Spin-current noise from fluctuation relations

We present fluctuation relations that connect spin-polarized current and noise in mesoscopic conductors. In linear response, these relations are equivalent to the fluctuation-dissipation theorem that relates equilibrium current-current correlations to the linear conductance. More interestingly, in the weakly nonlinear regime of transport, these relations establish a connection between the leading-order rectification spin conductance, the spin noise susceptibility and the third cumulant of spin current fluctuations at equilibrium. Our results are valid even for systems in the presence of magnetic fields and coupled to ferromagnetic electrodes.