Statistical thermodynamics of chiral skyrmions in a ferromagnetic material

Solitons are a challenging topic in condensed matter physics and materials science because of the interplay between their topological and physical properties and for the crucial role they play in topological phase transitions. Among them, chiral skyrmions hosted in ferromagnetic systems are axisymmetric solitonic states attracting a lot of attention for their dazzling physical properties and technological applications. In this paper, the equilibrium statistical thermodynamics of chiral magnetic skyrmions developing in a ferromagnetic material having the shape of an ultrathin cylindrical dot is investigated. This is accomplished by determining via analytical calculations for both Néel and Bloch skyrmions: (1) the internal energy of a single chiral skyrmion; (2) the partition function; (3) the free energy; (4) the pressure; and (5) the equation of state of a skyrmion diameters population. To calculate the thermodynamic functions for points (2)-(5), the derivation of the average internal energy and of the configurational entropy is crucial. Numerical calculations of the thermodynamic functions for points (1)-(5) are applied to Néel skyrmions. These results could advance the field of materials science with special regard to low-dimensional magnetic systems.