First-principles determined charge and orbital interactions in Fe$_3$O$_4$

TL;DR

This paper develops a DFT+U-based energy model to analyze charge and orbital interactions in Fe$_3$O$_4$, revealing a complex energy landscape with a new proposed ground state structure.

Contribution

It introduces a novel effective energy model for charge and orbital interactions in transition metal oxides, specifically applied to magnetite, incorporating both electronic and lattice effects.

Findings

Proposes a new ground state structure for Fe$_3$O$_4$.

Models interactions using electrostatics and Kugel-Khomskii exchange.

Identifies a complex energy landscape with frustration effects.

Abstract

The interactions between charge and orbitally ordered $d$-electrons are important in many transition metal oxides. We propose an effective energy model for such interactions, parameterized with DFT+U calculations, so that energy contributions of both electronic and lattice origin can be simultaneously accounted for. The model is applied to the low-temperature phase of magnetite, for which we propose a new ground state structure. The effective interactions on the B-lattice of Fe$_3$O$_4$ can be interpreted in terms of electrostatics and short-range Kugel-Khomskii exchange coupling. The frustration between optimal charge and orbital orderings leads to a complex energy landscape whereby the supercell for the charge ordering, orbital ordering and ionic displacements can all be different.