An improved magnetic memory system in which binary data are stored as cross-tie, Bloch-line pairs, which are serially propagated downstream along a cross-tie wall in a magnetizable layer by appropriate drive fields. The magnetizable layer is configured into a data track whose two opposing edges are formed into patterns of asymmetrically shaped edges which form successive narrow portions with wide portions therebetween, and which are formed about the geometric centerline of the data track. The improvement comprises forming a plurality of energy wells along the geometric centerline of the data track and, transverse to the geometric centerline of the data track in the areas of the narrow portions where the cross-ties are stored but not in the areas of the geometric centerline.