Charge-orbital ordering and Verwey transition in magnetite

Ultrafast generation of hidden phases via energy-tuned electronic photoexcitation in magnetite

Phase transitions occurring in nonequilibrium conditions can evolve through high-energy intermediate states inaccessible via equilibrium adiabatic conditions. Because of the subtle nature of such hidden phases, their direct observation is extremely challenging and requires simultaneous visualization of matter at subpicoseconds and subpicometer scales. Here, we show that a magnetite crystal in the vicinity of its metal-to-insulator transition evolves through different hidden states when controlled via energy-tuned ultrashort laser pulses. By directly monitoring magnetite's crystal structure with ultrafast electron diffraction, we found that upon near-infrared (800 nm) excitation, the trimeron charge/orbital ordering pattern is destroyed in favor of a phase-separated state made of cubic-metallic and monoclinic-insulating regions. On the contrary, visible light (400 nm) activates a photodoping charge transfer process that further promotes the long-range order of the trimerons by stabilizing the charge density wave fluctuations, leading to the reinforcement of the monoclinic insulating phase. Our results demonstrate that magnetite's structure can evolve through completely different metastable hidden phases that can be reached long after the initial excitation has relaxed, breaking ground for a protocol to control emergent properties of matter.

Verwey transition as evolution from electronic nematicity to trimerons via electron-phonon coupling

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step toward controlling material's properties. Since the proposal of charge order-induced MIT in magnetite Fe3O4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive. Recently, a trimeron order was found in the low-temperature structure of Fe3O4; however, the expected transition entropy change in forming trimeron is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here, we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature structure of bulk Fe3O4 and that, upon cooling, a competitive intertwining of charge and lattice orders arouses the Verwey transition. Our findings discover an unconventional type of electronic nematicity in correlated materials and offer innovative insights into the transition mechanism in Fe3O4 via the electron-phonon coupling.

Surface-Mediated Production of Complexed •OH Radicals and FeO Species as a Mechanism for Iron Oxide Peroxidase-Like Nanozymes

Fe₃ O₄ nanoparticles (NPs) with intrinsic peroxidase-like properties have attracted significant interest, although limited information is available on the definite catalytic mechanism. Here, it is shown that both complexed hydroxyl radicals (•OH) and high-valent FeO species are attributed primarily to the peroxidase-like catalytic activity of Fe₃ O₄ NPs under acid conditions rather than only being caused by free •OH radicals generated through the iron-driven Fenton/Haber-Weiss reactions as previously thought. The low energy barrier of OO bond dissociation of H₂ O₂ /•OOH (0.14 eV) and the high oxidation activity of surface FeO (0 eV) due to the reduced state of Fe on the surface of Fe₃ O₄ NPs thermodynamically favor both the •OH and FeO pathways. By contrast, high-valent FeO species are the key intermediates in the catalytic cycles of natural peroxidase enzymes. Moreover, it is demonstrated that the enzyme-like activity of Fe₃ O₄ NPs can be rationally regulated by modulating the size, surface structure, and valence of active metal atoms in the light of this newly proposed nanozyme catalytic mechanism.

Density Functional Studies on the Atomistic Structure and Properties of Iron Oxides: A Parametric Study

With the aim to find the best simulation routine to accurately predict the ground-state structures and properties of iron oxides (hematite, magnetite, and wustite) using density functional theory (DFT) with Hubbard-U correction, a significant amount of DFT calculations were conducted to investigate the influence of various simulation parameters (energy cutoff, K-point, U value, magnetization setting, smearing value, etc.) and pseudopotentials on the structures and properties of iron oxides. With optimized simulation parameters, the obtained equation of state, lattice constant, bulk moduli, and band gap is much closer to the experimental values compared with previous studies. Due to the strong coupling between the 2p orbital of O and the 3d orbital of Fe, it was found that Hubbard-U correction obviously improved the results for all three kinds of iron oxides including magnetite which has not yet been tested with U correction before, but the U value should be different for different oxides (3 ev, 4 ev, 4 ev for hematite, magnetite, and wustite, respectively). Two kinds of spin magnetism settings for FeO are considered, which should be chosen according to different calculation purposes. The detailed relationship between the parameter settings and the atomic structures and properties were analyzed, and the general principles for future DFT calculation of iron oxides were provided.

