Magnetic Skyrmions Under Confinement

Document Type

Article

Publication Date

12-1-2023

Abstract

We present a variational treatment of confined magnetic skyrmions in a minimal micromagnetic model of ultrathin ferromagnetic films with interfacial Dzylashinksii-Moriya interaction (DMI) in competition with the exchange energy, with a possible addition of perpendicular magnetic anisotropy. Under Dirichlet boundary conditions that are motivated by the asymptotic treatment of the stray field energy in the thin film limit we prove existence of topologically non-trivial energy minimizers that concentrate on points in the domain as the DMI strength parameter tends to zero. Furthermore, we derive the leading order non-trivial term in the Γ -expansion of the energy in the limit of vanishing DMI strength that allows us to completely characterize the limiting magnetization profiles and interpret them as particle-like states whose radius and position are determined by minimizing a renormalized energy functional. In particular, we show that in our setting the skyrmions are strongly repelled from the domain boundaries, which imparts them with stability that is highly desirable for applications. We provide explicit calculations of the renormalized energy for a number of basic domain geometries.

Identifier

85175831397 (Scopus)

Publication Title

Communications in Mathematical Physics

External Full Text Location

https://doi.org/10.1007/s00220-023-04864-w

e-ISSN

14320916

ISSN

00103616

First Page

1571

Last Page

1605

Issue

3

Volume

404

Grant

DMS-1908709

Fund Ref

Università di Pisa

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