Moving domain walls in magnetic nanowires

Kühn, Katharina

doi:10.1016/j.anihpc.2008.11.004

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…Γ-convergence results are also known in some other asymptotic regimes of nanowire where the stray-field contribution is still present in the Γ-limit functional, though as a local term (see e.g. [29,24,25,7]).…”

Section: γ-mentioning

confidence: 79%

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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Section: γ-mentioning

confidence: 79%

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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show abstract

“…The understanding of walls dynamics in one dimensional devices like ferromagnetic nanowires is very important for the applications, in particular for the storage of digital information (see [37]). For 3-dimensional models of nanowires, let us mention the works of Khün who constructs wall profiles for thin nanowires in [24] and [25]. For one dimensional models of nanowires, the description of walls motion is more complete (see [38] and the references given below).…”

Section: Contextmentioning

confidence: 99%