The influence of a large spin-polarized current on the coupled dynamics of vortices in spin-transfer nanooscillators with a diameter of 400 nm is investigated. New stationary modes of coupled oscillations of vortices have been discovered, both for the same and opposite polarities of their cores. The dependence of the frequency of stationary coupled oscillations of magnetic vortices on the magnitude of the spin-polarized current has been studied. The found effect can be used to increase the operating frequencies of spin-transfer nano-oscillators.

A ferromagnetic insulator proximate with a superconductor induces some spin asymmetry in superconducting correlations. Density of states (DoS) changes as a result of the induction of magnetization in superconductor (S) under the influence of the inverse proximity effect with the ferromagnetic insulator (FI). The study solves the Usadel equations numerically and calculates characteristic features of the density of states at the interface boundary and at the boundary with vacuum, caused by FI. The electron density of states was analyzed, showing significant singlet-to-triplet conversion, even for small values of the interface parameter (phi). In DoS, the zero bias peak tends to play a larger role than the spin-splitting of the BCS peaks. The features of the density of state obtained in this work can be measured experimentally.

We consider a spin valve composed of a superconducting film (S) between two ferromagnetic insulators (FI) on two sides. In the dirty limit, the superconductor is described by Usadel equations. Appropriate boundary conditions were chosen for two S-FI interfaces, which are described via the interface parameter spin mixing angle. By numerically solving the Usadel equations, the density of states (DOS) at different spin mixing angles was obtained. It was shown previously that the critical temperature of such an FI-S-FI structure depends on the mutual alignment of the FI layers’ magnetization. We follow the evolution of DOS at the change of misalignment of ferromagnets magnetization and probe the zero bias peak creation. The DOS characteristic features may give fruitful information about triplet superconducting components creation and interplay inside the S layer.

In the modern world, there's a notable trend towards the active miniaturization of electronic devices. With technological advances enabling the manipulation of nanostructures, there's an increasing focus on exploring quantum effects pivotal to such designs. One distinguishing feature of nanostructures is the quantum nature of the electron's energy spectrum. This spectrum becomes discrete in directions where electrons move. Depending on the direction of this confinement, structures can be categorized as nanoplates, quantum wires, or quantum dots. The properties of such structures can significantly differ from those observed in large-scale systems. When discussing superconductivity, particular emphasis is placed on its macroscopic quantum properties.The influence on electronic wave functions is reflected in the characteristics of the superconducting state on broader scales. The Bardeen-Cooper-Schrieffer (BCS) theory is frequently utilized to analyze these nanostructures. The Gor’kov equations method serves as a potent tool for tasks related to the BCS theory. For instance, it can determine the parameters of the superconducting state, critical temperature, and current. Components of these equations, like Green's functions, are associated with various system properties. Research in the early stages of superconductivity studies revealed that the critical temperature (Tc ) – the temperature at which a material transitions to a superconducting state – can differ significantly between thin films and bulk materials. Intriguingly, reducing the film's thickness can both decrease (e.g., in niobium) and increase (e.g., in aluminum) the Tc value. This study delves into the quantum size effect in thin aluminum films, paving the way for materials with higher transition temperatures. Such advancements can simplify and make the maintenance of superconducting systems more cost-effective. In this study, a theoretical relationship between the critical temperature of a thin aluminum film and its thickness was derived. The Green's function method was chosen, which hadn't been previously employed for this computation. This approach offers greater potential compared to other superconductivity theory methods, presenting extensive avenues for theoretical exploration in this domain. The authors are confident that this work will contribute to further research on quantum dimensional effects in low-dimensional superconducting structures.

The present study investigates the behavior of the Cooper pair wave function in a normal metal (NM) near superconductor-NM-junctions, specifically focusing on the ballistic regime at zero temperature. It is widely assumed that the wave function follows a power-law decay, with the decay exponents dependent on the system’s dimensionality. Our work reveals that the multiband nature of a compound significantly influences the damping degree of pair amplitudes in an NM, rendering it sensitive to the position of the Fermi level. To explore this phenomenon, we employ the numerical method of self-consistent Bogoliubov–de Gennes equations, utilizing a nanowire as a model for an electronic multiband system. By analyzing the obtained pair amplitudes, we extract relevant lengths and exponents that characterize the leakage of superconducting correlations. We further examine this phenomenon by varying the sample’s cross-sectional size and the superconducting coupling constant. Consequently, our findings demonstrate that the properties of a superconducting/NM junction’s proximity effect can be manipulated not only through temperature, total impurity and defect density, but also by controlling the position of the Fermi level. This tunability enables the transition from a long-range regime to a short-range one, providing valuable insights for designing and understanding such junctions in practical applications.

