The mineral magnetite (Fe3O4) 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 Fe2+ and Fe3+ ions1, but the ground state of the low-temperature phase has remained contentious2,3 because twinning of crystal domains hampers diffraction studies of the structure4. Recent powder diffraction refinements5,6,7 and resonant X-ray studies8,9,10,11,12 have led to proposals of a variety of charge-ordered and bond-dimerized ground-state models13,14,15,16,17,18,19. 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 FeO6 octahedra show that Verwey’s hypothesis is correct to a first approximation and that the charge and Fe2+ orbital order are consistent with a recent prediction17. 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.
Subscribe to Journal
Get full journal access for 1 year
only $3.83 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Verwey, E. J. W. Electronic conduction of magnetite (Fe3O4) and its transition point at low temperatures. Nature 144, 327–328 (1939)
Walz, F. The Verwey transition: a topical review. J. Phys. Condens. Matter 14, R285–R340 (2002)
Coey, M. Condensed-matter physics: charge-ordering in oxides. Nature 430, 155–157 (2004)
Iizumi, M. et al. Structure of magnetite (Fe3O4) below the Verwey transition-temperature. Acta Crystallogr. B 38, 2121–2133 (1982)
Wright, J. P., Attfield, J. P. & Radaelli, P. G. Long range charge ordering in magnetite below the Verwey transition. Phys. Rev. Lett. 87, 266401 (2001)
Wright, J. P., Attfield, J. P. & Radaelli, P. G. Charge ordered structure of magnetite Fe3O4 below the Verwey transition. Phys. Rev. B 66, 214422 (2002)
Blasco, J., Garcia, J. & Subias, G. Structural transformation in magnetite below the Verwey transition. Phys. Rev. B 83, 104105 (2011)
Goff, R. J., Wright, J. P., Attfield, J. P. & Radaelli, P. G. Resonant X-ray diffraction study of the charge ordering in magnetite. J. Phys. Condens. Matter 17, 7633–7642 (2005)
Nazarenko, E. et al. Resonant X-ray diffraction studies on the charge ordering in magnetite. Phys. Rev. Lett. 97, 056403 (2006)
Joly, Y. et al. Low-temperature structure of magnetite studied using resonant X-ray scattering. Phys. Rev. B 78, 134110 (2008)
Bland, S. R. et al. Full polarization analysis of resonant superlattice and forbidden X-ray reflections in magnetite. J. Phys. Condens. Matter 21, 485601 (2009)
Lorenzo, J. E. et al. Charge and orbital correlations at and above the Verwey phase transition in magnetite. Phys. Rev. Lett. 101, 226401 (2008)
Seo, H., Ogata, M. & Fukuyama, H. Aspects of the Verwey transition in magnetite. Phys. Rev. B 65, 085107 (2002)
Jeng, H. T., Guo, G. Y. & Huang, D. J. Charge-orbital ordering and Verwey transition in magnetite. Phys. Rev. Lett. 93, 156403 (2004)
Jeng, H. T., Guo, G. Y. & Huang, D. J. Charge-orbital ordering in low-temperature structures of magnetite: GGA+U investigations. Phys. Rev. B 74, 195115 (2006)
van den Brink, J. & Khomskii, D. I. Multiferroicity due to charge ordering. J. Phys. Condens. Matter 20, 434217 (2008)
Yamauchi, K., Fukushima, T. & Picozzi, S. Ferroelectricity in multiferroic magnetite Fe3O4 driven by noncentrosymmetric Fe2+/Fe3+ charge-ordering: first-principles study. Phys. Rev. B 79, 212404 (2009)
Zhou, F. & Ceder, G. First-principles determination of charge and orbital interactions in Fe3O4 . Phys. Rev. B 81, 205113 (2010)
Fukushima, T., Yamauchi, K. & Picozzi, S. Ab initio investigations of Fe2+/Fe3+ bond dimerization and ferroelectricity induced by intermediate site/bond-centered charge ordering in magnetite. J. Phys. Soc. Jpn 80, 014709 (2011)
Yoshida, J. & Iida, S. X-ray-diffraction study on low-temperature phase of magnetite. J. Phys. Soc. Jpn. 42, 230–237 (1977)
Kasama, T., Church, N. S., Feinberg, J. M., Dunin-Borkowski, R. E. & Harrison, R. J. Direct observation of ferrimagnetic/ferroelastic domain interactions in magnetite below the Verwey transition. Earth Planet. Sci. Lett. 297, 10–17 (2010)
Attfield, J. P. Charge ordering in transition metal oxides. Solid State Sci. 8, 861–867 (2006)
Verwey, E. J. W. & Heilmann, E. L. Physical properties and cation arrangement of oxides with spinel structures. 1. Cation arrangement in spinels. J. Chem. Phys. 15, 174–180 (1947)
Anderson, P. W. Ordering and antiferromagnetism in ferrites. Phys. Rev. 102, 1008–1013 (1956)
Downward, L. et al. Universal relationship between magnetization and changes in the local structure of La1-xCaxMnO3: evidence for magnetic dimers. Phys. Rev. Lett. 95, 106401 (2005)
Yang, M. H. et al. Anion order in perovskite oxynitrides. Nat. Chem. 3, 47–52 (2011)
Ikeda, N. et al. Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4 . Nature 436, 1136–1138 (2005)
Yamada, Y., Wakabayashi, N. & Nicklow, R. M. Neutron diffuse-scattering in magnetite due to molecular polarons. Phys. Rev. B 21, 4642–4648 (1980)
Shepherd, J. P., Koenitzer, J. W., Aragon, R., Sandberg, C. J. & Honig, J. M. Heat-capacity studies on single-crystal annealed Fe3O4 . Phys. Rev. B 31, 1107–1113 (1985)
We thank C. Morrison for supplying code for electrical polarization calculations, J. Honig for provision of the magnetite sample, the Leverhulme Trust for financial support, and EPSRC and STFC for financial support and provision of continuing access to ESRF.
The authors declare no competing financial interests.
About this article
Cite this article
Senn, M., Wright, J. & Attfield, J. Charge order and three-site distortions in the Verwey structure of magnetite. Nature 481, 173–176 (2012). https://doi.org/10.1038/nature10704
Physical Review B (2020)
Physical Sciences Reviews (2020)
SQUID-on-tip with single-electron spin sensitivity for high-field and ultra-low temperature nanomagnetic imaging
Advanced Functional Materials (2020)
Physica B: Condensed Matter (2020)