Seminars & Colloquia Calendar

MATHEMATICAL PHYSICS WEBINAR
RUTGERS UNIVERSITY

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Cyrill Muratov – Università di Pisa

Wednesday, August 7th, 10:45AM EDT 

Magnetic skyrmions: an overview

I will present an overview of the results on existence and asymptotic properties of magnetic skyrmions — particle-like topologically nontrivial two-dimensional spin textures that have been envisioned as bit encoding states in the emergent field of spintronics. Mathematically these are defined as topologically nontrivial maps of degree +1 from the plane to a sphere which minimize a micromagnetic energy containing the exchange, perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction (DMI) terms. In ultrathin films, the stray field energy simply renormalizes the anisotropy constant at leading order, but in finite samples it also produces additional non-trivial contributions at the sample edges, promoting nontrivial spin textures. Starting with the whole space problem, I will first discuss the existence of single skyrmions as global energy minimizers at sufficiently small DMI strength. Then, using the quantitative rigidity of the harmonic maps I will present the asymptotic characterization of single skyrmion profiles both in infinite and finite samples. Lastly, I will touch upon the question of existence of multi-skyrmion solutions as minimizers with higher topological degree and present recent existence results obtained jointly with T. Simon and V. Slastikov.