6 - Static properties of magnetic skyrmions

Abstract

Chiral skyrmions hosted in ferromagnetic systems are axisymmetric solitonic states attracting a lot of attention for their dazzling physical properties and technological applications in storage and neuromorphic computing. In this chapter, we review the static properties of chiral magnetic skyrmions focusing on the recent results obtained on the equilibrium thermodynamic properties of a population of skyrmion diameters by means of micromagnetic simulations and analytical calculations. This is accomplished taking into account the strict analogy of a skyrmion diameters population with the particles behavior in an ideal gas. The skyrmion energy can be modeled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann (MB) distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas MB molecules distribution of velocities at thermodynamic equilibrium. The analysis is applied to hedgehog-like or Néel magnetic skyrmions developing in a ferromagnetic material having the shape of an ultrathin cylindrical dot and can be extended to other types of ferromagnetic materials. The calculation of the skyrmion average energy and of the configurational entropy, due to thermally induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. Although 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. Despite magnetic skyrmions are planar structures, the advantages of the three-dimensional description are underlined. Finally, the use of skyrmions as information entropy carriers for a future potential technological application in the field of low-dimensional magnetic systems and skyrmionics is reviewed.