Abstract
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.
Highlights
The thermodynamic description of topological defects and topological phase transitions has been one of most important challenges of the modern condensed matter physics
Kosterlitz and Thouless deepened this type of investigation, arguing the existence of topological defects having the form of vortices in physical systems described by the XY model, such as superfluids [3,4,5]
They studied the thermodynamic behavior of these systems by means of the calculation of the Helmholtz free energy F showing that, for T→0 K and with increasing size, F can be minimized if no vortices appear, while above a critical temperature F is minimized if there is the formation of couples of unpaired vortices and anti-vortices
Summary
The thermodynamic description of topological defects and topological phase transitions has been one of most important challenges of the modern condensed matter physics. Kosterlitz and Thouless deepened this type of investigation, arguing the existence of topological defects having the form of vortices in physical systems described by the XY model, such as superfluids [3,4,5]. They studied the thermodynamic behavior of these systems by means of the calculation of the Helmholtz free energy F showing that, for T→0 K and with increasing size, F can be minimized if no vortices appear, while above a critical temperature F is minimized if there is the formation of couples of unpaired vortices and anti-vortices. On the basis of this analysis, they introduced the concept of defect-mediated topological phase transition in condensed matter physics systems, the so-called infinite-order Berezinskii–Kosterlitz–Thouless phase transition
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