Electrical Measurement of the Direct Spin Hall Effect in $\mathrm{Fe}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ Heterostructures

We report on an all-electrical measurement of the spin Hall effect in epitaxial $\mathrm{Fe}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures with $n$-type (Si) channel doping and highly doped Schottky tunnel barriers. A transverse spin current generated by an ordinary charge current flowing in the ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ is detected by measuring the spin accumulation at the edges of the channel. The spin accumulation is identified through the observation of a Hanle effect in the voltage measured by pairs of ferromagnetic Hall contacts. We investigate the bias and temperature dependence of the resulting Hanle signal and determine the skew and side-jump contributions to the total spin Hall conductivity.

Figure 1

(a) Micrograph of a spin Hall device with Fe contacts located $10\mu \mathrm{m}$ from the edges of the GaAs channel. The devices with contacts closer to the edges have a third contact in the center of the channel that is not used in this experiment. The contact pairs $ab$ and $cd$ are used to measure the spin accumulation. (b) Nonlocal spin valve (—) and Hanle effect (●) data obtained on a GaAs device at $T=60\mathrm{K}$ for $j_{\mathrm{Inj}}=8.2\times {10}^2\mathrm{A}/{\mathrm{cm}}^2$. Hanle data are shown for both parallel and antiparallel states of injector and detector. (c) The measured voltage $V_{ab}-V_{cd}$ for a GaAs device with Fe contacts $2\mu \mathrm{m}$ from the edges at $T=30\mathrm{K}$ for $j_x=5.7\times {10}^3\mathrm{A}/{\mathrm{cm}}^2$ in the two different parallel states ($\uparrow \uparrow$, ●) and ($\downarrow \downarrow$, ○). An offset voltage of 13.2 mV has been subtracted from both sets of data. (d) The same data after extraction of the spin Hall signal for both positive (●) and negative (○) currents. The spin Hall signal in the antiparallel state is shown as the solid line.

Figure 2

(a) SHE-induced polarization $P$ (●) as a function of magnetic field for the GaAs sample at $T=30\mathrm{K}$ and channel current $j_x=\pm 2.9\times {10}^3\mathrm{A}/{\mathrm{cm}}^2$. The solid curves (—) show fits to all contact separations with a single set of parameters. (b), (c), and (d) Data and fits for the ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ samples for $x=0.03$ (b), 0.05 (c), and 0.06 (d) under the same bias conditions. No signal was observed for the contact separations that are not shown. (e) Magnitude of the SHE signal as a function of distance from the edge of the channel for all four samples, normalized to $P_0$. The solid lines are curves generated from the fitting parameters found in (a)–(d).

Figure 3

(a) Dependence of ${\sigma }_{\mathrm{SH}}$ on the ${\sigma }_{xx}$ at $T=30\mathrm{K}$ for the $x=0$ (squares), 0.03 (circles), 0.05 (triangles), and 0.06 (diamonds) samples. A linear fit is used to determine $\gamma$ and ${\sigma }_{\mathrm{SJ}}$ for each sample. The fitting parameters are compiled in Table . (b) Temperature dependence of ${\sigma }_{\mathrm{SH}}$ from $T=30$ to 130 K (solid points) and predicted temperature dependence (curves).