Magnetism and the Trimeron Bond

First-Principles Calculations of Magnetite (Fe3O4) above the Verwey Temperature by Using Self-Consistent DFT + U + V

In this report, we have used the DFT + U + V approach, an extension of the DFT + U approach that takes into account both on-site and intersite interactions, to simulate structural, magnetic, and electronic properties together with the Fe and O K-edge XAS spectra of Fe3O4 above the Verwey temperature (Tv). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + U + V to DFT, DFT + U, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard U value for Feoct and Fetet at the DFT + U level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + U and DFT + U + V). The resulting Hubbard U and V parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + U + V can improve the structural, magnetic, and electronic properties of Fe3O4 compared to approximate DFT and DFT + U. In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe3O4 above Tv, since the Fermi level is found in the t2g band with a Feoct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe3O4 above the Tv.

Oxidation-State Dynamics and Emerging Patterns in Magnetite

Magnetite is an important mineral with many interesting applications related to its magnetic, electrical, and thermal properties. Typically studied by electronic structure calculations, these methods are unable to capture the complex ion dynamics at relevant temperatures, time, and length scales. We present a hybrid Monte Carlo/molecular dynamics (MC/MD) method based on iron oxidation-state swapping for accurate atomistic modeling of bulk magnetite, magnetite surfaces, and nanoparticles that captures the complex ionic dynamics. By comparing the oxidation-state patterns with those obtained from density functional theory, we confirmed the accuracy of our approach. Lattice distortions leading to the stabilization of excess charges and a critical surface thickness at which the oxidation states transition from ordered to disordered were observed. This simple yet efficient approach paves the way for elucidating aspects of oxidation-state ordering of inverse spinel structures in general and battery materials in particular.

Redox phase transformations in magnetite nanoparticles: impact on their composition, structure and biomedical applications

Magnetite nanoparticles (NPs) are one of the most investigated nanomaterials so far and modern synthesis methods currently provide an exceptional control of their size, shape, crystallinity and surface functionalization. These advances have enabled their use in different fields ranging from environmental applications to biomedicine. However, several studies have shown that the precise composition and crystal structure of magnetite NPs depend on their redox phase transformations, which have a profound impact on their physicochemical properties and, ultimately, on their technological applications. Although the physical mechanisms behind such chemical transformations in bulk materials have been known for a long time, experiments on NPs with large surface-to-volume ratios have revealed intriguing results. This article is focused on reviewing the current status of the field. Following an introduction on the fundamental properties of magnetite and other related iron oxides (including maghemite and wüstite), some basic concepts on the chemical routes to prepare iron oxide nanomaterials are presented. The key experimental techniques available to study phase transformations in iron oxides, their advantages and drawbacks to the study of nanomaterials are then discussed. The major section of this work is devoted to the topotactic oxidation of magnetite NPs and, in this regard, the cation diffusion model that accounts for the experimental results on the kinetics of the process is critically examined. Since many synthesis routes rely on the formation of monodisperse magnetite NPs via oxidation of wüstite counterparts, the modulation of their physical properties by crystal defects arising from the oxidation process is also described. Finally, the importance of a precise control of the composition and structure of magnetite-based NPs is discussed and its role in their biomedical applications is highlighted.

Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates

The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo₄¹³⁺ tetrahedron has been postulated as single-configuration a₁² e⁴ t₂⁵, where a₁, e, and t₂ are symmetry-adapted linear combinations of single-site Mo t_2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a₁² e⁴ t₂⁵ configuration. While spin-orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin-orbit operator and the g factors deviate from figures describing nominal t⁵ j_eff = 1/2 moments. As such, our data documents the dressing of a spin-orbit j_eff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials.

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.