B. Verkin Institute for Low Temperature Physics and Engineering

Using the method of SQUID magnetometry, the features of the antiferromagnet-ferromagnet thermomagnetic transition in arrays of the nanosized disks of Py/NiCu/Py synthetic antiferromagnets (SAFs) have been investigated. The effective interlayer interaction in individual SAFs “ferromagnet/diluted ferromagnet/ferromagnet” (F2/f/F1) changes from high-temperature antiferromagnetic to low-temperature ferromagnetic upon the transition at the Curie temperature TCf of the interlayer f. Temperature dependence of the magnetic parameters of individual layers and their effect on the features of the thermomagnetic transition are determined. The observed properties are important for the development of temperature-controlled nanoscale SAFs and multilayer nanostructures based on them.

The low-temperature dependence of the heat capacity of acrylonitrile-butadiene-styrene (ABS) polymer and its composite with thermally reduced graphene oxide was studied. The existence of a so-called “boson peak” characteristic of orientational and structural glasses was demonstrated. The boson peak appears in the form of a local maximum in the heat capacity curve displayed as C/T3 vs T at Tmax = 3.52 K. It was found that for both ABS polymer and its composite, as well as for a number of other substances of a crystalline and amorphous nature, the manifestation of the anomaly of the boson peak in the heat capacity has a universal character that is described by an empirical function Δ*. The value of Δ* depends on the magnitude of the anomaly in the heat capacity and the temperature of the boson peak manifestation. Thus, this study provides new physical information about the possible causes of the boson peak appearance in disordered materials and indicates the universality of boson peak anomaly for substances with short- and long-range order.

The effect of temperature variations over a wide range on the rheological properties of amorphous polymers with high rubber-like elasticity (elastomers) is discussed. A theoretical study of the transition from the deformation state of a warm elastomer to the state of a frozen one, the effects of structural-strain glass transition and forced elasticity was done. Two types of mechanical testing of polymer samples are considered in detail: slow tensile deformation at a constant rate and relaxation of the deforming stress after deformation stops. The study was carried out on the basis of the previously proposed molecular-kinetic model of the processes of highly elastic deformation of amorphous polymers and the corresponding nonlinear rheological equation (V. D. Natsik and H. V. Rusakova, Fiz. Nizk. Temp. 48, 281 (2022) [Low Temp. Phys. 48, 253 (2022)]).

The molecular dynamics method is applied to simulate the behavior of two-dimensional electron clusters of various shapes containing about 100 particles. The influence of a magnetic field on the effects of ordering and disordering (melting) in such clusters is studied. The field dependence of the rms displacements of particles in clusters is determined, and the trajectories of electron motion are found as functions of temperature and magnetic field. Ordering and disordering in clusters were fixed by the appearance of characteristic features in the rms displacements of electrons in the system. Hysteresis was observed in the field dependence of these displacements at a fixed temperature. The obtained data are compared with the results for root-mean-square displacements of electrons in a two-dimensional electronic infinite crystal. The qualitative agreement was found with these results; at the same time, the field dependence of root-mean-square displacements in an unbounded crystal is much weaker than in the clusters under study. The influence of the cluster shape on ordering transitions is studied, and it is found that the shape of a defect-free cluster does not affect the transition conditions. The distribution of electron velocities in clusters is studied for various magnetic fields.

The electrical breakdown of a dielectric nanolayer between film electrodes under the combined action of direct current and capacitor discharge current makes it possible to form Josephson bridges with a reproducible resistance exceeding 1 Ω. A new feature of the formation of a bridge during the electrical breakdown, which is preceded by a series of preliminary breakdowns (auto breakdowns) of a dielectric nanolayer, has been discovered. The mechanism of the process and the role of the cathode film's thickness in forming the bridge are discussed.

