First-principles study of spin spirals in the multiferroic $BiFeO_3$

We carry out density functional theory (DFT) calculations to explore the antiferromagnetic (AFM) spin cycloid in multiferroic BiFeO3 of the R3c ground state structure. We calculate the energy dispersion E(q) of cycloidal spin spirals along the high symmetry directions of the pseudo-cubic unit cell and find a flat AFM spin spiral (or cycloid) ground state with a periodicity of ∼80 nm, which is in good agreement with experiments. To investigate which structural distortion of the R3c phase is the driving mechanism for the stabilization of this cycloid, we further study three artificial phases: cubic, R3c, and R3m. In all cases, we find a large exchange frustration. The comparison between these phases provides detailed insight about how polarization and octahedral antiphase tilting affect the different magnetic interactions and the magnetic ground state in BiFeO3. In R3c BiFeO3, the magnetic ground state is driven by a competition between the frustrated exchange stemming from the hybridization between the elements Bi, Fe, O and the Dzyaloshinskii-Moriya (DM) interaction due to the Fe-Bi ferroelectric displacement. The cycloid appears to be stable because the anisotropy energy in R3c BiFeO3 is relatively small to enforce a collinear order.