The magnetization induced in a superconductor due to the reverse proximity effect is studied in hybrid structures containing a superconductor and a ferromagnetic insulator. The study was carried out within the method of semiclassical Green's functions, in which the Usadel equations are solved numerically with boundary conditions suitable for strongly spin-polarized ferromagnetic materials. The conversion of singlet superconducting correlations into triplet ones as a result of the proximity effect with a ferromagnet and its manifestation in the features of the electron density of states, induced magnetization, and suppression of the superconducting order parameter have been studied. It is shown that the magnetization can change sign inside the superconducting layer. The magnetization distribution is compared with the data obtained by the authors in previous works.

This paper presents a theoretical study of the dynamics of the induced magnetization and spin current arising in a layer of an impure superconductor due to the proximity to a ferromagnetic dielectric with a uniform periodically precessing magnetization. The dynamics of the observed physical quantities is described within the semi-classical Usadel–Floquet formalism, which makes it possible to study the effect of a periodic perturbation on an inhomogeneous superconducting system. The spatial distributions and temporal evolution of the induced magnetization and the superconducting spin current inside the superconductor layer are found from the numerical solutions of the system of Usadel–Floquet equations.

The main goal of the present work is the description of the dynamics of spin current and induced magnetization inside a superconducting film S that is in contact with a ferromagnetic insulator layer FI. Spin current and induced magnetization are calculated not only at the interface of the S/FI hybrid structure, but also inside the superconducting film. The new and interesting predicted effect is the frequency dependence of the induced magnetization with a maximum appearing at high temperatures. It is also shown that the increase of the magnetization precession frequency can drastically change the spin distribution of quasiparticles at the S/FI interface.

A detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with an intrinsic spiral magnetic order, which could result from competing isotropic exchanges or, if the crystal lattice breaks central symmetry, from asymmetric Dzyaloshinskii-Moriya exchange. Depending on the anisotropy, such a metal may change its magnetiza-tion either from a spiral to uniform order, as seen in Ho and Er, or in the direction of the spiral itself, as in crystals of the B20-type structure [such as MnSi, (Fe,Co)Si, FeGe, etc.]. The nonuniform mag-netic order controls the appearance of long-range triplet superconducting correlations at strong exchange fields, affecting the detailed character of the proximity effect. We show that the magnetic control of the spin-valve behavior can also be obtained from moderately low exchange fields (typically associated to negligible long-range triplet correlations), thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. Our numerical calculations reveal that the spin-valve effect is in fact magnified at moderately low exchange fields, when the exchange splitting in the spiral magnet is comparable to the superconducting gap, and the spiral period is less than or equal to the superconducting coherence length in the magnet multiplied by 2 pi.

The combined influence of a spin polarized current and an external magnetic field for switching the polarity of vortices in spin-transfer nanooscillators 400 nm in diameter is studied. A diagram is constructed of the dependence of the magnitude of the spin-polarized current on the magnitude of the magnetic field, which separately switches the polarity of the vortex in the magnetic layers of the spin-transfer nanooscillator.

There are many tasks solved by people that can be partially or completely automated. One of the most prom- ising tools for these purposes are artificial neural networks. Neural networks are a technology at the intersection of many disciplines: physics, mathematics, statistics, computer science and technology. They find application in a wide range of tasks, such as time series analysis, regression analysis, pattern recognition in images, etc. It is im- possible not to note an important feature of neural networks: to learn from data both with the participation of a teacher, and to go through the learning process without a teacher. This article discusses the basic terms and basic principles of the functioning of artificial neural networks. At the beginning, a mathematical model of the operation of an artificial neuron is given. The main constituent elements of an artificial neuron, such as synapses, inputs, axons, etc., are described. Some subtleties in optimization processes are generalized, and the main types of activa- tion functions are given. Examples of software implementations of neural networks are given, specific application cases are considered, their strengths are noted, as well as some limitations. Given the limitations, an alternative technology is presented: hardware implementations of artificial neural networks. A brief description of the use of neural networks in the world is given, after which the classification of hardware implementations is considered. Each class highlights the features of using such technologies, including strengths and weaknesses. At the end of the article, the question of the relevance of the problem of finding an element base for building hardware solutions in the field of artificial neural networks is raised, arguments are given in favor of the development of hardware solutions. It is shown that it is necessary to further develop the element base for the construction of artificial neu- ral networks.

