  Domain walls in a one-dimensional gapped easy-axis ferromagnet can exhibit
Bloch oscillations in an applied magnetic field. We investigate how exchange
couplings modify this behavior within an approximation based on noninteracting
domain-wall bound states. In particular, we obtain analytical results for the
spectrum and the dynamic structure factor, and show where in momentum space to
expect equidistant energy levels, the Wannier-Zeeman ladder, which is the
spectral signature of magnetic Bloch oscillations. We compare our results to
previous calculations employing a single domain-wall approximation, and make
predictions relevant for the material $CoCl2\cdot2H2O$.
