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Based on density functional theory (DFT) calculations including an on-siteHubbard $U$ term we investigate the effect of substrate-induced strain on theproperties of ferrimagnetic Fe$_2$O$_3$-FeTiO$_3$ solid solutions andheterostructures. While the charge compensation mechanism through formation ofa mixed \fetw, \feth-contact layer is unaffected, strain can be used to tunethe electronic properties of the system, e.g. by changing the position ofimpurity levels in the band gap. Straining hematite/ilmenite films at thelateral parameters of Al$_{2}$O$_{3}$(0001), commonly used as a substrate, isfound to be energetically unfavorable as compared to films onFe$_{2}$O$_{3}$(0001) or FeTiO$_{3}$(0001)-substrates.

Effect of strain on the stability and electronic properties of ferrimagnetic Fe$_{2-x}$Ti$_x$O$_3$ heterostructures from correlated band theory