Epitaxial Phases of BiMnO$_3$ from First Principles

Bulk BiMnO$_3$ is the only transition-metal perovskite oxide that is insulating and shows strong ferromagnetism. This distinctive behavior would make it a promising candidate as a magnetoelectric multiferroic if it was also a polar material, but experiments have shown that bulk BiMnO$_3$ has either a very small polarization (below 0.1~$\mu$C/cm$^2$) or, most likely, that it is a paraelectric. There is also experimental evidence that the polarization in BiMnO$_3$ {\em films} grown on SrTiO$_3$ can be as high as 20~$\mu$C/cm$^2$. Despite of the interest of these behaviors, the diagram of BiMnO$_3$ as a function of epitaxial strain has remained largely unexplored. In this article, we use first-principles to predict that both under enough compressive and tensile epitaxial strain BiMnO$_3$ films are ferroelectric with a giant polarization around 100~$\mu$C/cm$^2$. The phases displayed by the films are similar to those experimentally found for BiFeO$_3$ in similar conditions---at compressive strains, the film is supertetragonal with a large component of the polarization pointing out of plane, while at tensile strains the polarization points mostly in plane. Like in BiFeO$_3$ films, these phases are antiferromagnetic---the orbital ordering responsible for ferromagnetism in BiMnO$_3$ is absent in the polar phases. Our calculations also show that the band gap of some of these BiMnO$_3$ films is substantially smaller than gaps typically found in ferroelectric oxides, suggesting it may be a suitable material for photovoltaic applications.