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

Abstract

Based on ab initio density functional theory, we have investigated a microscopic mechanism that leads to Fe${}_B^{2+}$/Fe${}_B^{3+}$ 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${}_B^{2+}$/Fe${}_B^{3+}$ 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".