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.
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