Precursor effects and field-induced short-range order above the Verwey transition in single Fe3O4 crystals

The internal fields in single crystals of magnetite (Fe3O4) have been previously studied through muon-spin rotation (μSR). By Maximum-Entropy (ME) μSR, we analyze Fe3O4 μSR data with external fields parallel to the <111>, <110> or <100> axis. The ME peak-to-noise ratio is optimized by varying the filter time and time interval. Several μSR time series indicate a beat pattern. Using MEμSR, a second frequency signal is seen at non-zero fields in the temperature range above the Verwey transition (TV = ∼123 K). At zero field, MEμSR confirms with much-improved precision the existence of one frequency signal found earlier by curve fitting (CF) and Fourier transformation (FT). We compare our room temperature (RT) field-dependent MEμSR transforms for <110> Fe3O4 with those found at 205 K to study a second order phase transition at the Wigner temperature (TW = ∼247 K). At RT and 205 K for fields below the demagnetization field and parallel to <110> Fe3O4, a second MEμSR frequency is observed, missed by CF and FT. These extra magnetic fields fall on the extended magnetization curves below and above TW. At RT, a small field induces a short-range order similar to the precursor effects in the TV – TW interval. At 205 K within that precursor T-interval, we observe a comparable RT-disordered state. The existence of these additional internal fields is likely related to phonon-assisted 3d-electron(-spin) hopping and short-range order behaviors. Our MEμSR studies lead to a better understanding of the local magnetism in this Mott-Wigner glass.