The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modeled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution of velocities at thermodynamic equilibrium. The calculation of the skyrmion configurational entropy, due to thermally induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics.

• Received 12 March 2019
• Revised 14 May 2019
• Corrected 11 July 2019

DOI:https://doi.org/10.1103/PhysRevB.99.174440