Transition In Magnetite Research Articles

Charge-Orbital Ordering and Verwey Transition in Magnetite

Local density approximation + Hubbard U (LDA + U) band structure calculations reveal that magnetite (Fe3O4) forms an insulating charge-orbital-ordered state below the Verwey transition temperature. The calculated charge ordering is in good agreement with that inferred from recent experiments. We found an associated t(2g) orbital ordering on the octahedral Fe2+ sublattice. Such an orbital ordering results primarily from the on-site Coulomb interaction. This finding unravels such fundamental issues about the Verwey transition as the mechanism for the charge ordering and for the formation of the insulating gap, as well as the nonobedience of the Anderson's criterion for the charge ordering.

The Verwey transition in magnetite as studied by means of definite impurity doping

Abstract The effect of low-dose cation doping (0.005 < x < 0.08) of magnetite single crystals, Fe3-xMxO4 (M = Ni, Mg, Co, Al, Ti, Ga), has been studied by means of the magnetic after-effect (MAE) s...

The effect of perturbative interactions among localized electrons on the Verwey transition in magnetite

We modify the current Straessler–Kittel theory of phase transitions by allowing for weak perturbative interactions among electrons localized on adjacent lattice sites. The solutions obtained in the absence of such interactions are stable against the perturbative influences. However, the detailed quantitative modeling of the Verwey transition in magnetite requires that such interactions be taken into account.

Aspects of the Verwey transition in magnetite

A new mechanism of the Verway transition in magnetite (Fe3O4), which has been argued to be a charge ordering transition so far, is proposed. Based on the mean field calculations for the three band model of spinless fermions appropriate for the d electrons of the Fe ions on the B sites, it is indicated that the phase transition should be the bond dimerization due to the cooperative effects of strong electronic correlation and electron-phonon interaction. The results show that the ferro-orbital ordered state is stabilized in a wide temperature range due to the strong on-site Coulomb interaction between different t2g orbitals resulting in an effectively one-dimensional electronic state, which leads the system toward an insulating state by the Peierls lattice distortion with the period of two Fe(B) ions, i.e., bond dimerization. Furthermore, it is found that the interplay between such lattice distortion in the Fe(B) ions and the lattice elastic energy of the Fe(B)-O as well as the Fe(A)-O bonds gives rise to a competition between two different three-dimensional patterns for the bond dimerization, and can stabilize a complicated one with a large unit cell size. The results are compared with the known experimental facts.

Use of the Straessler–Kittel theory of phase transitions: thermodynamic properties and application to the Verwey transition

Abstract Thermodynamic quantities derived from the Straessler–Kittel theory of phase transitions are derived and evaluated. The applicability of these results to the Verwey transition of magnetite is briefly discussed.

Orbital ordering and bond dimerization in magnetite Fe3O4

A new mechanism of the Verway transition in magnetite (Fe3O4) is proposed. It is argued to be a bond dimerization transition due to the interplay between the strong inter-orbital on-site Coulomb interaction on the Fe sites stabilizing a ferro-orbital ordered state making the system one-dimensional, and the electron–phonon interaction which results in the Peierls lattice distortion. Furthermore, discussions on the total elastic energy of the lattice lead us to a complicated lattice distortion pattern with large unit cell size in accordance with the experiments.

Metallization of magnetite (Fe3O4) under high pressure

Electrical resistivity measurements have been made on a good qualified single crystalline magnetite (Fe3O4) at temperatures from 300 down to 3.0 K under pressure up to 10 GPa. A steep change in resistivity at the Verwey transition temperature has been observed at pressure below 6.5 GPa, which shows a quite distinct result reported in prior work. Moreover, the Verwey transition temperature has been found to decrease nonlinearly with increasing pressure and it disappears at around 8 GPa. Above 8 GPa magnetite exhibits metallic behavior. The residual-resistivity ratio of the metallic state is observed to be more than 350. This finding of a metallic ground state in magnetite provides insight into the understanding of the Verwey transition in magnetite.

Possible influence of electron — lattice interactions on the Verwey transition in magnetite

In the paper crystal lattice influence on the Verwey transition in magnetite related compounds is discussed based on the experimental activity of our group. Heat capacity studies indicate the distinct low temperature lattice properties of slightly doped magnetite from those with higher dopant concentration. Neutron scattering lattice examination and the elastic constants studies are then performed to further study this conjecture. Our main conclusion is that the Verwey transition in magnetite can not be understood and described without strong involvement of lattice dynamics.

Infrared and Raman studies of the Verwey transition in magnetite

We present infrared and Raman measurements of magnetite (Fe_3O_4). This material is known to undergo a metal-insulator and a structural transition (Verwey transition) at T_V=120K. At temperatures below T_V, we observe a strong gap-like suppression of the optical conductivity below 1000 cm^-1. The structural aspect of the Verwey transition demonstrates itself by the appearance of additional infrared- and Raman-active phonons. The frequencies of the infrared-active phonons show no significant singularities at the transition whereas their linewidths increase. The frequency and linewidth of the Raman-active phonon at 670 cm^-1 changes abruptly at the transition. For T<T_V, we observe fine structures in the infrared and Raman spectra which may indicate strong anharmonicity of the system below the transition. Our estimate of the effective mass of the carriers above the transition to be about 100 m, where m is the free electron mass. Our measurements favor a polaronic mechanism of conductivity and underline the importance of the electron-phonon interaction in the mechanism of the Verwey transition.

