Properties of mixed transition metal oxides: MM′O3 in corundum-type structures (M,M′=Al,Ti,V,Cr,and Fe)

The growing interest of modern technologies in oxide materials is in part due to the possibility of their doping and/or mixing, which often leads to artificial compounds with tunable properties, such as the gap width or the band edge positions. However, engineering of mixed oxide materials requires a better fundamental understanding of their structural, electronic, and ordering properties, well beyond low doping levels, and with reference to their parent materials. In the present work, a series of mixed $M{M}^{\ensuremath{'}}{\mathrm{O}}_{3}$ oxides $(M,{M}^{\ensuremath{'}}=\text{Al},\text{Ti},\text{V},\text{Cr},\text{Fe})$ in three corundum-type structures---ilmenite, ${\mathrm{LiNbO}}_{3}$, and C---is studied by means of first-principles DFT+$U$ simulations. We find that regardless of the precise atomic structure, the local structural and electronic characteristics of most of the compounds are very close to those of their parent corundum ${M}_{2}{\mathrm{O}}_{3}$ oxides. The two noticeable exceptions are ${\mathrm{TiVO}}_{3}$ and ${\mathrm{TiFeO}}_{3}$, for which the structural, electronic, and magnetic characteristics are consistent with a mixing-induced change of the cation oxidation states. We show that this actual oxidoreduction process can be rationalized by analyzing the relative band edge positions of the parent oxides. The formation energies of these mixed oxides correlate well with the experimental evidence and, within a mean-field approximation, allow predicting the thermodynamics of solid solutions ${M}_{2\ensuremath{-}2x}{M}_{2x}^{\ensuremath{'}}{\mathrm{O}}_{3}$ at finite temperature.