  Here we suggest a novel hybrid spin noise spectroscopy technique, which is
sensitive to the spin Hall effect. It is shown that, while the standard
spin-spin correlation function is not sensitive to the spin Hall effect,
spin-transverse voltage and transverse voltage-voltage correlation functions
provide the missing sensitivity being linear and quadratic in the spin Hall
coefficient, respectively. The correlation between transverse voltage and spin
fluctuations appears as a result of spin-charge coupling fundamental for the
spin Hall effect. We anticipate that the proposed method could find
applications in the studies of spin-charge coupling in semiconductors.
