Resonant x-ray diffraction studies on the charge ordering in magnetite

Ultrafast generation of hidden phases via energy-tuned electronic photoexcitation in magnetite

Phase transitions occurring in nonequilibrium conditions can evolve through high-energy intermediate states inaccessible via equilibrium adiabatic conditions. Because of the subtle nature of such hidden phases, their direct observation is extremely challenging and requires simultaneous visualization of matter at subpicoseconds and subpicometer scales. Here, we show that a magnetite crystal in the vicinity of its metal-to-insulator transition evolves through different hidden states when controlled via energy-tuned ultrashort laser pulses. By directly monitoring magnetite's crystal structure with ultrafast electron diffraction, we found that upon near-infrared (800 nm) excitation, the trimeron charge/orbital ordering pattern is destroyed in favor of a phase-separated state made of cubic-metallic and monoclinic-insulating regions. On the contrary, visible light (400 nm) activates a photodoping charge transfer process that further promotes the long-range order of the trimerons by stabilizing the charge density wave fluctuations, leading to the reinforcement of the monoclinic insulating phase. Our results demonstrate that magnetite's structure can evolve through completely different metastable hidden phases that can be reached long after the initial excitation has relaxed, breaking ground for a protocol to control emergent properties of matter.

A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator

The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of thes-dexchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.

Verwey-Type Charge Ordering and Site-Selective Mott Transition in Fe4O5 under Pressure

The metal–insulator transition driven by electronic correlations is one of the most fundamental concepts in condensed matter. In mixed-valence compounds, this transition is often accompanied by charge ordering (CO), resulting in the emergence of complex phases and unusual behaviors. The famous example is the archetypal mixed-valence mineral magnetite, Fe₃O₄, exhibiting a complex charge-ordering below the Verwey transition, whose nature has been a subject of long-time debates. In our study, using high-resolution X-ray diffraction supplemented by resistance measurements and DFT+DMFT calculations, the electronic, magnetic, and structural properties of recently synthesized mixed-valence Fe₄O₅ are investigated under pressure to ∼100 GPa. Our calculations, consistent with experiment, reveal that at ambient conditions Fe₄O₅ is a narrow-gap insulator characterized by the original Verwey-type CO. Under pressure Fe₄O₅ undergoes a series of electronic and magnetic-state transitions with an unusual compressional behavior above ∼50 GPa. A site-dependent collapse of local magnetic moments is followed by the site-selective insulator-to-metal transition at ∼84 GPa, occurring at the octahedral Fe sites. This phase transition is accompanied by a 2+ to 3+ valence change of the prismatic Fe ions and collapse of CO. We provide a microscopic explanation of the complex charge ordering in Fe₄O₅ which “unifies” it with the behavior of two archetypal examples of charge- or bond-ordered materials, magnetite and rare-earth nickelates (RNiO₃). We find that at low temperatures the Verwey-type CO competes with the “trimeron”/“dimeron” charge ordered states, allowing for pressure/temperature tuning of charge ordering. Summing up the available data, we present the pressure–temperature phase diagram of Fe₄O₅.

Magnetism and the Trimeron Bond

A review of progress in understanding the Verwey transition in magnetite (Fe₃O₄) over the past decade is presented. This electronic and structural transition at T _V ≈ 125 K was reported in 1939 and has since been a contentious issue in magnetism. Long range Fe²⁺/Fe³⁺ charge ordering has been confirmed below the transition from crystal structure refinement, and Fe²⁺ orbital ordering and formation of trimerons through weak bonding of Fe²⁺ states to two Fe neighbors has been discovered. This model has accounted for many spectroscopic observations such as the ⁵⁷Fe NMR frequencies. The trimeron lifetime has been measured, and trimeron soft modes have been observed. The origin of the first to second order crossover of Verwey transitions in doped magnetites has been revealed by a nanoparticle study. Electronic and structural fluctuations are found to persist to temperatures far above T _V and local structural distortions track the bulk magnetization, disappearing at the 850 K Curie transition. New binary mixed-valent iron oxides discovered at high pressure are found to have electronic transitions and orbital molecule ground states similar to those of magnetite.

Crystal Orbital Overlap Population and X-ray Absorption Spectroscopy

We present an extension of an ab initio numerical tool calculating X-ray absorption spectroscopies and crystal orbital overlap populations at the same time. Density functional theory is used to calculate the electronic structure in both occupied (valence to core X-ray emission spectroscopy) and nonoccupied states (i.e., X-ray absorption near the edge structure and X-ray magnetic circular dichroism) and to evaluate the orbital overlap typifying the covalency between neighboring atoms. We show how the different features in the experimental spectra can be correlated to the chemical bonds around the absorbing atoms in several examples including acrylonitrile molecules, rutile TiO₂, Li₂RuO₃ high-energy density cathode, ZnO, and anti-ferromagnetic V₂O₃.

