A reduced model for precessional switching of thin-film nanomagnets   under the influence of spin-torque
  We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin-current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane magnetization angle in a weakly damped regime. We then apply this model to study the experimentally relevant problem of switching of an elliptical element when the spin-polarization has a component perpendicular to the film plane, restricting the reduced model to a macrospin approximation. The macrospin ordinary differential equation is treated analytically as a weakly damped Hamiltonian system, and an orbit-averaging method is used to understand transitions in solution behaviors in terms of a discrete dynamical system. The predictions of our reduced model are compared to those of the full Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin. 
Ross G. Lund, Gabriel D. Chaves O'Flynn, Andrew D. Kent, Cyrill B.   Muratov
cond-mat.mes-hall cond-mat.mtrl-sci