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co-emergence ofmagnetic order and structural fluctuations

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The nature of the Verwey transition occurring at TV ≈ 125 K in magnetite (Fe3O4) has been an outstanding problem over many decades. A complex low temperature electronic order was recently discovered and associated structural fluctuations persisting above TV are widely reported, but the origin of the underlying correlations and hence of the Verwey transition remains unclear. Here we show that local structural fluctuations in magnetite emerge below the Curie transition at TC ≈ 850 K, through X-ray pair distribution function analysis. Around 80% of the low temperature correlations emerge in proportion to magnetization below TC. This confirms that fluctuations in Fe-Fe bonding arising from magnetic order are the primary electronic instability and hence the origin of the Verwey transition. Such hidden instabilities may be important to other spin-polarised conductors and orbitally degenerate materials

Short-range structural correlations above the Verwey transition1,2,3,4 were reported in early diffuse scattering studies of magnetite5, and their persistence up to at least room temperature has been studied recently6 and corroborated by observations of anomalous phonon broadening7, a charge gap from optical and photoelectron spectroscopies8,9, and magnetic excitations driven by polaronic distortions in resonant inelastic X-ray scattering data10. Analysis of the interatomic pair distribution function (PDF)11 derived from total X-ray scattering data is a simple method for exploring local structure that is highly sensitive to the displacements of metal atoms associated with the formation of orbital molecules, metal–metal-bonded clusters such as the trimerons observed in magnetite12. Persistence of orbital molecules far above their long-range electronic ordering transitions has been discovered from X-ray PDF studies of Li2RhO413, Li2RuO314, AlV2O415, and GaV2O416

Experimental details are in the “Methods” section. Total X-ray scattering data from a highly stoichiometric sample of magnetite were recorded from 90 to 923 K. Representative scattering intensity S(Q) plots and the derived PDFs G(r) are shown in Fig. 1. The monoclinic superstructure adopted by magnetite below TV is very complex with 168 small (<0.24 Å) displacements of atoms from their positions in the high temperature cubic spinel structure3. To fit the PDFs over all temperatures, we have used this monoclinic supercell with lattice parameters adjusted to a cubic metric and with each of the 168 atomic coordinates given by p = pu + fV(pd − pu) where pu is the coordinate from an undistorted high-temperature cubic crystal structure refinement and pd is the coordinate in the distorted 90 K structure reported previously3. fV is a Verwey shift parameter that describes the set of constrained structural displacements, such that fV = 0 corresponds to the cubic spinel structure without any local distortions and fV = 1 describes the full magnitude of distortions in the 90 K magnetite superstructure3. Comparative views of the fV = 0 and fV = 1 structures are shown in ref. 4. Three values of fV were determined at each temperature by fitting the structural model to three successive regions of the PDF corresponding approximately to distances from atoms to their neighbours in the same unit cell (First Unit Cell range, covering all interatomic distances for r < 9.36 Å) and similarly to atoms in the Second and Third Unit Cell regions. The structural models and fitting procedure are further described in “Methods”, and fits to data and their sensitivity to changing fV are shown in Fig. 2

co-emergence ofmagnetic order and structural fluctuations

X-ray scattering data for magnetite. a Scattering intensities S(Q) for magnetite at three representative temperatures. b Pair distribution functions G(r) derived from S(Q) data in a. Typical thermal effects leading to loss of high-Q features in S(Q) and broadening of G(r) peaks are observed

Fitting of magnetite pair distribution functions (PDFs). a, b Comparison of fits of a the cubic (residual Rw = 15.6%) and b the monoclinic superstructure (Rw = 11.6%) models to the 90 K PDF. The visible improvement of the fit to the r ≈ 3 Å peak measuring nearest neighbour Fe–Fe (and O–O) distances and lowering of Rw demonstrates sensitivity to the monoclinic Verwey superstructure distortions. PDF data are open blue circles, fits are red curves and the difference is below in green. c Rw as a function of the Verwey shift parameter fV from fits to the First Unit Cell region of the high-temperature PDFs. The well-defined minimum seen at fV ≈ 0.8 for the 498 K fits becomes more shallow and moves to zero at the highest temperatures, as plotted in Fig. 3b. This subtle change of local structure can be seen in the shift in the maximum of the 3 Å peak to slightly longer r (inset), consistent with the loss of Fe–Fe distances shortened through trimeron bonding

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Ore processing plant means that extracts and purifies some elements in the raw ore through a series of complex ore beneficiation flow and professional beneficiation equipment. The refined concentrate powder is mainly used in metallurgy and industry base. Processing capacity: 0.2~8 m³/min Applied material: Copper, Iron

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