This note is dedicated to Professor B.I. Kochelaev on the occasion of his 90th anniversary.

An effective operator of the interaction of the orbital moment of d-electrons with the magnetic field is derived by combining the method of secondary quantization with the technique of irreducible tensor operators. It is found that in addition to renormalization of the matrix elements of the total orbital momentum L there are new terms in the Hamiltonian of the interaction with the magnetic field. The effects are numerically calculated by the example of the ground term of Fe²⁺ ions in Fe₂Mo₂O₈. Additional magnetic dipole transitions with ∆M = ±3 and ∆M = ±2 are allowed when the magnetic field is directed along the c-axis of the crystal and in the perpendicular orientation, respectively.

A mini auto-review of relaxation function theory with paramagnon excitations for doped S = 1/2 two-dimensional Heisenberg antiferromagnetic system is given in view of magnetic response of high-T_c copper oxide superconductors as obtained by nuclear magnetic resonance (NMR) and resonant inelastic X-ray scattering (RIXS). It is shown that RIXS data analysis is affected by approximations made for dynamic spin susceptibility and thus depends on paramagnon damping. The results of the theory give fair agreement without especially adjusted parameters to RIXS data for Y-Ba-Cu-O and Nd(La)-Ba(Sr)-Cu-O family compounds.

Hydroxyapatite (HAp) is an attractive material for creating biocompatible implants owing to its osteoregenerative properties, elemental and phase similarity to bone tissue. The flexible structure of the material allows the introduction of ionic impurities to improve physicochemical and biological characteristics while maintaining the space symmetry group. Rare earth ions are a new step in improving compounds to create luminescent bioimaging agent for application in diagnostics imaging medicine. Nanosized powder of HAp doped with cerium ions (Ce-HAp) was obtained in order to study the impurity localization and its oxidizing state with conventional and pulsed electron paramagnetic resonance (EPR) at X-band. Undoped and doped HAp powders were synthesized via precipitation technique. It was revealed, that Ce-HAp powders after synthesis and heating exhibit luminescence in visible wavelength range (380 and 420 nm) that confirms the presence of Ce³⁺ in HAp structure. Heating of Ce-HAp in the air atmosphere results in formation of CeO₂ with low intensity of luminescence. EPR spectra of the doped sample confirms the Ce³⁺ incorporation into HAp structure. The powder-like EPR lineshape for the obtained powders can be simulated with g_∥ = 3.47 and g_⊥ = 0.51.

In this report, we compare the analysis of electron spin resonance (ESR) studies of Berezinskii-Kosterlitz-Thouless (BKT) correlations in the spin S = 1 Ni²⁺-based layered honeycomb antiferromagnets BaNi₂X₂O₈ with X = V, P and As. Moreover, we investigate the effect of doping on the BKT correlations by the substitution of Ni²⁺ by spin S = 1/2 Cu²⁺ ions in BaNi₂V₂O₈.

This study establishes precise links between the fractional integral of the RL-type and the averaging technique of a smooth function over 1D-fractal sets. These findings were previously reported in the works [1], [2]. To draw in the interest of other experts operating in the NMR/EPR zones, it is helpful to repeat them again. The physical meaning of these acquired formulas is explained and numerical verifications are performed with the purpose of confirming the analytical results. Furthermore, results were achieved for a combination of fractal circuits with a discrete set of fractal dimensions that were generalized. We suppose that these new results help understand deeper the intimate links between fractals and fractional integrals of different types, especially in applications of the fractional operators in complex systems.

The primary benefit of incorporating a ferroelectric material into a complex heterostructure lies in the ability to manipulate various properties of the entire system using an external electric field. Specifically, the electric field can alter the polarization direction within the ferroelectric material, thereby influencing its structural properties. These structural changes, in turn, affect the electronic and magnetic properties of the neighboring material. The interfacial phenomena are of significant interest due to their potential to provide enhanced functionality in next-generation electronic devices. Inspired by the concept of employing ferroelectrics in heterostructure components, this study investigates the two-dimensional electron gas (2DEG) and the impact of ferroelectric polarization direction onto the electronic and magnetic properties. Lastly the presence of magnetoelectric coupling (ME) within the model systems of LaMnO₃/BaTiO₃ and LaMnO₃/PbTiO₃ heterostructures using density functional theory calculations was examined.

