Shot Noise Induced by Nonequilibrium Spin Accumulation

When an electric current passes across a potential barrier, the partition process of electrons at the barrier gives rise to the shot noise, reflecting the discrete nature of the electric charge. Here we report the observation of excess shot noise connected with a spin current which is induced by a nonequilibrium spin accumulation in an all-semiconductor lateral spin-valve device. We find that this excess shot noise is proportional to the spin current. Additionally, we determine quantitatively the spin-injection-induced electron temperature by measuring the current noise. Our experiments show that spin accumulation driven shot noise provides a novel means of investigating nonequilibrium spin transport.

Figure 1

(a) Current noise at $T=0$ for $\mathrm{\Delta }\mu =400\mu \mathrm{eV}$, when a nonmagnetic detector electrode is used [11]. The inset shows the schematic energy diagram. The dotted curve indicates shot noise without spin accumulation. (b) Current noise when a ferromagnetic contact is used on one side of the tunneling barrier as a detector electrode ($\alpha =0.75$ and $\beta =0.25$).

Figure 2

(a) Schematic diagram of the sample and measurement system. Six (Ga,Mn)As electrodes ($E1$ to $E6$) are placed on the $n$-GaAs channel, where $E2$ ($4\mu \mathrm{m}\times 50\mu \mathrm{m}$ size) is an injection electrode, while either $E3$, $E4$, or $E5$ ($0.5\mu \mathrm{m}\times 50\mu \mathrm{m}$ size) is a detection electrode. The center-to-center spacing between the neighboring electrodes is $5\mu \mathrm{m}$. Schematic spatial dependence of each chemical potential in the $n$-GaAs channel is illustrated. (b) Typical nonlocal voltage signal for $I_{\mathrm{inj}}=-23\mu \mathrm{A}$. A peak observed around the zero magnetic field is induced by dynamic nuclear spin polarization (DNP) [23]. This effect is irrelevant to the present result, as the noise measurement was performed outside of the DNP region. (c) Schematic energy diagram at the detection electrode in the presence of $eV$ and $\mathrm{\Delta }\mu$.

Figure 3

(a) Measured $S$ at $E3$ as a function of $V$ for $\mathrm{P}$ and $\mathrm{A}\mathrm{P}$ configurations for several injection currents. The curves are offset vertically by $1\times {10}^{-26}{\mathrm{A}}^2/\mathrm{Hz}$ for clarity. The dotted curve is the fitted curve from Eq. (1). The error bar for each point is $\pm 0.4\times {10}^{-27}{\mathrm{A}}^2/\mathrm{Hz}$. (b) $B$ dependence of $S$ measured with keeping $V$ constant ($V=-6.8\mathrm{mV}$) for $I_{\mathrm{inj}}=0,-9$, and $-23\mu \mathrm{A}$ (from bottom to top). The thick arrows denote the magnetization directions of $E2$ and $E3$. (c) $S_S$ versus $I_S$ for the bias region ($|eV|>\mathrm{\Delta }\mu /2$, $2k_{\mathrm{B}}T$) for several injection currents and for different detection electrodes. The dashed line is the linear relation with $F=0.77$. The inset shows the counterpart of the main graph for $S_C$ versus $I_C$.

Figure 4

(a) $I_{\mathrm{inj}}$ dependence of the extracted $k_{\mathrm{B}}\mathrm{\Delta }{T}_e$ and $\mathrm{\Delta }\mu$ at detector $E3$. (b) $L$ dependence of $k_{\mathrm{B}}\mathrm{\Delta }{T}_e$ and $\mathrm{\Delta }\mu$ for $I_{\mathrm{inj}}=-23\mu \mathrm{A}$.