  We have studied the magnetic field dependence of far-infrared active magnetic
modes in a single ferroelectric domain \BFO/ 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 \DM/ 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.