Heat capacity signature of frustrated trimerons in magnetite

Recently it has been proposed that the long-range electronic order formed by trimerons in magnetite should be frustrated due to the great degeneracy of arrangements linking trimerons. This result has important consequences as charge ordering from the condensed minority band electrons leads to a complex 3D antiferro orbital order pattern. Further more, the corner sharing tetrahedra structure of spinel B-sites supports frustration for antiferromagnetic alignments. Therefore frustration due to competing interactions will itself induce disorder and very likely frustration in the spin orientations. Here we present very low temperature specific heat data that show two deviations to the magnons and phonons contributions, that we analyze in terms of Schottky-type anomalies. The first one is associated with the thermal activation across both ferroelastic twin and ferromagnetic anti-phase domains. The second Schottky-type anomaly displays an inverse (1/H) field dependence which is a direct indication of the disordered glassy network with macroscopically degenerated singular ground states.

Dielectric-Screening Reduction-Induced Large Transport Gap in Suspended Sub-10 nm Graphene Nanoribbon Functional Devices

The predicted quasiparticle energy gap of more than 1 eV in sub-6 nm graphene nanoribbons (GNRs) is elusive, as it is strongly suppressed by the substrate dielectric screening. The number of techniques that can produce suspended high-quality and electrically contacted GNRs is small. The helium ion beam milling technique is capable of achieving sub-5 nm patterning; however, the functional device fabrication and the electrical characteristics are not yet reported. Here, the electrical transport measurement of suspended ≈6 nm wide mono- and bilayer GNR functional devices is reported, which are obtained through sub-nanometer resolution helium ion beam milling with controlled total helium ion budget. The transport gap opening of 0.16-0.8 eV is observed at room temperature. The measured transport gap of the different edge orientated GNRs is in good agreement with first-principles simulation results. The enhanced electron-electron interaction and reduced dielectric screening in the suspended quasi-1D GNRs and anti-ferromagnetic coupling between opposite edges in the zigzag GNRs substantiate the observed large transport gap.

Jahn-Teller distortion driven magnetic polarons in magnetite

The first known magnetic mineral, magnetite, has unusual properties, which have fascinated mankind for centuries; it undergoes the Verwey transition around 120 K with an abrupt change in structure and electrical conductivity. The mechanism of the Verwey transition, however, remains contentious. Here we use resonant inelastic X-ray scattering over a wide temperature range across the Verwey transition to identify and separate out the magnetic excitations derived from nominal Fe²⁺ and Fe³⁺ states. Comparison of the experimental results with crystal-field multiplet calculations shows that the spin–orbital dd excitons of the Fe²⁺ sites arise from a tetragonal Jahn-Teller active polaronic distortion of the Fe²⁺O₆ octahedra. These low-energy excitations, which get weakened for temperatures above 350 K but persist at least up to 550 K, are distinct from optical excitations and are best explained as magnetic polarons.

The Verwey transition of magnetite is complex due to the coexistence of strong correlations and electron-phonon coupling. Here, the authors use resonant inelastic X-ray scattering to show evidence for magnetic polarons in magnetite and provide insight into the nature of the transition.

The Verwey structure of a natural magnetite

A remarkably complex electronic order of Fe(2+)/Fe(3+) charges, Fe(2+) orbital states, and weakly metal-metal bonded Fe3 units known as trimerons, was recently discovered in stoichiometric magnetite (Fe3O4) below the 125 K Verwey transition. Here, the low temperature crystal structure of a natural magnetite from a mineral sample has been determined using the same microcrystal synchrotron X-ray diffraction method. Structure refinement demonstrates that the natural sample has the same complex electronic order as pure synthetic magnetite, with only minor reductions of orbital and trimeron distortions. Chemical analysis shows that the natural sample contains dopants such as Al, Si, Mg and Mn at comparable concentrations to extraterrestrial magnetites, for example, as reported in the Tagish Lake meteorite. Much extraterrestrial magnetite exists at temperatures below the Verwey transition and hence our study demonstrates that the low temperature phase of magnetite represents the most complex long-range electronic order known to occur naturally.

