A high-temperature expansion method for calculating paramagnetic exchange interactions

The method for calculating the isotropic exchange interactions in the paramagnetic phase is proposed. It is based on the mapping of the high-temperature expansion of the spin-spin correlation function calculated for the Heisenberg model onto Hubbard Hamiltonian one. The resulting expression for the exchange interaction has a compact and transparent formulation. The quality of the calculated exchange interactions is estimated by comparing the eigenvalue spectra of the Heisenberg model and low-energy magnetic part of the Hubbard model. By the example of quantum rings with different hopping setups we analyze the contributions from the different part of the Hubbard model spectrum to the resulting exchange interaction.Comment: 8 pages, 8 figure

Monte Carlo study of magnetic nanoparticles adsorbed on halloysite Al2Si2O5(OH)4Al_2Si_2O_5(OH)_4 nanotubes

We study properties of magnetic nanoparticles adsorbed on the halloysite surface. For that a distinct magnetic Hamiltonian with random distribution of spins on a cylindrical surface was solved by using a nonequilibrium Monte Carlo method. The parameters for our simulations: anisotropy constant, nanoparticle size distribution, saturated magnetization and geometrical parameters of the halloysite template were taken from recent experiments. We calculate the hysteresis loops and temperature dependence of the zero field cooling (ZFC) susceptibility, which maximum determines the blocking temperature. It is shown that the dipole-dipole interaction between nanoparticles moderately increases the blocking temperature and weakly increases the coercive force. The obtained hysteresis loops (e.g., the value of the coercive force) for Ni nanoparticles are in reasonable agreement with the experimental data. We also discuss the sensitivity of the hysteresis loops and ZFC susceptibilities to the change of anisotropy and dipole-dipole interaction, as well as the 3d-shell occupation of the metallic nanoparticles; in particular we predict larger coercive force for Fe, than for Ni nanoparticles.Comment: 10 pages, 12 figure

Bimeron nanoconfined design

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.Comment: 5 pages, 7 figure

Profile approach for recognition of three-dimensional magnetic structures

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

Supervised learning magnetic skyrmion phases

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 ferromag- netic, 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.Comment: 9 pages, 14 figures. Accepted for publication in Physical Review

Reconstruction of classical skyrmions from Anderson towers: quantum Darwinism in action

The development of the quantum skyrmion concept is aimed at expanding the scope of the fundamental research and practical applications for classical topologically-protected magnetic textures, and potentially paves the way for creating new quantum technologies. Undoubtedly, this calls for establishing a connection between a classical skyrmion and its quantum counterpart: a skyrmion wave function is an intrinsically more complex object than a non-collinear configuration of classical spins representing the classical skyrmion. Up to date, such a quantum-classical relation was only established on the level of different physical observables, but not for classical and quantum states per se. In this work, we show that the classical skyrmion spin order can be reconstructed using only the low-energy part of the spectrum of the corresponding quantum spin Hamiltonian. This can be done by means of a flexible symmetry-free numerical realization of Anderson's idea of the towers of states (TOS) that allows one to study known, as well as unknown, classical spin configurations with a proper choice of the loss function. We show that the existence of the TOS in the spectrum of the quantum systems does not guarantee a priori that the classical skyrmion magnetization profile can be obtained as an outcome of the actual measurement. This procedure should be complemented by a proper decoherence mechanism due to the interaction with the environment. The later selects a specific combination of the TOS eigenfunctions before the measurement and, thus, ensures the transition from a highly-entangled quantum skyrmionic state to a classical non-collinear magnetic order that is measured in real experiments. The results obtained in the context of skyrmions allow us to take a fresh look at the problem of quantum antiferromagnetism.Comment: 15 pages, 10 figure

Green-function method in the theory of ultraslow electromagnetic waves in an ideal gas with Bose-Einstein condensates

We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.Comment: 15 pages, 6 figure

Monte Carlo study of magnetic nanoparticles adsorbed on halloysite Al2Si2O5(OH)4 nanotubes

This work was supported by the Russian Science Foundation, Grant 15-12-20021. Details of this research were published and available at Ref. [4]

Tunable dimer systems of cobalt atoms on phosphorene

In this work we report on a comprehensive study of a dimer system, two cobalt atoms on phosphorene surface. Since each cobalt atom can be stabilized in high- and low-spin states, the couplings in this dimer system can be tuned. More specifically, it was shown that applying a small bias voltage one can change interaction between two atoms within dimer from ferro-magnetic to antiferromagnetic and vice versa.This work was supported by the Russian Science Foundation, Grant No. 17-72-20041

Correlation effects in insulating surface nanostructures

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 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, the relative 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 on important role of dynamical correlations in the interaction between adatoms on a surface.Comment: 8 pages, 8 figure