Observation of Intrinsic Inverse Spin Hall Effect

We report observation of intrinsic inverse spin Hall effect in undoped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well before the first electron-hole scattering event. Generation of the transverse current in the scattering-free ballistic transport regime provides unambiguous evidence for the intrinsic inverse spin Hall effect.

Figure 1

The GaAs quantum-well sample is simultaneously illuminated by two laser pulses with angular frequencies of $\omega$ and $2\omega$ [waves in panels (a) and (b)]. Quantum interference between one-photon absorption of the $2\omega$ pulse and the two-photon absorption of the $\omega$ pulse [vertical arrows in panel (b)] causes spin-up (orange spheres) and spin-down (blue spheres) electrons to be excited with opposite wave vectors, forming a pure spin current along $\widehat{x}$. Initially, the two spin systems overlap in space [panel (c)]. After a short period of time, they separate by a small distance $\Delta x$ [panel (d)], resulting in a spin density $S$ with a derivativelike profile along $\widehat{x}$ [panel (e)]. Because of the inverse spin Hall effect, both spin systems move along $\widehat{y}$, causing the whole electron density profile ($N$) to move a distance $\Delta y$ (positive or negative) from the origin. The resulting electron accumulation $\Delta N$ has a derivativelike profile along $\widehat{y}$ [panel (f)].

Figure 2

Panel (a) shows the profile of the electron density ($N$) measured by scanning the probe spot in the $x\mathrm{\text{−}}y$ plane with a probe delay of 0.5 ps. The sample temperature is 10 K and the peak carrier density is $6\times {10}^{16}{\mathrm{cm}}^{-3}$. The spin density ($S$) and the electron accumulation ($\Delta N$) measured by scanning the probe spot along the horizontal line shown in panel A are plotted as the solid squares in panel (b) and the solid circles in panel (c), respectively. Solid squares and solid circles in panels (d) and (e) show these two quantities measured by scanning the probe spot along the vertical line shown in panel (a). Panel (f) shows the deduced $\Delta x$ (solid squares) and $\Delta y$ (solid circles) as a function of the probe delay. All the open symbols in panels (b)–(f) show corresponding results obtained with a higher peak carrier density of $2.4\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 3

Panels (a) and (b) show measurements of sample $B$ that correspond to Figs. 2b, 2e, respectively, with a fixed probe delay of 0.2 ps. Panels (c) and (d) corresponds to Fig. 2f, but from samples $B$ and $C$, respectively, both measured at $x=y=1\mu \mathrm{m}$. Panel (e) is the same as panel (d) but measured at a different probe position ($x=1$, $y=-1\mu \mathrm{m}$).