Electronic phase transitions in ultrathin magnetite films

Magnetite (Fe3O4) shows singular electronic and magnetic properties, resulting from complex electron-electron and electron-phonon interactions that involve the interplay of charge, orbital and spin degrees of freedom. The Verwey transition is a manifestation of these interactions, with a puzzling connection between the low temperature charge ordered state and the dynamic charge fluctuations still present above the transition temperature. Here we explore how these rich physical phenomena are affected by thin film geometries, particularly focusing on the ultimate size limit defined by thicknesses below the minimum bulk unit cell. On one hand, we address the influence of extended defects, such as surfaces or antiphase domains, on the novel features exhibited by thin films. On the other, we try to isolate the effect of the reduced thickness on the electronic and magnetic properties. We will show that a distinct phase diagram and novel charge distributions emerge under reduced dimensions, while holding the local high magnetic moments. Altogether, thin film geometries offer unique possibilities to understand the complex interplay of short- and long-range orders in the Verwey transition. Furthermore, they arise as interesting candidates for the exploitation of the rich physics of magnetite in devices that demand nanoscale geometries, additionally offering novel functionalities based on their distinct properties with respect to the bulk form.

Speed limit of the insulator-metal transition in magnetite

As the oldest known magnetic material, magnetite (Fe3O4) has fascinated mankind for millennia. As the first oxide in which a relationship between electrical conductivity and fluctuating/localized electronic order was shown, magnetite represents a model system for understanding correlated oxides in general. Nevertheless, the exact mechanism of the insulator-metal, or Verwey, transition has long remained inaccessible. Recently, three-Fe-site lattice distortions called trimerons were identified as the characteristic building blocks of the low-temperature insulating electronically ordered phase. Here we investigate the Verwey transition with pump-probe X-ray diffraction and optical reflectivity techniques, and show how trimerons become mobile across the insulator-metal transition. We find this to be a two-step process. After an initial 300 fs destruction of individual trimerons, phase separation occurs on a 1.5±0.2 ps timescale to yield residual insulating and metallic regions. This work establishes the speed limit for switching in future oxide electronics.

Anharmonicity due to electron-phonon coupling in magnetite

We present the results of inelastic x-ray scattering for magnetite and analyze the energies and 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 Δ(5) symmetries broaden in a nonlinear way with decreasing T when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points, which suggests the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered by a combination of these experimental results with 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 the electron charge fluctuations condensing in the low-symmetry phase.

Microscopic theory of resonant soft-x-ray scattering in materials with charge order: the example of charge stripes in high-temperature cuprate superconductors

We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.

Effect of surface polishing and oxidization induced strain on electronic order at the Verwey transition in Fe3O4

Following the controversy between two previous publications (Lorenzo et al 2008 Phys. Rev. Lett. 101 226401 and Garcia et al 2009 Phys. Rev. Lett. 102 176405), we report on the influence of mechanical polishing, and subsequent sample storage, on the electronic order at the Verwey transition of highly pure magnetite, Fe(3)O(4), by resonant x-ray scattering. Contrary to expectations, mechanically polishing the surface induces an inhomogeneous micron deep dead layer, probably of powdered Fe(3)O(4). In addition, we have found that polishing the sample immediately before the experiment influences and favors the appearance of long range order electronic correlations, whereas samples polished well in advance have their electronic order quenched. Conversely, lattice distortions associated with the Verwey transition appear less affected by the surface state. We conclude that mechanical polishing induces stresses at the surface that may propagate into the core of the single crystal sample. These strains relax with time, which affects the different order parameters, as measured by x-ray resonant diffraction.

Polaron physics and crossover transition in magnetite probed by pressure-dependent infrared spectroscopy

The optical properties of magnetite at room temperature were studied by infrared reflectivity measurements as a function of pressure up to 8 GPa. The optical conductivity spectrum consists of a Drude term, two sharp phonon modes, a far-infrared band at around 600 cm(-1) and a pronounced mid-infrared absorption band. With increasing pressure both absorption bands shift to lower frequencies and the phonon modes harden in a linear fashion. Based on the shape of the MIR band, the temperature dependence of the dc transport data, and the occurrence of the far-infrared band in the optical conductivity spectrum, the polaronic coupling strength in magnetite at room temperature should be classified as intermediate. For the lower energy phonon mode an abrupt increase of the linear pressure coefficient occurs at around 6 GPa, which could be attributed to minor alterations of the charge distribution among the different Fe sites.

