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We designed and modeled a nonvolatile memory device that utilizes the Rashba spin-orbit coupling (SOC) to write data onto a free ferromagnetic (FM) layer and uses the tunneling magnetoresistive (TMR) effect for data read-back. The magnetic RAM (MRAM) device consists of a free (switchable) FM multilayer stack, in which a large internal electric field is induced at the interfaces between the oxide and the FM layer. In the FM layer, data writing by magnetization switching occurs via the Rashba-induced spin torque, while the data reading process in the system could be fulfilled via the current-perpendicular-to-plane TMR response. A general equation of motion for the local moments has been obtained by formally deriving the SU(2) spin-orbit gauge field arising due to SOC and the critical current density is estimated to be 1.2 ×108 A/cm2. Micromagnetic simulations were performed to demonstrate the Rashba-induced switching mechanism. By choosing or fabricating alloys with a lower magnetocrystalline anisotropy and enhancing the Rashba coupling strength via surface or interfacial engineering, the critical current may be further reduced to well below 107 A/cm2, a level that may enable the practical realization of a single-layer Rashba-induced magnetization switching memory.