In this work we theoretically investigate the spin dynamics of superconducting condensate proximity coupled with the single FMR mode uniform periodical precessing magnetization. The theoretical model of the inverse proximity effect is built within quasicalssical formalism using time-dependent Usadel equations. Frequency representation of Usadel equations allows to turn non-stationary periodic problem to the stationary one. We numerically solve the derived frequency-dependent Usadel equations and calculate non-stationary distributions of the spin supercurrent and induced magnetization inside the superconductor/ferromagnetic insulator hybrid structure.

We propose a superconducting spin valve based on a Josephson junction with B20-family magnetic metal as a barrier material. Our analysis shows that the states of this element can be switched by reorienting the intrinsic non-collinear magnetization of the spiral magnet. This reorientation modifies long-range spin-triplet correlations and thereby strongly influences the critical Josephson current. Compared to superconducting spin valves proposed earlier, our device has the following advantages: (a) it contains only one barrier layer, which makes it easier to fabricate and control; (b) its ground state is stable, which prevents uncontrolled switching; (c) it is compatible with devices of low-T Josephson electronics. This device may switch between two logical states which exhibit two different values of critical current, or its positive and negative values. I.e. 0- π switch is achievable on a simple Josephson junction.

We propose a method to control a bilayer superconducting spin valve (SSV) which does not perturb its superconducting state and is suitable for energy saving cryogenic electronics. This SSV consists of a superconducting layer and a helimagnetic layer of B20 family compounds, namely, Nb and spiral antiferromagnet MnSi. Thanks to unique properties of MnSi—broken inversion symmetry and cubic crystal lattice—there are a few ground state magnetic configurations with different directions of the magnetic spiral, divided by a potential barrier. Superconductivity in such a bilayer is controlled by the reorientation of the spiral vector in the MnSi layer, which leads to a change in the critical temperature of the Nb layer due to the proximity effect. The switching is proposed to be carried out by a several hundred ps in duration magnetic field pulse of several kOe in magnitude. Such a pulse does not destroy the superconducting state of the Nb layer by itself but leads to the excitation of magnons in the MnSi layer, which triggers the reorientation process of the magnetic spiral. After the completion of this process, the Nb layer switches into a normal state. Inverse switching returns the spiral to the initial state, opening the valve and turning on the superconducting state. The system can be switched there and back by a magnetic field of opposite signs along one direction in the layers plane, which allows an easy control. The switching time is estimated as several nanoseconds, which coincides with the scales of the STT-MRAM recording time.

The magnetization in a superconductor induced due to the inverse proximity effect is investigated in hybrid bilayers containing a superconductor and a ferromagnetic insulator or a strongly spin-polarized ferromagnetic metal. The study is performed within a quasiclassical Green function framework, wherein Usadel equations are solved with boundary conditions appropriate for strongly spin-polarized ferromagnetic materials. A comparison with recent experimental data is presented. The singlet to triplet conversion of the superconducting correlations as a result of the proximity effect with a ferromagnet is studied.

The detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with intrinsic spiral magnetic order, which may be the result of a competitive exchange or of an asymmetric Dzyaloshinsky-Moriya exchange following from the central symmetry breaking of the crystal lattice. Depending on the anisotropy, this metal may change its magnetization either from a spiral to uniform order, as in Ho and Er, or in the direction of the spiral itself, as in B20 family crystals. Very recently, a new way of controlling the superconducting spin valve has been developed: the change of the magnetic order may also be triggered by magnonic relaxation processes, thus merging superconducting spintronics and magnonics. The nonuniform magnetic order controls the appearance of long-range triplet superconducting correlations (LRTC), which change the conditions of the proximity effect, enabling an external magnetic control of the superconducting critical temperature. We show that magnetic control of the spin-valve behavior can also be obtained for moderately low exchange energies thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. The competition between these two mechanisms yields different behaviors of the spin-valve effect. Our numerical calculations show that at low exchange fields (as in MnSi) the spin valve effect may be quite significant. They suggest the switching behavior of the superconducting spin valve to be better optimized for B20 family compounds allowing magnonic control.

The joint effect of the spin polarized current and an external magnetic field on the dynamics of magnetization in vortex spin-transfer nano-oscillators with a diameter of 400 nm is investigated. For the numerical calculation of the coupled dynamics of magnetic vortices, the SpinPM software package for micromagnetic modeling was used. The dependence of the frequency of stationary coupled oscillations of vortices on the magnitude of the magnetic field, which determines the operating frequency range of a tunable vortex spin-transfer nano-oscillator.