Hubbard U correction on magnetic interactions and Curie temperatures of FeO, Fe2O3, and Fe3O4

Abstract

Nanosized ferromagnets hold great potential for the development of nanoscale spintronic devices. In this study, the structural, electronic and magnetic properties of FeO, Fe${}_2$O${}_3$, and Fe${}_3$O${}_4$ are investigated using density functional theory (DFT) calculations with and without Hubbard U correction. The inclusion of the Hubbard U term is crucial for accurately capturing the strong electron–electron correlations in iron oxides, which significantly affect their electronic and magnetic behaviors, including the Curie temperature. For FeO, the PBEsol calculations predict a metallic band structure, while the PBEsol+U calculations yield a band gap of 2.08 eV. Similarly, for Fe${}_2$O${}_3$, the band gap increases from 0.59 eV with PBEsol to 2.50 eV with PBEsol+U, and for Fe${}_3$O${}_4$, it changes from metallic to 1.71 eV when the Hubbard U correction is applied. The magnetic moments for Fe atoms also show a significant improvement with the inclusion of the Hubbard U correction. In FeO, the magnetic moment increases from 3.21 ${\mu }_{\text{B}}$ with PBEsol to 3.38 ${\mu }_{\text{B}}$ with PBEsol+U. For Fe${}_2$O${}_3$, the values change from 3.15 ${\mu }_{\text{B}}$ to 3.85 ${\mu }_{\text{B}}$, and for Fe${}_3$O${}_4$, from 3.32 ${\mu }_{\text{B}}$ to 3.75 ${\mu }_{\text{B}}$. These results bring the calculated values closer to the experimental observations. The Curie temperatures, calculated using magnetic exchange constants determined from the Green function method, also highlight the impact of the Hubbard U correction. For FeO, the Curie temperature dramatically decreases from 825 K with PBEsol to 330 K with PBEsol+U. In Fe${}_2$O${}_3$, it is slightly reduced from 1230 K to 1180 K, while for Fe${}_3$O${}_4$, it decreases from 1120 K to 960 K. These results underline the critical role of electron–electron correlations in accurately predicting the electronic and magnetic properties of iron oxides.