Frenkel pair formation energy for cubic Fe3O4in DFT + U calculations

The cubic phase of magnetite is stabilized above the Verwey transition temperature of about 120 K via a complex electron-phonon interaction that is still not very well understood. In this work using the DFT + U method we describe our attempt to calculate point defect formation energies for this cubic phase in the static approximation. The electronic structure calculations and atomic relaxation peculiarities are discussed in this context. Only the cubic phase model with a small band gap and charge disproportionation (Fe²⁺/Fe³⁺) gives an adequate point defect formation energies, not the semi-metallic model. The relaxation of the local defect atomic structure and the relaxation of the surrounding crystal matrix are analyzed. Point defects cause only local perturbations of atomic positions and charge-orbital order. After analysis of the supercell size effects for up to 448 atoms, we justify the use of small supercells with 56 atoms to make calculations for the cubic phase. The extensive experimental results of Dieckmannet alon defects in magnetite at high temperature are deployed for comparison of our DFT + U results on Frenkel pair formation energies.

Verwey-Type Charge Ordering and Site-Selective Mott Transition in Fe4O5 under Pressure

The metal-insulator transition driven by electronic correlations is one of the most fundamental concepts in condensed matter. In mixed-valence compounds, this transition is often accompanied by charge ordering (CO), resulting in the emergence of complex phases and unusual behaviors. The famous example is the archetypal mixed-valence mineral magnetite, Fe3O4, exhibiting a complex charge-ordering below the Verwey transition, whose nature has been a subject of long-time debates. In our study, using high-resolution X-ray diffraction supplemented by resistance measurements and DFT+DMFT calculations, the electronic, magnetic, and structural properties of recently synthesized mixed-valence Fe4O5 are investigated under pressure to ∼100 GPa. Our calculations, consistent with experiment, reveal that at ambient conditions Fe4O5 is a narrow-gap insulator characterized by the original Verwey-type CO. Under pressure Fe4O5 undergoes a series of electronic and magnetic-state transitions with an unusual compressional behavior above ∼50 GPa. A site-dependent collapse of local magnetic moments is followed by the site-selective insulator-to-metal transition at ∼84 GPa, occurring at the octahedral Fe sites. This phase transition is accompanied by a 2+ to 3+ valence change of the prismatic Fe ions and collapse of CO. We provide a microscopic explanation of the complex charge ordering in Fe4O5 which "unifies" it with the behavior of two archetypal examples of charge- or bond-ordered materials, magnetite and rare-earth nickelates (RNiO3). We find that at low temperatures the Verwey-type CO competes with the "trimeron"/"dimeron" charge ordered states, allowing for pressure/temperature tuning of charge ordering. Summing up the available data, we present the pressure-temperature phase diagram of Fe4O5.

Cohesive properties of PbBi/Fe3O4 and PbBi/(Fe,Cr)3O4 interfaces

First principles calculations reveal that the effects of PbBi on the cohesive properties of Fe₃O₄ and (Fe,Cr)₃O₄: PbBi can reduce the cohesive strength of the oxides, and the contents of O and Cr on the O-terminated oxide side play a significant role in the cohesive properties of the PbBi/Fe₃O₄ and PbBi/(Fe,Cr)₃O₄ interfaces. Specifically, the performance of oxidation decreases more significantly under the conditions of insufficient oxygen, and a high ratio of Cr of the subsurface of oxides can lead to the reduction of the cohesive properties of O-terminated interfaces. Calculations also show that the Pb-O-terminated interfaces are energetically favorable and are more stable than the Bi-O-terminated surfaces due to the strong bond of Pb-O, while the Bi-Cr and Bi-Fe interfaces are more stable than the Pb-Cr and Pb-Fe interfaces. Moreover, it is found that the stability and cohesion of the PbBi/Fe₃O₄ and PbBi/(Fe,Cr)₃O₄ interfaces will decrease when the oxygen concentration is insufficient or the degree of wetting of PbBi of oxides is low, and the PbBi/Fe₃O₄ interface is more sensitive to these conditions. The bond-dissociation energies and electronic structures provide a deep understanding of various interface properties, and the obtained results are in good agreement with experimental measurements in the literature.

Localized surface electromagnetic waves in CrI3-based magnetophotonic structures

Resulting from strong magnetic anisotropy two-dimensional ferromagnetism was recently shown to be stabilized in chromium triiodide, CrI₃, in the monolayer limit. While its properties remain largely unexplored, it provides a unique material-specific platform to unveil its electromagnetic properties associated with coupling of modes. Indeed, trigonal symmetry in the presence of out-of-plane magnetization results in a non-trivial structure of the conductivity tensor, including the off-diagonal terms. In this paper, we study the surface electromagnetic waves localized in a CrI₃-based structure using the results of ab initio calculations for the CrI₃ conductivity tensor. In particular, we provide an estimate for the critical angle corresponding to the surface plasmon polariton generation in the Kretschmann-Raether configuration by a detailed investigation of reflectance spectrum as well as the magnetic field distribution for different CrI₃ layer thicknesses. We also study the bilayer structure formed by two CrI₃ layers separated by a SiO₂ spacer and show that the surface plasmon resonance can be achieved at the interface between CrI₃ and air depending on the spacer thickness.

