Electronic structure and magnetism in Fe₃O₄ and Cr₃O₄

We investigate the electronic structure and magnetism of Iron (II, III) oxide (Fe₃O₄) called magnetite and Chromium (II, III) Oxide (Cr₃O₄) to explore and understand the fundamental physics behind their physical properties and their applicability to magnetism and quantum-based technologies. The Fe₃O₄ has Fe in both octahedral and tetrahedral sites providing two competing structures in its crystal. The same structural behavior is expected and observed in more complex Cr₃O₄. We explore and predict how the 3D bulk of these transition metal oxides and their single-layer 2D counterparts behave in terms of magnetic ordering and magnetic phase transition. Fe ions interacting magnetically with non-similar sites, namely the interacting octahedral/tetrahedral pairs, yield antiferromagnetic ordering, whereas the interaction of the octahedral-to-octahedral ions is ferromagnetic, resulting in the overall ferromagnetic ordering. The comparative study of Fe₃O₄ with Cr₃O₄ is primarily interesting because of the contrasting filling of 3d orbitals in respective Fe and Cr compositions.