Shot noise of spin current

We report a theoretical investigation of shot noise of spin current without an accompanying charge current. For a two-probe spin pump, both cross- and autocorrelations are needed to characterize the noise. The corresponding Fano factors measure the spin unit of the quasiparticles in the spin current. The shot noise also detects open channels for spin transport, and can have qualitatively different behavior compared with the shot noise of charge current.