Heat capacity signature of frustrated trimerons in magnetite

Recently it has been proposed that the long-range electronic order formed by trimerons in magnetite should be frustrated due to the great degeneracy of arrangements linking trimerons. This result has important consequences as charge ordering from the condensed minority band electrons leads to a complex 3D antiferro orbital order pattern. Further more, the corner sharing tetrahedra structure of spinel B-sites supports frustration for antiferromagnetic alignments. Therefore frustration due to competing interactions will itself induce disorder and very likely frustration in the spin orientations. Here we present very low temperature specific heat data that show two deviations to the magnons and phonons contributions, that we analyze in terms of Schottky-type anomalies. The first one is associated with the thermal activation across both ferroelastic twin and ferromagnetic anti-phase domains. The second Schottky-type anomaly displays an inverse (1/H) field dependence which is a direct indication of the disordered glassy network with macroscopically degenerated singular ground states.

Orbital ordering and magnetism in layered Perovskite Ruthenate Sr2RuO4

Local density approximation plus on-site Coulomb interaction U electronic structure calculations reveal that layered perovskite oxide Sr₂RuO₄ exhibits the ferromagnetic (FM) half-metallic ground state, which is nearly degenerate with the antiferromagnetic (AFM) phase with a slightly higher total energy. The nearly degenerate FM/AFM total energies provide a reasonable explanation for the experimentally observed spin-fluctuation. In addition, a dumbbell-shape 4d − t_2g recombined d_xz − d_yz orbital ordering on the Ru sublattice is obtained owing to the on-site Coulomb interaction U associated with the elongated RuO₆ octahedron local structure. The discovered orbital ordering is robust against the spin-orbit interaction as well as the surface terminations. Our findings unravel the on-site Coulomb correlation as the driving force of the Ru-4d orbital ordering as well as the inherent magnetic degeneracy.

Shaping Magnetite Nanoparticles from First Principles

Iron oxide magnetic nanoparticles (NPs) are stimuli-responsive materials at the forefront of nanomedicine. Their realistic finite temperature simulations are a formidable challenge for first-principles methods. Here, we use density functional tight binding to open up the required time and length scales and obtain global minimum structures of Fe_{3}O_{4} NPs of realistic size (1400 atoms, 2.5 nm) and of different shapes, which we then refine with hybrid density functional theory methods to accomplish proper electronic and magnetic properties, which have never been accurately described in simulations. On this basis, we develop a general empirical formula and prove its predictive power for the evaluation of the total magnetic moment of Fe_{3}O_{4} NPs. By converting the total magnetic moment into the macroscopic saturation magnetization, we rationalize the experimentally observed dependence with shape. We also reveal interesting reconstruction mechanisms and unexpected patterns of charge ordering.

Electronic transport properties and magnetoresistance in the Fe3O4/SiO2/p-Si heterostructure with an in-plane current geometry

In traditional electronic devices, the electronic charge is manipulated to realize different functions. The fascinating control of electronic spin in conventional semiconductors increases the probability of occurrence of spin-dependent transport properties. Herein, the injection of electronic spin into a Si wafer with in-plane geometry was achieved by Fe3O4, which acted as a spin injector. At high temperatures, the resistivity of Fe3O4 is far less than that of a p-Si wafer. Moreover, above 190 K, the current-voltage (I-V) characteristic and magnetoresistance (MR) of the proposed heterostructure are dominated by the intrinsic properties of a polycrystalline Fe3O4 film, and the in-plane current flows in the Fe3O4 layer. Due to the increased resistivity of Fe3O4 at low temperatures, the in-plane conductive channel gradually switches from Fe3O4 to Si. The spin injection from Fe3O4 results in a spin-polarized space charge region in p-Si. The heterostructure shows an MR of up to -76.1% at 90 K due to the spin-dependent transport of electrons in p-Si. With a further decrease in temperature, the I-V characteristic of the heterostructure shows negative differential resistance below 80 K due to band bending at the Fe3O4/SiO2/p-Si interface.

