Mode coupling in spin torque oscillators

A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator. Examples are observed mode-hopping or mode coexistence. There has been some intial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we derive such a theory starting with the Landau-Lifshitz-Gilbert equation for magnetization dynamics. We compare our results with the single-mode theory, and show how it is a natural extension of that theory to include mode interactions.