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 timescale 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.
Bibliographical noteFunding Information:
J.C. thanks FONDECYT (Chile) for financial support through Grant No. 1210297. F.U. thanks FONDECYT (Chile) for financial support through Postdoctoral Grant No. 3180227. C.P. acknowledges support from the CM-iLab. A.C. acknowledges support from the CODEV Seed Money Programme of the École Polytechnique Fédérale de Lausanne (EPFL), and the support of the Design Engineering Center at UAI.
© 2021 American Physical Society.