Giant Spin Accumulation in Silicon Nonlocal Spin-Transport Devices

Although the electrical injection, transport, and detection of spins in silicon have been achieved, the induced spin accumulation is much smaller than expected and desired, limiting the potential impact of Si-based spintronic devices. Here, using nonlocal spin-transport devices with an $n$-type Si channel and $\mathrm{Fe}/\mathrm{MgO}$ magnetic tunnel contacts, we demonstrate that it is possible to create a giant spin accumulation in Si, with the spin splitting reaching 13 meV at 10 K and 3.5 meV at room temperature. The nonlocal spin signals are in good agreement with a numerical evaluation of spin injection and diffusion that explicitly takes the size of the injector contact into account. The giant spin accumulation originates from the large tunnel spin polarization of the $\mathrm{Fe}/\mathrm{MgO}$ contacts (53% at 10 K and 18% at 300 K) and from the spin-density enhancement that is achieved by using a spin injector with a size comparable to the spin-diffusion length of the Si. The ability to induce a giant spin accumulation enables the development of Si spintronic devices with a large magnetic response.

Figure 1

Structural characterization of the $\mathrm{Si}/\mathrm{MgO}/\mathrm{Fe}$ tunnel contact. RHEED patterns of (a) the Si surface having a $c(2\times 4)$ reconstruction after in situ annealing at $700°\mathrm{C}$, (b) the MgO(001) layer deposited at $300°\mathrm{C}$, and (c) the Fe(001) layer deposited at $200°\mathrm{C}$. In each case, the patterns along the [100] and [110] azimuths are shown. Note that the azimuth labels for the Fe are interchanged because the Fe lattice is rotated by 45° with respect to the MgO and Si lattices. (d) Low-magnification and (e) high-resolution cross-sectional TEM images of the junction.

Figure 2

Spin transport in the Si nonlocal device and giant spin accumulation. (a) Schematic layout of the nonlocal device with dimensions indicated. (b) Nonlocal spin signals $V_{\mathrm{NL}}$ measured on device $B$ in spin-valve geometry and Hanle geometry with the external magnetic field applied, respectively, in plane ($B_Y$) along the long axis of the FM contacts or perpendicular to the sample plane ($B_Z$). The narrow FM strip ($0.6\mu \mathrm{m}$) is used as the injector, and the spin accumulation in the Si is detected using the wide FM contact ($1.8\mu \mathrm{m}$). The $B_Y$ is either swept from plus to minus (green symbols) or in the opposite direction (dark blue symbols). The wide (narrow) FM contact reverses its magnetization at a smaller (larger) value of $B_Y$. The injected current $I$ is $+1\mathrm{mA}$ (current density $J={+4.2\mathrm{kA}/\mathrm{cm}}^2$, electrons flowing from FM into the Si), and an offset of about 3 mV is subtracted from the measured signals. $T=10\mathrm{K}$. (c),(d) Nonlocal spin-valve signals measured on device $A$ at 10 K and at 300 K, using the wide FM strip ($1.2\mu \mathrm{m}$) as the injector and the narrow FM strip ($0.4\mu \mathrm{m}$) as the nonlocal detector. Indicated are the values of the spin accumulation under the detector contact (either positive or negative) extracted from $V_{\mathrm{NL}}=P_{\det }\mathrm{\Delta }\mu /2e$ using $P_{\det }$ is 53% at 10 K and 18% at 300 K. The $J$ is $+12.5\mathrm{kA}/{\mathrm{cm}}^2$ ($I=+6\mathrm{mA}$) at 10 K and $+8.3\mathrm{kA}/{\mathrm{cm}}^2$ ($I=+4\mathrm{mA}$) at 300 K. The origin of the cusp around zero field in (c) is not understood.

