Detection of Electrically Modulated Inverse Spin Hall Effect in an $\mathrm{Fe}/\mathrm{GaAs}$ Microdevice

We report the detection of the inverse spin Hall effect (ISHE) in $n$-gallium arsenide ($n$-GaAs) combined with electrical injection and modulation of the spin current. We use epitaxial ultrathin-$\mathrm{Fe}/\mathrm{GaAs}$ injection contacts with strong in-plane magnetic anisotropy. This allows us to simultaneously perform Hanle spin-precession measurements on an Fe detection electrode and ISHE measurements in an applied in-plane hard-axis magnetic field. In this geometry, we can experimentally separate the ordinary from the spin-Hall signals. Electrical spin injection and detection are combined in our microdevice with an applied electrical drift current to modulate the spin distribution and spin current in the channel. The magnitudes and external field dependencies of the signals are quantitatively modeled by solving drift-diffusion and Hall-cross response equations.

Figure 1

(a) Schematics of the device. (b) Nonlocal signal $V_{\mathrm{NL}}$ measured at bias current $I_B=100\mu \mathrm{A}$ in field $B_y$ applied along the Fe easy axis. The left (right) black arrow in each pair of arrows indicates the magnetization state of the detection (injection) Fe electrode. (c) The difference between $V_{\mathrm{NL}}$ at antiparallel and parallel configurations of magnetization in the injection and detection Fe electrode as a function of $I_B$. (d) Symmetrized Hanle measurement of $V_{\mathrm{NL}}$ at $I_B=300\mu \mathrm{A}$ in hard-axis field $B_x$. (e) Antisymmetrized ISHE signal, $V_H$, under same experimental conditions as in (d).

Figure 2

(a) The two nearly identical curves (blue and black) show the measured raw data $V_H^{\uparrow }$, obtained by setting the magnetization in the Fe injection electrode in the positive easy-axis orientation, with a subtracted linear background of 0.3 $\mu$V/mT, and the pure spin signal $V_H^m$ obtained by $V_H^m=(V_H^{\uparrow }-V_H^{\downarrow })/2$. The curve which is antisymmetric with respect to the $x$-axis (red) shows the antisymmetrized signal $V_H^{\mathrm{as}}(B)=[V_H^m(B)-V_H^m(-B)]/2$. (b) Symmetrized $V_{\mathrm{NL}}$ measured in the out-of-plane hard-axis field $B_z$. (c) and (d) are the schematics of the experimental setups. (e) Antisymmetrized ISHE data for the in-plane hard-axis field measurements. The curve with the minimum at negative fields (black) corresponds to the spin current direction in the experimental setup of panel (c). The curve with the maximum at negative fields (red) corresponds to the spin current direction in the experimental setup of panel (d).

Figure 3

(a) Schematics of the experimental setup. (b) and (c) show the experimental symmetrized nonlocal spin-valve and antisymmetrized ISHE signals in the in-plane hard-axis field measured at constant spin-injection bias current $I_B=300\mu \mathrm{A}$ and at three different drift currents $I_D$ depicted in (a). (d) and (e) are the calculations of the nonlocal spin-valve and ISHE signals.