# Slim Ibrahim: Phase Transition threshold and stability of magnetic skyrmions

**Time: **
Tue 2023-10-24 14.00 - 15.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Slim Ibrahim

**Abstract:**

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.)