2013/07/15 by Bin Hu, Hu, Bin, X. R. Wang +2
Computer Science · Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Dynamics and Pattern Formation #Physics of Superconductivity and Magnetism #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.1307.3825
9 pages. arXiv admin note: text overlap with arXiv:1304.2439
openalex publication_date 2013/07/15 · arxiv created 2013/07/20 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A powerful mathematical method for front instability analysis that was recently developed in the field of nonlinear dynamics is applied to the 1+1 (spatial and time) dimensional Landau-Lifshitz-Gilbert (LLG) equation. From the essential spectrum of the LLG equation, it is shown that the famous Walker rigid body propagating domain wall (DW) is not stable against the spin wave emission. In the low field region only stern spin waves are emitted while both stern and bow waves are generated under high fields. By using the properties of the absolute spectrum of the LLG equation, it is concluded that in a high enough field, but below the Walker breakdown field, the Walker solution could be convective/absolute unstable if the transverse magnetic anisotropy is larger than a critical value, corresponding to a significant modification of the DW profile and DW propagating speed. Since the Walker solution of 1+1 dimensional LLG equation can be realized in experiments, our results could be also used to test the mathematical method in a controlled manner.