Charge Ordering In Magnetite Research Articles

Dual-stage structural response to quenching charge order in magnetite

The Verwey transition in magnetite (Fe3O4 ) is the prototypical metal-insulator transition and has eluded a comprehensive explanation for decades. A major element of the challenge is the complex interplay between charge order and lattice distortions. Here we use ultrafast electron diffraction (UED) to disentangle the roles of charge order and lattice distortions by tracking the transient structural evolution after charge order is melted via ultrafast photoexcitation. A dual stage response is observed in which X3, X1, and Delta5 type structural distortions occur on markedly different timescales of 0.7 to 3.2 ps and longer than 3.2 ps. We propose that these distinct timescales arise because X3 type distortions strongly couple to the trimeron charge order, whereas the Delta5-distortions are more strongly associated with monoclinic to cubic distortions of the overall lattice. Our work aids in clarifying the charge lattice interplay using UED method and illustrates the disentanglement of the complex phases in magnetite.

Kinetics of the charge ordering in magnetite below the Verwey temperature

In this work the kinetics of the charge ordering in magnetite (Fe3O4) below the Verwey transition temperature TV is investigated in time and energy domain. After excitation by a one-second voltage pulse to destruct the charge-ordered state below TV, an alternating current (AC) is used to perturb its recovery process. Upon warming up to above a temperature Tr(< TV) the charge order recovers despite the ac perturbation, because the temperature-dependent relaxation time becomes shorter than the polarity change of the ac. From the frequency dependence of Tr(f), an activation energy of ΔE = 126 meV is extracted. Below Tr the real part of the ac conductance Greal follows the relation Greal ∼ fα with α = 0.98 ± 0.18, suggesting that the charge reordering is driven by correlated hopping transport. The relaxation time τ = 1/f(Tr) of the charge-ordered state is determined for temperatures between 70 and 98 K and is extrapolated to τ(TV) = 1.6 ms, continuously slowing down its dynamics as the temperature is decreased.

Coulombic charge ice

We consider a classical model of charges $\pm q$ on a pyrochlore lattice in the presence of long range Coulomb interactions. This model first appeared in the early literature on charge order in magnetite. In the limit where the interactions become short-ranged, the model has a ground state with an extensive entropy and dipolar charge-charge correlations. When long range interactions are introduced, the exact degeneracy is broken. We study the thermodynamics of the model and show the presence of a correlated charge liquid within a temperature window in which the physics is well described as a liquid of screened charged defects. The structure factor in this phase, which has smeared pinch points at the reciprocal lattice points, may be used to detect charge ice experimentally. In addition, the model exhibits fractionally charged excitations $\pm q/2$ which are shown to interact via a $1/r$ potential. At lower temperatures, the model exhibits a transition to a long-range ordered phase. We are able to treat the Coulombic charge ice model and the dipolar spin ice model on an equal footing by mapping both to a constrained charge model on the diamond lattice. We find that states of the two ice models are related by a staggering field which is reflected in the energetics of these two models. From this perspective we can understand the origin of the spin ice and charge ice ground states as coming from a dipolar model on a diamond lattice. We study the properties of charge ice in an external electric field finding that the correlated liquid is robust to the presence of a field in contrast to the case of spin ice in a magnetic field. Finally, we comment on the transport properties of Coulombic charge ice in the correlated liquid phase.

Electronic structure and charge ordering in magnetite: implications for the Fe3O4 (001)–water interface

Electronic structure calculations on atomistic models of magnetite (Fe3O4) provide valuable insight into the structure and properties that dictate the behaviour of magnetite under environmental conditions. The charge ordering in the bulk oxide controls the reactivity of the exposed surfaces, but it has been difficult to measure experimentally or predict theoretically. We use spin-polarised density functional theory to calculate the structure of bulk Fe3O4 and its (001) and (111) surface terminations. We then present an ab initio thermodynamics approach to determine the most energetically favourable clean and hydroxylated surface terminations of Fe3O4 (001). We present results on molecular water adsorption and heterolytic dissociation at both quarter- and half-monolayer coverage for Fe3O4 (001). Our calculations suggest that the tetrahedral (001) surface termination is the most energetically stable across all oxygen chemical potentials, and that water molecules preferentially dissociate at the surface. The calculated hydroxylated and hydrated surface terminations, as obtained from careful consideration of the charge ordering in the bulk, serve as a strong basis for future studies of the electrical double layer at the mineral–water interface.

