THz spectroscopy of spin waves in multiferroic BiFeO$_3$ in high magnetic fields

We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain BiFeO$_3$ crystal at low temperature. The modes soften close to the critical field of 18.8\,T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31\,T. A microscopic model that includes two Dzyaloshinskii-Moriya interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. The good agreement of theory with experiment suggests that the proposed model provides the foundation for future technological applications of this multiferroic material.