Interfacial magnetic skyrmions are topological spin textures which have been proposed for use as information carriers in spintronic devices 1. Hence, it is vital that their creation, annihilation, and motion can be accurately controlled 1. Still, their thermal stability and interactions with lattice defects are not fully understood. Recently, many groups studied the skyrmion creation/annihilation energy paths by reconstructing associated free energy landscapes (FELs) and calculating the minimum energy paths, by combining micromagnetic simulations with an enhanced sampling technique called the nudged elastic band method (NEBM) 2. However, micromagnetics and NEBM do not fully account for thermal effects. In addition, most computational models assume defect-free material interfaces with idealized magnetic parameters; while lattice defects alter the skyrmion dynamics and show potential to be used as pinning, destruction/creation points in future devices.

To address these, we use atomic scale magnetic simulations combined with an enhanced sampling technique named metadynamics to reconstruct non-trivial FELs of certain skyrmion degrees of freedom called as collective variables (CVs) in metadynamics. Metadynamics systematically adds a potential bias on the CVs to sample states outside of the thermodynamic equilibrium and explore the whole configurational space 3,4. Traditionally, this has been used to understand how molecules bind to surfaces. Recently, metadynamics has been used in magnetism to study simple situations such as the temperature dependence of anisotropy CVs 5. We use it to explore how spin textures interact with defects. Thus, we demonstrate that metadynamics can be extensively used in computational magnetism to study the behaviour of spin textures by selecting appropriate CVs. Mainly, we use metadynamics to study the thermal stability of skyrmions, via studying the annihilation/creation energy barriers as a function of temperature. Additionally, we investigate how various defects modify these FELs and their associated energy barriers. Ultimately, we explore if certain defects alter the skyrmion stability, trap/repel skyrmions, disturb their motion and prevent/help their creation/annihilation.

References
1 A. Fert, N. Reyren, V. Cros, Nat Rev Mater 2, 17031 (2017) 2 D. Cortés-Ortuño, W. Wang, M. Beg, et al. Sci Rep 7, 4060 (2017) 3 A. Laio, L. Parrinello, PNAS 99, 20 (2002) 4 G. Bussi, A. Laio, Nat Rev Phys 2, 200–212 (2020). 5 B. Nagyfalusi, L. Udvardi, L. Szunyogh, Phys. Rev. B 100, 174429 (2019)