Numerical simulation of magnetic skyrmions on flat lattices

Abstract

We studied several types of flat lattices with direct exchange and Dzyaloshinskii-Moriya interaction between spins: a honeycomb lattice with 3 nearest neighbours (NN), a square lattice with 4 NN and a hexagonal or triangular lattice with 6 NN. For the analysis of data obtained during the Monte Carlo simulation, a convolutional neural network was used for the recognition of different phases of the spin system which was dependent on simulation parameters such as DMI and external magnetic field (Hz). Based on these data, the phase diagrams (Hz, D) for the different lattices were plotted. The various states of the systems under observation were visualised and the boundaries between the different phases were defined as a spiral, a skyrmion and others. The data from the numerical experiments will be used in further studies to determine the model parameters of the systems for the formation of a stable skyrmion state and the development of methods for controlling skyrmions in a magnetic film.

Calculation of Order Parameter and Critical Exponents of the Spin Glass in the Frame of Edwards-Anderson Model

“…It was shown that the search for GS of spin glasses in a three-dimensional lattice belongs to the NP-complete problem. As a result, many numerical approaches were proposed, such as, for example, genetic algorithms, cluster-exact approximation, renormalization-group approaches, Monte-Carlo methods are developed, such as multicanonical modeling, parallel tempering, the Metropolis algorithm and others [2,3,4].…”