We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the single-hidden-layer neural network that only relies on the z projections of the spins. In this setup one needs a limited set of magnetic configurations to distinguish ferromagnetic, skyrmion and spin spiral phases, as well as their different combinations in transitional areas of the phase diagram. The network trained on the configurations for square-lattice Heisenberg model with Dzyaloshinskii-Moriya interaction can classify the magnetic structures obtained from Monte Carlo calculations for triangular lattice and vice versa. The second approach we apply, a minimum distance method performs a fast and cheap classification in cases when a particular configuration is to be assigned to only one magnetic phase. The methods we propose are also easy to use for analysis of the numerous experimental data collected with spin-polarized scanning tunneling microscopy and Lorentz transmission electron microscopy experiments.

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We study the role of static and dynamical Coulomb correlation effects on the electronic and magnetic properties of individual Mn, Fe, and Co adatoms deposited on the CuN surface. For these purposes, we construct a realistic Anderson model, solve it by using the finite-temperature exact diagonalization method, and compare the calculated one-particle spectral functions with the LDA + U densities of states. In contrast to Mn/CuN and Fe/CuN, the cobalt system tends to form the electronic excitations at the Fermi level. Based on the calculated magnetic response functions, transverse relaxation times for the magnetic moments of impurity orbitals are estimated. To study the effect of the dynamical correlations on the exchange interaction in nanoclusters, we solve the two-impurity Anderson model for the Mn dimer on the CuN surface. It is found that the experimental exchange interaction can be well reproduced by employing U = 3 eV, which is two times smaller than the value used in static mean-field LDA + U calculations. This suggests an important role of dynamical correlations in the interaction between adatoms on a surface. To estimate the correlated exchange interaction in the general case we derive a simple and transparent analytical expression demonstrating that the renormalization of the electronic spectrum due to dynamical correlations leads to a rescaling of the magnetic interactions compared to density functional results.

We report on the stabilization of the topological bimeron excitations in confined geometries. The Monte Carlo simulations for a ferromagnet with a strong Dzyaloshinskii-Moriya interaction revealed the formation of a mixed skyrmion-bimeron phase. The vacancy grid created in the spin lattice drastically changes the picture of the topological excitations and allows one to choose between the formation of a pure bimeron and skyrmion lattice. We found that the rhombic plaquette provides a natural environment for stabilization of the bimeron excitations. Such a rhombic geometry can protect the topological state even in the absence of the magnetic field.

We propose an approach for low-dimensional visualisation and classification of complex topological magnetic structures formed in magnetic materials. Within the approach one converts a three-dimensional magnetic configuration to a vector containing the only components of the spins that are parallel to the z axis. The next crucial step is to sort the vector elements in ascending or descending order. Having visualized profiles of the sorted spin vectors one can distinguish configurations belonging to different phases even with the same total magnetization. For instance, spin spiral and paramagnetic states with zero total magnetic moment can be easily identified. Being combined with a simplest neural network our profile approach provides a very accurate phase classification for three-dimensional magnets characterized by complex multispiral states even in the critical areas close to phases transitions. By the example of the skyrmionic configurations we show that profile approach can be used to separate the states belonging to the same phase.