}}$ at $E=0.6$ mV/$\mu$m for (a) bilayer and (b) single-layer samples with the calculated well potential and the associated wave functions. (c) Device configuration sketching the spatial separation of opposite spins.

Figure 2

(a) $B_{\text{ext}}$ scans of the KR signal at different probe positions. The dashed lines show the Hanle curve fits. (b) Spatial dependence of the KR amplitude at $B_{\text{ext}}=0$. (c) Spin lifetime fitted in (a). Probe power: 150 $\mu$W, and $V_{\text{rms}}=2.5$ V.

Figure 3

(a) One-dimensional spatial profile as a function of $B_{\text{ext}}$ measured with 2.5 mW probe power. (b) Line cuts in (a) for the polarization peak positions. (c) Positive peak dependence on the applied voltage. The dashed lines show the Hanle curve fits.

Figure 4

(a) Dependence of $B_{\text{in}}$, $B_{1/2}$, and KR amplitude on $E$. The lines are a guide to the eyes and the data point size represents the error bar. (b) Inversion of the positive polarization peak by switching the source-drain contacts. The labels indicate the geometry compared to Fig. 1 ($+i$). (c) One-dimensional SHE spatial profile as a function of $B_{\text{ext}}$ with unidirectional $E$.