Abstract: A cross-tie random access memory comprising: a thin film magneto-resistive material having spaced memory locations defining memory elements, the thin film being configured for each memory element to include, when the memory element is in one binary state, a plurality of contiguous magnetic domains, each having a direction extending in the plane of the thin film, each memory element being configured, when the memory element is in the other state, to include a reverse path portion within each of the plurality of magnetic domains having a direction extending in the plane of the film, each path portion being bounded on one side by a Bloch-line and on the opposite side by a cross-tie.