DFT insight into the effect of potassium on the adsorption, activation and dissociation of CO2 over Fe-based catalysts

Catalytic conversion of CO2 including hydrogenation has attracted great attention as a method for chemical fixation of CO2 in combination with other techniques such as CO2 capture and storage. Potassium is a well-known promotor for many industrial catalytic processes such as in Fischer-Tropsch synthesis. In this work, we performed density functional theory (DFT) calculations to investigate the effect of potassium on the adsorption, activation, and dissociation of CO2 over Fe(100), Fe5C2(510) and Fe3O4(111) surfaces. The function of K was analyzed in terms of electronic interactions between co-adsorbed CO2 and K-surfaces which showed conspicuous promotion in the presence of K of the adsorption and activation of CO2. The adsorption strength of CO2 on these surfaces ranks as oct2-Fe3O4(111) > Fe(100) > Fe5C2(510). Generally, we observed a direct proportional correlation between the adsorption strength and the charges on the adsorbates. Adding K on the catalyst surface also reduces the kinetic barrier for CO2 dissociation. CO2 dissociation is more facile to occur on Fe(100) and Fe5C2(510) in the presence of K whereas the Fe3O4(111) surfaces impede CO2 dissociation regardless of the existence of K. Instead, a stable CO3- species is formed upon CO2 adsorption on Fe3O4(111) which will be directly hydrogenated when sufficient H* are available on the surface. Our results highlight the origin of the promotion effect of potassium and provide insight for the future design of K-promoted Fe-based catalysts for CO2 hydrogenation.

Giant thermal hysteresis in Verwey transition of single domain Fe3O4 nanoparticles

Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe₃O₄ is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe₃O₄ nanoparticles exhibits size-dependent thermal hysteresis in magnetization, ⁵⁷Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience.

Verwey-type charge ordering transition in an open-shell p-electron compound

The Verwey transition in Fe₃O₄, a complex structural phase transition concomitant with a jump in electrical conductivity by two orders of magnitude, has been a benchmark for charge ordering (CO) phenomena in mixed-valence transition metal materials. CO is of central importance, because it frequently competes with functional properties such as superconductivity or metallic ferromagnetism. However, the CO state in Fe₃O₄ turned out to be complex, and the mechanism of the Verwey transition remains controversial. We demonstrate an archetypical Verwey-type transition in an open p-shell anionic mixed-valence compound using complementary diffraction and spectroscopic techniques. In Cs₄O₆, a phase change from a cubic structure with a single crystallographic site for the molecular O₂^x- building units to a tetragonal structure with ordered superoxide O₂^- and peroxide O₂^2- entities is accompanied by a drastic drop in electronic conductivity and molecular charge fluctuation rates. The simple CO pattern of molecular units and the lack of magnetic order suggest Cs₄O₆ as a model system for disentangling the complex interplay of charge, lattice, orbital, and spin degrees of freedom in Verwey-type CO processes.

Water adsorption on the Fe3O4(111) surface: dissociation and network formation

Water adsorption on Fe₃O₄(111) is studied in detail using infrared spectroscopy, temperature programmed desorption, micro-calorimetry and density functional theory.

The structural, magnetic and optical properties of TMn@(ZnO)42 (TM = Fe, Co and Ni) hetero-nanostructure

The magnetic transition-metal (TM) @ oxide nanoparticles have been of great interest due to their wide range of applications, from medical sensors in magnetic resonance imaging to photo-catalysis. Although several studies on small clusters of TM@oxide have been reported, the understanding of the physical electronic properties of TM_n@(ZnO)₄₂ is far from sufficient. In this work, the electronic, magnetic and optical properties of TM_n@(ZnO)₄₂ (TM = Fe, Co and Ni) hetero-nanostructure are investigated using the density functional theory (DFT). It has been found that the core-shell nanostructure Fe₁₃@(ZnO)₄₂, Co₁₅@(ZnO)₄₂ and Ni₁₅@(ZnO)₄₂ are the most stable structures. Moreover, it is also predicted that the variation of the magnetic moment and magnetism of Fe, Co and Ni in TM_n@ZnO₄₂ hetero-nanostructure mainly stems from effective hybridization between core TM-3d orbitals and shell O-2p orbitals, and a magnetic moment inversion for Fe₁₅@(ZnO)₄₂ is investigated. Finally, optical properties studied by calculations show a red shift phenomenon in the absorption spectrum compared with the case of (ZnO)₄₈.

