Faraday kinks connecting parametric waves in magnetic wires

Abstract

Kinks are domain walls connecting symmetric equilibria and emerge in several branches of science. Here, we report topological kinks connecting Faraday-type waves in a magnetic wire subject to dissipation and a parametric injection of energy. We name these structures Faraday kinks. The wire magnetization is excited by a time-dependent magnetic field and evolves according to the one-dimensional Landau–Lifshitz–Gilbert equation. In the case of high magnetic anisotropy and low energy injection and dissipation, this model is equivalent to a perturbative sine-Gordon equation, which exhibits 2π kinks that connect uniform states. We show that kinks connecting Faraday-type waves also exist in the damped and parametrically driven sine-Gordon equation, corresponding to the localized structures observed in the magnetic system. The solutions are robust; indeed, the bifurcation diagram reveals that kinks are stable, independently if the Faraday patterns are standing waves or have a dynamic amplitude or phase. Analysis of the nearly integrable limit of the sine-Gordon equation, as well as its description in terms of a fast and a slow variable, i.e., the Kapitza limit, provide a useful interpretation of the kink as a non-parametric emitter that barely alters the fast standing waves. The existence of topological kinks connecting Faraday-type waves in the parametrically driven and damped Landau–Lifshitz–Gilbert and sine-Gordon equations, which model magnetic media, forced pendulum chains, and Josephson junctions, among other systems, suggest the universality of this self-organized structure.