Shot noise of spin current in ferromagnet-normal-metal systems

We propose a three-terminal spin-valve setup, to determine experimentally the spin- dependent shot noise, which carries information on the spin- relaxation processes. Based on a spin- dependent Boltzmann-Langevin approach, we show that the spin Fano factor, defined as the spin shot noise to the mean charge current, strongly depends on the spin-flip scattering rate in the normal wire. While in the parallel configuration the spin Fano factor always decreases below its unpolarized value with increasing spin injection, for the antiparallel case it varies nonmonotonically. We also show that in contrast to the charge current Fano factor, which varies appreciably only in the antiparallel case, the spin Fano factor allows for a more sensitive determination of the spin-flip scattering rate.