Spin-Transfer-Driven Magnetization Dynamics

Abstract

This chapter deals with the analytical study of dynamics driven by the joint action of applied magnetic fields and spin-polarized current injection. Most experimental work and theoretical analysis in this area are concerned with three-layer structures consisting of a “pinned” magnetic layer with a fixed magnetization, a nonmagnetic spacer, and a “free” magnetic layer. The generalization of the Landau–Lifshitz–Gilbert (LLG) equation to the case of spin-polarized current injection is discussed. It is stressed that the addition of the spin-transfer term does not affect the conservation of the magnetization magnitude and the normalized LLC–Slonczewski equation describes the magnetization dynamics on the unit sphere. The phenomenon of self-oscillations (limit cycles) is also studied. The physical origin of self-oscillations is the balancing out of the energy dissipation due to the damping by the energy influx due to the spin-polarized current injection. This balancing occurs not locally in time, but rather over one precessional period. To identify the precessional trajectories over which this balancing occurs, the appropriate Melnikov function is introduced. The chapter concludes with the discussion of axially symmetric nanopillar devices when the directions of the applied dc magnetic field and the easy axes of the free and pinned layers are normal to the plane of the layers.