Origin of magnetic anisotropy and spiral spin order in multiferroic BiFeO3

The first-principles calculations and thermodynamic modeling are combined to investigate the magnetic properties of BiFeO3. Our calculations indicate that the single-ion anisotropy and the anisotropic superexchange coupling contribute the same magnitude to the easy-magnetization-plane anisotropy. We show that the competition between the isotropic superexchange and the Dzyaloshinskii-Moriya interaction [I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)] of the nearest-neighbor Fe spins provides the microscopic mechanism for the origin of the long period spiral spin order, and the induced spontaneous magnetization exhibits a sinusoidal arrangement under the spiral order.