The influence of a finite bandwidth on the Verwey transition inmagnetite

The role of the band structure in the Verwey transition in magnetite(Fe3O4) has been analysed within the framework of an exactly solvabletwo-band model based on an effective interionic Coulomb potential splittingthe 3d band of the t2g electrons. The model predicts an instability ofthe Verwey order below a certain ratio β/W of the Coulomb interactionparameter β and the bandwidth W. This instability can be understood interms of a clear physical picture showing the impossibility of constructing aself-consistent ordered charge distribution in this case. A resemblance to theCullen-Callen criterion is evident. It is shown as well that the influence ofthe band structure on the Verwey temperature vanishes rapidly when β/Wincrease beyond its critical value. Band-structure effects do provide anexplanation, however, for the discontinuity in the Verwey temperature as afunction of the concentration of cation dopants or the oxygen stoichiometry,which marks the transition from a first- to a second-order Verwey transition.In this respect, the model reproduces the experimental data quantitatively.Fits obtained by application of the model yield values of 0.037-0.04 eV forthe Coulomb gap and 0.012-0.014 eV for the bandwidth. The obtained values ofthe bandwidth are typical for a strongly localized electron system and supporta polaronic band picture.

Mössbauer characterization of iron oxides and (oxy)hydroxides: the present state of the art

Mossbauer spectroscopy is a powerful direct technique for the identification and quantification of iron oxides and (oxy)hydroxides in soils and sediments. However, further characterization with respect to structural properties such as crystallinity, Al substitution, stoichiometry, water content, etc. is rather limited. With some examples of synthetic and natural goethite and hematite sample series it is illustrated that the hyperfine parameters depend on much more structural features than the Al content and crystallinity alone. Neither the Morin transition in hematite nor the Verwey transition in magnetite is directly applicable for analytical purposes in natural samples.

Quantum State Model of the Verwey Transition in Magnetite

Previous analyses of the Verwey transition in magnetite have been placed on a firm footing by a consistent analysis of the statistical properties of an array of quantum states associated with ferrous or ferric ions in octahedrally coordinated interstices of the spinel lattice. This collection is represented by an assembly of bonds and sites. Individual sites can be in one of three configurations: empty, as in the Fe3+ state, trapped, or polaronic if in the Fe2+ state. On neglect of high-energy states involving electron occupation of neighboring lattice sites, one arrives at an analytic equation of state for the order parameter in its dependence on temperature, which can be solved numerically. This equation is sufficiently flexible to handle both the first- and second-order transitions by appropriate changes in parameters. The present theory rationalizes the experimentally observed changes in the order of the Verwey transition that result from alterations in the sample stoichiometry.

PAC measurements of the Verwey transition in magnetite

Perturbed angular correlation (PAC) experiments with implanted 111In tracers have recently been used to investigate magnetic phase transitions in metal oxides. Here we report on PAC measurements for 111Cd in polycrystalline Fe3O4 in the neighborhood of the Verwey phase transition (TV≈ 120 K). Perturbed angular correlation spectra were taken for implanted 111In probes at temperatures between 9 and 850 K. The two observed Larmor frequencies are attributed to the two possible cation sites in the cubic inverse spinel lattice. For T > 120 K, the temperature dependence of both Larmor frequencies follows a Curie–Weiss power law ωL(T)/ ωL(0)=(1-T/TN)β, with the parameters TN=848(2) K and β= 0.392(2). At the Verwey temperature we find a rapid change of both Larmor frequencies, with ωL1 increasing from 178(2) MHz at 120 K to 191(4) MHz at 100 K, and ωL2 decreasing from 173(4) MHz to 151(5) MHz. The Verwey transition also affects the widths of the frequency distributions, which more or less double below TV. This possibly indicates the presence of several components with Larmor frequencies similar to those found in the previous Mossbauer data, or for electronic after-effects correlated with the semiconductivity of magnetite below TV.

The role of volume effects in the Verwey transition inmagnetite

Fe2+/Fe3+ ordering in magnetite is described in terms of a simple mean-field approach based on an effective interionic Coulomb potential. It is shown that first-order electronic order-disorder transformations, as reported in the literature, can only be reproduced when the dependence of the interionic potential on the unit-cell dimensions is taken into account. In this case the first-order transitions can then be viewed as the result of an interplay between the lattice-deformation energy and the free-energy contribution related to the electronic ordering of the octahedral Fe lattice. Furthermore, the effect of the lattice deformation by hydrostatic pressure on the Verwey transition can be successfully explained to some extent within the context of the same framework. In comparison to experimental data available from the literature, the mean-field approach developed in this paper yields very acceptable results with respect to both qualitative and quantitative aspects, thus opening an interesting new viewpoint on the mechanism of the Verwey transition.

