Controlled Quasi-Latitudinal Solutions for Ultra-Fast Spin-Torque Magnetization Switching

Abstract

The aim of this paper is to present a novel class of time-dependent controls to realize ultra-fast magnetization switching in nanomagnets driven by spin-torques produced by spin-polarized electric currents. Magnetization dynamics in such complex systems is governed by the Landau–Lifshitz–Slonczewski equation which describes the precessional motion of (dimensionless) magnetization vector on the unit-sphere. The relevant case of nanoparticles with uniaxial anisotropy having in-plane easy and intermediate axes as well as out-of-plane hard axis is considered. By exploiting the characteristic smallness of damping and spin-torque intensity, the complexity of the magnetic system’s dynamic is dealt with by employing tools borrowed from Hamiltonian Perturbation Theory. More precisely, the aforementioned controls are constructed via suitable perturbative tools in a way to realize approximate latitudinal solutions (i.e. motions on a sphere in which the out-of-plane magnetization component stays constant) with the effect to fast “switch” the system from one stationary state to another. The possibility to keep a (“small”) bounded value of the out-of-plane coordinate throughout this process of “transfer” turns out to be advantageous in the applications as it sensibly reduces the post-switching relaxation oscillations that may cause the failure of switching in real samples. Further relevant quantitative results on the behavior of the solutions during the pre- and post-switching stages (termed “expulsion” and “attraction”, respectively) are given as a by-product. A selection of validating numerical experiments is presented alongside the corresponding theoretical results.