Spin Transfer Torques in Ultra-Scaled MRAM Cells

Abstract

Modern magnetoresistive random access memory (MRAM) cells with single-digit nanometer diameters, utilize a combination of perpendicular interface-induced and shape-driven out-of-plane anisotropy in a free layer (FL) consisting of several ferromagnetic parts separated by tunnel barriers and/or nonmagnetic spacers. To accurately evaluate the torques acting in such a structure, we generalized the coupled spin and charge drift-diffusion transport approach to account for a number of tunnel barriers (TB) or spacers separating the elongated ferromagnetic pieces. The inclusion of the tunneling magnetoresistance effect is achieved by modeling the TB as a poor conductor with a conductivity locally dependent on the relative magnetization orientation of the ferromagnetic layers. The TB parameters are calibrated to reproduce the expected torque magnitudes in magnetic tunnel junctions (MTJ). To reproduce the spin transfer torques acting on a FL in a MTJs with several TBs and spacers, a special treatment of the spin current is proposed. In elongated FLs, position-dependent torques are present in the ferromagnetic pieces due to non-homogeneous magnetization. We show that, with the proposed approach, composite FLs with several TBs are treated on equal footing. Our simulations of the magnetization dynamics in composite elongated FLs agree well with recent experimental demonstrations of switching of ultra-scaled MRAM cells.