A method of and an apparatus for magneto-resistively detecting information in a cross-tie memory system is disclosed. The detector includes a first conductive element, which is the terminating portion of an electrically-conducting wide-narrow edged propagating drive line, and second and third conductive elements that are serially aligned along a magnetic, serrated-edged data track, which three conductive elements form two gaps therebetween. The two gaps are oriented along the data track at respective narrow portions, a first narrow portion which may support a cross-tie but which second narrow portion will not support a cross-tie. A differential sense amplifier is coupled across the two gaps using the second narrow portion as a reference segment to differentially detect the presence vel non of a cross-tie in the first narrow portion.