Figure 3

Calculated spin accumulation. (a) Spatial profiles of the spin accumulation for different widths of the FM injector contact. Solid lines are the exact profile obtained from expression (1), whereas the dashed lines are for the approximation of the injector as a line of infinitesimal width placed at the center of the injector [located between $x=0$ (right edge) and $x=-W_{\mathrm{inj}}$ (left edge, indicated by the short colored vertical lines)]. (b) Magnitude of the spin accumulation at the edge of the FM injector contact as a function of the contact width. The thick blue line is for the full numerical calculation using expression (1), whereas the thin green line is for the line injector approximation. For (a) as well as (b), we use ${\mathrm{L}}_{\mathrm{SD}}=1.0\mu \mathrm{m}$, and the spin accumulation is normalized to the maximum value at the center of a very wide contact ($W_{\mathrm{inj}}\gg L_{\mathrm{SD}}$).

Figure 4

Calculated spin signal and experimental data for different injector contact width. (a) Nonlocal spin-valve signals at 10 K for device $A$ at $J={+6.3\mathrm{kA}/\mathrm{cm}}^2$ using either the narrow FM strip as the injector and the wider FM strip as the nonlocal detector (left panel, $I=+1\mathrm{mA}$), or vice versa (right panel, $I=+3\mathrm{mA}$), as indicated by the schematic diagrams of the measurement configuration. (b) The same for device $C$ at $J={+2.1\mathrm{kA}/\mathrm{cm}}^2$ (left panel, $I=+0.66\mathrm{mA}$; right panel $I=+2\mathrm{mA}$). (c) Calculated spin signal versus position produced by the spin accumulation in the Si for different widths of the FM injector contact (solid lines) and experimental data (symbols) for devices $A$, $B$, and $C$ obtained in two configurations (either using the narrow FM strip as the injector and the wider FM strip as the detector, or vice versa). The injector is located between $x=0$ (right edge) and $x=-W_{\mathrm{inj}}$ (left edge, indicated by the short colored vertical lines). The experimental data are compared to the calculated spin signal at the center of the detector, which is located at $x>0$. The best agreement with the data is obtained using $L_{\mathrm{SD}}=2.2\mu \mathrm{m}$ and $P=53\%$ in the calculation. (d) Calculated spin signal (solid line) at the right edge of the injector ($x=0$) versus the width of the injector contact compared to the values (symbols) derived from the experimental data by compensating for the exponential decay between $x=0$ and the center of the detector.

Figure 5

Nonlocal Hanle measurements and extracted spin lifetime. Nonlocal Hanle measurements for parallel (blue open circles) and antiparallel (pink open circles) orientation of the magnetization of the injector and the detector, for different devices and width of the injector, as indicated. The solid black lines correspond to the numerically calculated Hanle signal at the center of the detector using ${\tau }_s=18\mathrm{ns}$, which simultaneously provides a good fit for all data sets. $T=10\mathrm{K}$.

Figure 6

Spin transport in Si at room temperature. (a) Nonlocal spin signals at $T=300\mathrm{K}$ for device $A$ using either the narrow FM strip as the injector and the wider FM strip as the nonlocal detector (left panels, $J={+7.5\mathrm{kA}/\mathrm{cm}}^2$, $I=+1.2\mathrm{mA}$), or vice versa (right panels, $J={+4.2\mathrm{kA}/\mathrm{cm}}^2$, $I=+2\mathrm{mA}$), as indicated by the schematic diagrams of the measurement configuration. The top panels display the spin signal for the spin-valve geometry, the bottom panels for the Hanle geometry. The fits to the Hanle data (solid black lines) are obtained using ${\tau }_s=2.5\mathrm{ns}$. Note the factor of 4 difference in the vertical scale between the left and right panels. (b) Spin signal at 300 K calculated as a function of position in the Si channel for different widths of the FM injector contact (solid lines), and experimental data (symbols) for devices $A$ and $C$ obtained in two configurations (either using the narrow FM strip as the injector and the wider FM strip as the detector, or vice versa). The best agreement with the data is obtained for $L_{\mathrm{SD}}=1.0\mu \mathrm{m}$ and $P=18\%$. (c) Nonlocal spin signals versus temperature for device $A$ for two configurations (pink symbols) together with previous data taken from Ref. [12] (dark blue symbols) and Ref. [16] (dark green symbols).