Spin torque driven dynamics of a coupled two layer structure: interplay between conservative and dissipative coupling

TL;DR

This paper develops an analytical and numerical model for the nonlinear spin wave dynamics in a two-layer coupled system, highlighting the role of dissipative coupling and explaining the frequency shift transition observed experimentally.

Contribution

It introduces a novel analytical description incorporating dissipative effects into the phase dynamics of coupled spin systems, validated by numerical simulations.

Findings

Dissipative coupling significantly influences the phase dynamics.

The model explains the redshift to blueshift frequency transition.

High mode hybridization is necessary for blueshift regime.

Abstract

In this manuscript the general concepts of spin wave theory are adapted to the dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the non-linear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most basic features of the dynamics of coupled systems. Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e. high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed.