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Equilibrium thermodynamic properties of chiral skyrmions in a ferromagnetic material

Roberto Zivieri

Chiral skyrmions forming in ferromagnetic systems are axisymmetric solitonic states attracting a lot of attention within the condensed matter community for their dazzling physical properties. In this study, the statistical and equilibrium thermodynamic properties of chiral magnetic skyrmions in a ferromagnetic material is investigated. This is accomplished by determining via analytical and numerical calculations: 1) The confi gurational entropy 2) The internal energy; 3) The partition function; 4) The free energy 5) The pressure The key result of this work is the derivation of an equation of state for a skyrmion diameters population and of the corresponding pressure that is compared to the well-known one of the ideal gas. For the calculation of the thermodynamic functions, it is used the analogy of a skyrmion diameters population with the three-dimensional Maxwell-Boltzmann distribution of particles of an ideal gas. The pressure of the Néel skyrmions population with skyrmion number S = -1 as a function of the volume V of the skyrmion diameters population at fi xed T. pressure p vs. volume V in the absence of an external bias fi eld for different isotherms is displayed. There is the dramatic increase of p with decreasing V below a given volume, depending on the temperature T. For a skyrmion of reduced size, the pressure exerted on the region of the ferromagnet just outside the skyrmion core is very high if compared to a skyrmion of intermediate size. Moreover, at fi xed volume, pressure reduces with reducing the skyrmion temperature in a way similar to that of the particles of an ideal gas. The pressure curve in the presence of an external magnetic fi eld shifts towards lower values. These results could advance the fi eld of materials science with special regard to low-dimensional magnetic systems.