The microscopic model of BiFeO3

Many years and great effort have been spent constructing the microscopic model for the room temperature multiferroic BiFeO₃. However, earlier models implicitly assumed that the cycloidal wavevector $q$ was confined to one of the three-fold symmetric axes in the hexagonal plane normal to the electric polarization. Because recent measurements indicate that $q$ can be rotated by a magnetic field, it is essential to properly treat the anisotropy that confines $q$ at low fields. We propose that the anisotropy energy $-K_3{S}^6{\sin }^6\theta \cos 6\varphi$ confines the wavevectors $q$ to the three-fold axis $\varphi =0$ and $\pm 2\pi /3$ within the hexagonal plane with $\theta =\pi /2$.