All-electrical measurements of direct spin Hall effect in GaAs with Esaki diode electrodes

We report on measurements of direct spin Hall effect in a lightly $n$-doped GaAs channel with conductivity below 2000 Ω${}^{-1}$ m${}^{-1}$. As spin detecting contacts, we employed highly efficient ferromagnetic Fe/(Ga,Mn)As/GaAs Esaki diode structures. We investigate bias and temperature dependence of the measured spin Hall signal and evaluate the value of total spin Hall conductivity and its dependence on channel conductivity and temperature. From the results, we determine skew scattering and side-jump contribution to the total spin Hall conductivity and compare it with the results of experiments on higher conductive $n$-GaAs channels [Garlid, Hu, Chan, Palmstrøm, and Crowell, Phys. Rev. Lett. 105, 156602 (2010)]. As a result, we conclude that both skewness and side jump contribution cannot be treated as fully independent of the conductivity of the channel.

Figure 1

(a) Micrograph of a spin Hall device with experimental layout. A pair of ferromagnetic contacts ($a$ and $b$) is placed at the Hall cross at a distance $L$ from the channel edges. Voltage $V_{\mathrm{ab}}$ and Hall voltage $V_{\mathrm{cd}}$ is measured as a function of in-plane field ${\mathbf{B}}_{\mathrm{y}}$, in the presence of charge current $j_{\mathrm{x}}$. (b) $V_{\mathrm{ab}}$ as a function of ${\mathbf{B}}_{\mathrm{y}}$ for $j_{\mathrm{x}}$ $=$ 1.7 × 10${}^3$ A/cm${}^2$ for initial orientation of magnetizations along $+x$ (solid black symbols) and $-x$ (open red symbols) directions. (c) Spin Hall voltage $V_{\mathrm{SH}}$ vs ${\mathbf{B}}_{\mathrm{y}}$ for the same current amplitude for both positive (solid black symbols) and negative (open red symbols) current directions after removing the background as described in the text.

Figure 2

(a)–(c) Spin Hall voltage V${}_{\mathrm{SH}}$ as a function of ${\mathbf{B}}_{\mathrm{y}}$ at $T$ $=$ 4.2 K and for $j_{\mathrm{x}}$ $=$ 1.7 × 10${}^3$ A/cm${}^2$ for three different values of a distance between contact and the channel edge. Solid lines represent fits with the same set of parameters. (d) Magnitude of the spin Hall signal Δ$V_{\mathrm{SH}}$ vs distance between contact and the channel edge with the extracted value of the spin diffusion length λ${}_{\mathrm{sf}}$.

Figure 3

(a)–(c) Spin Hall voltage V${}_{\mathrm{SH}}$ as a function of ${\mathbf{B}}_{\mathrm{y}}$ at $T$ $=$ 4.2 K for three different channel current densities $j_{\mathrm{x}}$ corresponding to different conductivities σ${}_{\mathrm{xx}}$. We plot both experimental data (symbols) and corresponding fits (red line). (d) Dependence of the spin Hall conductivity on σ${}_{\mathrm{xx}}$ extracted from our measurements at $T$ $=$ 4.2 K (full symbols) and taken from Ref. 10 (open symbols, $T$ $=$ 30 K). From the linear interpolation (solid line) with Eq. (3), we obtain the value of skewness parameter γ $=$ 4 × 10${}^{-4}$ and side jump contribution σ${}_{\mathrm{SJ}}$ ≈ 0.6 Ω${}^{-1}$m${}^{-1}$. From the linear fit shown for Ref. 10 data, one gets γ $=$ 4 × 10${}^{-3}$ and σ${}_{\mathrm{SJ}}$ ≈ −12 Ω${}^{-1}$m${}^{-1}$. (Inset) Zoom of our data.

Figure 4

(a)–(c) Spin Hall voltage $V_{\mathrm{SH}}$ as a function of ${\mathbf{B}}_{\mathrm{y}}$ at three different temperature values $T$ for current density $j_{\mathrm{x}}$ $=$ 1.7 × 10${}^3$A/cm${}^2$; (d) temperature dependence of σ${}_{\mathrm{SH}}$ for $j_{\mathrm{x}}$ $=$ 1.7 × 10${}^3$A/cm${}^2$. Displayed are the experimental results (black squares) and predicted values (red triangles), derived from Eq. (3) using measured $n$($T$) and σ${}_{\mathrm{xx}}$($T$). Lines are just guides for the eye.