The dependencies on strain and oxygen vacancies of the ferroelectric
polarization and the weak ferromagnetic magnetization in the multiferroic
material bismuth ferrite, BiFeO_3, are investigated using first principles
density functional theory calculations. The electric polarization is found to
be rather independent of strain, in striking contrast to most conventional
perovskite ferroelectrics. It is also not significantly affected by oxygen
vacancies, or by the combined presence of strain and oxygen vacancies. The
magnetization is also unaffected by strain, however the incorporation of oxygen
vacancies can alter the magnetization slightly, and also leads to the formation
of Fe^{2+}. These results are discussed in light of recent experiments on
epitaxial films of BiFeO_3 which reported a strong thickness dependence of both
magnetization and polarization.Comment: 9 pages, 3 figure