Relationship between multiple degrees of freedom and oxygen interstitial ordering in rare earth ferrites

Oxygen interstitials and vacancies, as two kinds of common defects in oxide system, usually play an important role in tuning the microstructure and properties of materials. To understand the tuning mechanism resulting from oxygen doping, the precise positions of these point defects and interaction between them and with other degrees of freedom need to be solved. Here, we report how such information can, for the first time, be obtained from the rare earth ferrite LuFe₂O_4+x by high-resolution electron microscopy, atomic-resolution spectroscopy and DFT calculations. The oxygen interstitial ordering and related lattice, charge, spin ordering form a new modulation structure, described by the same modulation vector. Meanwhile, we prove the modulation structure can be affected by changing the oxygen interstitial ordering. The interaction between oxygen interstitials and multiple degrees of freedom presented here provide a direct insight into tuning mechanism of oxygen doping in non-stoichiometric oxide systems.