Experimental evaluation of the spin-Hall conductivity in Si-doped GaAs

We performed photoinduced inverse spin-Hall effect (ISHE) measurements on Si-doped bulk GaAs at room temperature. The spin current is optically injected in the sample by means of circularly polarized light and is detected through spin-dependent scattering by Si impurities, which provide an electromotive field ${\mathbf{E}}_{\mathrm{ISHE}}$ close to the sample surface. We measured the ISHE signal as a function of the incident photon energy, and we determined the corresponding averaged spin current, flowing through the sample, to experimentally determine the spin-Hall conductivity.

Figure 1

Experimental geometry for ISHE measurements on the Si-doped GaAs(001) sample. The ISHE electromotive force $\Delta V_{\mathrm{ISHE}}$ is the voltage difference between the two Au electrodes. $\theta$ is the angle between the direction of the incident photons, represented by the unit vector ${\mathbf{u}}_{\mathbf{k}}$, and the normal to the sample surface, whereas, $\varphi$ is the angle in the $xy$ plane set between the projection of ${\mathbf{u}}_{\mathbf{k}}$ in the $xy$ plane and the $x$ axis.

Figure 2

(a) The ISHE electromotive force $\Delta V_{\mathrm{ISHE}}$ (black dots) as a function of the angle $\varphi$ (the straight red line represents a cosine fit). Data are taken at $T=300\mathrm{K},\theta ={65}^{\circ },h\nu =1.7\mathrm{eV}$ and with an excitation power of $w_{\mathrm{exc}}\approx 30\mathrm{mW}$, taking into account the GaAs reflection coefficient; (b) the ISHE signal as a function of the incident photon energy in the 1.42–1.8-eV energy range for $\theta ={65}^{\circ }$ and $\varphi =0$. The values are normalized with respect to $w_{\mathrm{exc}}$. The dashed red arrow shows the GaAs energy band gap $E_{\mathrm{g}}=1.42\mathrm{eV}$ at room temperature.

Figure 3

Calculated spin-diffusion length $L_{\mathrm{s}}$ (black line) and $I_{\mathrm{ISHE}}/\gamma$ (red line), defined in Eq. (3) as a function of the incident photon energy in the 1.42–1.8-eV range.

Figure 4

Spin-Hall angle $\gamma$ at room temperature, extrapolated from the experimental data of Fig. 2b. The inset shows an enlargement of the $\gamma$ values near $E_{\mathrm{g}}$.