Energy domain versus time domain precursor fluctuations above the Verwey transition in magnetite

We study the dynamics and interactions of the critical fluctuations of the Verwey transition in magnetite (Fe3O4) in the pretransition region by means of inelastic neutron scattering experiments on a natural single crystal. We find that a Delta(5) mode interacts strongly with a central peak of order parameter fluctuations, whose width is determined by the order parameter coherence time. This is compared with pump-probe experiments, which we formerly explained in terms of fluctuation-assisted stimulated Raman scattering. Our estimates of the order parameter correlation time from experiments in the energy domain (inelastic neutron scattering experiments) and in the time domain (pump-probe experiments) coincide, thus giving further credit to our previous interpretation of pump-probe experiments and confirming that the Verwey transition is of the order-disorder type, without phonon softening.