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.

/pdf/electron-states-magnetism-and-the-verwey-transition-in-563i3iv6uy.pdf

Electron states, magnetism, and the Verwey transition in magnetite

Publisher Summary This chapter discusses the progress in spinel ferrite research. A large number of oxides with a metal–oxygen ratio of 0.75 as composition is known to crystallize into the spinel structure. Among these oxides, magnetite Fe 3 O 4 is an important compound, from which the spinel ferrites can be derived by partial substitution of the iron ions by other cations. Between most of the spinel oxides solid solutions can be formed, which means that a great variety of spinel oxides is possible. The simple spinel ferrites are those ferrites in which x = 0 and the bivalent metal ion is Mg or Cd or one of the bivalent transition metal elements Mn, Fe, Co, Ni, Cu, and Zn. Partial solid solutions of the simple ferrites are also possible with compounds that either do not exist or that do not have the spinel structure. A great variety in the chemical composition of spinel ferrites is possible. The diversity in composition results into a large range of physical properties that permits the tuning of the properties for specific applications and makes spinel ferrites of particular interest.

Chapter 3 Progress in spinel ferrite research

We present a detailed study of the spin-dependent electronic structure of thin epitaxial magnetite films of different crystallographic orientations. Using spin- and angle-resolved photoelectron spectroscopy at room temperature, we determine for epitaxial Fe3O4(111) films a maximum spin polarization value of −(80 ± 5)% near EF. The spin-resolved photoelectron spectra for binding energies between 1.5 eV and EF show good agreement with the spin-split band structure from density functional theory (DFT) calculations which predict an overall energy gap in the spin-up electron bands in high symmetry directions, thus providing evidence for the half-metallic ferromagnetic state of Fe3O4 in the [111] direction. In the case of the Fe3O4(100) surface, both the spin-resolved photoelectron spectroscopy experiments and the DFT density of states give evidence for a half-metal to metal transition: the measured spin polarization of about −(55 ± 10)% at EF and the theoretical value of −40% are significantly lower than the −100% predicted by local spin density approximation (LSDA) calculations for the bulk magnetite crystal as well as the −(80 ± 5)% obtained for the Fe3O4(111) films. The experimental findings were corroborated by DFT calculations as due to a surface reconstruction leading to the electronic states in the majority-spin band gap and thus to the reduced spin polarization.

/pdf/magnetite-a-search-for-the-half-metallic-state-28448d1fmz.pdf

Magnetite: a search for the half-metallic state

We study the first-order Verwey transition in single-crystal ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$ using high-resolution temperature-dependent (100--300 K) photoemission spectroscopy. The near-Fermi-level (${\mathit{E}}_{\mathit{F}}$) spectrum exhibits a clear gap of \ensuremath{\sim}70 meV in the occupied part of the density of states (DOS) in the low-temperature semiconducting phase. The gap is closed above the transition temperature ${\mathit{T}}_{\mathit{V}}$=122 K, establishing a metal-semiconductor transition. The Fe 3d derived features arising from ${\mathrm{Fe}}^{3+}$ (${\mathit{e}}_{\mathit{g}}^{2}$) majority- and ${\mathrm{Fe}}^{2+}$ (${\mathit{t}}_{2\mathit{g}}^{1}$) minority-spin states responsible for the transition retain their character just above the transition but merge into a single feature by 300 K. Simultaneously, the DOS at ${\mathit{E}}_{\mathit{F}}$ increases systematically in the metallic phase. The results indicate the existence of, and a gradual change in, the short-range order for Tg${\mathit{T}}_{\mathit{V}}$, which causes the nonmetalliclike electrical conductivity observed just above ${\mathit{T}}_{\mathit{V}}$.

High-resolution photoemission spectroscopy of the Verwey transition in Fe3O4.

We propose a ‘molecular polaron’ model which describes the properties of valance fluctuations in Fe3O4 above the Verwey transition temperature. The molecular polaron is dynamically coupled cluster, or a vibronic state associated with two electrons in four-site molecular orbitals coupled to local vibrational modes with T2g symmetry. The lifetime of a molecular polaron is assumed to be long enough to induce a strain field around it. That is, each molecular polaron is considered to be ‘dressed’ by an instantaneous strain field. Based on this model, neutron Huang scattering due to the strain field around independent molecular polarons has been calculated. The observed patterns of neutron diffuse scatteringagree quite well with the calculated patterns, which seems to ensure the validity of the proposed model.

Y. Yamada

Papers

Molecular polarons and valence fluctuations in Fe3O4