Statistical properties and configurational entropy of a two-dimensional Néel magnetic skyrmions population

The study of the thermodynamic properties of topological defects is important not only for understanding their magnetic properties but also for suggesting novel applications. In this paper, the statistical and statistical thermodynamic properties of a population of Néel magnetic skyrmion diameters hosted in an ultrathin cylindrical dot is determined within a two-dimensional analytical approach. The statistical properties such as the skyrmion size are calculated in the region of skyrmion metastability and are compared with the ones obtained using a recent three-dimensional analytical approach based on the analogy with the Maxwell–Boltzmann distribution of dilute gas molecules. The investigations of the statistical thermodynamic properties focus on the calculation of the configurational entropy at thermodynamic equilibrium determined in the continuous limit from the Boltzmann order function. While the statistical properties are quantitatively similar passing from the two-dimensional to the three-dimensional approach, the configurational entropy calculated from the two-dimensional skyrmions distribution is considerably lower than the one obtained from the three-dimensional skyrmions distribution. Because of the strong resemblance between the statistical configurational entropy and Jaynes’s information entropy, it is suggested to use magnetic skyrmions as temperature and external field dependent information entropy carriers for a future potential technological application in the field of low-dimensional magnetic systems and skyrmionics.