Charge order and three-site distortions in the Verwey structure of magnetite

The mineral magnetite (Fe(3)O(4)) undergoes a complex structural distortion and becomes electrically insulating at temperatures less than 125 kelvin. Verwey proposed in 1939 that this transition is driven by a charge ordering of Fe(2+) and Fe(3+) ions, but the ground state of the low-temperature phase has remained contentious because twinning of crystal domains hampers diffraction studies of the structure. Recent powder diffraction refinements and resonant X-ray studies have led to proposals of a variety of charge-ordered and bond-dimerized ground-state models. Here we report the full low-temperature superstructure of magnetite, determined by high-energy X-ray diffraction from an almost single-domain, 40-micrometre grain, and identify the emergent order. The acentric structure is described by a superposition of 168 atomic displacement waves (frozen phonon modes), all with amplitudes of less than 0.24 ?ngstr?ms. Distortions of the FeO(6) octahedra show that Verwey's hypothesis is correct to a first approximation and that the charge and Fe(2+) orbital order are consistent with a recent prediction. However, anomalous shortening of some Fe-Fe distances suggests that the localized electrons are distributed over linear three-Fe-site units, which we call 'trimerons'. The charge order and three-site distortions induce substantial off-centre atomic displacements and couple the resulting large electrical polarization to the magnetization. Trimerons may be important quasiparticles in magnetite above the Verwey transition and in other transition metal oxides.