title: Charge order and three-site distortions in the Verwey structure of magnetite.
abstract: 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 ångströms. 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.
authors.affiliation: Centre for Science at Extreme Conditions and School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JZ, UK.
authors.forename: Mark S
authors.initials: MS
authors.lastname: Senn
authors.forename: Jon P
authors.initials: JP
authors.lastname: Wright
authors.forename: J Paul
authors.initials: JP
authors.lastname: Attfield