A method of and an apparatus for reading out the information that is stored in a magnetizable layer that is formed of a thin film in which data are stored as inverted Neel wall sections about associated Bloch-lines along a cross-tie wall. The apparatus utilizes a magnetizable layer which is configured into a strip whose two opposing edges are, along its longitudinal axis, formed into mirror-imaged, spaced-apart, repetitive, asymmetrically-shaped patterns which repetitive patterns are formed of successive narrow portions that form wide portions therebetween. The repetitive patterns, when suitable magnetic fields are coupled thereto, form a cross-tie wall along the longitudinal axis of the strip while structuring the cross-ties along the cross-tie wall at the narrow portions and the Bloch-lines along the cross-tie walls and between the adjacent narrow portions. One of the repetitive patterns is configured into a sharp film whose longitudinal axis is transverse the strip's longitudinal axis and whose transverse axis is along the strip's longitudinal axis. The sharp film, in the area extending beyond the strip's two opposing edges, comprises an open flux path film that possesses the characteristic of shape anisotropy providing a magnetic easy axis that is generally oriented along the sharp film's longitudinal axis and along which the sharp film's remanent magnetization resides wherein for all points on the sharp film's edge the angle .beta.' between the sharp film's edge and the sharp film's longitudinal axis is equal to or greater than 0.degree. and less than 45.degree.. Also disclosed is a detector that is associated with the sharp film for reading out the orientation of the sharp film's remanent magnetization along the sharp film's easy axis.