To achieve a fundamental understanding of the multiferroic behavior and electronic properties of intrinsic vacancies in $\mathrm{BiFe}{\mathrm{O}}_3$, here we performed first-principles calculations based on hybrid Hartree-Fock density functional theories, which can accurately describe defect electronic structures. Oxygen vacancies, which behave as deep donors with high concentrations under oxygen-poor conditions, reduce the magnetic moments at neighboring Fe ions in the neutral state, while charged oxygen vacancies induce additional ferroelectric polarizations. Cation vacancies, on the other hand, are likely to form under oxygen-rich conditions and result in multiferroic properties distinct from those induced by oxygen vacancies. Bi vacancies act as triple-shallow acceptors and strongly suppress spontaneous polarization regardless of charge states, while Fe vacancies locally interfere with both electric and spin polarization and are thus regarded as multiferroic singular points in $\mathrm{BiFe}{\mathrm{O}}_3$. A rich variety of the multiferroic behavior of vacancies can be systematically understood from the localized/delocalized features of defect states, and the different formation conditions for vacancies provide a strategy to tailor the multiferroic properties of $\mathrm{BiFe}{\mathrm{O}}_3$ through control of the concentration and charge states of vacancies.

• Received 28 October 2015
• Revised 20 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.174107