Quantifying spatiotemporal patterns in classical and quantum systems out of equilibrium

A rich variety of nonequilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in many-body systems of completely different nature. In this work we provide a solution to this problem by adopting a structural complexity measure to quantify spatiotemporal patterns in the time-dependent digital representation of a system. On the basis of very limited amount of data our approach allows us to distinguish different dynamical regimes and define critical parameters in both classical and quantum systems. By the example of the discrete time crystal realized in nonequilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings, which can be considered as a valuable alternative to previous studies based on the calculations of qubit correlation functions.

Probing Diffusive Dynamics of Natural Tubule Nanoclays with Machine Learning

Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically important properties is natural and cannot be artificially reproduced one-to-one in the laboratory? The situation becomes even more complicated when we are interested in exploring stochastic properties of a natural system and only a limited set of noisy experimental data is available. In this paper we address these problems by exploring diffusive motion of some natural clays, halloysite and sepiolite, in a liquid environment. By using a combination of dark-field microscopy and machine learning algorithms, a quantitative theoretical characterization of the nanotubes' rotational diffusive dynamics is performed. Scanning the experimental video with the gradient boosting tree method, we can trace time dependence of the diffusion coefficient and probe different regimes of nonequilibrium rotational dynamics that are due to contacts with surfaces and other experimental imperfections. The method we propose is of general nature and can be applied to explore diffusive dynamics of various biological systems in real time.

Nature of the magnetic moment of cobalt in ordered FeCo alloy

The magnets are typically classified into Stoner and Heisenberg type, depending on the itinerant or localized nature of the constituent magnetic moments. In this work, we investigate theoretically the behaviour of the magnetic moments of iron and cobalt in their B2-ordered alloy. The results based on local spin density approximation for the density functional theory (DFT) suggest that the Co magnetic moment strongly depends on the directions of the surrounding magnetic moments, which usually indicates the Stoner-type mechanism of magnetism. This is consistent with the disordered local moment picture of the paramagnetic state, where the magnetic moment of cobalt gets substantially suppressed. We argue that this is due to the lack of strong on-site electron correlations, which we take into account by employing a combination of DFT and dynamical mean-field theory (DMFT). Within LDA + DMFT, we find a substantial quasiparticle mass renormalization and a non Fermi-liquid behaviour of Fe-3dorbitals. The resulting spectral functions are in very good agreement with measured spin-resolved photoemission spectra. Our results suggest that local correlations play an essential role in stabilizing a robust local moment on Co in the absence of magnetic order at high temperatures.

Multiscale structural complexity of natural patterns

Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.

Heisenberg-exchange-free nanoskyrmion mosaic

Isotropic Heisenberg exchange naturally appears as the main interaction in magnetism, usually favouring long-range spin-ordered phases. The anisotropic Dzyaloshinskii-Moriya interaction arises from relativistic corrections and is a priori much weaker, even though it may sufficiently compete with the isotropic one to yield new spin textures. In this work, we challenge this well-established paradigm, and propose to explore a Heisenberg-exchange-free magnetic world. In this case, the Dzyaloshinskii-Moriya interaction induces magnetic frustration in two dimensions, from which the competition with an external magnetic field results in a new mechanism producing skyrmions of nanoscale size. A single nanoskyrmion can already be stabilized in a few-atom cluster, and may then be used as LEGO^® block to build a large magnetic mosaic. The realization of such topological spin nanotextures in sp- and p -electron compounds or in ultracold atomic gases would open a new route toward robust and compact magnetic memories.

Structural phase transitions in VSe2: energetics, electronic structure and magnetism

First principles calculations of the magnetic and electronic properties of VSe₂ describing the transition between two structural phases (H,T) were performed.

Molecular dynamics of the halloysite nanotubes

We report large-scale and long-time molecular dynamics simulations demonstrating the transformation of a single kaolin alumosilicate sheet to a halloysite nanotube. The models we consider contain up to 5 × 10⁵ atoms, which is two orders of magnitude larger than that used in previous theoretical works. It was found that the temperature plays a crucial role in the formation of the rolled geometry of the halloysite. For the models with periodic boundary conditions, we observe the tendency to form twin-tube structures, which is confirmed experimentally by atomic force microscopy imaging. The molecular dynamics calculations show that the rate of the rolling process is very sensitive to the choice of the winding axis and varies from 5 ns to 25 ns. The effects of the open boundary conditions and the initial form of the kaolin alumosilicate sheet are discussed. Our simulation results are consistent with experimental TEM and AFM halloysite tube imaging.

