  Using THz spectroscopy, we show that the spin-wave spectrum of multiferroic
BiFeO$_3$ in its high-field canted antiferromagnetic state is well described by
a spin model that violates rhombohedral symmetry. We demonstrate that the
monoclinic distortion of the canted antiferromagnetic state is induced by the
single-ion magnetoelastic coupling between the lattice and the two nearly
anti-parallel spins. The revised spin model for BiFeO$_3$ contains two new
single-ion anisotropy terms that violate rhombohedral symmetry and depend on
the direction of the magnetic field.