Direct observation of charge ordering in magnetite using resonant multiwave x-ray diffraction

Charge disproportion at octahedral Fe sites in magnetite was observed at low temperature using two inversion-symmetry related three-wave resonant x-ray diffraction, 022-311 and 002-̅3̅1, near the iron K edge. Both of the three-wave cases involve the (002) forbidden-weak reflection. The self-normalized three-wave to two-wave (002) diffraction intensity ratio automatically cancels the self-absorption effect and leads to direct determination of charge disproportion for magnetite below 120 K. This approach provides a more direct and effective way for extracting charge-ordering information.

Structural distortion, charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X-ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high-quality Fe(3)O(4) single crystals and thin films grown on MgO by using resonant X-ray scattering at the Fe K-edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e(-) with [0 0 1] and [1 1 0] cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a-b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low-temperature crystal structure refined in the non-polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.

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 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.

On the correlation between the X-ray absorption chemical shift and the formal valence state in mixed-valence manganites

Here the correlation between the chemical shift in X-ray absorption spectroscopy, the geometrical structure and the formal valence state of the Mn atom in mixed-valence manganites are discussed. It is shown that this empirical correlation can be reliably used to determine the formal valence of Mn, using either X-ray absorption spectroscopy or resonant X-ray scattering techniques. The difficulties in obtaining a reliable comparison between experimental XANES spectra and theoretical simulations on an absolute energy scale are revealed. It is concluded that the contributions from the electronic occupation and the local structure to the XANES spectra cannot be separated either experimentally or theoretically. In this way the geometrical and electronic structure of the Mn atom in mixed-valence manganites cannot be described as a bimodal distribution of the formal integer Mn(3+) and Mn(4+) valence states corresponding to the undoped references.

Full polarization analysis of resonant superlattice and forbidden x-ray reflections in magnetite

Despite being one of the oldest known magnetic materials, and the classic mixed valence compound, thought to be charge ordered, the structure of magnetite below the Verwey transition is complex and the presence and role of charge order is still being debated. Here, we present resonant x-ray diffraction data at the iron K-edge on forbidden (0, 0, 2n+1)(C) and superlattice [Formula: see text] reflections. Full linear polarization analysis of the incident and scattered light was conducted in order to explore the origins of the reflections. Through simulation of the resonant spectra we have confirmed that a degree of charge ordering takes place, while the anisotropic tensor of susceptibility scattering is responsible for the superlattice reflections below the Verwey transition. We also report the surprising result of the conversion of a significant proportion of the scattered light from linear to nonlinear polarization.

Direct observation of charge order and an orbital glass state in multiferroic LuFe2O4

Geometrical frustration of the Fe ions in LuFe2O4 leads to intricate charge and magnetic order and a strong magnetoelectric coupling. Using resonant x-ray diffraction at the Fe K edge, the anomalous scattering factors of both Fe sites are deduced from the (h/3 k/3 l/2) reflections. The chemical shift between the two types of Fe ions equals 4.0(1) eV corresponding to full charge separation into Fe2+ and Fe3+. The polarization and azimuthal angle dependence of the superlattice reflections demonstrate the absence of differences in anisotropic scattering revealing random orientations of the Fe2+ orbitals characteristic of an orbital glass state.

Is the Verwey transition in Fe(3)O(4) magnetite driven by a Peierls distortion?

In this viewpoint article we analyse recent crucial structural, optical and transport experiments on Fe(3)O(4) magnetite across the Verwey transition at T(V)∼120-125 K. We find that all the relevant experimental data are consistent with a model of a Peierls distortion in the cubic spinel lattice, and likewise, some of them evidence against the original and still distributed hypothesis of the long range charge ordering origin of the Verwey transition. An estimated Peierls transition temperature (T(P)) is comparable with T(V). The Peierls model provides new insight into the electronic properties of magnetite. Application of the Peierls model to some other systems is briefly discussed also.

Reexamination of the temperature dependences of resonant reflections in highly stoichiometric magnetite

We have studied the temperature dependences of the so-called charge and orbital ordering reflections in the neighborhood of the Verwey transition by means of resonant x-ray scattering at the Fe K and L edges on a high purity single crystal of magnetite. Contrary to recently published results [J. E. Lorenzo, Phys. Rev. Lett. 101, 226401 (2008)10.1103/PhysRevLett.101.226401], we show that all the reflections studied disappear simultaneously at the Verwey transition for both edges, on and off resonance. This means that there is no correlation between the Verwey (123.5 K) and the spin-reorientation (130 K) transitions and that the resonant reflections are driven by the lattice distortions.

