  We measure the low-frequency thermal fluctuations of pure spin current in a
Platinum film deposited on yttrium iron garnet via the inverse spin Hall effect
(ISHE)-mediated voltage noise as a function of the angle $\alpha$ between the
magnetization and the transport direction. The results are consistent with the
fluctuation dissipation theorem in terms of the recently discovered spin Hall
magnetoresistance (SMR). We present a microscopic description of the $\alpha$
dependence of the voltage noise in terms of spin current fluctuations and ISHE.
