Dissipation and quantum propagation of bloch walls

Bloch walls in mesoscopic ferromagnets are shown to tunnel coherently between periodically arranged pinning sites and to form a band similar to a Bloch electron in a crystal lattice. Eliminating the spin wave degrees of freedom we derive an effective action for the Bloch wall position. The dissipative term in this action involves a spectral function with a gap and therefore damping due to spin waves is negligible at low temperatures. It is shown that the Berry phase gives rise to a spin-parity-dependent shift in the dispersion. We show that this band structure can give rise to Bloch oscillations of the magnetization in response to a static external field, which provides a magnetic analog to the Josephson effect.