Semiclassical theory of spin-polarized shot noise in mesoscopic diffusive conductors

We study fluctuations of spin-polarized currents in a three-terminal spin-valve system consisting of a diffusive normal-metal wire connected by tunnel junctions to three ferromagnetic terminals. Based on a spin-dependent Boltzmann-Langevin equation, we develop a semiclassical theory of charge and spin currents and the correlations of the current fluctuations. In the three-terminal system, we show that current fluctuations are strongly affected by the spin-flip scattering in the normal metal and the spin polarizations of the terminals, which may point in different directions. We analyze the dependence of the shot noise and the cross-correlations on the spin-flip scattering rate in the full range of the spin polarizations and for different magnetic configurations. Our results demonstrate that noise measurements in multiterminal devices allow us to determine the spin-flip scattering rate by changing the polarizations of the ferromagnetic terminals.

Figure 1

A schematic picture of the three-terminal spin valve. A diffusive wire of length $L$ is connected to three ferromagnetic terminals via the tunnel junctions.

Figure 2

Fano factor $F$ versus the spin-flip scattering intensity $\lambda =L∕{\mathit{\ell }}_{sf}$ for a given magnitude of the polarization in $\mathrm{F}$ terminals, but different configurations and for different values of the tunnel conductances $g=g_i∕g_N$. For the configurations with $p_2=p_3$ the corresponding cross-correlation is obtained via $S_{23}∕\mid I_{c1}\mid =(F-1)∕4$.

Figure 3

Fano factor $F$ versus the magnitude of spin polarization $p$ of the terminals in the limit of the small spin flip-scattering intensity $\lambda =L∕{\mathit{\ell }}_{sf}\to 0$. The results are shown for different configurations of the polarizations and different values of the tunnel conductances $g$.

Figure 4

Fano factor $F$ versus the spin-flip scattering intensity $\lambda =L∕{\mathit{\ell }}_{sf}$ for different polarizations $p_1$ in the terminal ${\mathrm{F}}_1$ and perfect polarizations in the other two terminals ${\mathrm{F}}_2$, ${\mathrm{F}}_3$, $p_2=p_3=1$. The columns I–III correspond to different values of the tunnel contact conductances $g=g_i∕g_N$. Here the crosscorrelations are related to the Fano factor via $S_{23}∕\mid I_{c1}\mid =(F-1)∕4$. For an explanation of the various plots, see the text.

Figure 5

Cross-correlations of the current measured between terminals ${\mathrm{F}}_2$ and ${\mathrm{F}}_3$ for the antiparallel configuration of the polarizations $p_2=-p_3$ and for different contact conductances $g=g_i∕g_N$. The polarization of ${\mathrm{F}}_1$, $p_1=1$ and the magnitude of the magnetizations $\mid p_2\mid =\mid p_3\mid$ vary in each column.