Band Gap in Magnetite above Verwey Temperature Induced by Symmetry Breaking

Magnetite exhibits a famous phase transition, called Verwey transition, at the critical temperature T_V of about 120 K. Although numerous efforts have been devoted to the understanding of this interesting transition, up to now, it is still under debate whether a charge ordering and a band gap exist in magnetite above T_V. Here, we systematically investigate the charge ordering and the electronic properties of magnetite in its cubic phase using different methods based on density functional theory: DFT+U and hybrid functionals. Our results show that, upon releasing the symmetry constraint on the density but not on the geometry, charge disproportionation (Fe²⁺/Fe³⁺) is observed, resulting in a band gap of around 0.2 eV at the Fermi level. This implies that the Verwey transition is probably a semiconductor-to-semiconductor transition and that the conductivity mechanism above T_V is small polaron hopping.

Survival of Verwey transition in gadolinium-doped ultrasmall magnetite nanoparticles

We have demonstrated that the Verwey transition, which is highly sensitive to impurities, survives in anisotropic Gd-doped magnetite nanoparticles. Transmission electron microscopy analysis shows that the nanoparticles are uniformly distributed. X-ray photoelectron spectroscopy and EDS mapping analysis confirm Gd-doping on the nanoparticles. The Verwey transition of the Gd-doped magnetite nanoparticles is robust and the temperature dependence of the magnetic moment (zero field cooling and field cooling) shows the same behaviour as that of the Verwey transition in bulk magnetite, at a lower transition temperature (∼110 K). In addition, irregularly shaped nanoparticles do not show the Verwey transition whereas square-shaped nanoparticles show the transition. Mössbauer spectral analysis shows that the slope of the magnetic hyperfine field and the electric quadrupole splitting change at the same temperature, meaning that the Verwey transition occurs at ∼110 K. These results would provide new insights into understanding the Verwey transition in nano-sized materials.

Jahn-Teller distortion driven magnetic polarons in magnetite

The first known magnetic mineral, magnetite, has unusual properties, which have fascinated mankind for centuries; it undergoes the Verwey transition around 120 K with an abrupt change in structure and electrical conductivity. The mechanism of the Verwey transition, however, remains contentious. Here we use resonant inelastic X-ray scattering over a wide temperature range across the Verwey transition to identify and separate out the magnetic excitations derived from nominal Fe²⁺ and Fe³⁺ states. Comparison of the experimental results with crystal-field multiplet calculations shows that the spin–orbital dd excitons of the Fe²⁺ sites arise from a tetragonal Jahn-Teller active polaronic distortion of the Fe²⁺O₆ octahedra. These low-energy excitations, which get weakened for temperatures above 350 K but persist at least up to 550 K, are distinct from optical excitations and are best explained as magnetic polarons.

The Verwey transition of magnetite is complex due to the coexistence of strong correlations and electron-phonon coupling. Here, the authors use resonant inelastic X-ray scattering to show evidence for magnetic polarons in magnetite and provide insight into the nature of the transition.

Surface Termination of Fe3O4(111) Films Studied by CO Adsorption Revisited

Although the (111) surface of Fe₃O₄ (magnetite) has been investigated for more than 20 years, substantial controversy remains in the literature regarding the surface termination proposed based on structural and adsorption studies. The present article provides density functional theory results that allow to rationalize experimental results of infrared reflection-absorption spectroscopy and temperature-programmed desorption studies on CO adsorption, thus leading to a unified picture in which the Fe₃O₄(111) surface is terminated by a ¹/₄ monolayer of tetrahedrally coordinated Fe³⁺ ions on top of a close-packed oxygen layer as previously determined by low energy electron diffraction. However, surface defects play a crucial role in adsorption properties and may dominate chemical reactions on Fe₃O₄(111) when exposed to the ambient.

Biaxial strain effect induced electronic structure alternation and trimeron recombination in Fe3O4

The Verwey transition in Fe₃O₄ is the first metal-insulator transition caused by charge ordering. However, the physical mechanism and influence factors of Verwey transition are still debated. Herewith, the strain effects on the electronic structure of low-temperature phase (LTP) Fe₃O₄ with P2/c and Cc symmetries are investigated by first-principles calculations. LTP Fe₃O₄ with each space group has a critical strain. With P2/c, Fe₃O₄ is sensitive to the compressive strain, but it is sensitive to tensile strain for Cc. In the critical region, the band gap of LTP Fe₃O₄ with both two symmetries linearly increases with strain. When strain exceeds the critical value, DOS of spin-down t_2g electron at Fe(B4) with P2/c and Fe(B42) with Cc changes between d_x2_-y2 and d_xz + d_yz. The trimerons appear in Cc can be affected by strain. With a compressive strain, the correlation of trimeron along x and y axes is strengthened, but broken along the face diagonal of Fe_B4O₄, which is opposite at the tensile strains. The results suggest that the electronic structure of Fe₃O₄ is tunable by strain. The narrower or wider band gap implies a lower or higher transition temperature than its bulk without strains, which also gives a glimpse of the origin of charge-orbital ordering in Fe₃O₄.

