On the stationary solution of the Landau-Lifshitz-Gilbert equation on a nanowire with constant external magnetic field

2024/05/29 by Guillaume Ferriere, Ferriere, Guillaume
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.18829

openalex publication_date 2024/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider an infinite ferromagnetic nanowire, with an energy functional E with easy-axis in the direction e₁ and a constant external magnetic field H_ext = h₀ e₁ along the same direction. The evolution of its magnetization is governed by the Landau-Lifshitz-Gilbert equation (LLG) associated to E. Under some assumptions on h₀, we prove the existence of stationary solutions with the same limits at infinity, their uniqueness up to the invariances of the equation and the instability of their orbits with respect to the flow. This property gives interesting new insights of the behavior of the solutions of (LLG), which are completed by some numerical simulations and discussed afterwards, in particular regarding the stability of 2-domain wall structures proven in \citeCote_Ferriere_₂DW and more generally the interactions between domain walls.

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