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Spectral signatures of magnetic Bloch oscillations in one-dimensional easy-axis ferromagnets

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 $CoCl2\cdot2H2O$.