Spin-Hall Voltage over a Large Length Scale in Bulk Germanium

We exploit the spin-Hall effect to generate a uniform pure spin current in an epitaxial $n$-doped Ge channel, and we detect the electrically induced spin accumulation, transverse to the injected charge current density, with polar magneto-optical Kerr microscopy at a low temperature. We show that a large spin density up to $400\mu {\mathrm{m}}^{-3}$ can be achieved at the edges of the $100\text{−}\mu \mathrm{m}$-wide Ge channel for an applied electric field lower than $5\mathrm{mV}/\mu \mathrm{m}$. We find that the spin density linearly decreases toward the center of the Ge bar, due to the large spin diffusion length, and such a decay is much slower than the exponential one observed in III–V semiconductors, allowing very large spin accumulations over a length scale of tens of micrometers. This lays the foundation for multiterminal spintronic devices, where different spin voltages can be exploited as inputs for magnetologic gates on the same Ge platform.

Figure 1

(a) 2D optical reflectivity map at $T=20\mathrm{K}$ of the $n$-doped Ge channel, grown on a high-resistivity Si(001) substrate. (b) Geometry of the SHE: A constant positive (negative) electric field $E_{+(-)}$ is applied along the $x$ axis between the two Ni Ohmic contacts of the Ge channel, resulting in a negative (positive) pure spin current ${\mathbf{J}}_{\mathrm{s}}$ along the $y$ axis. (c) Scheme of the spin electrochemical potential along the Ge channel width ($y$ axis) given by the SHE. (d) Sketch of the magneto-optical Kerr microscopy setup. BS, beam splitter; PEM, photoelastic modulator; PD, photodiode.

Figure 2

(a) Average of 40 line profiles of the optical reflectivity $R$ (top panel) and the Kerr ellipticity ${\vartheta }_{\mathrm{ell}}$ (bottom panel) across the Ge channel for an applied positive $E_{+}$ (red dots) and negative $E_{(-)}$ (black dots) uniform electric field $E_{+(-)}=4.7\mathrm{mV}/\mu \mathrm{m}$. The scanned area is $40\times 130\mu {\mathrm{m}}^2$. ${\vartheta }_{\mathrm{ell}}$ is shown in the range between $y=-42$ and $42\mu \mathrm{m}$. (b) Difference of the Kerr ellipticity profiles in (a) (left $y$ axis) and electrically induced spin density $n_s$ across the Ge channel (right $y$ axis), as obtained from the calibration procedure described in Supplemental Material, Sec. C [29]. The dashed light blue line is a linear fit of the experimental data from Eq. (1).

Figure 3

Kerr ellipticity map across the Ge channel, obtained as the difference between measurements with opposite applied electric field $E_{+(-)}=4.7\mathrm{mV}/\mu \mathrm{m}$. The scanned area is $40\times 84\mu {\mathrm{m}}^2$ around the center of the sample, corresponding to a region where the reflectivity $R$ is flat. Measurements have been performed at $T=20\mathrm{K}$ with an incident power of $W=2\mathrm{mW}$.

Figure 4

(a) Electrically induced spin density $n_s$ across the Ge channel width as a function of the applied electric field. The dashed red line represents a linear fit of the experimental data from Eq. (1). (b) Spin-Hall conductivity ${\sigma }_{\mathrm{SH}}$ of the Ge channel as a function of the applied electric field at $T=20\mathrm{K}$. The light blue area identifies the averaged value of ${\sigma }_{\mathrm{SH}}$, weighed with the experimental error. (c) Spin current density $J_s$ for $y=0$ at $T=20\mathrm{K}$, estimated through the spin drift-diffusion model of Eq. (1) from the experimental data set in (a). (d) Electrically induced spin density $n_s$ for a unit electric field and $y=42\mu \mathrm{m}$ as a function of the temperature. The red dashed line corresponds to the estimated temperature dependence of the spin diffusion length $L_s$ (see Supplemental Sec. B [29]). Inset: Spin-Hall conductivity ${\sigma }_{\mathrm{SH}}$ of the Ge channel as a function of the temperature.