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

Neural network agent playing spin Hamiltonian games on a quantum computer

Quantum computing is expected to provide new promising approaches for solving the most challenging problems in material science, communication, search, machine learning and other domains. However, due to the decoherence and gate imperfection errors modern quantum computer systems are characterized by a very complex, dynamical, uncertain and fluctuating computational environment. We develop an autonomous agent effectively interacting with such an environment to solve magnetism problems. By using the reinforcement learning the agent is trained to find the best-possible approximation of a spin Hamiltonian ground state from self-play on quantum devices. We show that the agent can learn the entanglement to imitate the ground state of the quantum spin dimer. The experiments were conducted on quantum computers provided by IBM. To compensate the decoherence we use local spin correction procedure derived from a general sum rule for spin-spin correlation functions of a quantum system with even number of antiferromagnetically-coupled spins in the ground state. Our study paves a way to create a new family of the neural network eigensolvers for quantum computers.Comment: Local spin correction procedure was used to compensate real device errors; comparison with variational approach was adde

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

Estimating Patterns of Classical and Quantum Skyrmion States

In this review we discuss the latest results concerning development of the machine learning algorithms for characterization of the magnetic skyrmions that are topologically-protected magnetic textures originated from the Dzyaloshinskii-Moriya interaction that competes Heisenberg isotropic exchange in ferromagnets. We show that for classical spin systems there is a whole pool of machine approaches allowing their accurate phase classification and quantitative description on the basis of few magnetization snapshots. In turn, investigation of the quantum skyrmions is a less explored issue, since there are fundamental limitations on the simulation of such wave functions with classical supercomputers. One needs to find the ways to imitate quantum skyrmions on near-term quantum computers. In this respect, we discuss implementation of the method for estimating structural complexity of classical objects for characterization of the quantum skyrmion state on the basis of limited number of bitstrings obtained from the projective measurements