  Combined resistance noise and muon-spin relaxation ($\mu$SR) measurements of
the ferromagnetic semiconductor HgCr$_2$Se$_4$ suggest a degree of
magnetoelectric coupling and provide evidence for the existence of isolated
magnetic polarons. These form at elevated temperatures and undergo a
percolation transition with a drastic enhancement of the low-frequency
1/$f$-type charge fluctuations at the insulator-to-metal transition at $\sim 95
- 98$ K in the vicinity of the magnetic ordering temperature $T_C \sim 105 -
107$ K. Upon approaching the percolation threshold from above, the strikingly
unusual dynamics of a distinct two-level fluctuator superimposed on the $1/f$
noise can be described by a slowing down of the dynamics of a nanoscale
magnetic cluster, a magnetic polaron, when taking into account an effective
radius of the polaron depending on the spin correlation length. Coinciding
temperature scales found in $\mu$SR and noise measurements suggest changes in
the magnetic dynamics over a wide range of frequencies and are consistent with
the existence of large polarized and domain-wall-like regions at low
temperatures, that result from the freezing of spin dynamics at the magnetic
polaron percolation transition.
