Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation

Abstract

We report the development, implementation and complete experimental vindication of a model for complex dynamical behaviors in spin wave envelopes propagating in nonlinear, dissipative driven, damped systems. These backward volume spin waves evolve under attractive nonlinearity in active magnetic thin film-based feedback rings where the major loss mechanisms present in the film are directly compensated by periodic linear amplification. Such a quasi-conservative evolution allows for the self-generation of spin waves and the observation of long-time behaviors $\mathcal{O}(\mathrm{ms})$ which persist for hundreds to tens of thousands of the fundamental round trip time $\mathcal{O}(100~\mathrm{ns})$. The cubic-quintic complex Ginzburg-Landau equation is developed as a predictive, descriptive model for the evolution of spin wave envelopes. Over 180000 nodes hours of computation are used to execute more than 10000 simulations in order characterize the model's six dimensional parameter space. This exploration of parameter space was conducted in full generality, spanning a minimum of eight orders of magnitude for each of three loss terms and five orders of magnitude for higher order nonlinearities. Nine distinct classes of behavior were identified, including four categories of dynamical pattern formation. This work contains the first predicted long time dynamical behaviors for spin waves and analogous physical systems. All four categories of dynamical pattern formation that were identified numerically were then cleanly realized experimentally. Additionally we observed the first known examples of dynamical behaviors for dark solitary waves self-generated under attractive nonlinearity. Our experimental verification of these dynamical regimes show that such ideas are not simply theoretical but in fact occur in the real physical world and are observable in an approachable, tunable spin-wave system which matches the conditions of many other real-world physical systems. It further established that the relatively simple cubic-quintic complex Ginzburg-Landau equation provides a highly accurate, effective, and predictive description of complex spin wave dynamics and should replace the commonly used nonlinear Schr\"odinger equation for these systems. Finally, simulations which model the ring dynamics on the scale round trips were conducted using 130000 node hours over 3000 unique numerical simulations. This yielded a robust general solution for stable bright solitary wave trains evolving under periodic amplification which is the numerical equivalent to the bright solitary wave train initial condition perturbed experimentally to generate soliton fractals and chaotic solitons. Using this novel dynamical equilibrium as an initial condition we developed a mechanism for the generation of bright soliton fractals. Our experimental and numerical works on complex spin wave envelopes in magnetic thin films suggest these systems provide for an approachable, table top, experiment for the study of fundamental nonlinear wave physics. The cubic-quintic complex Ginzburg-Landau model further provides for means for both prediction and verification of results. The physics reported here are expected to be wildly applicable to related fields of physics that are described by isomorphic forms of our model. This includes fields such as nonlinear optics, nonlinear hydrology and Bose-Einstein condensation.