Nanoscale Size Effects on Push-Pull Fe-O Hybridization through the Multiferroic Transition of Perovskite ϵ-Fe₂O₃

Multiferroics have tremendous potential to revolutionize logic and memory devices through new functionalities and energy efficiencies. To reach their optimal capabilities will require better understanding and enhancement of the ferroic orders and couplings. Herein, we use ϵ-Fe₂O₃ as a model system with a simplifying single magnetic ion. Using 15, 20, and 30 nm nanoparticles, we identify that a modified and size-dependent Fe-O hybridization changes the spin-orbit coupling and strengthens it via longer octahedra chains. Fe-O hybridization is modified through the incommensurate phase, with a unique two-step rearrangement of the electronic environment through this transition with attraction and then repulsion of electrons around tetrahedral Fe. Interestingly, size effects disappear in the high-temperature phase where the strongest Fe-O hybridization occurs. By manipulating this hybridization, we tune and control the multiferroic properties.