Phase transition thresholds and chiral magnetic fields of general degree

TL;DR

This paper analyzes phase transition thresholds and magnetic field effects in a 2D micromagnetic model, revealing new stability phenomena and classifying energy minimizers across topological degrees.

Contribution

It determines minimal energies for various degrees, proves minimizer uniqueness for specific degrees, and uncovers new stability transitions in the Landau--Lifshitz model.

Findings

Identified two types of phase transitions in the model.

Proved uniqueness of minimizers for degrees 0 and -1.

Discovered a new stability transition driven by Zeeman energy.

Abstract

We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of phase transitions consistent with physical observations. In addition, we prove the uniqueness of the energy minimizer in degrees $0$ and $-1$, and nonexistence of minimizers for all other degrees. Finally, we show that the homogeneous state remains stable even beyond the threshold at which the skyrmion loses stability, and we uncover a new stability transition driven by the Zeeman energy.