Impurity effects upon the Verwey transition in magnetite

Magnetite single crystals ${\mathrm{Fe}}_{3\ensuremath{-}x}{M}_{x}{\mathrm{O}}_{4}$ doped with $M=\mathrm{Ni},$ Co, Mg, Al, Ga, and Ti were grown and annealed under a controlled atmosphere to produce homogeneous and oxygen stoichiometric samples. The cation vacancy concentration of the samples was proved to be lower than ${10}^{\ensuremath{-}6}$ by means of magnetic disaccommodation spectroscopy. The Verwey temperature shift as function of the substituent concentration was determined from the temperature dependence of the resistivity. The systematics of the transition temperature shift as function of the concentration and nature of the substituents is indicative that the mechanism of the transition is related to the second-neighbor Coulomb interaction of the cations on the octahedral sites.

Electrostatically driven charge-ordering in Fe2OBO3

Charge-ordering is an important phenomenon in conducting metal oxides: it leads to metal–insulator transitions1 in manganite perovskites (which show ‘colossal’ magnetoresistances), and the Verwey2 transition in magnetite (in which the material becomes insulating at low temperatures when the conduction electrons freeze into a regular array). Charge-ordered ‘stripes’ are found in some manganites3,4 and copper oxide superconductors5; in the latter case, dynamic fluctuations of the stripes have been proposed6 as a mechanism of high-temperature superconductivity. But an important unresolved issue is whether the charge-ordering in oxides is driven by electrostatic repulsions between the charges (Wigner crystallization7), or by the strains arising from electron–lattice interactions (such as Jahn–Teller distortions) involving different localized electronic states. Here we report measurements on iron oxoborate, Fe2OBO3, that support the electrostatic repulsion charge-ordering mechanism: the system adopts a charge-ordered state below 317 K, in which Fe2+ and Fe3+ ions are equally distributed over structurally distinct Fesites. In contrast, the isostructural manganese oxoborate, Mn2OBO3, has been previously shown8 to undergo charge-ordering through Jahn–Teller distortions. We therefore conclude that both mechanisms occur within the same structural arrangement.

Single-particle gap above the Verwey transition inFe3O4

The Verwey transition in magnetite, ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$, has been studied using temperature-dependent high-resolution photoemission spectroscopy. On heating through the transition temperature ${\mathrm{T}}_{\mathrm{V}}$ the band gap is not collapsed, but is merely reduced by \ensuremath{\sim}50 meV, showing that a metal-insulator transition does not occur. The change in the gap is perfectly consistent with the two orders of magnitude conductivity jump at ${\mathrm{T}}_{\mathrm{V}}$. Thus even above ${\mathrm{T}}_{\mathrm{V}}$ short-range charge ordering rather than site equivalency dominates the single-particle excitations and the electrical properties. We also point out important implications for efforts to model the electrical transport above ${\mathrm{T}}_{\mathrm{V}}$.

Analysis of the Verwey transition in magnetite

A review is presented of work carried out in the author's laboratory concerning the thermodynamic and electrical transport phenomena in magnetite. The need for careful compositional control of single crystal growth is emphasized. With increasing deviations from the ideal Fe 3O 4 composition the Verwey transition suddenly shifts from the first order to a higher order regime. This hitherto unrecognized feature is documented by a variety of experimental techniques and is rationalized in terms of a single formalism based on a mean field theoretic approach. The agreement between theory and experiment is very good. Various aspects of the theoretical analysis are discussed in detail; the formalism is of much more general appreciability than the limited use to which it was put in the resolution of the Verwey problem.

Verwey transition in magnetite: Finite-temperature mean-field solution of the Cullen-Callen model.

Verwey transition in magnetite is studied by solving the Cullen-Callen spinless one-band model at finite temperature, extending the work of Cullen and Callen from the T=0 to T\ensuremath{\ne}0 regime. A complete phase diagram of the model in the (U/t,T) plane is presented here, which exhibits three phases---a disordered phase and two ordered phases, one multiply ordered and one singly ordered. It is also explicitly shown that the transitions from the disordered phase to the ordered phases are of the first-order type, and they are entropy driven. I also find that for the transition temperature near the experimental value of 120 K, the transition is from the disordered state to the multiply ordered state, and not to the singly ordered state.

Verwey transition in magnetite: Mean-field solution of the three-band model

The nature of the Verwey transition in magnetite (Fe3O4) within a three-band spinless model Hamiltonian is examined. These bands, which arise from the minority-spin t2g orbitals on the Fe(B) sublattice, are occupied by half an electron per Fe(B) atom. The Verwey order–disorder transition is studied as a function of the ratio of the intersite Coulomb repulsion U1 and the bandwidth W. It is found that the electrons are ordered beyond the critical value of U1/W≊0.25 in essential agreement with the results of the one-band Cullen–Callen model. For larger values of U1/W, a Verwey-like order is exhibited where the electrons occupy alternate (001) planes. The model predicts a transition from the metallic to the semiconducting state with the band gap increasing linearly with U1 beyond the transition point.