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We employ a finite element discretization scheme to solve numerically the coupled spin and charge transport equations in spin-transfer torque magnetoresistive random access memory cells. To adapt the drift-diffusion formalism to the case of a magnetic tunnel junction, we model the tunnel barrier as a material with a low magnetization-dependent conductivity and a large spin diffusion constant. This generalized spin and charge drift-diffusion approach is applied to determine the torques entering the Landau-Lifshitz-Gilbert equation to describe the magnetization dynamics. In particular, the switching times under a fixed voltage, a fixed current, and a fixed current density are compared.
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Simone Fiorentini, Johannes Ender, Mohamed Mohamedou, Siegfried Selberherr, Roberto L. de Orio, Wolfgang Goes, Viktor Sverdlov, "Comprehensive modeling of coupled spin-charge transport and magnetization dynamics in STT-MRAM cells," Proc. SPIE 11470, Spintronics XIII, 114701B (20 August 2020); https://doi.org/10.1117/12.2567480