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

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.

From Thermodynamics to Information: Landauer’s Limit and Negentropy Principle Applied to Magnetic Skyrmions

“…Exploiting this physical analogy with ideal gases, an analytical MB distribution for a 3D skyrmion diameter population [7,9] was proposed, and it was found an excellent agreement between the micromagnetic and the analytical results [7]. This analogy was also extended to the 2D skyrmion diameter distribution [8]. From the analogy with the 3D MB distribution of an ideal gas, the Gaussian distribution at the thermodynamic equilibrium at a given T and H for both 3D and 2D skyrmion diameter distribution can be written in the form…”

“…The skyrmion energy was calculated from the microscopic micromagnetic Hamiltonian as a spatial integral of the skyrmion energy density within the thin-film limit including exchange, interfacial DMI, magnetostatic and perpendicular anisotropy contributions, and external magnetic field interaction [7][8][9]. Within this model, the exchange interaction among spins forming the magnetic skyrmion was rigorously taken into account.…”

“…It has also been proposed the employment of magnetic skyrmions as information entropy carriers suggesting a data communication system based on the coding of information entropy [6]. This investigation stemmed from the theoretical and numerical exploration of the thermodynamic properties of magnetic skyrmions [7][8][9][10]. In this respect, the link between the physical and information entropies has been a subject matter of several studies [11][12][13][14][15].…”

“…In this perspective article, this kind of investigation was applied to magnetic skyrmions. The aim of this study was threefold: 1) to show that Landauer's limit is expressed in terms of variation of negentropy for a Néel skyrmion; 2) to show that the generalized second principle of thermodynamics based on Brillouin's negentropy principle can be applied to a Néel skyrmion; and 3) to explain the interplay between information and negentropy and vice versa of a Néel skyrmion [6,8]. This discussion could open the route in prospect for a new way of storing and coding information by using magnetic topological defects.…”

Topological Spin Textures and Their Applications

“…For example, both theoretical and experimental works have suggested that skyrmions can be used as key components in conventional spintronic devices, such as racetrack-type memory and logic computing gates [2][3][4][5][6]. Recent works also suggested that skyrmions can be used for unconventional applications, including information entropy holders [7,8], random bit generators [9], and neuromorphic computing [10]. Moreover, some recent theoretical reports have pointed out the possibility that skyrmions can be used as qubits for quantum computing [11].…”