This review encompasses the story of the Verwey transition in magnetite over a period of about 90 years, from its discovery up to the present. Despite this long period of thorough investigation, the intricate multi-particle system Fe3O4 with its various magneto-electronic interactions is not completely understood, as yet - although considerable progress has been achieved, especially during the last two decades. It therefore appeared appropriate to subdivide this retrospect into three eras: (I) from the detection of the effect to the Verwey model (1913-1947), being followed by a period of: (II) checking, questioning and modification of Verwey's original concepts (1947-1979). Owing to prevailing under-estimation of the role of crystal preparation and qualitiy control, this period is also characterized by a series of uncertainties and erroneous statements concerning the reaction order (one or two) and type of the transition (multi-stage or single stage). These latter problems, beyond others, could definitely be solved within era (III) (1979 to the present) - in favour of a first-order, single-stage transition near 125 K - on the basis of experimental and theoretical standards established in the course of a most inspiring conference organized in 1979 by Sir Nevill Mott in Cambridge and solely devoted to the present topic. Regarding the experimental field of further research, the remarkable efficiency of magnetic after-effect (MAE) spectroscopy as a sensitive probe for quality control and investigation of low-temperature (4 K Tv) into a Wigner crystal (T<Tv), describes most adequately the various low-temperature mechanisms in Fe3O4 in terms of tunnelling and variable range hopping of small polarons. On the other hand, the well-elaborated Ihle-Lorenz model, assuming a superposition of polaron-band and -hopping conductivity, is in better agreement with the high-temperature data (Tv<T<600 K).

https://iopscience.iop.org/article/10.1088/0953-8984/14/12/203/pdf

The Verwey transition - a topical review

Using density-functional calculations, we examine the electronic structure of magnetite in the spinel crystal structure in order to gain insight into the nature of the Verwey transition. The calculated cohesive and magnetic properties are in agreement with experimental results. The magnetic structure is analyzed using a Stoner model as well as from calculations within the framework of the local-spin-density approximation to the density-functional theory. The calculations show a minority-spin band at the Fermi energy consisting of ${\mathit{t}}_{2\mathit{g}}$ orbitals on the Fe(B) sublattice. These results suggest a three-band spinless model Hamiltonian for the description of the Verwey transition. The hopping integrals and the electron interaction parameters entering the model Hamiltonian are calculated using the ``constrained'' density-functional theory. The calculated parameters are consistent with the electronic origin of the Verwey transition.

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Electron states, magnetism, and the Verwey transition in magnetite

X-ray diffraction is used to show that the structural distortion of magnetite below 125 kelvin is to a first approximation caused by charge ordering of its constituent iron ions, but that the localized electrons are distributed over three iron sites to form ‘trimeron’ quasiparticles. In a letter to Nature in 1939, Evert Johannes Willem Verwey described the first example of a low-temperature charge-ordering transition in a solid — the Verwey transition — in the mineral magnetite, Fe3O4 (see go.nature.com/3h2pp1
 ). This phenomenon has since been observed in other transition metal oxides, yet despite decades of study, the precise structure of the charge-ordered state in magnetite has remained elusive. The complex structural distortions that characterize the Verwey state have now been determined, revealing an anomalous shortening of some inter-atomic distances. These are suggestive of an unusual charge configuration in which the localized electrons are each distributed over three neighbouring Fe sites. 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 angstroms. 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.

/pdf/charge-order-and-three-site-distortions-in-the-verwey-heqx84vnel.pdf

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

Inorganic compounds with the AB2X4 spinel structure have been studied for many years, because of their unusual physical properties The spinel crystallographic structure, first solved by Bragg in 1915, has cations occupying both tetrahedral (A) and octahedral (B) sites Interesting physics arises when the B-site cations become mixed in valence Magnetite (Fe3O4) is a classic and still unresolved example, where the tendency to form ordered arrays of Fe2+ and Fe3+ ions competes with the topological frustration of the B-site network The CuIr2S4 thiospinel is another example, well known for the presence of a metal-insulator transition at 230 K with an abrupt decrease of the electrical conductivity on cooling accompanied by the loss of localized magnetic moments Here, we report the determination of the crystallographic structure of CuIr2S4 below the metal-insulator transition Our results indicate that CuIr2S4 undergoes a simultaneous charge-ordering and spin-dimerization transition-a rare phenomenon in three-dimensional compounds Remarkably, the charge-ordering pattern consists of isomorphic octamers of Ir83+S24 and Ir84+S24 (as isovalent bi-capped hexagonal rings) This extraordinary arrangement leads to an elegant description of the spinel structure, but represents an increase in complexity with respect to all the known charge-ordered structures, which are typically based on stripes, slabs or chequerboard patterns

Formation of isomorphic Ir3+ and Ir4+ octamers and spin dimerization in the spinel CuIr2S4.

This review puts in doubt the classical description of the Verwey (metal–insulator) transition in magnetite on the basis of the wide set of experiments carried out over the last 60 years. We re-analyse here the most relevant experiments used to study the Verwey transition from the point of view of their degree of agreement with the proposed Fe2+–Fe3+ charge ordering model. We will consider three groups of experimental studies, according to their capability of detecting different ionic species and/or a charge periodicity: (1) Experiments which have been interpreted using the charge ordering model as the starting point though they are not able to demonstrate its validity. This is the case for macroscopic properties such as the electrical resistivity, the heat capacity and the magnetic properties. (2) Experiments which can distinguish different types of Fe ions, such as Mossbauer, nuclear magnetic resonance (NMR) and electronic spectroscopies. However, we show that they are not able to associate them with a specific valence (2+ or 3+ in our case) and, in some cases, they observe more than two different kinds of iron atoms. (3) Diffraction (x-ray, neutron and electron) experiments, which are the most conclusive ones for determining a periodic ordering of different entities. These experiments, instead, point to the lack of ionic charge ordering. We will focus, in particular, on the discussion of the results of some recent x-ray resonant scattering experiments carried out on magnetite that directly prove the lack of ionic charge ordering in such mixed valence oxide. Furthermore, we also reconsider some so-called Verwey-type transition metal oxides in terms of the applicability of the Verwey charge ordering model. We show that a complete charge disproportionation (δ) is not experimentally observed in any of these compounds, the maximum δ being less than 0.5 e−. Regarding the theoretical framework, we will outline some relevant implications for the description of the physics of 3d transition metal oxides of this critical re-examination of the experimental facts on magnetite. Electronic localization should then occur involving more than one transition metal atom, so the definition of ionic d states loses its meaning in mixed valence transition metal oxides.

http://iopscience.iop.org/article/10.1088/0953-8984/16/7/R01/pdf

M. Iizumi

Papers

Structure of magnetite (Fe3O4) below the Verwey transition temperature