A method for implementing miniaturization of magnetic random access memory (MRAM) and a magnetic memory using single domain switching by direct current are provided. The magnetic memory preferably includes a half-circle or U-shaped architecture with an exchange biasing pad, such as a FeMn exchange biasing pad that effectively generates a head-to-head magnetization configuration. The magnetic memory also includes nanometer scale notches in order to minimize magnetostatic interaction between a single domain memory element and the spin current sources and to effectively trap the magnetic domain wall. Reading the bit can be carried out by anisotropic magnetoresistance, or by other means of determining the magnetization orientation through resistance measurements, such as a spin valve or a magnetic tunneling junction.