A micro magnetic analysis, has been performed for ultra dense magnetoresistive memory cells employing giant magnetoresistive materials that have array densities from 2/spl times/10/sup 8/ to 10/sup 9/ elements per square cm. The analysis shows that as elements are made smaller, it is necessary to increase the effective anisotropy constant by increasing the demagnetizing factor in the long dimension of the element (or by finding GMR materials with large anisotropy fields). With diminishing cell size, exchange torque becomes progressively more important, and depending in detail on the thickness of the magnetic and separation layers, the layers ultimately act semi-coherently. Cell widths are eventually limited to values between 0.05 and 0.1 microns by thermal considerations because the smaller cells require progressively larger word and sense fields. The analysis assumed GMR elements made from magnetic layers 50 to 60 Angstroms thick of Ni, Fe, Co alloys with Cu, Ag, or Au separation layers of 15 to 30 Angstroms and with a magnetoresistive coefficient of 6 to 9%. >