Metastability of Wall Configurations in Ferromagnetic Nanowires

Carbou, Gilles

doi:10.1137/13090568x

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…Here we mention only that the Landau-Lifschitz theory of ferromagnetizm requires coupling of equations (1.1) and (1.2) with the Maxwell equations in the whole space. They need not be introduced in this paper because in one-dimensional domain the effect of coupling is incorporated in the term βg(M )f (M ), see [19] for details. Finally, we note that the case of one-dimensional domain while being relatively simple (contrary to the multidimensional case, smooth solutions exist) is important for physics of ferromagnetism and applications of ferromagnetic nanowires, see [19].…”

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confidence: 99%

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

Brzeźniak

Gołdys

Jegaraj

2017

Arch Rational Mech Anal

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We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property. Next, we prove the large deviations principle for small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is compactness, or weak to strong continuity, of the solution map for a deterministic Landau-Lifschitz equation, when considered as a transformation of external fields. We then apply this large deviations principle to show that small noise can cause magnetisation reversal. We also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise. The problem is motivated by applications of ferromagnetic nanowires to the fabrication of magnetic memories.

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confidence: 99%

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

Brzeźniak

Gołdys

Jegaraj

2017

Arch Rational Mech Anal

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“…A precise description of all these non-planar solutions could help us to prove that the solutions M l 0 and M k,λ 0 are isolated. This could be of great help in demonstrating true instability results instead of linear instability theorems (see Theorems 6,7,and 8).…”

Section: Discussionmentioning

confidence: 99%

“…where R(ϕ) is defined by (8). By projection of the mobile frame (M 1 k,λ (θ ), M 2 ), we construct a one-parameter family V(ϕ) of static solutions for (20) given by:…”

Section: B Proof Of Theoremmentioning

confidence: 99%

“…This property plays an important role in numerical data storage since the information is encoded by the localization of DWs (see [2,15,20]). Because of these potential applications, DW dynamics in ferromagnetic wires is intensively investigated as well in Physics (see [16,19,[23][24][25][26][27]) as in Mathematics (see [3,8,10,17,22]). In [12,14,18], DW dynamics and magnetization reversal in ferromagnetic rings are investigated.…”

Section: Introductionmentioning

confidence: 99%

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Stability of steady states in ferromagnetic rings

Moussaoui

Rachi

2022

Journal of Mathematical Physics

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“…Earlier stability results (for 2 perturbation) were obtained by Carbou and Labbé [6] for static domain walls (called Bloch walls), in the absence of applied field. Jizzini [22] establishes 1 stability under a constant applied field (up to the optimal size), without proving any exponential decay, see also [4,5]. These cited works are done in the absence of DMI, i.e., = 0.…”

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confidence: 99%

Asymptotic stability of precessing domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction

Côte¹,

Ignat²

2022

Preprint

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RAPHAËL CÔTE AND RADU IGNAT A. We consider a ferromagnetic nanowire and we focus on an asymptotic regime where the Dzyaloshinskii-Moriya interaction is taken into account.First we prove a dimension reduction result via Γ-convergence that determines a limit functional defined for maps : R → S 2 in the direction 1 of the nanowire. The energy functional is invariant under translations in 1 and rotations about the axis 1 . We fully classify the critical points of finite energy when a transition between − 1 and 1 is imposed; these transition layers are called (static) domain walls.The evolution of a domain wall by the Landau-Lifshitz-Gilbert equation associated to under the effect of an applied magnetic field ℎ( ) 1 depending on the time variable gives rise to the so-called precessing domain wall. Our main result proves the asymptotic stability of precessing domain walls for small ℎ in ∞ ([0, +∞)) and small 1 (R) perturbations of the static domain wall, up to a gauge which is intrinsic to invariances of the functional .

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Metastability of Wall Configurations in Ferromagnetic Nanowires

Abstract: In this paper we consider a one dimensional model of ferromagnetic nanowire subject to a non constant electromagnetic field. Taking into account the ratio between the exchange length and the length of the wire, we prove that the wall configurations are persistent in a large time interval.

Cited by 7 publications

References 33 publications

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

Stability of steady states in ferromagnetic rings

Asymptotic stability of precessing domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction

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