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We study the dynamics and interactions of the critical fluctuations of the Verwey transition in magnetite (${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$) in the pretransition region by means of inelastic neutron scattering experiments on a natural single crystal. We find that a ${\mathrm{\ensuremath{\Delta}}}_{5}$ 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.

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