Generating Spin Currents in Semiconductors with the Spin Hall Effect

We investigate electrically induced spin currents generated by the spin Hall effect in GaAs structures that distinguish edge effects from spin transport. Using Kerr rotation microscopy to image the spin polarization, we demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current, which can drive spin polarization nearly 40 microns into a region in which there is minimal electric field. Using a model that incorporates the effects of spin drift, we determine the transverse spin drift velocity from the magnetic field dependence of the spin polarization.

Figure 1

(a) Measurement schematic and experimental geometry. We take the center of the channel to be the origin $O$. (b) Kerr rotation as a function of magnetic field at $(x,y)=(26\mu \mathrm{m},0\mu \mathrm{m})$. Line is a Lorentzian fit from which the amplitude and spin lifetime can be determined. (c) (top) Spin polarization amplitude as a function of position measured for the channel (black) and with $10\mu \mathrm{m}$ (red), $20\mu \mathrm{m}$ (green), and $40\mu \mathrm{m}$ (blue) side arms. (bottom) Spin coherence time as a function of position. Data are taken at $T=30\mathrm{K}$ and $V=6\mathrm{V}$.

Figure 2

(a) Measurements of the channel with a $20\mu \mathrm{m}$ side arm at $T=30\mathrm{K}$. The edges of the main mesa are at $x=-30\mu \mathrm{m}$ and $x=+30\mu \mathrm{m}$. Top panel is a color plot of Kerr rotation as a function of magnetic field and position for $V=6\mathrm{V}$. Middle panel shows the amplitude as a function of position for $V=2\mathrm{V}$ (blue), 4 V (red), and 6 V (black). Bottom panel shows the spin coherence time as a function of position for $V=2\mathrm{V}$ (blue), 4 V (red), and 6 V (black). (b) Measurements of the channel with a $40\mu \mathrm{m}$ side arm at $T=30\mathrm{K}$. Top panel is a color plot of spin polarization as a function of magnetic field and position for $V=6\mathrm{V}$. Middle panel shows the amplitude as a function of position for $V=4\mathrm{V}$ (red) and 6 V (black). Bottom panel shows the spin coherence time as a function of position for $V=4\mathrm{V}$ (red) and 6 V (black). For the color plots, a vertical offset is subtracted from each magnetic field scan.

Figure 3

(a) Measurement schematic showing sample dimensions. $P$ indicates the position $(x,y)=(0\mu \mathrm{m},-50\mu \mathrm{m})$. (b) Kerr rotation as a function of magnetic field for three different $x$ positions at $y=-50\mu \mathrm{m}$ on the $40\mu \mathrm{m}$ side arm. Taking $x=0\mu \mathrm{m}$ to be the center of the channel, the edges of the main channel are at $x=-30\mu \mathrm{m}$ and $x=+30\mu \mathrm{m}$ ($w=60\mu \mathrm{m}$). Measurements are shown for $x=40\mu \mathrm{m}$ ($P_1$, red), $x=50\mu \mathrm{m}$ ($P_2$, blue), and $x=60\mu \mathrm{m}$ ($P_3$, green). Solid black lines are calculated from a model that accounts for spin drift, as described in the text. The same values for $S_0$, ${\tau }_s$, $v_{\mathrm{sd}}$, and $D$ are used for all three curves. (c) Amplitude of Kerr rotation measured as a function of longitudinal position $y$ for $x=-26\mu \mathrm{m}$ (purple), $x=26\mu \mathrm{m}$ (orange), $x=36\mu \mathrm{m}$ (cyan), and $x=56\mu \mathrm{m}$ (magenta). These positions are shown as dashed lines in part (a) of this figure. One contact edge is located at $y=-158\mu \mathrm{m}$, and the edges of the side arm are at $y=-70\mu \mathrm{m}$ and $y=-30\mu \mathrm{m}$. Data are taken at $T=30\mathrm{K}$ and $V=6\mathrm{V}$.

Figure 4

(a) Measurement schematic showing a channel that splits into two smaller channels. $O$ indicates the origin. (b) Kerr rotation amplitude as a function of transverse position $x$ for longitudinal positions $y=28\mu \mathrm{m}$ (black), $y=18\mu \mathrm{m}$ (red), $y=8\mu \mathrm{m}$ (blue), $y=-2\mu \mathrm{m}$ (green), $y=-12\mu \mathrm{m}$ (orange), and $y=-22\mu \mathrm{m}$ (purple). The sample edges are at $x=-50\mu \mathrm{m}$, $x=-5\mu \mathrm{m}$, $x=5\mu \mathrm{m}$, and $x=50\mu \mathrm{m}$. (c) Kerr rotation amplitude as a function of $y$ for $x=-10\mu \mathrm{m}$ (blue) and $x=10\mu \mathrm{m}$ (red) showing spin diffusion along the direction of the applied electric field. Data are taken at $T=30\mathrm{K}$ and $V=6\mathrm{V}$.