English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We characterize skyrmions in ultrathin ferromagnetic films as localminimizers of a reduced micromagnetic energy appropriate for quasitwo-dimensional materials with perpendicular magnetic anisotropy andinterfacial Dzyaloshinskii-Moriya interaction. The minimization is carried outin a suitable class of two-dimensional magnetization configurations thatprevents the energy from going to negative infinity, while not imposing anyrestrictions on the spatial scale of the configuration. We first demonstrateexistence of minimizers for an explicit range of the model parameters when theenergy is dominated by the exchange energy. We then investigate the conformallimit, in which only the exchange energy survives and identify the asymptoticprofiles of the skyrmions as degree 1 harmonic maps from the plane to thesphere, together with their radii, angles and energies. A byproduct of ouranalysis is a quantitative rigidity result for degree $\pm 1$ harmonic mapsfrom the two-dimensional sphere to itself.

archive for rational mechanics and analysis

A quantitative description of skyrmions in ultrathin ferromagnetic films  and rigidity of degree $\pm1$ harmonic maps from $\mathbb{R}^2$ to  $\mathbb{S}^2$