The influence of liquid Pb-Bi on the anti-corrosion behavior of Fe3O4: a first-principles study

In this work, the influence of Pb and Bi atoms on the anti-corrosion behavior of the oxide film (Fe3O4) formed on steel surface is investigated based on first-principles calculations. Through calculations of the formation energies, we find that Pb and Bi atoms can promote the formation of point defects, such as interstitial atoms and vacancies in Fe3O4. Besides, the effects of the concentration of Pb (or Bi) and pressure on the formation of these defects are also studied. Our results depict that a high density of Pb (or Bi) and compression pressure can promote the formation of defects in Fe3O4 significantly. Furthermore, the energy barriers for Pb and Bi atom migration in Fe3O4 are also estimated using the climbing image nudge elastic band (CI-NEB) method, which implies that Pb and Bi can diffuse more easily in Fe3O4 compared to Fe. Our results reveal the underlying mechanism of how Pb and Bi influence the anti-corrosion ability of oxide films in an accelerate driven system (ADS). It is instructive for improving the corrosion resistance of the oxide films in the ADS.

Reversed ageing of Fe3O4 nanoparticles by hydrogen plasma

Magnetite (Fe₃O₄) nanoparticles suffer from severe ageing effects when exposed to air even when they are dispersed in a solvent limiting their applications. In this work, we show that this ageing can be fully reversed by a hydrogen plasma treatment. By x-ray absorption spectroscopy and its associated magnetic circular dichroism, the electronic structure and magnetic properties were studied before and after the plasma treatment and compared to results of freshly prepared magnetite nanoparticles. While aged magnetite nanoparticles exhibit a more γ-Fe₂O₃ like behaviour, the hydrogen plasma yields pure Fe₃O₄ nanoparticles. Monitoring the temperature dependence of the intra-atomic spin dipole contribution to the dichroic spectra gives evidence that the structural, electronic and magnetic properties of plasma treated magnetite nanoparticles can outperform the ones of the freshly prepared batch.

Electronic structures of greigite (Fe3S4): A hybrid functional study and prediction for a Verwey transition

Greigite (Fe₃S₄) is a ferrimagnetic mineral with vital functions in both the bio-geochemical cycle and novel technological applications. However, the ground state electronic structure of this material has not been fully characterized by either experiment or theory. In the present study, ab initio calculations using the hybrid functional method have been performed to investigate the electronic structure and magnetic properties. It is found that the cubic structure observed under ambient temperature is a half metal and is metastable. A more stable monoclinic structure slightly distorted from the cubic form is found. The structural distortion is induced by charge ordering and associated with a metal-to-insulator transition, resulting in a semiconductive ground state with a bandgap of ~0.8 eV and a magnetic moment of 4 μB per formula unit. The results predict, similar to the magnetite (Fe₃O₄), a Verwey transition may exist in greigite, although it has not yet been observed experimentally.

Temperature Dependence of Magnetically Active Charge Excitations in Magnetite across the Verwey Transition

We study the electronic structure of bulk single crystals and epitaxial films of Fe_{3}O_{4}. Fe 2p core level spectra show clear differences between hard x-ray (HAX) and soft x-ray photoemission spectroscopy (PES). The bulk-sensitive spectra exhibit temperature (T) dependence across the Verwey transition, which is missing in the surface-sensitive spectra. By using an extended impurity Anderson full-multiplet model-and in contrast to an earlier peak assignment-we show that the two distinct Fe species (A and B site) and the charge modulation at the B site are responsible for the newly found double peaks in the main peak above T_{V} and its T-dependent evolution. The Fe 2p HAXPES spectra show a clear magnetic circular dichroism (MCD) in the metallic phase of magnetized 100-nm-thick films. The model calculations also reproduce the MCD and identify the contributions from magnetically distinct A and B sites. Valence band HAXPES shows a finite density of states at E_{F} for the polaronic half metal with a remnant order above T_{V} and a clear gap formation below T_{V}. The results indicate that the Verwey transition is driven by changes in the strongly correlated and magnetically active B-site electronic states, consistent with resistivity and optical spectra.

