On the stationary solution of the ...
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Title :
On the stationary solution of the Landau-Lifshitz-Gilbert equation on a nanowire with constant external magnetic field
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English keyword(s) :
ferromagnetism
numerical simulation
Landau-Lifshitz-Gilbert equation
stationary solution
instability
numerical simulation
Landau-Lifshitz-Gilbert equation
stationary solution
instability
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
We consider an infinite ferromagnetic nanowire, with an energy functional $E$ with easy-axis in the direction $e_1$ and a constant external magnetic field $H_{ext} = h_0 e_1$ along the same direction.The evolution of its ...
Show more >We consider an infinite ferromagnetic nanowire, with an energy functional $E$ with easy-axis in the direction $e_1$ and a constant external magnetic field $H_{ext} = h_0 e_1$ 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 $h_0$, 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 \cite{Cote_Ferriere__2DW} and more generally the interactions between domain walls.Show less >
Show more >We consider an infinite ferromagnetic nanowire, with an energy functional $E$ with easy-axis in the direction $e_1$ and a constant external magnetic field $H_{ext} = h_0 e_1$ 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 $h_0$, 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 \cite{Cote_Ferriere__2DW} and more generally the interactions between domain walls.Show less >
Language :
Anglais
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Submission date :
2024-05-30T12:21:10Z
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