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Combined resistance noise and muon-spin relaxation ($\mu$SR) measurements ofthe ferromagnetic semiconductor HgCr$_2$Se$_4$ suggest a degree ofmagnetoelectric coupling and provide evidence for the existence of isolatedmagnetic polarons. These form at elevated temperatures and undergo apercolation transition with a drastic enhancement of the low-frequency1/$f$-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 strikinglyunusual 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 nanoscalemagnetic cluster, a magnetic polaron, when taking into account an effectiveradius of the polaron depending on the spin correlation length. Coincidingtemperature scales found in $\mu$SR and noise measurements suggest changes inthe magnetic dynamics over a wide range of frequencies and are consistent withthe existence of large polarized and domain-wall-like regions at lowtemperatures, that result from the freezing of spin dynamics at the magneticpolaron percolation transition.

Probing the magnetic polaron state in the ferromagnetic semiconductor  HgCr$_2$Se$_4$ with resistance fluctuation and muon-spin spectroscopy  measurements