Layer-dependent dopant stability and magnetic exchange coupling of iron-doped MoS2 nanosheets

Using density-functional theory calculations including a Hubbard U term we explore structural stability, electronic and magnetic properties of Fe-doped MoS2 nanosheets. Unlike previous reports, the geometry and the stability of Fe dopant atoms in MoS2 nanosheets strongly depend on the chemical potential and the layer number of sheets. The substitution Fe dopant atoms at the Mo sites are energetically favorable in monolayer MoS2 and the formation of intercalated and substitutional Fe complexes are preferred in bilayer and multilayer ones under the S-rich regime that is a popular condition for the synthesis of MoS2 nanosheets. We find that the Fe dopants prefer to the ferromagnetic coupling in monolayer MoS2 and the antiferromagnetic coupling in bilayer and multilayer ones, suggesting the layer dependence of magnetic exchange coupling (MEC). The transition of MEC in Fe-doped MoS2 sheets induced by the change of layer number arises from the competition mechanism between the double-exchange and superexchange couplings. The findings provide a route to facilitate the design of MoS2-based diluted magnetic semiconductors and spintronic devices.

BaMn9II(VO4)6(OH)2: a homospin ferrimagnet with a broken spinel-lattice of B-sites

A new homospin ferrimagnet BaMn₉^II(VO₄)₆(OH)₂ exhibits a unique structural feature with a reverse triangular dipyramid Mn₇ spin lattice, in which such a lattice can be considered as a broken spin lattice of B-sites in spinel compounds.

The dipole moment of the spin density as a local indicator for phase transitions

The intra-atomic magnetic dipole moment - frequently called 〈T_z〉 term - plays an important role in the determination of spin magnetic moments by x-ray absorption spectroscopy for systems with nonspherical spin density distributions. In this work, we present the dipole moment as a sensitive monitor to changes in the electronic structure in the vicinity of a phase transiton. In particular, we studied the dipole moment at the Fe²⁺ and Fe³⁺ sites of magnetite as an indicator for the Verwey transition by a combination of x-ray magnetic circular dichroism and density functional theory. Our experimental results prove that there exists a local change in the electronic structure at temperatures above the Verwey transition correlated to the known spin reorientation. Furthermore, it is shown that measurement of the dipole moment is a powerful tool to observe this transition in small magnetite nanoparticles for which it is usually screened by blocking effects in classical magnetometry.

Electronic ferroelectricity induced by charge and orbital orderings

After the revival of the magnetoelectric effect which took place in the early 2000s, the interest in multiferroic materials displaying simultaneous presence of spontaneous long-range magnetic and dipolar order has motivated an exponential growth of research activity, from both the experimental and theoretical perspectives. Within this context, and relying also on the rigorous formulation of macroscopic polarization as provided by the Berry-phase approach, it has been possible to identify new microscopic mechanisms responsible for the appearance of ferroelectricity. In particular, it has been realized that electronic spin, charge and orbital degrees of freedom may be responsible for the breaking of the space-inversion symmetry, a necessary condition for the appearance of electric polarization, even in centrosymmetric crystal structures. In view of its immediate potential application in magnetoelectric-based devices, many efforts have been made to understand how magnetic orderings may lead to ferroelectric polarization, and to identify candidate materials. On the other hand, the role of charge and orbital degrees of freedom, which have received much less attention, has been predicted to be non-negligible in several cases. Here, we review recent theoretical advances in the field of so-called electronic ferroelectricity, focusing on the possible mechanisms by which charge- and/or orbital-ordering effects may cause the appearance of macroscopic polarization. Generally, a naive distinction can be drawn between materials displaying almost localized electrons and those characterized by a strong covalent character and delocalized electrons. As for the latter, an intuitive understanding of basic mechanisms is provided in the framework of tight-binding model Hamiltonians, which are used to shed light on unusual charge/orbital effects in half-doped manganites, whereas the case of magnetite will be thoroughly discussed in light of recent progress pointing to an electronic origin of its proposed ferroelectric and magnetoelectric properties.

Electronic structure near cationic defects in magnetite

We used the DFT + U method to describe the modification of the physical properties induced by cationic point defects in cubic magnetite Fe3O4. We considered the case of Fe vacancies and interstitial atoms in non-stoichiometric magnetite, and of Frenkel defects in a stoichiometric crystal. For each of these defects, we give results on the modification of the magnetic moment of atoms near the defect. We describe the local reorganization of the electric charge which is responsible for changes in the average oxidation degree of Fe atoms. We show that gap states, when they exist, do not destroy the half-metallic character of magnetite. Fe defects, however, change the filling of bands crossing the Fermi level and must be mostly responsible for a decrease in the magnetization.

