Surface Verwey transition in magnetite

We report density functional studies of the (001) surface of magnetite that account for local Coulomb interactions. Iron cations in the surface layers exhibit charge and t2g orbital ordering that is coupled with the lattice strains. Orbital ordering is present for various surface stoichiometries and causes opening of the band gap Eg approximately 0.3 eV at the surface, such that the (001) surface of Fe3O4 remains insulating also in the high temperature cubic phase. The (radical 2 x radical 2)R45 degrees surface reconstruction is related to orbital ordering.     

Origin of the Verwey transition in magnetite

Comprehensive x-ray powder diffraction studies were carried out in magnetite in the 80-150 K and 0-12 GPa ranges with a membrane-driven diamond anvil cell and helium as a pressure medium. Careful data analyses have shown that a reversible, cubic to a distorted-cubic, structural transition takes place with increasing pressure, within the (P,T) regime below the Verwey temperature TV(P). The experimental documentation that TV(P)=Tdist(P) implies that the pressure-temperature-driven metal-insulator Verwey transition is caused by a gap opening in the electronic band structure due to the crystal-structural transformation to a lower-symmetry phase. The distorted-cubic insulating phase comprises a relatively small pressure-temperature range of the stability field of the cubic metallic phase that extends to 25 GPa.     

PAC measurements of the Verwey transition in magnetite

Hyperfine Interactions - Perturbed angular correlation (PAC) experiments with implanted 111In tracers have recently been used to investigate magnetic phase transitions in metal oxides. Here we...     

Optic spin-waves in magnetite near the Verwey transition

The energies of optic spin waves at a zone centre and a (001) zone boundary have been measured in a natural crystal of magnetite at temperatures in the neighbourhood of the Verwey transition. The energies of these spin waves increased by 0.5 ± 0.4and 0.9 ± 0.5 meV respectively on cooling through the transition and therefore do not exhibit a strong change as a consequence of the ordering of the Fe²⁺ and Fe³⁺ ions at the transition.     

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.     

Verwey ordering on magnetite as a co-operative Jahn-Teller transition

Verwey ordering of Fe²⁺ and Fe³⁺ on alternate planes along [001] direction occurring at 119° K is considered uniquely as a collective Jahn-Teller transition. The model predicts two successive second-order transitions, as a result of simultaneous coupling to both shear distortion and optical phonon mode. Expected elastic constant anomalies are calculated. The insulating state thus obtained at T = 0, does not invoke electron-electron correlation on near-neighbor sites.     

Magnetic properties of magnetite thin films close to the Verwey transition

Temperature dependence of the magnetic properties of magnetite thin film across the Verwey transition has been investigated. As the temperature is decreased, the magnetization of the film in a fixed field showed a sharp decrease close to the Verwey transition temperature (T_v). The M–H loops of the film have been recorded at various temperatures below and above T_v. It is found that film does not saturate at any temperature and saturation becomes more difficult below T_v. While cooling through T_v, the extrapolated value of magnetization to infinite field (Q), calculated from the numerical fit 4πM=Q [1−(H*/H)^1/2], does not show a drop, but the coefficient indicating difficulty in saturation (H*) shows a sharp rise as does the coercivity.     

Electronic structure and hyperfine fields in non-stoichiometric magnetite above the Verwey transition

The NMR spectra of ⁵⁷Fe nuclei were measured below and above the Verwey transition temperature T_V in single crystal samples of Fe_3(1?δ)O₄ (0?δ?0.009). The measured crystals were grown from the melt using the cold crucible technique. In a cubic phase above T_V the satellite structure induced by vacancies in the octahedral sublattice is clearly resolved. The satellite lines originate from those iron nuclei in the tetrahedral sublattice that are nearest to the vacancy. Temperature dependence of satellite lines indicates that the presence of vacancy leads to a redistribution of the electrons in octahedral sublattice and the appearance of iron ions possessing appreciable orbital momentum.     

Electrical properties of nanocrystalline magnetite with large non-stoichiometry, near Verwey transition

DC electrical measurements were carried out on compacted powders of magnetite with an average particle diameter of 50 nm over the temperature range 10-300 K. The non-stoichiometry was estimated from Mossbauer spectroscopy analysis. High-resolution X-ray diffraction studies in the temperature range 93-300 K did not show any phase transition. There was a drastic change in resistivity around 80 K but no discontinuity thereof. Electrical resistivity vs. temperature data were analysed on the basis of Mott's small polaron and variable-range hopping models, respectively. The Verwey temperature as estimated from this analysis was 93 K. From voltage-current characteristics it was concluded that there was a small intrinsic gap at the Fermi level above the transition temperature and the same increased drastically below the transition temperature. This was ascribed to a transition from short-range order to long-range order as the temperature was lowered.     

