A magneto-resistive random access memory includes a MOS transistor having a first gate and source and drain junctions on a substrate, a lower electrode connected to the source junction, a first magnetic layer on the lower electrode, a dielectric barrier layer including aluminum and hafnium on the first magnetic layer which, together with the first magnetic layer, form a potential well, a second magnetic layer on the dielectric barrier layer opposite the first magnetic layer, an upper electrode on the second magnetic layer, a second gate interposed between the first gate and the lower electrode to control the magnetic data of one of the first and second magnetic layers, and a bit line positioned orthogonal to the first gate and electrically connected to the upper electrode. Improved characteristics of the barrier layer increase a magnetic resistance ratio and improve data storage capacity of the magneto-resistive random access memory.