Phase Transitions in Epitaxial (-110) BiFeO$_3$ Films from First Principles*

The effect of misfit strain on properties of epitaxial BiFeO$_3$ films that are grown along the pseudo-cubic [$\bar{1}$10] direction, rather than along the ``usual'' [001] direction, is predicted from density functional theory. These films adopt the monoclinic $Cc$ space group for compressive misfit strains smaller in magnitude than $\simeq$1.6\% and for any investigated tensile strain. In this $Cc$ phase, both polarization and the axis about which antiphase oxygen octahedra tilt rotate {\it within} the epitaxial plane as the strain varies. Surprisingly and unlike in (001) films, for compressive strain larger in magnitude than $\simeq$1.6\%, the polarization vanishes and two orthorhombic phases of $Pnma$ and $P2_12_12_1$ symmetry successively emerge via strain-induced transitions. The $Pnma$-to-$P2_12_12_1$ transition is a rare example of a so-called pure ``gyrotropic'' phase transition, and the $P2_12_12_1$ phase exhibits original interpenetrated arrays of ferroelectric vortices and antivortices. This work is mostly supported by ONR Grants N00014-08-1-0915 and N00014-07-1-0825 (DURIP). *S. Prosandeev, Igor A. Kornev, and L. Bellaiche, Phys. Rev. Lett. 107, 117602 (2011).