Mode coupling in spin torque oscillators

• Deriving equations for coupled modes in spin torque oscillators.
• Including Hamiltonian formalism and elimination of three–magnon processes.
• Thermal bath of magnons central to mode coupling.
• Numerical examples of circular and elliptical devices.

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, such as observed mode-hopping or mode coexistence. There has been some initial 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 rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.