Power dependence of pure spin current injection by quantum interference

We investigate the power dependence of pure spin current injection in GaAs bulk and quantum-well samples by a quantum interference and control technique. Spin separation is measured as a function of the relative strength of the two transition pathways driven by two laser pulses. By keeping the relaxation time of the current unchanged, we are able to relate the spin separation to the injected average velocity. We find that the average velocity is determined by the relative strength of the two transitions in the same way as in classical interference. Based on this, we conclude that the density of injected pure spin current increases monotonically with the excitation laser intensities. The experimental results are consistent with theoretical calculations based on Fermi’s golden rule.

Figure 1

(Color online) Quantum interference and control technique to inject pure spin current. Two laser pulses with angular frequencies $\omega$ and $2\omega$ incident on a semiconductor along $+\widehat{z}$ direction (panel a). Electrons are excited from the valence band (VB) to the conduction band (CB) via one-photon absorption of the $2\omega$ and two-photon absorption of the $\omega$ pulses (vertical arrows in panel b). When the $\omega$ and $2\omega$ pulses are linearly polarized along $\widehat{x}$ and $\widehat{y}$ directions, respectively, quantum interference causes spin-up electrons (balls with an up arrow) to be preferentially excited to $k$ states along $+\widehat{x}$ direction, with an equal number of spin-down electrons (balls with a down-arrow) to opposite $k$ states (panel b). In real space, electrons with opposite spin orientations move with opposite velocities (horizontal arrows in panel a), forming a pure spin current.

Figure 2

(Color online) (a) Experimental setup for injection and detection of pure spin current. See text for details. (b) Upon injection, spin-up and spin-down electrons have identical spatial profiles (Gaussian shaped solid and dotted curves) with a height of $H$ and a width of $w$ (full width at half maximum), but with opposite average velocities (horizontal arrows). (c) After the transport, the two profiles separate by a distance $d$ (spin separation). The resulting spin density $\left(s\right)$ has a derivativelike profile, with a height $h$ related to $d$ by Eq. (6).

Figure 3

(Color online) Spatial profiles of the total electron density $n=n_{\uparrow }+n_{\downarrow }$ (squares, left axis) injected in the GaAs bulk sample at room temperature and the spin density $s=n_{\uparrow }-n_{\downarrow }$ (circles, right axis) that resulted from spin transport. $x=0$ is defined as when the pump and probe spots overlap. A spin separation of 44 nm can be deduced from these profiles.

Figure 4

(Color online) Spin separation measured as a function of $n_{\omega }/n_{2\omega }$ by using the procedure summarized in Fig. 3. In each set of measurements, the total electrons density is kept constant when $n_{\omega }/n_{2\omega }$ is varied. The squares, circles, and triangles show data measured from the bulk sample at room temperature, with the total electron density at the center of the profile of 1.4, 2.5, and $5.5\times {10}^{17}{\text{cm}}^{-3}$, respectively. The diamonds represent data measured from the quantum-well sample at 80 K, with the total electron density of $1.0\times {10}^{17}{\text{cm}}^{-3}$. The data sets shown as squares, triangles, and diamonds are scaled by multiplying factors of 1.30, 1.42, and 0.28, respectively, so that all the fitted curves by Eq. (3) overlap, shown as the solid line.