Spin and charge drift-diffusion in ultra-scaled MRAM cells

Abstract

We presented a modeling approach to accurately describe the charge and spin currents, the torques, and the magnetization dynamics in ultra-scaled MRAM cells consisting of several elongated pieces of ferromagnets separated by multiple tunnel barriers. We showed how the fully 3D spin and charge drift-diffusion equations can be supplied with appropriate conditions at the tunneling layer to reproduce the TMR effect as well as the angular and voltage dependence of the torque expected in MTJs. We reported how an iterative solution of the charge and spin accumulation equations can be employed to account for the GMR effect. The advantage of the proposed approach is the possibility of computing all the torque contributions from a unified expression, so that the interactions between them can be evaluated, and the torque acting in the presence of multiple layers of varying thickness is automatically accounted for, even for non-uniform magnetization distributions. We demonstrated that the Slonczewski and Zhang and Li torques are not additive and must be derived from the spin accumulation to account for their interplay and correctly describe the torques on textured magnetization in elongated FLs with several MgO TBs. Finally, we applied the presented method to switching simulations of MRAM cells with elongated and composite FLs. The obtained results validate the use of the proposed simulation approach as support for the design of advanced ultra-scaled MRAM cells.