Ab initio investigation of Fe$^{2+}$/Fe$^{3+}$ dimerization and ferroelectricity in multiferroic magnetite: role of electronic correlations

TL;DR

This study uses ab initio density functional theory to reveal how electronic correlations induce Fe$^{2+}$/Fe$^{3+}$ dimerization and ferroelectricity in charge-ordered magnetite, highlighting hybridization effects and a specific charge ordering pattern.

Contribution

It demonstrates the microscopic mechanism behind ferroelectricity in magnetite, emphasizing the role of electronic correlations and hybridization in a noncentrosymmetric structure.

Findings

Fe$^{2+}$/Fe$^{3+}$ dimerization is driven by hybridization effects.

Ferroelectric polarization is significant along the b axis.

Ferroelectricity originates from intermediate site/bond-centered charge ordering.

Abstract

Based on ab initio density functional theory, we have investigated a microscopic mechanism that leads to Fe$^{2+}_{B}$/Fe$^{3+}_{B}$ dimerization and consequent ferroelectricity in charge ordered Fe$_{3}$O$_{4}$ with $P2$ symmetry. In addition to the simple inter-site Coulomb repulsion, quantum hybridization effects are invoked to explain the Fe$^{2+}_{B}$/Fe$^{3+}_{B}$ bond dimerization. Our results, based on the generalized gradient approximation + Hubbard $U$ (GGA+$U$) method, indicate that noncentrosymmetric $P2$ magnetite shows a finite and sizeable ferroelectric polarization along the $b$ crystalline axis. From the $U$ dependence of polarization, we conclude that the origin of ferroelectricity in $P2$ Fe$_{3}$O$_{4}$ lies in the recently proposed "intermediate site/bond-centered charge ordering".