Equilibrium thermodynamic properties of chiral skyrmions in ferromagnetic materials*

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 hedgehog and vortex-like skyrmions: 1) the internal energy of a single chiral skyrmion; 2) the skymion radius depending on magnetic and geometric parameters; 3) the skyrmion configurational entropy; 4) the partition function; 5) the free energy; 6) the pressure and 7) the equation of state of a skyrmion diameters population. For the calculation of the thermodynamic functions we nake the analogy between the skyrmion diameters population and the three-dimensional Maxwell-Boltzmann distribution of particles of an ideal gas [1]. It is shown that, in correspondence of the average skyrmion volumes, the pressure curves of the skyrmion diameters population intersect the pressure curves of the ideal gas at different temperatures. These results could advance the field of materials science with special regard to skyrmionics.
[1] R. Zivieri et al., Phys. Rev. B 99, 174440 (2019).