# Tunable mode coupling in nano-contact spin torque oscillators

## TL;DR

This paper develops a theoretical framework with rate equations to analyze tunable linear and nonlinear mode coupling in nano-contact spin torque oscillators, explaining multimode behaviors observed experimentally.

## Contribution

It derives explicit expressions for mode coupling terms and maps the dynamics onto a phase space, advancing understanding of multimode interactions in spin torque oscillators.

## Key findings

- Mode coupling depends on external magnetic field and temperature.
- Phase space analysis reveals manifolds of periodic orbits and fixed points.
- The model explains mode-hopping and coexistence phenomena.

## Abstract

Recent experiments on spin torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode-coexistence, mode-hopping, and temperature-driven cross-over between modes. Initial multimode theory has indicated that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nano-contact spin torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space, and demonstrate in the phase portraits, how the manifolds of periodic orbits and fixed points vary with external magnetic field as well as with temperature.