Bloch oscillations of magnetic solitons in anisotropic spin-$\frac{1}{2}$ chains

We study the quantum dynamics of solitonlike domain walls in anisotropic spin-$\frac{1}{2}$ chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e., the domain walls oscillate along the chain with a finite Bloch frequency and amplitude. In the presence of the field, the Bloch band, with a continuum of extended states, breaks up into the Wannier-Zeeman ladder—a discrete set of equally spaced energy levels. We calculate the dynamical structure factor $S^{\mathrm{zz}}(q,\omega )$ in the one-soliton sector at finite frequency, wave vector, and temperature, and find sharp peaks at frequencies which are integer multiples of the Bloch frequency. We further calculate the uniform magnetic susceptibility and find that it too exhibits peaks at the Bloch frequency. We identify several candidate materials where these Bloch oscillations should be observable, for example, via neutron-scattering measurements. For the particular compound ${\mathrm{CoCl}}_2{\mathrm{\cdot }2\mathrm{H}}_2\mathrm{O}$ we estimate the Bloch amplitude to be on the order of a few lattice constants, and the Bloch frequency on the order of 100 GHz for magnetic fields in the Tesla range and at temperatures of about 18 K.