  In quantum dots made from materials with nonzero nuclear spins, hyperfine
coupling creates a fluctuating effective Zeeman field (Overhauser field) felt
by electrons, which can be a dominant source of spin qubit decoherence. We
characterize the spectral properties of the fluctuating Overhauser field in a
GaAs double quantum dot by measuring correlation functions and power spectra of
the rate of singlet-triplet mixing of two separated electrons. Away from zero
field, spectral weight is concentrated below 10 Hz, with 1/f^2 dependence on
frequency, f. This is consistent with a model of nuclear spin diffusion, and
indicates that decoherence can be largely suppressed by echo techniques.
