Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Spin-Transfer Torque

We study the Landau–Lifshitz–Gilbert equation for the dynamics of a magnetic vortex system. We include the spin-torque effects of an applied spin current, and we rigorously derive an equation of motion (“Thiele equation”) for vortices if the current is not too large. Our method of proof strongly utilizes the geometry of the problem in order to obtain the necessary energy estimates.

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