Decisive Role of the Defect-Clustering Effect in the Variation of Magnetic Order in Diluted Magnetic Binary Metal Oxides

Above room temperature T_c, magnetism is becoming viable in diluted magnetic semiconductors, which show different magnetic orders, depending on the dopant type and their fabrication method. However, how the defects can influence the magnetic properties remains unclear at the atomic level. In this article, by taking the Co-doped tetragonal MO₂ (t-MO₂, M = Ti, Sn, Hf, and Zr) as an example, the density functional theory-based investigations show that the magnetic order is mainly decided by the defect clustering effect, following a “defect-distance-based” defect correlation principle. It is found that the distance between two defects (Co-Co) leads to an alteration of magnetic order, where SnO₂ and ZrO₂ show antiferromagnetic (AFM) behavior when the nearest Co-Co distance lies within one octahedron, while a larger distance gives rise to the ferromagnetic (FM) state. In contrast, TiO₂ exhibits an AFM state at the neighboring Co-Co configuration with the nearest Co-Co distance larger than one octahedra, while HfO₂ showed an opposite trend as that of TiO₂. Furthermore, the position of oxygen vacancies mainly affects the magnitude of magnetization instead of magnetic order. We believe this work would significantly advances the understanding of defect chemistry and condensed matter physics related to diluted FM-AFM systems.