Statistical Properties and Configurational Entropy of a Two-Dimensional Néel Magnetic Skyrmions Population

Roberto Zivieri

doi:10.3390/app10010352

Abstract

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 investigation 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.

Highlights

Magnetic skyrmions are axisymmetric topological solitons hosted in ferromagnetic materials stabilized by the Dzyaloshinskii–Moriya interaction (DMI), a relativistic exchange interaction [3,4]
In early 2000, Bogdanov and Rößler developed a phenomenological theory of chiral symmetry breaking in magnetic thin films and multilayers, and they predicted the formation of skyrmions in magnetic thin films and multilayers stabilized by induced
Regarding the statistical thermodynamic properties, the analysis focuses on the calculation of the configurational entropy as a function of the temperature T and of the external bias field in a 2D framework

Summary

Introduction

Magnetic skyrmions are axisymmetric topological solitons hosted in ferromagnetic materials (see [1,2] and references therein) stabilized by the Dzyaloshinskii–Moriya interaction (DMI), a relativistic exchange interaction [3,4]. There are two types of DMI, the interfacial DMI (IDMI) stabilizing chiral Néel (hedgehog-like) and the bulk DMI stabilizing Bloch (vortex-like) skyrmions. In early 2000, Bogdanov and Rößler developed a phenomenological theory of chiral symmetry breaking in magnetic thin films and multilayers, and they predicted the formation of skyrmions in magnetic thin films and multilayers stabilized by induced. Afterwards, it has been theoretically demonstrated that skyrmion structures can be formed as spontaneous ground states in magnetic metals with DMI interactions without the need of applying external fields or the presence of defects [6].

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