  We report on a novel spin-charge fluctuation in the all-in-all-out pyrochlore
magnet Cd$_2$Os$_2$O$_7$, where the spin fluctuation is driven by the
conduction of thermally excited electrons/holes and associated fluctuation of
Os valence. The fluctuation exhibits an activation energy significantly greater
than the spin-charge excitation gap and a peculiar frequency range of
$10^{6}$--$10^{10}$ s$^{-1}$. These features are attributed to the hopping
motion of carriers as small polarons in the insulating phase, where the polaron
state is presumably induced by the magnetoelastic coupling via the strong
spin-orbit interaction. Such a coupled spin-charge-phonon fluctuation manifests
as a part of the metal-insulator transition that is extended over a wide
temperature range due to the modest electron correlation comparable with other
interactions characteristic for 5$d$-subshell systems.
