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The stability of magnetic skyrmions has been investigated in the past, butmostly in the absence of thermal fluctuations. However, thermal spinfluctuations modify the magnetic properties (exchange stiffness,Dzyaloshinskii-Moriya interaction (DMI) and anisotropy) that define skyrmionstability. Thermal magnons also excite internal skrymion dynamics, deformingthe skyrmion shape. Entropy has also been shown to modify skyrmion lifetimes inexperiments, but is absent or approximated in previous studies. Here we usemetadynamics to calculate the free energy surface of a magnetic thin film interms of the topological charge and magnetization. We identify the free energyminima corresponding to different spin textures and the lowest energy pathsbetween the ferromagnetic and single skyrmion states. We show that at lowtemperatures the lowest free energy barrier is a skyrmion collapse process.However, this energy barrier increases with temperature. An alternative path,where a singularity forms on the skrymion edge, has a larger free energybarrier at low temperatures but decreases with increasing temperature andeventually becomes the lowest energy barrier.

Metadynamics calculations of the effect of thermal spin fluctuations on skyrmion stability