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A drift-diffusion approach to coupled spin and charge transport has been commonly applied to determine the spin-transfer torque acting on the magnetization in metallic valves. This approach, however, is not suitable to describe the predominant tunnel transport in magnetic tunnel junctions. In this work we present a coupled Finite Element solution to the spin and charge drift–diffusion equations. We demonstrate that by introducing a magnetization dependent resistivity one can successfully reproduce the resistance dependence on the magnetization orientation in the ferromagnetic layers. We then investigate the dependence of the resulting torques on system parameters, and show that the approach is able to reproduce the torque magnitude expected in a magnetic tunnel junction. As a unique set of equations is used for the entire structure, this constitutes an efficient Finite Element based approach to describe the magnetization dynamics in emerging spin-transfer torque memories.

We demonstrate by means of numerical simulations the switching of a perpendicularly magnetized free layer by spin–orbit torques based on a two-pulse switching scheme with improved writing power efficiency. In this scheme, the first pulse selects the cell, while the second pulse completes the switching deterministically. It is shown that the magnitude of the second current pulse can be reduced to about 50% of the critical current and the switching remains reliable with a switching time of 300 ps. With such a significant current reduction the writing power required for switching decreases by 40%, which results in a very energy efficient scheme. In addition, we develop a reinforcement learning approach to optimize the pulse configuration with the goal of achieving the shortest switching time. With this approach a switching time of 146 ps has been obtained, a reduction of 50% in relation to the non-optimized configuration. These research findings confirm that reinforcement learning is a promising tool to simplify and automate the search for a faster, energy efficient scheme in the two-pulse switching approach.

We investigate the robustness of a purely electrical field-free switching of a perpendicularly magnetized free layer based on SOT. The effective magnetic field which leads to deterministic switching of a rectangular as well as of a square free layer is created dynamically by a two-current pulse scheme. It is demonstrated that the switching is very robust, being insensitive to fluctuations of the write pulses’ durations and to relatively large variations of the heavy metal wires’ dimensions. Furthermore, it remains reliable for a wide range of synchronization failures between the pulses. The combination of a rectangular free layer shape with a partial overlap with the second current line accelerates the switching of the cell allowing a fast, 0.25 ns, switching.