We present the simulation results of magnetic 2D and 3D structures with direct (for both of them) and Dzyaloshinskii-Moriya (DMI) (for 2D lattice) interactions in the frame of the Heisenberg model. We have adapted the multipath Metropolis algorithm for systems with complex types of exchange interactions and rough energy landscapes. We show the temperature behavior of magnetization, energy, and heat capacity, and reveal its critical temperatures and order parameter.
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.
In this paper, we present the results of a numerical simulation of thermodynamics for the array of Classical Heisenberg spins placed on a 2D square lattice, which effectively represents the behaviour of a single layer. Using the Metropolis algorithm, we show the temperature behaviour of the system with a competing Heisenberg and Dzyaloshinskii-Moriya interaction (DMI) in contrast with the classical Heisenberg system. We show the process of nucleation of the skyrmion depending on the value of the external magnetic field. We proposed the controlling method for the movement of skyrmions.
The results of numerical calculations of the thermodynamic properties of multilayer films with alternating magnetic and non-magnetic layers were presented. Computer simulation of such structures within the frame of the classical Heisenberg model was carried out by Monte Carlo methods. The processes of magnetization reversal of multilayer structures in external magnetic fields were investigated.
We utilize the Metropolis algorithm to obtain statistical averages of the domain wall length in a FePt granular structure after remagnetization is performed by an ultrashort polarized laser impulse. We propose and check the cluster-size-based order parameter, which along with magnetization, shows the domain wall length, and as a consequence, the average cluster size in the system. We treat the inverse Faraday effect as an external directed magnetic field and show impulse time- and laser power- dependent estimates within the Heisenberg model.
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