  The stability of magnetic skyrmions has been investigated in the past, but
mostly in the absence of thermal fluctuations. However, thermal spin
fluctuations modify the magnetic properties (exchange stiffness,
Dzyaloshinskii-Moriya interaction (DMI) and anisotropy) that define skyrmion
stability. Thermal magnons also excite internal skrymion dynamics, deforming
the skyrmion shape. Entropy has also been shown to modify skyrmion lifetimes in
experiments, but is absent or approximated in previous studies. Here we use
metadynamics to calculate the free energy surface of a magnetic thin film in
terms of the topological charge and magnetization. We identify the free energy
minima corresponding to different spin textures and the lowest energy paths
between the ferromagnetic and single skyrmion states. We show that at low
temperatures 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 energy
barrier at low temperatures but decreases with increasing temperature and
eventually becomes the lowest energy barrier.
