Analysis and PDE Seminar: Skyrmions and stability of degree ±1 harmonic maps from the plane to the two-dimensional sphere

Seminar | August 26 | 4:10-5 p.m. | 939 Evans Hall

 Thilo Simon, New Jersey Institute of Technology

 Department of Mathematics

Skyrmions are topologically nontrivial patterns in the magnetization of extremely thin ferromagnets. Typically thought of as stabilized by the so-called Dzyaloshinskii-Moriya interaction (DMI), or antisymmetric exchange interaction, arising in such materials, they are of great interest in the physics community due to possible applications in memory devices.

In this talk, I will characterize skyrmions as local minimizers of a two-dimensional limit of the full micromagnetic energy, augmented by DMI and retaining the nonlocal character of the stray field energy. In the regime of dominating Dirichlet energy, I will provide rigorous predictions for their size and "wall angles". The main tool is a quantitative stability result for harmonic maps of degree ± 1 from the plane to the two-dimensional sphere, relating the energy excess of any competitor to the homogeneous H¹-distance to the closest harmonic map. This is joint work with Anne Bernand-Mantel and Cyrill B. Muratov.

 tdepoyfe@math.berkeley.edu