Competing phases in BiFeO\$\_3\$ thin films under compressive epitaxial strain

Combining density-functional calculations and x-ray diffraction experiments, we show that BiFeO3 epitaxially grown under compressive strain on cubic substrates evolves from the monoclinic Cc phase (resulting from the strain-induced deformation of the ground-state rhombohedral R3c phase) to the monoclinic Cm phase with increasing misfit, the transition being at about -4.5\%/-5.5\%. Moreover, the polarization of the Cc phase only rotates (instead of increasing) for misfit strain ranging from 0\% to -4\%, due to a strong coupling between polar displacements and oxygen octahedra tilts. This strong interaction is of interest for multiferroics where usually both structural degrees of freedom coexist.