Significant modulation of electrical spin accumulation by efficient thermal spin injection

We have investigated the dc bias current dependence of the nonlocal spin valve signal in CoFeAl/Cu lateral spin valves. The spin signal is found to increase monotonically with the bias current. Surprisingly, the modulation amplitude from $-1$ mA to 1 mA exceeds 30 percent of the spin signal at low bias current. From the analysis based on the one-dimensional spin diffusion model and considering the bias-current heating effect, we find that the contribution of the thermal spin injection is much larger than the influence of the reduction of the spin diffusion length due to the Joule heating. We also show that the second harmonic lock-in signal precisely extracts the contribution of the thermal spin injection from the mixed spin signal.

Figure 1

(a) SEM image of the fabricated LSV device consisting of two CoFeAl wires and a single Cu channel strip. (b) Representative nonlocal spin signal observed in CFA/Cu LSV under the ac current of $I_0=140\mu \mathrm{A}$ without the dc current. The dash and solid curves correspond to forward and backward field sweeps, respectively. (c) First harmonic spin signal without dc current as a function of interval distance $L$. The solid red curve is obtained by fitting Eq. (2) to the experimental points.

Figure 2

Field dependence of the first harmonic signal with the dc bias currents (a) $+1$ mA, (b) 0 mA, and (c) $-1$ mA. (d) First harmonic spin signal $R_{\mathrm{S}}^{1\mathrm{f}}$ as a function of dc bias current $\left(I_{\mathrm{dc}}\right)$ for the CFA/Cu LSV with the interval distance 400 nm. The solid line corresponds to the fitting curve based on Eq. (4).

Figure 3

Field dependence of the second harmonic voltage for the ac currents (a) 0.21 mA, (b) 0.53 mA, and (c) 0.84 mA. (d) Second harmonic spin voltage $V_{\mathrm{S}}^{2\mathrm{f}}=V_{\mathrm{P}}^{2\mathrm{f}}-V_{\mathrm{AP}}^{2\mathrm{f}}$ and (e) base voltage of second harmonic $V_{\mathrm{B}}^{2\mathrm{f}}=(V_{\mathrm{P}}^{2\mathrm{f}}+V_{\mathrm{AP}}^{2\mathrm{f}})/2$ as a function of AC bias current $\left(I_0\right)$. The solid red curves represent the fitting parabolic curve.

Figure 4

First harmonic spin signal $R_{\mathrm{S}}^{1\mathrm{f}}$ as a function of dc bias current $\left(I_{\mathrm{dc}}\right)$ for the Py/Cu LSV. The solid line corresponds to the fitting curve based on Eq. (4). The inset shows the representative field dependence of the spin signal for $(I_{\mathrm{dc}}=0)$.