Cisternas, J., & Concha, A. (2024). Searching nontrivial magnetic equilibria using the deflated Newton method. Chaos Solitons Fractals, 179, 114468.
Abstract: Nonlinear systems that model physical experiments often have many equilibrium configurations, and the number of these static solutions grows with the number of degrees of freedom and the presence of symmetries. It is impossible to know a priori how many equilibria exist and which ones are stable or relevant, therefore from the modeler's perspective, an exhaustive search and symmetry classification in the space of solutions are necessary. With this purpose in mind, the method of deflation (introduced by Farrell as a modification of the classic Newton iterative method) offers a systematic way of finding every possible solution of a set of equations. In this contribution we apply deflated Newton and deflated continuation methods to a model of macroscopic magnetic rotors, and find hundreds of new equilibria that can be classified according to their symmetry. We assess the benefits and limitations of the method for finding branches of solutions in the presence of a symmetry group, and explore the high dimensional basins of attraction of the method in selected 2 dimensional sections, illustrating the effect of deflation on the convergence.

Mellado, P., Concha, A., Hofhuis, K., & Tapia, I. (2023). Intrinsic chiral field as vector potential of the magnetic current in the zigzag lattice of magnetic dipoles. Sci. Rep., 13(1), 1245.
Abstract: Chiral magnetic insulators manifest novel phases of matter where the sense of rotation of the magnetization is associated with exotic transport phenomena. Effective control of such phases and their dynamical evolution points to the search and study of chiral fields like the DzyaloshinskiiMoriya interaction. Here we combine experiments, numerics, and theory to study a zigzag dipolar lattice as a model of an interface between magnetic inplane layers with a perpendicular magnetization. The zigzag lattice comprises two parallel sublattices of dipoles with perpendicular easy plane of rotation. The dipolar energy of the system is exactly separable into a sum of symmetric and antisymmetric longrange exchange interactions between dipoles, where the antisymmetric coupling generates a nonlocal DzyaloshinskiiMoriya field which stabilizes winding textures with the form of chiral solitons. The DzyaloshinskiiMoriya interaction acts as a vector potential or gauge field of the magnetic current and gives rise to emergent magnetic and electric fields that allow the manifestation of the magnetoelectric effect in the system.
