  We present the results of inelastic x-ray scattering for magnetite and
analyze the energies and spectral widths of the phonon modes with different
symmetries in a broad range of temperature 125<T<293 K. The phonon modes with
X_4 and Delta_5 symmetries broaden in a nonlinear way with decreasing
temperature when the Verwey transition is approached. It is found that the
maxima of phonon widths occur away from high-symmetry points which indicates
the incommensurate character of critical fluctuations. Strong phonon
anharmonicity induced by electron-phonon coupling is discovered within ab
initio calculations which take into account local Coulomb interactions at Fe
ions. It (i) explains observed anomalous phonon broadening, and (ii)
demonstrates that the Verwey transition is a cooperative phenomenon which
involves a wide spectrum of phonons coupled to charge fluctuations condensing
in the low-symmetry phase.
