How the aggregation of oxygen vacancies in rutile-based ${\mathrm{TiO}}_{2-\delta }$ phases 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 Magnéli 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.

Figure 1

Formation enthalpies $\mathrm{\Delta }{H}_{\mathrm{f}}$ [see Eq. (4)] of vacancy orderings in the rutile crystal structure resulting from a DFT-based (solid red circles) CE fit (open blue diamonds). The black solid line marks the CE ground states. For comparison, the DFT formation enthalpies of the Magnéli phase are also displayed (open green circles).

Figure 2

Relaxed ${\mathrm{Ti}}_4{\mathrm{O}}_7$ Magnéli structure. Overcoordinated ${\mathrm{O}}_{\mathrm{ovc}}$ atoms (orange) form quasi-one-dimensional channels in [111]. All Ti atoms (blue) retain sixfold coordination. Fully coordinated oxygen atoms appear in red. The crystallographic (121) shear plane (see text for affinity to rutile) is shaded blue.

Figure 3

Relaxed structure of the isolated ${\mathrm{V}}_{\mathrm{O}}$ arrangement predicted for 5% ${\mathrm{V}}_{\mathrm{O}}$ concentration. The missing oxygen atom induces three undercoordinated Tiⁱⁱⁱ ions, marked in green.

Figure 4

Planes of ${\mathrm{V}}_{\mathrm{O}}$ relax into Tiⁱⁱⁱ linked by overcoordinated ${\mathrm{O}}_{\mathrm{ovc}}$ atoms. For more details and the denotation, see text.

Figure 5

(a) Spin-polarized densities of states of isolated ${\mathrm{V}}_{\mathrm{O}}$ (see Fig. 3), (b) the Magnéli phase ${\mathrm{Ti}}_4{\mathrm{O}}_7$, and (c) the prototypical planar ${\mathrm{V}}_{\mathrm{O}}$ arrangements found for 16.7% ${\mathrm{V}}_{\mathrm{O}}$ concentration (see Fig. 4).