The profile of chiral skyrmions of small radius

Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulae for the solution of the correspon...

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Bibliographic Details
Published in:Nonlinearity 2020-07, Vol.33 (7), p.3395-3408
Main Authors: Komineas, Stavros, Melcher, Christof, Venakides, Stephanos
Format: Article
Language:English
Subjects:
Dzyaloshinskii-Moriya interaction
magnetic skyrmion
micromagnetics
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Summary:Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulae for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively large anisotropy). The matching of these two fields leads to a formula for the skyrmion radius as a function of the DM parameter. The derived solutions show the different length scales which are present in the skyrmion profiles. The picture is thus created of a chiral skyrmion that is born out of a Belavin-Polyakov solution with an infinitesimally small radius, as the DM parameter is increased from zero. The skyrmion retains the Belavin-Polyakov profile over and well-beyond the core before it assumes an exponential decay; the profile of an axially-symmetric Belavin-Polyakov solution of unit degree plays the role of the universal core profile of chiral skyrmions.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ab81eb