Stable and unstable trajectories in a dipolar chain

TL;DR

This paper investigates the stability and dynamics of magnetic dipole chains, revealing how unstable solutions influence hysteresis, and demonstrates the existence of domain wall structures through experiments and bifurcation analysis.

Contribution

It provides a comprehensive bifurcation analysis of stable and unstable solutions in dipolar chains, linking symmetry changes to hysteresis and introducing experimental validation of domain wall states.

Findings

Unstable solutions shape hysteresis loops in the system.

Boundary basin entropy indicates fractal structures depend on damping.

Experimental confirmation of domain wall solutions at macroscale.

Abstract

In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping time scale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale.