  We investigate the strain dependence of the ferroelectric polarization and
the structure of the ferroelectric domain walls in the layered
perovskite-related barium fluorides, BaMF$_4$ (M=Mg, Zn). The unusual
"geometric ferroelectricity" in these materials is driven by the softening of a
single polar phonon mode consisting of rotations of the MF$_6$ octahedra
accompanied by polar displacements of the Ba cations, and in contrast to
conventional ferroelectrics involves minimal electronic rehybridization. We
therefore anticipate a different strain dependence of the polarization, and
alternative domain wall structures compared with those found in conventional
ferroelectric materials. Using first-principles calculations based on density
functional theory (DFT) within the general gradient approximation (GGA), we
calculate the variation of the crystal structure and the ferroelectric
polarization under both compressive and tensile strain. We perform structural
relaxations of neutral domain walls between oppositely oriented directions of
the ferroelectric polarization and calculate their corresponding energies to
determine which are most likely to form. We compare our results to literature
values for conventional perovskite oxides to provide a source of comparison for
understanding the ferroelectric properties of alternative non-oxide materials
such as the barium fluorides.
