Measuring spin accumulations with current noise

We investigate the time-dependent fluctuations of the electric current injected from a reservoir with a nonequilibrium spin accumulation into a mesoscopic conductor. We show how the current noise power directly reflects the magnitude of the spin accumulation in two easily noticeable ways. First, as the temperature is lowered, the small-bias noise saturates at a value determined by the spin accumulation. Second, in the presence of spin-orbit interactions in the conductor, the current noise exhibits a sample-dependent mesoscopic asymmetry under reversal of the electric current direction. These features provide for a purely electric protocol for measuring spin accumulations.

Figure 1

Three-terminal quantum dot connected to two unpolarized electron reservoirs (labeled 1 and 2) and one reservoir (3) with a nonequilibrium spin accumulation. Top right inset: a ferromagnetic reservoir with an equilibrium spin accumulation (a case we do not consider in this paper).

Figure 2

Current noise in a two-terminal conductor vs applied bias voltage for a spin accumulation of $\delta \mu =400$ $\mu$eV in a single lead (solid lines) or no spin accumulation in either lead (dashed lines). (a) $T=0$ K and $N=10$. (b) $T=1$ K and $N=10$. (c) Second derivative of the data in panel (b). (d) Typical asymmetry in the current noise as a function of applied bias for $T=1$ K and $N=2$.