Origin of the twofold and fourfold symmetric anisotropic magnetoresistance in epitaxial Fe3O4 films

The angular dependence of anisotropic magnetoresistance (AMR) in epitaxial Fe3O4 films on several kinds of substrates has been investigated to explore the nature of AMR. All the measurements show that the dependence of AMR on the angle between current and magnetic field is the superimposition of sinusoidal twofold and fourfold symmetric AMR. The AMR in epitaxial Fe3O4 films is controlled by magnetic anisotropy and antiphase boundaries (APBs). The twofold and fourfold symmetric AMR originate from the scattering far away from the APBs and that near the APBs, respectively, which is consistent with the physical picture of magnetoresistance in epitaxial Fe3O4 films. The magnetic anisotropy, such as the uniaxial anisotropy induced by the step terraces and shape geometry, is closely related to the twofold symmetric AMR. The fourfold symmetric AMR is based on magnetocrystalline anisotropy and probably not correlated with the charge order in magnetite, which was verified by the fourfold symmetric AMR in octahedral-site doped epitaxial Ni0.3Fe2.7O4 films.

Direct Observation oft2gOrbital 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.

Correlation between Surface Structure and Charge Ordering in Magnetite(001) Studied by Scanning Tunneling Microscopy and Spectroscopy

We report the observation on the charge ordering of Fe ions in a magnetite(Fe3O4)(001) film surface by scanning tunneling microscopy and spectroscopy (STM/STS) with a nonmagnetic W tip. The Fe3O4(001) film surface exhibits a B-plane termination with a (√2 × √2)R45° reconstruction. Fe cation rows running along the [110] direction show a wavelike structure. The (√2 × √2)R45° surface reconstruction is originated from the wavelike Fe rows. The current imaging tunneling spectroscopy image shows alternation of two different kinds of current peak with a separation of about 0.6 nm. Each current peak arises from the same local density of states (LDOS) of two Fe ions. The presence of Fe dimers with two different kinds of LDOS provides evidence for the charge ordering of Fe ions with different charge states. STM and STS using a nonmagnetic W tip allow us to correlate the charge ordering pattern with the surface structure.

Investigation of the presence of charge order in magnetite by measurement of the spin wave spectrum

Inelastic neutron scattering results on magnetite $({\mathrm{Fe}}_{3}{\mathrm{O}}_{4})$ show a large splitting in the acoustic spin wave branch, producing a $7\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ gap midway to the Brillouin zone boundary at $\mathbf{q}=(0,0,1∕2)$ and $\ensuremath{\hbar}\ensuremath{\omega}=43\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The splitting occurs below the Verwey transition temperature, where a metal-insulator transition occurs simultaneously with a structural transformation, supposedly caused by the charge ordering on the iron sublattice. The wavevector $(0,0,1∕2)$ corresponds to the superlattice peak in the low symmetry structure. The dependence of the magnetic superexchange on changes in the crystal structure and ionic configurations that occur below the Verwey transition affect the spin wave dispersion. To better understand the origin of the observed splitting, several Heisenberg models intended to reproduce the pair-wise variation of the magnetic superexchange arising from both small crystalline distortions and charge ordering were studied. None of the models studied predicts the observed splitting, whose origin may arise from charge-density wave formation or magnetoelastic coupling.

