Trimeron-phonon coupling in magnetite

Abstract

Using density functional theory, we study the lattice dynamical properties of magnetite (Fe3O4) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and phonon density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic Cc structure revealing the strong coupling between charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise which, remarkably, can be understood assuming that the strong trimeron-phonon coupling can be extended above the Verwey transition, with lattice dynamics influenced by the short-range trimeron order instead of the average cubic structure. Our results establish the validity of trimerons (and trimeron-phonon coupling) in explaining the physics of magnetite much beyond their original formulation.

Frenkel pair formation energy for cubic Fe$_3$O$_4$ in DFT+U calculations

“…Also, there are no significant structural changes after atomic relaxation at a fixed lattice constant. However, the cation magnetic moments in the DFT+U symmetric case are higher than in DFT, and they are similar to the data reported recently 23,35 .…”

“…At a sufficiently high Hubbard parameter U eff the asymmetric ground state gives the differences between di-and trivalent B-cations and a band gap that is confirmed in calculations with hybrid functionals 27 . At the same time, no differences between di-and trivalent B-cations and no band gap are found in other recent DFT+U studies of the magnetite cubic phase 23,35 . This may indicate that the ground state obtained within the symmetric ansatz for electronic structure was used in these studies (the authors did not provide the details).…”

Electronic phase separation: Recent progress in the old problem

“…Lattice symmetry is unchanged but different strains from the electronic orders probably drive the phase separation. Indeed, as it is shown in in [176], the trimeron-phonon interaction is rather strong, thus determining the specific features of the ground state. However, for the phase separation in charge ordered materials, a deviation from the stoichiometry may be needed [177].…”

“…Then, it is convenient to pass to the momentum representation of Hamiltonian (176). As a result, we find [30,64]…”

Magnetism and the Trimeron Bond

“… 27 Recent phonon calculations for the Cc structure have shown good agreement with inelastic neutron, X-ray, and nuclear scattering data, revealing strong trimeron–phonon coupling, especially for trimerons oriented parallel to the axes of the monoclinic Cc cell. 28 …”