Analytical approach to current-driven self-oscillations in Landau–Lifshitz–Gilbert dynamics

Abstract

Nonlinear magnetization dynamics in uniformly magnetized bodies subject to spin-polarized current, is described by Landau–Lifshitz–Gilbert (LLG) equation with an additional spin-transfer torque term. The resulting magnetization dynamics may exhibit self-oscillatory regimes, i.e. limit cycles. By using the fact that spin-transfer torque and Gilbert damping are small perturbations of the conservative LLG dynamics, the analysis of limit cycles is carried out by an appropriate perturbation method known as Melnikov-function technique. The technique is then applied to the analysis of a typical current-driven switching process in magnetic thin film. Analytical formulas for frequency, amplitude of limit cycles in function of the injected current are derived along with critical values of current which characterized the switching process. Finally, the accuracy of the perturbative technique is tested by comparing analytical results with numerical solutions.