Observation of large spin accumulation voltages in nondegenerate Si spin devices due to spin drift effect: Experiments and theory

A large spin accumulation voltage of more than 1.5 mV at 1 mA, i.e., a magnetoresistance of 1.5 Ω, was measured by means of the local three-terminal magnetoresistance in nondegenerate Si-based lateral spin valves (LSVs) at room temperature. This is the largest spin accumulation voltage measured in semiconductor-based LSVs. The modified spin drift–diffusion model, which successfully accounts for the spin drift effect, explains the large spin accumulation voltage and significant bias-current-polarity dependence. The model also shows that the spin drift effect enhances the spin-dependent magnetoresistance in the electric two-terminal scheme. This finding provides a useful guiding principle for spin metal-oxide-semiconductor field-effect transistor operations.

Figure 1

(a) Schematic of the Si-based LSV. Two Fe ferromagnetic electrodes (FE1, FE2) are placed in contact with two Al nonmagnetic electrodes (NE1, NE2). A MgO barrier is used to realize a large spin accumulation in the Si channel. Average of phosphorous was approximately $2\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$. (b) A schematic of the electrochemical potential of up and down spins in an NC and FEs. An electric field generates a charge current, $I$, from FE1 to FE2, resulting in spin injection and extraction at the NC/FE2 and FE1/NC interfaces, respectively. A spin accumulation in NC is generated due to the spin injection and extraction, resulting in a spin-dependent voltage drop (spin injection: $D_V$ and spin extraction: $E_V$) at the interfaces, which induce a two-terminal magnetoresistance effect.

Figure 2

(a) Local three-terminal magnetoresistances (L-3T MR) in the nondegenerate Si-based LSV measured at room temperature (RT). The currents of the upper and lower panels were +1 mA (spin extraction condition) and −1 mA (spin injection condition), respectively. The distance, $d$, between FE1 and FE2 in Fig. 1 was 1.85 μm. The blue and red circles show the results obtained under different magnetic field sweep directions. (b) Hanle effect signals measured in the L-3T MR scheme at RT, where the magnetic field direction was perpendicular to the plane. The current was +1 mA. The raw data under parallel (red) and antiparallel (blue) configurations are shown in the inset, and the difference in the Hanle signal between antiparallel and parallel configurations is shown in the main panel. The fit with Eq. (1) is shown by the black solid line.

Figure 3

L-3T MRs of two different devices, B and C, measured at +1 mA. The distance, $d$, between FE1 and FE2 of the devices B and C was 2.00 and 2.75 μm, respectively.

Figure 4

(a) A schematic of the Si-based LSV for calculation of spin accumulation voltage. (b)–(g) The spin-dependent voltage $V_{3\uparrow (\downarrow )}\left(x_F\right)$ of up (red) and down (blue) spins under parallel (solid line) and antiparallel (broken line) configurations calculated using Eqs. (4) and (5), (b) without and (e) with the spin drift effect, and the spin accumulation voltage detected at FE2 (spin injection condition), and FE1 (spin extraction condition), calculated with Eqs. (2, 3, 4, 5) with (c), (d) and without (f), (g) the spin drift effect. Calculated to be less than −12 is plotted in the same color (purple).

Figure 5

(a) Schematic of degenerate Si-based LSV. L-3T MR measured at (b) +3 mA (spin extraction condition, $E_V/I$) and (c) −3 mA (spin injection condition, $D_V/I)$. (d) The raw data of L-3T MR at −3 mA. All measurements were conducted at RT.

Figure 6

(a) Schematic of Cu-based LSV. L-3T MR signals in Cu-based LSV measured at (b) $+2\mathrm{mA}\left(E_V/I\right)$ and (c) $-2\mathrm{mA}\left(D_V/I\right)$. (d) Nonlocal voltage signal measured at −3 mA. All measurements were conducted at RT.

Figure 7

Bias-current dependence of $\mathrm{\Delta }{E}_V$ of (a) nondegenerate Si-, (b) degenerate Si-, and (b) Cu-based LSV measured at RT. Solid lines are the theoretical calculations using Eqs. (2, 3, 4, 5).

Figure 8

Bias-current dependence of two-terminal magnetoresistance calculated using Eqs. (2, 3, 4, 5) both with (red) and without (blue) the spin drift effect. The conductivities of the channel are (a) $1\times {10}^7$, (b) $1\times {10}^6$, (c) $1\times {10}^5$, and (d) $1\times {10}^4{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$, respectively.