In a magnetoresistive random access memory (MRAM), a magnetic tunnel junction (MTJ) (54) cell is stacked with an asymmetric tunnel device (56). This device, when used in a crosspoint MRAM array, improves the sensing of the state or resistance of the MTJ cells. Each MTJ cell has at least two ferromagnetic layers (42, 46) separated by an insulator (44). The asymmetric tunnel device (56) is electrically connected in series with the MTJ cell and is formed by at least two conductive layers (48, 52) separated by an insulator (50). The asymmetric tunnel device may be a MIM (56), MIMIM (80) or a MIIM (70). Asymmetry results from conducting electrons in a forward biased direction at a significantly greater rate than in a reversed biased direction. Materials chosen for the asymmetric tunnel device are selected to obtain an appropriate electron tunneling barrier shape to obtain the desired rectifying current/voltage characteristic.