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We study the magnetization dynamics of thin-film magnetic elements within-plane magnetization subject to a spin-current flowing perpendicular to thefilm plane. We derive a reduced partial differential equation for the in-planemagnetization angle in a weakly damped regime. We then apply this model tostudy the experimentally relevant problem of switching of an elliptical elementwhen the spin-polarization has a component perpendicular to the film plane,restricting the reduced model to a macrospin approximation. The macrospinordinary differential equation is treated analytically as a weakly dampedHamiltonian system, and an orbit-averaging method is used to understandtransitions in solution behaviors in terms of a discrete dynamical system. Thepredictions of our reduced model are compared to those of the fullLandau--Lifshitz--Gilbert--Slonczewski equation for a macrospin.

A reduced model for precessional switching of thin-film nanomagnets under the influence of spin-torque