The technological requirement for ever more efficient materials for the energy and electronics sectors has led to the consideration of numerous compositionally and structurally complicated systems. These systems include solid solutions that are difficult to model using electronic structure calculations because of the numerous possibilities in the arrangement of atoms in supercells. The plethora of such possible arrangements leads to extensive and large numbers of potential supercells, and this renders the investigation of defect properties practically intractable. We consider recent advances in oxide interfaces where studies have demonstrated that it is feasible to tune their defect processes effectively. In this review, we aim to contribute to the ongoing discussion in the community on simple, efficient and tractable ways to realise research in solid solutions and oxide interfaces. The review considers the foundations of relevant thermodynamic models to extract point defect parameters and the special quasirandom structures method to model the supercell of solid solutions. Examples of previous work are given to highlight these methodologies. The review concludes with future directions, systems to be considered and a brief assessment of the relevant methodologies.

We study the eigenvalue distribution of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the analog of the population covariance matrix is now a function of random data matrices (synaptic weight matrices in the deep neural network terminology). The problem has been treated in recent work [J. Pennington, S. Schoenholz and S. Ganguli, The emergence of spectral universality in deep networks, Proc. Mach. Learn. Res. 84 (2018) 1924–1932, arXiv:1802.09979] by using the techniques of free probability theory. Since, however, free probability theory deals with population covariance matrices which are independent of the data matrices, its applicability in this case has to be justified. The justification has been given in [L. Pastur, On random matrices arising in deep neural networks: Gaussian case, Pure Appl. Funct. Anal. (2020), in press, arXiv:2001.06188] for Gaussian data matrices with independent entries, a standard analytical model of free probability, by using a version of the techniques of random matrix theory. In this paper, we use another version of the techniques to extend the results of [L. Pastur, On random matrices arising in deep neural networks: Gaussian case, Pure Appl. Funct. Anal. (2020), in press, arXiv:2001.06188] to the case where the entries of the data matrices are just independent identically distributed random variables with zero mean and finite fourth moment. This, in particular, justifies the mean field approximation in the infinite width limit for the deep untrained neural networks and the property of the macroscopic universality of random matrix theory in this case.

Specific heat ${C}_{B}$ of a ${\mathrm{TbAl}}_{3}{({\mathrm{BO}}_{3})}_{4}$ crystal was studied for 50 mK $<T<$ 300 K with emphasis on $T<1$ K where a phase transition was found at ${T}_{c}=0.68$ K. Nuclear, nonphonon (${C}_{m}$), and lattice contributions to ${C}_{B}$ were separated. Lowering of ${T}_{c}$ with an increase in magnetic field parallel to the easy magnetization axis $({B}_{\ensuremath{\parallel}})$ was found. It was established that ${C}_{m}$ and a Gr\"uneisen ratio depend on ${B}_{\ensuremath{\parallel}}$ and $T$ in a way characteristic of systems in which a classical transition is driven by quantum fluctuations (QFs) to a quantum critical point at $T=0$ by tuning a control parameter (${B}_{\ensuremath{\parallel}}$). The ${B}_{\ensuremath{\parallel}}\ensuremath{-}T$ phase diagram was constructed, and the dynamical critical exponent $0.82\ensuremath{\le}z\ensuremath{\le}0.96$ was assessed. Nature of the transition was not established explicitly. Magnetization studies point at the ferromagnetic ordering of ${\mathrm{Tb}}^{3+}$ magnetic moments, however, lowering of ${T}_{c}$ with increase in ${B}_{\ensuremath{\parallel}}$ is opposite to the classical behavior. Hence, a dominant role of QFs was supposed.

Given an infinite countable discrete amenable group Γ \Gamma , we construct explicitly sharply weak mixing nonsingular Poisson Γ \Gamma -actions of each Krieger’s type: I I I λ III_\lambda , for λ ∈ [ 0 , 1 ] \lambda \in [0,1] , and I I ∞ II_\infty . The result is new even for Γ = Z \Gamma =\mathbb {Z} . As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ \Gamma -actions and infinite direct product of finite type systems of each possible Krieger’s type.