Discovery of Stable Short-Range Order in High-Entropy Oxides Assisted with Bayesian Optimization

High-entropy oxides (HEOs), first proposed in 2015, are a novel class of materials attracting significant attention because of their potential to exhibit unexpected physical properties arising from the random mixing of multiple elements. To elucidate these properties from the perspective of electronic states, theoretical calculations are indispensable. However, specifying precise atomic configurations poses a substantial challenge because of the inherent configurational disorder of HEOs. Conventional computational models typically assume idealized randomness, thus failing to adequately represent the realistic short-range order (SRO) observed experimentally. In this study, a methodology is developed to identify stable SRO by optimizing metal atom arrangements in a representative rocksalt-type HEO, (NiMgCuCoZn)O. Simple descriptors based on neighboring metal atom pairs were extracted, and first-principles calculations were performed on selected structures within the exploration space. Bayesian optimization was then applied to efficiently identify stable configurations, ultimately pinpointing an exceptionally stable structure. Prediction models using second-nearest-neighbor descriptors, capable of capturing atomic arrangements along the crystal axes, demonstrated higher predictive accuracy than those using nearest-neighbor descriptors. In addition, analyses of the identified stable structures revealed that a cooperative Jahn-Teller effect involving Cu-O pairs significantly contributes to structural stability. The proposed method for identifying stable SRO is expected to provide deeper insights into the stability mechanisms of HEOs and to facilitate more accurate and realistic theoretical computations.