Magnetism of coupled spin tetrahedra in ilinskite-type KCu5O2(SeO3)2Cl3

Synthesis, thermodynamic properties, and microscopic magnetic model of ilinskite-type KCu5O2(SeO3)2Cl3 built by corner-sharing Cu4 tetrahedra are reported, and relevant magnetostructural correlations are discussed. Quasi-one-dimensional magnetic behavior with the short-range order around 50 K is rationalized in terms of weakly coupled spin ladders (tubes) having a complex topology formed upon fragmentation of the tetrahedral network. This fragmentation is rooted in the non-trivial effect of the SeO3 groups that render the Cu-O-Cu superexchange strongly ferromagnetic even at bridging angles exceeding 110°.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Band filling dependence of the Curie temperature in CrO2

Rutile CrO2 is an important half-metallic ferromagnetic material, which is also widely used in magnetic recording. In an attempt to find the conditions, which lead to the increase of the Curie temperature (T C), we study theoretically the band-filling dependence of interatomic exchange interactions in the rutile compounds. For these purposes, we use the effective low-energy model for the magnetic t 2g bands, derived from the first-principles electronic structure calculations in the Wannier basis, which is solved by means of dynamical mean-field theory. After the solution, we calculate the interatomic exchange interactions, by using the theory of infinitesimal spin rotations, and evaluate T C. We argue that, as far as the Curie temperature is concerned, the band filling realized in CrO2 is far from being the optimal one and much higher T C can be obtained by decreasing the number of t 2g electrons (n) via the hole doping. We find that the optimal n is close to 1, which should correspond to the case of VO2, provided that it is crystallized in the rutile structure. This finding was confirmed by using the experimental rutile structure for both CrO2 and VO2 and reflects the general tendency towards ferromagnetism for the narrow-band compounds at the beginning of the band filling. In particular, our results suggest that the strong ferromagnetism can be achieved in the thin films of VO2, whose crystal structure is controlled by the substrate.

Nonfrustrated interlayer order and its relevance to the Bose-Einstein condensation of magnons in BaCuSi2O6

Han purple (BaCuSi2O6) is not only an ancient pigment, but also a valuable model material for studying Bose-Einstein condensation of magnons in high magnetic fields. Using precise low-temperature structural data and extensive density-functional calculations, we elucidate magnetic couplings in this compound. The resulting magnetic model comprises two types of nonequivalent spin dimers, in excellent agreement with the Cu63,65 nuclear magnetic resonance data. We further argue that leading interdimer couplings connect the upper site of one dimer to the bottom site of the contiguous dimer, and not the upper-to-upper and bottom-to-bottom sites, as assumed previously. This finding is verified by inelastic neutron scattering data and implies the lack of frustration between the layers of spin dimers in BaCuSi2O6, thus challenging existing theories of the two-dimensional-like Bose-Einstein condensation of magnons in this compound.

First-order transition between a small gap semiconductor and a ferromagnetic metal in the isoelectronic alloy FeSi1-xGex

The contrasting ground states of isoelectronic, isostructural FeSi and FeGe are explained within an extended local density approximation scheme (LDA+U) by an appropriate choice of the Coulomb repulsion U on the Fe sites. A minimal two-band model with interband interactions leads to a phase diagram for the alloys FeSi1-xGex. A mean field approximation gives a first-order transition between a small gap semiconductor and a ferromagnetic metal as a function of magnetic field, temperature, and concentration x. Unusually the transition from metal to insulator is driven by broadening, not narrowing, the bands and it is the metallic state that shows magnetic order.

[The basic principles for the analytical study of epidemic-control measures in the modelling of epidemic processes]

For prognostication of epidemic aerogenic infections with the help of mathematical modeling the authors propose to regard the testing population as a unity of the following streams: susceptible to infection, embraced with emergency vaccination, just vaccinated, protected with the measures of specific or emergency vaccination. Each stream has its own equation which is analogous in its structure to the epidemic dynamics modeling made by O. V. Baroian and L. A. Rvachev, and besides this has correction coefficients which depict the grade of the mobility downtrend due to prophylactic measures. The model built on the bases of the proposed methods makes it possible to determine the level and dynamics of morbidity depending on the volume and efficiency of each sanitary measure described in it.