Charge-orbital ordering and Verwey transition in magnetite measured by resonant soft X-ray scattering

We report experimental evidence for the charge-orbital ordering in magnetite below the Verwey transition temperature T(V). Measurements of O K-edge resonant x-ray scattering on magnetite reveal that the O 2p states in the vicinity of the Fermi level exhibit a charge-orbital ordering along the c axis with a spatial periodicity of the doubled lattice parameter of the undistorted cubic phase. Such a charge-orbital ordering vanishes abruptly above T(V) and exhibits a thermal hysteresis, correlating closely with the Verwey transition in magnetite.     

Magnetic properties and Verwey transition of quasi-one-dimensional magnetite nanowire arrays assembled in alumina templates

Magnetite (Fe₃O₄) has been successfully assembled into anodic alumina templates by an electrochemical method followed by a heat-treating process. Here, we report on the magnetic properties of these so formed nanowires and the Verwey transition measured by vibrating sample magnetometer and SQUID. A Mössbauer spectrum was collected to verify the magnetic orientation of the wires, and a tilt of the moment of 45° with respect to the wire axis was found. These wires show perpendicular magnetic anisotropy mainly due to the average easy axis of the grains pointing along the wire axis. The temperature dependence of the coercity, remanence, and the magnetization undergo a major change at 50 K, induced by the Verwey transition, which occurs at a temperature much lower than for bulk materials (120 K). The behavior of the magnetization in the vicinity of 50 K as well as its field-dependent properties was interpreted using the magneto-electronic model.     

Magnetic dipolar and electric quadrupolar effects on the Mössbauer spectra of magnetite above the Verwey transition

Mössbauer spectroscopic studies (⁵⁷Fe) of powdered magnetite have been undertaken between 120 K and 880 K. Below the magnetic transition temperature (T _C=839.5 K) three six-line patterns have been fitted to our experimental spectra. The broadening of the B-pattern is explained by two magnetically non-equivalent B-site irons, suggesting broadening due to electron hopping to be negligible. In the paramagnetic state the electric quadrupole splittings of iron at A-and B-sites are found to be constant, independent of temperature, having the values zero and 0.16 mm/s, respectively. The centroid shifts, on the other hand, show above 700 K large deviations from the calculated second order Doppler shift. It is proposed that the deviations arise from a variation in band overlap. The temperature variation of the magnetic fields is found to be proportional to the sublattice magnetization. The difference in the magnetic fields at the two non-equivalent B-sites is measured to be 1.1 T at 310 K.     

Verwey transition in magnetite at high pressure: A new quantum critical point at the onset of metallization

We provide a detailed physical discussion of the existence of a quantum critical point (QCP) at the metallization threshold of an almost stoichiometric magnetite, with the critical pressure . A presence of an additional crossover or a critical line separating metallic and semiconducting states is proposed. A connection of the critical behavior to that of a spinless-fermion model with coupling of fermions to the lattice distortion is outlined.     

Isotope and pressure effects on the Verwey temperature of magnetite

The isotope and pressure effects on the Verwey temperature of magnetite have been explained with the assumption that the transition is due to the condensation of an active phonon mode which is responsible for its transport properties in the high-temperature phase.     

Ferrimagnetic/ferroelastic domain interactions in magnetite below the Verwey transition: Part II. Micromagnetic and image simulations

Micromagnetic simulations have been used to explore the interaction between ferrimagnetic domain walls (DWs) and ferroelastic twin walls (TWs) below the Verwey transition in magnetite (Fe₃O₄). Simulations were performed using a thin-foil geometry in order to replicate the domain patterns observed experimentally using transmission electron microscopy. The magnetic microstructure is shown to be highly sensitive to the physical dimensions and crystallographic orientation of the foil, the spatial distribution and crystallographic classification of the TWs and the temperature/field history of the sample. A method to calculate the phase shift of a beam of electrons passing through the micromagnetic simulations is applied. The resulting phase maps provide a robust interpretation of experimental images obtained using Fresnel-mode Lorentz microscopy and off-axis electron holography. The interaction between ferrimagnetic and ferroelastic DWs during field cycling provides an explanation for the low-temperature ‘field-memory effect’ in magnetite.     

Spin moment over 10-300 K and delocalization of magnetic electrons above the Verwey transition in magnetite

In order to probe the magnetic ground state, we have carried out temperature-dependent magnetic Compton scattering experiments on an oriented single crystal of magnetite (Fe₃O₄), together with the corresponding first-principles band theory computations to gain insight into the measurements. An accurate value of the magnetic moment μ_S associated with unpaired spins is obtained directly over the temperature range of 10-300 K. μ_S is found to be non-integral and to display an anomalous behavior with the direction of the external magnetic field near the Verwey transition. These results reveal how the magnetic properties enter the Verwey energy scale via spin-orbit coupling and the geometrical frustration of the spinel structure, even though the Curie temperature of magnetite is in excess of 800 K. The anisotropy of the magnetic Compton profiles increases through the Verwey temperature T_v and indicates that magnetic electrons in the ground state of magnetite become delocalized on Fe B-sites above T_v.