Math @ Duke

Publications [#347413] of Stephanos Venakides
Papers Published
 Komineas, S; Melcher, C; Venakides, S, The profile of chiral skyrmions of small radius,
Nonlinearity, vol. 33 no. 7
(July, 2020),
pp. 33953408, IOP Publishing [doi]
(last updated on 2021/05/15)
Abstract: Chiral skyrmions are stable particlelike solutions of the LandauLifshitz equation for ferromagnets with the DzyaloshinskiiMoriya (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 farfield and nearfield 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 BelavinPolyakov solution with an infinitesimally small radius, as the DM parameter is increased from zero. The skyrmion retains the BelavinPolyakov profile over and wellbeyond the core before it assumes an exponential decay; the profile of an axiallysymmetric BelavinPolyakov solution of unit degree plays the role of the universal core profile of chiral skyrmions.


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