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The results of a comprehensive and systematic ab-initio based ground-statesearch for the structural arrangement of oxygen vacancies in rutile phaseTiO$_2$ provide new insights into their memristive properties. We find that Ovacancies tend to form planar arrangements which relax into structuresexhibiting metallic behavior. These meta-stable arrangements are structurallyakin to, yet distinguishable from the Magn\'eli phase. They exhibit a morepronounced metallic nature, but are energetically less favorable. Our resultsconfirm a clear structure-property relationship between segregated oxygenvacancy arrangement and metallic behavior in reduced oxides.

How the aggregation of oxygen vacancies in rutile based TiO$_{2-\delta}$ phases causes memristive behavior