Collective Electron Theory of the Metal‐Semiconductor Transition in Magnetite
01 Mar 1970-Journal of Applied Physics (American Institute of PhysicsAIP)-Vol. 41, Iss: 3, pp 879-880
TL;DR: In this article, the Verwey transition in magnetite is described on a band model, with the electrons selfconsistently breaking the symmetry by ordering in the self-induced Coulomb potential.
Abstract: The Verwey transition in magnetite is described on a band model, with the electrons self‐consistently breaking the symmetry by ordering in the self‐induced Coulomb potential. The order parameter is the difference in occupation numbers on alternate sites. There is a gap in the single‐particle excitation spectrum, and the gap and order parameter undergo a second‐order phase transition. The theory is BCS‐like, with the Verwey temperature being given in the weak‐coupling limit by an exponential in the reciprocal of the density of states at the Fermi level.
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TL;DR: The story of the Verwey transition in magnetite over a period of about 90 years, from its discovery up to the present, can be subdivided into three eras as mentioned in this paper.
Abstract: 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
623 citations
TL;DR: Using density-functional calculations, a three-band spinless model Hamiltonian is suggested for the description of the Verwey transition using a Stoner model as well as from calculations within the framework of the local-spin-density approximation to the density- functional theory.
Abstract: 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.
610 citations
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TL;DR: In this paper, a review of the current status of knowledge regarding the surfaces of the iron oxides, magnetite (Fe3O4), maghemite (γ-Fe2O3), haematite (α-Fe 2O3, and wustite (fe1−xO) is reviewed.
445 citations
Cites background from "Collective Electron Theory of the M..."
...long-range charge order established amongst the Fe2+ and Fe3+ cations. Subsequently, most conduction models have been based on either band conduction and/or small-polaron hopping. In the band picture [54] the two Fe oct atoms per formula unit distribute their 11 d-electrons across two distinct bands, with ten spin-down electrons occupying a lower energy band, and one electron the higher energy band. T...
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TL;DR: In this paper, the degree of stoichiometry in magnetite is quantitatively measured by determining the ratio of Fe2+ to Fe3+ using powder X-ray diffraction (pXRD).
Abstract: A solid solution can exist of magnetite (Fe3O4) and maghemite (γ-Fe2O3), which is commonly referred to as nonstoichiometric or partially oxidized magnetite. The degree of stoichiometry in magnetite is quantitatively measured by determining the ratio of Fe2+ to Fe3+. Magnetite stoichiometry ( x = Fe2+/Fe3+) strongly influences several physical properties, including the coercitivity, sorption capacity, reduction potential, and crystalline structure. Magnetite stoichiometry has been extensively studied, although very little work exists examining the stoichiometry of nanoparticulate samples (<<100 nm); when the stoichiometry was measured for nanoparticulate samples, it was not validated with a secondary technique. Here, we review the three most common techniques to determine magnetite stoichiometry: (1) acidic dissolution; (2) Mossbauer spectroscopy; and (3) powder X-ray diffraction (pXRD), specifically with nanoparticulate samples in mind. Eight samples of nonstoichiometric magnetite were synthesized with x ranging from 0 to 0.50 and with the particle size kept as similar as possible (BET specific surface area = 63 ± 7 m2/g; particle size ≈ 20 nm). Our measurements indicate excellent agreement between stoichiometries determined from Mossbauer spectra and by acidic dissolution, suggesting that Mossbauer spectroscopy may be a useful means for estimating magnetite stoichiometry in nanoparticulate, multi-phases samples, such as those found in the environment. A significant linear correlation was also observed between the unit-cell length ( a ) of magnetite measured by pXRD and magnetite stoichiometry, indicating that pXRD may also be useful for determining particle stoichiometry, especially for mixed phased samples.
206 citations
TL;DR: In this article, the Hartree-Fock approximation is used to describe the band overlap or Wilson transition, which occurs when a conduction band overlaps a valence band; this is discussed in § 2 and for noncrystalline systems in § 15.
Abstract: An account is given of some of the mechanisms which can lead to a transition from a metallic to a nonmetallic state, when a parameter such as the interatomic distance or temperature is varied. The simplest of these is the band overlap or Wilson transition, which occurs when a conduction band overlaps a valence band; this is discussed in § 2 and for noncrystalline systems in § 15. These transitions can be described in the Hartree-Fock approximation. If the insulating property is due essentially to the repulsion between electrons (e2/r12), then the nonmetallic state is normally antiferromagnetic. The possibility of describing it by normal band theory with a spin-dependent potential is discussed in § 5. It is emphasized that antiferromagnetism can exist in the metallic state, and that the conditions for the appearance of conductivity and the disappearance of antiferromagnetism are not always the same. The nonmetallic behaviour, that is the existence of a Hubbard gap, normally persists above the Neel temperature (as in NiO), as does the gap in some metals, but not in chromium. Disordered systems, such as doped semiconductors, are discussed; here in the metallic state we suggest that the two Hubbard bands overlap, and that the metal-nonmetal transition can be described as an Anderson transition (§ 16). This model gives a simple explanation of the negative magnetoresistance. In some materials a transition occurs which does not involve magnetic moments or structural change, and for d bands, following Halperin and Rice, and Weger, we introduce the concept of an `orbital orientation wave' in degenerate d bands (§§ 5, 19.3, 19.4). A number of specific materials are discussed.
148 citations
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TL;DR: The low-temperature transition in magnetite is due to the ordering of the ferrous and ferric ions in the octahedral interstices of the spinel lattice as mentioned in this paper.
Abstract: The low-temperature transition in magnetite, according to Verwey, is due to the ordering of the ferrous and ferric ions in the octahedral interstices of the spinel lattice. This arrangement would require a symmetry change from cubic to orthorhombic. X-ray diffraction indicates and electric conductivity and magnetization measurements confirm that the transition leads to an orthorhombic structure. An external magnetic field applied while cooling through the transition establishes a preferred orientation for the $c$ axis throughout the whole crystal. Below the transition this $c$ axis can be switched to a new direction by a strong magnetic field, a process involving a co-operative rearrangement of the ferrous ions in new sites and relatively large changes in dimensions. In stoichiometric, synthetic, single crystals the transition occurs at 119.4\ifmmode^\circ\else\textdegree\fi{}K and is marked by an abrupt decrease in the conductivity by a factor of 90 in a temperature interval of 1\ifmmode^\circ\else\textdegree\fi{}. No thermal hysteresis is observed. The conductivity of a crystal cooled in a strong magnetic field is anisotropic below the transition as given by the relation $\ensuremath{\sigma}=A+B(1+{cos}^{2}\ensuremath{\theta})$, where $\ensuremath{\theta}$ is the angle between the $c$ axis and the direction of measurement. The ratio $\frac{B}{(A+B)}$ increases rapidly as the crystal is cooled to 90\ifmmode^\circ\else\textdegree\fi{}K, indicating a progressive increase in the long-range order. The $c$ axis is the direction of easy magnetization below the transition, and the anisotropy energy is very much larger below than above; the anisotropy constants have been determined at 85\ifmmode^\circ\else\textdegree\fi{}K.
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