Abstract
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.
Highlights
Using MEμSR, a second frequency signal is seen at non-zero fields in the temperature range above the Verwey transition (TV = ∼123 K)
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 Fe3O4 with those found at 205 K to study a second order phase transition at the Wigner temperature (TW = ∼247 K)
Summary
Magnetic anomalies, observed between TV and the Wigner temperature (TW ≈ 247 K) show, Fe3O4 can be considered a Wigner electron glass.. Our studies support the phonon-assisted electron-spin hopping model and the Mott-Wigner glass description of Fe3O4.5. An external field (Bext) dependency for Fe3O4 at RT for the B // shows that the frequencies follow an expected linear trend with a slope of 13.55 MHz/kOe and Bdem = ∼ 0.9 kOe. The broadening with increasing Bext was interpreted as two frequency signals. External field dependence of μSR frequencies for B // at 205 K shows that two frequency signals follow the expected linear parallel trends with slopes of 13.55 MHz/kOe with both a Bdem of about 0.5 kOe and a 5-MHz shift. FT & CF studies indicated only one frequency signal. The relaxation rates at 205 K are much smaller; smaller errors in frequency are seen at 205 K compared to those at RT
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