Using first-principles calculations, we predict a unique $\mathrm{BiFe}{\mathrm{O}}_3$ (BFO) phase, which is coined $I$-BFO, with layered characteristics based on the ilmenite structure. The interactions between interlayer bismuth atoms make it easy to exfoliate monolayer BFO with a configuration in which Bi ions are above and below two-dimensional (2D) iron-oxygen octahedra sharing common edges. The calculated phonon spectra reveal the dynamic stability of both bulk and monolayer forms of $I$-BFO. Combining total energy computation and crystal structure search, we corroborate that the $I$-BFO monolayer maintains the lowest-energy ground state, as compared to other 2D BFO exfoliations. We also discover that monolayer $I$-BFO is a robust antiferromagnetic material with a Néel temperature ($T_N$) of 4 K in the fully relaxed case. Such $T_N$ can be prominently improved by strain, for example, $T_N=25\mathrm{K}$ at 6% tension. Furthermore, our electronic structure calculations with PBE and hybrid HSE functionals show the $I$-BFO monolayer to be an indirect-gap semiconductor. Finally, we indicate that other ternary $AB{\mathrm{O}}_3$ compounds also have the potential to produce layered materials from the ilmenite structure. This work thus provides guidance to explore unconventional layered materials, and further broadens the application of BFO and other promising ilmenite oxides in two dimensions.

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• Geometric & topological phases
• Density functional calculations
• Electronic structure