Origin of the Verwey transition in magnetite: Group theory, electronic structure, and lattice dynamics study

Abstract

The Verwey phase transition in magnetite has been analyzed using the group theory methods. It is found that two order parameters with the symmetries X3 and ∆5 induce the structural transformation from the high-temperature cubic to the low-temperature monoclinic phase. The coupling between the order parameters is described by the Landau free energy functional. The electronic and crystal structure for the cubic and monoclinic phases were optimized using the ab initio density functional method. The electronic structure calculations were performed within the generalized gradient approximation including the on-site interactions between 3d electrons at iron ions -the Coulomb element U and Hund's exchange J. Only when these local interactions are taken into account, the phonon dispersion curves, obtained by the direct method for the cubic phase, reproduce the experimental data. It is shown that the interplay of local electron interations and the coupling to the lattice drives the phonon order parameters and is responsible for the opening of the gap at the Fermi energy. Thus, it is found that the metal-insulator transition in magnetite is promoted by local electron interactions, which significantly amplify the electron-phonon interaction and stabilize weak charge order coexisting with orbital order of the occupied t2g states at Fe ions. This provides a scenario to understand the fundamental problem of the origin of the Verwey transition in magnetite.

Probing the non-equilibrium transient state in magnetite by a jitter-free two-color X-ray pump and X-ray probe experiment

“…23: It is a result of local destruction of electronic order induced by secondary excitations. We note that the structural relaxation, which is expected to occur on times of $⪆$105 fs and $⪆$65 fs, 28,29 is not observable in our data, e.g., as a second time scale. In an earlier experiment, we found that when probing the (0 0 $\frac{1}{2}$) peak at the Fe- L 2,3 resonance, i.e., when sensitive to electronic order like in the present experiment, structural relaxation is visible as a shift of the peak position on the detector 23 .…”

“…Indeed, sub-300 fs structural dynamics have also been found in other transition-metal oxides 26,27 . For the structural part of the Verwey transition, the dominant Δ 5 und X 3 phonons 28,29 allow us to estimate a structural relaxation time, which we assume to be at least of the order of one quarter of their phonon oscillation period, yielding $\ge$ 105 fs and $\ge$ 65 fs, respectively 30 . These time scales also define the temporal resolution needed to observe dynamical decoupling.…”

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

“…Different U eff values have been proposed for Fe 3 d orbitals in different materials ( e.g . a much larger U eff value of 3.2 eV was used for magnetite31). The U eff value is also dependent on the exchange correlation functional used32.…”

Structural transformation in magnetite below the Verwey transition

“…Despite the fact that this structure is only a first approach, accounting for only a quarter of the actual cell, recent calculations still use it to explain the Verwey transition within a scheme of pseudo-Fe 2+ /Fe 3+ charge and orbital orderings. [14][15][16][17][18] To sum up, the lack of an accurate determination of the magnetite structure below T V has obviated a reliable characterization of the CO developed at the metal-insulator transition, if any. This is because of the enormous difficulty involved in solving its crystal structure at low temperature.…”