Magnetization Reversal of a Nanoparticle by Electric Current Pulse via Spin-orbit Torque

We theoretically study the influence of a predominant field like spin-orbit torque on the magnetization switching of small devices with a uniform magnetization. An electric current in the heavy-metal layer of a spin-orbit-torque magnetic random access memory (SOT-MRAM) with a ferromagnet/heavy-metal bilayer at its centre produces a pure spin current via the spin-Hall effect that flows perpendicularly into the magnetic layer which is already known by us. Using the optimum control theory, it is shown that by properly structuring both in-plane components of the current pulse, the energy cost of the spin-orbit torque driven reversal of a nanomagnet with perpendicular anisotropy may be greatly decreased. we study the magnetization reversal strategy by a minimal electric current pulse for realistic materials. we identify energy efficient switching pulses by applying a systematic approach based on the optimal control theory. To make the most of the pulse optimization, we apply constraints on the pulse shape as a polarized cosine chirp pulse (CCMP) and consider independent variations of both in-plane components of the current. We obtain a complete analytical solution for optimal control paths (OCPs) of field free magnetization switching, i.e., the reversal trajectories minimizing the energy cost associated with joule heating, and derive optimal switching pulses from the obtained OCPs. We obtain analytically the time dependence of the ideal switching pulse that minimizes the energy cost of joule heating in terms of the material properties and the necessary reversal time. the magnetization can be switched deterministically without the need for an external help field. It is possible to find the ideal reversal time that strikes a balance between energy efficiency and switching speed. The spin-orbit torque is shown to have a sweet-spot balance between the field like and damping like components. This balance allows for an especially effective switching by a cosine-chirped spinning current pulse, whose duration need to be precisely regulated. The proposed switching scheme is numerically verified by micromagnetic simulations to be effective in devices. Switching without any external assist field is of great interest for the application of spin-orbit torques to magnetic memories. 

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