Theory of Bloch-line and Bloch-wall motion

A theory of Bloch‐line (BL) dynamics in magnetic bubble materials is proposed and applied to the problem of domain collapse with a small number of BLs. We derive from the Landau‐Lifshitz‐Gilbert equation the dynamic reaction force, composed of gyrotropic and viscous terms, on a single moving BL. From this follows easily the wall mobility for equally spaced BLs. However, we show that BLs tend to cluster statically at distances comparable to the BL width. If the BLs are clustered on one side of a circular‐cylinder domain, then a change of the bias field causes the centers of bubble and cluster to move on spiral trajectories. The predicted displacement of the bubble center is large enough for visual confirmation, but the bound on coervicity required to confirm the spiral shape may be too stringent. The collapse mobility for the clustered case is typically much greater than that for the case of uniform spacing. The theory is supported by collapse‐time data of Malozemoff for a garnet film of medium viscosity (α=0.12). In garnets of low viscous damping of $\text{(α≲0.01)}$ we predict that coercivity H_c gives rise to nonlinearity of the velocity‐drive relation, with a characteristic ``knee'' veolcity, (2/π)γH_cr, for collapse of a domain of radius r.