Charge and orbital correlations at and above the Verwey phase transition in magnetite

The subtle interplay among electronic degrees of freedom (charge and orbital orderings), spin and lattice distortion that conspire at the Verwey transition in magnetite (Fe3O4) is still a matter of controversy. Here, we provide compelling evidence that these electronic orderings are manifested as a continuous phase transition at the temperature where a spin reorientation takes place at around 130 K, i.e., well above TV approximately 121 K. The Verwey transition seems to leave the orbital ordering unaffected whereas the charge ordering development appears to be quenched at this temperature and the temperature dependence below TV is controlled by the lattice distortions. Finally, we show that the orbital ordering does not reach true long range (disorder), and the correlation length along the c-direction is limited to 100 angstroms.

Electrically driven phase transition in magnetite nanostructures

Magnetite (Fe3O4), an archetypal transition-metal oxide, has been used for thousands of years, from lodestones in primitive compasses to a candidate material for magnetoelectronic devices. In 1939, Verwey found that bulk magnetite undergoes a transition at TV approximately 120 K from a high-temperature 'bad metal' conducting phase to a low-temperature insulating phase. He suggested that high-temperature conduction is through the fluctuating and correlated valences of the octahedral iron atoms, and that the transition is the onset of charge ordering on cooling. The Verwey transition mechanism and the question of charge ordering remain highly controversial. Here, we show that magnetite nanocrystals and single-crystal thin films exhibit an electrically driven phase transition below the Verwey temperature. The signature of this transition is the onset of sharp conductance switching in high electric fields, hysteretic in voltage. We demonstrate that this transition is not due to local heating, but instead is due to the breakdown of the correlated insulating state when driven out of equilibrium by electrical bias. We anticipate that further studies of this newly observed transition and its low-temperature conducting phase will shed light on how charge ordering and vibrational degrees of freedom determine the ground state of this important compound.

Direct observation of t2g orbital ordering in magnetite

Using soft-x-ray diffraction at the site-specific resonances in the Fe L2,3 edge, we find clear evidence for orbital and charge ordering in magnetite below the Verwey transition. The spectra show directly that the (001/2) diffraction peak (in cubic notation) is caused by t2g orbital ordering at octahedral Fe2+ sites and the (001) by a spatial modulation of the t2g occupation.

Zener double exchange from local valence fluctuations in magnetite

Magnetite (Fe3O4) is a mixed valent system where electronic conductivity occurs on the B site (octahedral) iron sublattice of the spinel structure. Below T(V)=123 K, a metal-insulator transition occurs which is argued to arise from the charge ordering of 2+ and 3+ iron valences on the B sites (Verwey transition). Inelastic neutron scattering measurements show that optical spin waves propagating on the B site sublattice (approximately 80 meV) are shifted upwards in energy above T_{V} due to the occurrence of B-B ferromagnetic double exchange in the mixed valent phase. The double exchange interaction affects only spin waves of Delta(5) symmetry, not all modes, indicating that valence fluctuations are slow and the double exchange is constrained by short-range electron correlations above T(V).

Surface Verwey transition in magnetite

We report density functional studies of the (001) surface of magnetite that account for local Coulomb interactions. Iron cations in the surface layers exhibit charge and t2g orbital ordering that is coupled with the lattice strains. Orbital ordering is present for various surface stoichiometries and causes opening of the band gap Eg approximately 0.3 eV at the surface, such that the (001) surface of Fe3O4 remains insulating also in the high temperature cubic phase. The (radical 2 x radical 2)R45 degrees surface reconstruction is related to orbital ordering.

Mechanism of the Verwey transition in magnetite: Jahn-Teller distortion and charge ordering patterns

We have performed density functional calculations with on-site Coulomb repulsion corrections of systems that may be involved in the Verwey transition in magnetite (Fe(3)O(4)). We find that the lowest energy solution for the minority spin wavefunction in the cubic cell involves orbitally ordered Fe-d and O-p states, which breaks cubic symmetry. This leads to partial charge ordering that triggers a Jahn-Teller distortion and band-gap opening. Our results show this to be the essential mechanism of the Verwey transition. Applying ionic relaxation within a larger tetragonal cell, three patterns of charge ordering are compared and a Pmca pattern matching x-ray data is found to be the most stable.

Mechanism of the Verwey transition in magnetite

By combining ab initio results for the electronic structure and phonon spectrum with the group theory, we establish the origin of the Verwey transition in Fe3O4. Two primary order parameters with X3 and Delta5 symmetries are identified. They induce the phase transformation from the high-temperature cubic to the low-temperature monoclinic structure. The on-site Coulomb interaction U between 3d electrons at Fe ions plays a crucial role in this transition--it amplifies the coupling of phonons to conduction electrons and thus opens a gap at the Fermi energy.