Two scenarios of spin-transfer switching and criteria for the corresponding threshold currents

It is useful to classify the spin-transfer switching events according to the scenarios of equilibrium destabilization: a local transformation or an equilibrium merging. We derive an invariant expression for the critical current of local transformation, discuss the critical current of merging, and consider the competition of the two scenarios. The critical current of saddle-point stabilization is also derived. Our results provide a intuitive picture for the behavior of spin-transfer devices, allowing one to make qualitative predictions and understand the limitations of some frequently used approximations.