Anharmonicity due to electron-phonon coupling in magnetite

We present the results of inelastic x-ray scattering for magnetite and analyze the energies and widths of the phonon modes with different symmetries in a broad range of temperature 125 < T < 293 K. The phonon modes with X(4) and Δ(5) symmetries broaden in a nonlinear way with decreasing T when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points, which suggests the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered by a combination of these experimental results with ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to the electron charge fluctuations condensing in the low-symmetry phase.

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

Symmetry of orbital order in Fe3O4 studied by Fe L(2,3) resonant x-ray diffraction

We studied the symmetry of the Fe 3d wave function in magnetite below the Verwey temperature T(V) with resonant soft-x-ray diffraction. Although the lattice structure of the low-temperature phase of Fe(3)O(4) is well described by the pseudo-orthorhombic Pmca with a slight monoclinic P2/c distortion, we find that the 3d wave function does not reflect the Pmca symmetry, and its distortion toward monoclinic symmetry is by far larger than that of the lattice. The result supports a scenario in which the Verwey transition involves the ordering of t(2g) orbitals with complex-number coefficients.

Structural distortion, charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X-ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high-quality Fe(3)O(4) single crystals and thin films grown on MgO by using resonant X-ray scattering at the Fe K-edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e(-) with [0 0 1] and [1 1 0] cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a-b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low-temperature crystal structure refined in the non-polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.

Magnetite (Fe3O4): a new variant of relaxor multiferroic?

The electric polarization, dielectric permittivity, magnetoelectric effect, heat capacity, magnetization and ac susceptibility of magnetite films and polycrystals were investigated. The electric polarization of magnetite films with saturation values between 4 and 8 μC cm(-2) was found to vanish between 32 and 38 K, but in polycrystals no phase transition was detected in this range by heat capacity. Both types of samples showed magnetoelectric effects at low temperatures below a frequency-dependent crossover. This is interpreted as arising from multiferroic relaxor behavior.

Charge order and three-site distortions in the Verwey structure of magnetite

The mineral magnetite (Fe(3)O(4)) undergoes a complex structural distortion and becomes electrically insulating at temperatures less than 125 kelvin. Verwey proposed in 1939 that this transition is driven by a charge ordering of Fe(2+) and Fe(3+) ions, but the ground state of the low-temperature phase has remained contentious because twinning of crystal domains hampers diffraction studies of the structure. Recent powder diffraction refinements and resonant X-ray studies have led to proposals of a variety of charge-ordered and bond-dimerized ground-state models. Here we report the full low-temperature superstructure of magnetite, determined by high-energy X-ray diffraction from an almost single-domain, 40-micrometre grain, and identify the emergent order. The acentric structure is described by a superposition of 168 atomic displacement waves (frozen phonon modes), all with amplitudes of less than 0.24 ångströms. Distortions of the FeO(6) octahedra show that Verwey's hypothesis is correct to a first approximation and that the charge and Fe(2+) orbital order are consistent with a recent prediction. However, anomalous shortening of some Fe-Fe distances suggests that the localized electrons are distributed over linear three-Fe-site units, which we call 'trimerons'. The charge order and three-site distortions induce substantial off-centre atomic displacements and couple the resulting large electrical polarization to the magnetization. Trimerons may be important quasiparticles in magnetite above the Verwey transition and in other transition metal oxides.

First-principles analysis of electron correlation, spin ordering and phonons in the normal state of FeSe 1-x

We present first-principles density-functional-theory-based calculations to determine the effects of the strength of on-site electron correlation, magnetic ordering, pressure and Se vacancies on phonon frequencies and electronic structure of FeSe(1 - x). The theoretical equilibrium structure (lattice parameters) of FeSe depends sensitively on the value of the Hubbard parameter U of on-site correlation and magnetic ordering. Our results suggest that there is a competition between different antiferromagnetic states due to comparable magnetic exchange couplings between first- and second-neighbor Fe sites. As a result, a short range order of stripe antiferromagnetic type is shown to be relevant to the normal state of FeSe at low temperature. We show that there is a strong spin-phonon coupling in FeSe (comparable to its superconducting transition temperature) as reflected in large changes in the frequencies of certain phonons with different magnetic ordering, which is used to explain the observed hardening of a Raman-active phonon at temperatures (∼100 K) where magnetic ordering sets in. The symmetry of the stripe antiferromagnetic phase permits an induced stress with orthorhombic symmetry, leading to orthorhombic strain as a secondary order parameter at the temperature of magnetic ordering. The presence of Se vacancies in FeSe gives rise to a large peak in the density of states near the Fermi energy, which could enhance the superconducting transition temperature within the BCS-like picture.