Microscopic Model for the Spectroscopic Modes of Multiferroic BiFeO$_{3}$ in a Magnetic Field

The zone-center modes measured by THz spectroscopy [1] provide the most detailed information available about the very small microscopic interactions responsible for the cycloid in multiferroic BiFeO$_{3}$. While a Dzaloshinskii-Moriya (DM) interaction perpendicular to the electric polarization \textbf{P} produces the cyloidal period, a DM interaction along \textbf{P} produces the small tilt in the cycloid, which leads to the weak ferromagnetic moment of the canted phase above a critical field of about 18 T. A microscopic model that includes both DM interactions as well as easy-axis anisotropy along \textbf{P} quantitatively predicts the field dependence of the spectroscopic frequencies [2]. Comparison with the measured frequencies indicates that only one of the three cycloidal domains survives above about 6 T.\\[4pt] [1] U. Nagel, R.S. Fishman, T. Katuwal, H. Engelkamp, D. Talbayev, H.T. Yi, S.-W. Cheong, and T. Room, \textit{Phys. Rev. Lett.} \textbf{110}, 257201 (2013)\\[0pt] [2] R.S. Fishman, \textit{Phys. Rev. B} \textbf{87}, 224419 (2013).