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Finite Element Method Approach to MRAM Modeling

Spin-transfer torque magnetoresistive random access memory (STT-MRAM) is among the most promising candidates for emerging memories. Thus, reliable simulation tools are mandatory to provide an important aid for understanding and improving the design of such devices. In this work we are concerned with the simulation of STT-MRAM. The well-known Landau-Lifshitz-Gilbert (LLG) equation describes the magnetization dynamics. Since we are dealing with STT-MRAM, an additional torque term must be added to the LLG equation. The torque acting on the magnetization is generated by the nonequilibrium spin accumulation due to the electric current flowing through the structure. The partial differential LLG equation with the additional torque computed from the spin accumulation is solved using the highly efficient finite element method (FEM). We implemented several time integration schemes using an open-source FEM library. In order to verify and calibrate the FEM implementation, we compared it to a finite difference method (FDM) implementation used as a reference. By properly tailoring the time integration scheme and the time step size, almost identical simulation results as with the FDM are achieved. Proper calibration is essential in order to simulate a more realistic multi-layer structure with a composite switching layer consisting of ferromagnetic layers separated by nonmagnetic buffers.