Faraday kinks connecting parametric waves in magnetic wires

• Published in: Communications in nonlinear science & numerical simulation Vol. 131; p. 107841
• Main Authors: Leon, Alejandro O., Berríos-Caro, Ernesto, León, Alejandra, Clerc, Marcel G.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2024
• Subjects: Faraday waves; Magnetic domain walls; Nonlinear magnetization dynamics; Parametrically driven systems; Topological Kinks; Faraday waves; Magnetic domain walls; Topological Kinks; Parametrically driven systems; Nonlinear magnetization dynamics
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.107841

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. •Faraday kinks are domain walls separating parametric waves.•Faraday kinks emerge in parametrically driven magnetic wires and sine-Gordon equation.•Faraday kinks are topologically protected loops in the circumferential phase space.