Charting the Skyrmion Free-Energy Landscape

Abstract

Chiral magnets with Dzyaloshinskii-Moriya interactions feature a rich phase diagram with a variety of thermodynamical phases. These include helical and conical spin arrangements and topologically charged objects such as (anti)skyrmions. Crucially, due to hysteresis effects, the thermodynamical phases can co-exist at any given temperature and external magnetic field, typically leading to metastability of, e.g., the material's topological phase. In this work, we use Monte Carlo simulations to study these effects. We compute the relative free energies of co-existing states, enabling us to determine the ground state at all values of the external parameters. We also introduce a method to estimate the activation energy, i.e. the height of the energy barrier that separates the topological phase from the ground state. This is one of the key ingredients for the determination of the skyrmion lifetime, which is relevant for technological applications. Finally, we prescribe predicting the system's evolution through any path in the space of external parameters. This can serve as a guideline to prepare the magnetic material in any desired phase or even trigger a phase transition in an experimental setup.