How the aggregation of oxygen vacancies in rutile-basedTiO2−δphases causes memristive behavior

The results of a comprehensive and systematic ab initio based ground-state search for the structural arrangement of oxygen vacancies in rutile phase ${\mathrm{TiO}}_{2}$ provide new insights into their memristive properties. We find that O vacancies tend to form planar arrangements which relax into structures exhibiting metallic behavior. These metastable arrangements are structurally akin to, yet distinguishable from, the Magn\'eli phase. They exhibit a more pronounced metallic nature but are energetically less favorable. Our results confirm a clear structure-property relationship between segregated oxygen vacancy arrangement and metallic behavior in reduced oxides.