Analysis Seminar

Phase Transition threshold and stability of magnetic skyrmions

Speaker: Slim Ibrahim, University of Victoria

Location: Warren Weaver Hall 1314

Date: Tuesday, December 5, 2023, 2:30 p.m.


After a very brief intro to chiral magnets, I will examine the stability of vortex-like configurations known as magnetic skyrmions. These correspond to critical points of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya (DM) interactions. From an earlier work of Doring and Melcher, it is known that the skyrmion is a ground state when the coefficient of the DM term is small. In my talk, I will quantify  an explicit critical threshold of that coefficient above which the skyrmion becomes unstable, while stable below it. In addition, in the unstable regime, I will show how the infimum of energy is not bounded from below, by giving an explicit counterexample with a sort of helical-shape configuration. This mathematically explains the occurrence of phase transition observed in some experiments. This is a joint work with I. Shimizu (Osaka, U.)


Special Analysis Seminar.