Resonant x-ray diffraction study of the charge ordering in magnetite

Powder x-ray diffraction patterns of magnetite(Fe3O4) have been recorded at 90 K, below the Verwey transition, at three wavelengths in the pre- tomid-edge region of the 7.1 keV Fe K absorption. Simultaneous fitting of these profiles hasbeen used to refine the anomalous scattering coefficients for the octahedral B site ironatoms. The refined values give direct evidence for a significant degree (46%) ofFe2+/Fe3+ charge ordering in magnetite, and provide new constraints on the number of possible chargeordered models.

Ab initiostudy of charge order inFe3O4

We present a self-interaction corrected local spin-density study of the electronic structure and possible charge order of magnetite ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}.$ The issue of charge order in magnetite is explored in both cubic and orthorhombic structures, the latter being an approximation to the true, low-temperature, monoclinic structure. We find that the Verwey charge ordered phase is not the ground-state solution for this compound either in cubic or orthorhombic structure. We conclude that the structural distortions, more than localization/delocalization correlations, are responsible for the charge disproportionation in the low-temperature phase.

Long range charge ordering in magnetite below the Verwey transition.

The crystal structure of Fe(3)O(4) below the 122 K Verwey transition has been refined using high-resolution x-ray and neutron powder diffraction data. The refinements give direct evidence for charge ordering (CO) over four independent octahedral Fe sites, two with a charge of +2.4 and the other two of +2.6. CO schemes consistent with our model do not meet the widely accepted Anderson condition of minimum electrostatic repulsion. Instead we propose that CO is driven primarily by a [001] electronic instability, which opens a gap at the transition through a charge density wave mechanism.

Electrostatically driven charge-ordering in magnetite below the Verwey temperature

This work describes the stability of different charge models for magnetite, Fe 3O 4, below the Verwey temperature (T V). Thirty-seven configurations allowed by the Anderson condition are analysed by means of Madelung calculations, including models proposed by Verwey, Mizoguchi and Zuo. A new approach based on summation over cubic cells is applied that ensured rapid convergence of lattice sums. The lowest Madelung energy has been found for the model in which coupled chains of Fe 2+ and Fe 3+ ions form structures parallel to the c-axis. These structures are similar to double helices having a period of twice the cubic lattice constant. Thus it has been shown, contrary to previous studies, that the Coulomb energy alone is sufficient to stabilize the charge order involving doubling of the c-axis.

Charge ordering in magnetite at low temperatures.

The ordering of the ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions on the octahedral sites of magnetite (${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$) at temperatures below the Verwey metal-insulator transition has been studied by quantitative high-energy transmission electron diffraction. We find that there are ten independent charge-ordering models (including the Verwey model) for the low-temperature structure that satisfy the Anderson condition if the symmetry is Cc (monoclinic). Dynamical electron diffraction patterns are simulated and compared with experiment for these charge-ordering models, using atomic coordinates obtained from neutron diffraction work. We find that one of these ten charge-ordering models agrees best with experiment and that the electrons in this model form a characteristic wave. Our calculations of electron correlation energy show that this model has the second lowest energy, while the Verwey model has the lowest. This indicates the importance of electron-phonon interactions in stabilizing the structure.

Partial charge ordering in magnetite

Abstract It is shown that recent models of the charge ordering in magnetite which can explain a- and b-axis doubling are likely to be unstable, even below the Verwey temperature, to the formation of a partially ordered structure which accords with single-crystal neutron results.

Polarization Screening Effect on the Charge Ordering in Magnetite

On the basis of the pure ionic model the charge ordering in magnetite is studied with due account of the wa vevector-dependent polarization -screening effect. The Verwey ordering (Tf,) is found to be unstable for the electronic polarizability of oxygens larger than [ac] c =0.91A', where the stablest charge-ordering pattern must be of X, symmetry. It is also shown that one fourth of the total modes of the charge fluctuation are nearly degenerate at the critical polarizability [ae] 0 •