Euler equation of the optimal trajectory for the fastest magnetization reversal of nano-magnetic structures

Abstract

Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary Stoner particle under an external magnetic field and a spin-polarized electric current, differential equations for the optimal reversal trajectory, along which the magnetization reversal is the fastest one among all possible reversal routes, are obtained. We show that this is a Euler-Lagrange problem with constrains. The Euler equation of the optimal trajectory is useful in designing a magnetic field pulse and/or a polarized electric current pulse in magnetization reversal for two reasons. 1) It is straightforward to obtain the solution of the Euler equation, at least numerically, for a given magnetic nano-structure characterized by its magnetic anisotropy energy. 2) After obtaining the optimal reversal trajectory for a given magnetic nano-structure, finding a proper field/current pulse is an algebraic problem instead of the original nonlinear differential equation.

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Cited by in corpus (10)

• Field-induced domain wall propagation velocity in magnetic nanowires
• Breaking the current density threshold in spin-orbit-torque magnetic random access memory
• Fast domain wall propagation under an optimal field pulse in magnetic nanowires
• Subnanosecond magnetization reversal of magnetic nanoparticle driven by chirp microwave field pulse
• Optimal control of magnetization reversal in a monodomain particle by means of applied magnetic field
• Thermally assisted magnetization reversal of a magnetic nanoparticle driven by a down-chirp microwave field pulse
• Zero-field magnetization reversal of two-body Stoner particles with dipolar interaction
• Fast magnetization reversal of a magnetic nanoparticle induced by cosine chirp microwave field pulse
• Spin transfer torque enhancement in dual spin valve in the ballistic regime
• Shape anisotropy effect on magnetization reversal induced by linear down chirp pulse