  We use first-principles calculations based on density functional theory to
investigate the interplay between oxygen vacancies, A-site cation size /
tolerance factor, epitaxial strain, ferroelectricity and magnetism in the
perovskite manganite series, AMnO3 (A=Ca2+, Sr2+, Ba2+). We find that, as
expected, increasing the volume through either chemical pressure or tensile
strain generally lowers the formation energy of neutral oxygen vacancies
consistent with their established tendency to expand the lattice. Increased
volume also favors polar distortions, both because competing rotations of the
oxygen octahedra are suppressed and because coulomb repulsion associated with
cation off-centering is reduced. Interestingly, the presence of ferroelectric
polarization favors ferromagnetic over antiferromagnetic ordering due to
suppressed antiferromagnetic superexchange as the polar distortion bends the
Mn-O-Mn bond angles away from the optimal 180deg. Intriguingly, we find that
polar distortions compete with the formation of oxygen vacancies, which have a
higher formation energy in the polar phases; conversely the presence of oxygen
vacancies suppresses the onset of polarization. In contrast, oxygen vacancy
formation energies are lower for ferromagnetic than antiferromagnetic orderings
of the same structure type. Our findings suggest a rich and complex phase
diagram, in which defect chemistry, polarization, structure and magnetism can
be modified using chemical potential, strain, and electric or magnetic fields.