In this study, we report an experimental attempt to resolve whether ferromagnetism of graphite nanoflakes is an intrinsic phenomenon or it solely originates from impurities. A comparative study of either a nominally undoped or intentionally contaminated with NiO or Gd₂O₃ samples was performed. We show, first, that a detectable by X-ray diffraction contamination may occur via the agate mortar/pestle working surfaces if prior to sample dispersion it was used for grinding of hard oxides. Second, we find a systematic trend in a development of a FM component of all three samples under vacuum annealing at 400 or 800^◦C. Third, we notice that the samples notably contaminated with NiO or Gd₂O₃ do not reveal any drastic enhancement in ferromagnetism with respect to the sample free from intentional doping, contrary to an expectation related to nickel and gadolinium oxides reduction to metallic ferromagnetic at room temperature state. As a result, we conclude that ferromagnetism of graphite nanoflakes is probably an intrinsic phenomenon that could be stimulated slightly by NiO or Gd₂O₃ impurities, though an impact of the agate (SiO₂) contamination itself may also play a role.

The electronic structure and optical properties of the MoS₂/WS₂ planar heterostructure are studied based on density functional theory. Compared with single-layer MoS₂ and WS₂, the MoS₂/WS₂ heterostructure has an indirect and very narrow band gap. In the visible region of the light spectrum, the maximum values of dielectric constant, refractive index and attenuation coefficient for MoS₂/WS₂ are shifted to the blue region of the spectrum.

This article is a brief overview of our recent work on theoretical studies of the interaction of magnetism and superconductivity in nanostructures. General approaches to the analysis of this interaction are discussed and the unified essence of the problem is revealed: the search for new phenomena and effects in such systems. Various aspects of this problem are considered, including proximity effects, solitary superconductivity, and inhomogeneous superconducting states. Approaches based on the properties of the band structure and Fermi surface for ferromagnets and superconductors in contact are considered in the context of predicting possible effects and explaining observed phenomena. The possibilities of further research in this area are discussed in order to expand our understanding of the physics of magnetic superconductors and develop new technologies based on them.

The results of studies of BaFe₂As₂ single crystals doped with cobalt by means of resistivity and microwave absorption measurement are reported. A theoretical description of the behavior of the microwave absorption amplitude is made taking into account the temperature dependence of resistivity, magnetic susceptibility and the lifetime of spin fluctuations. An assumption has been made that the deviation from the linear dependence of resistivity on temperature at T < 100 K is not related to the electron-electron scattering mechanism, but it is due to the appearance of nematic fluctuations. Estimates of the rate of scattering by spin fluctuations indicate their nematic nature at temperatures near the structural transition.

Two methods for calculating the superconducting transition critical temperature of superconductor / ferromagnetic metal heterostructures in the dirty limit are compared. The first method relies on an approximation where the order parameter is assumed to be constant within each superconducting layer. The second method does not use any approximations and involves a numerical iterative process where the critical temperature and the order parameter distribution are jointly searched for in each iteration. Using these methods, we study various heterostructures involving a ferromagnetic and superconducting layers, including case where the ferromagnetic layer is split into domains.

This work examines the conductivity properties of point contact magnetic tunnel junctions taking into account gradients of the electrochemical potentials at the ferromagnetic metal/dielectric interface. The calculations were carried out for spin-polarized currents at arbitrary ratio the point magnetic tunnel junction size and the mean free paths of conduction electrons under the applied voltage conditions. Current-voltage characteristics were obtained for symmetrical and asymmetrical point junctions.

We analyse the possibility of the appearance of spontaneous currents in proximated superconducting/normal metal (S/N) heterostructure when Cooper pairs penetrate into the normal metal from the superconductor. In particular, we calculate the free energy of the S/N structure. We show that whereas the free energy of the N film F_N in the presence of the proximity effect increases compared to the normal state, the total free energy, which includes the boundary term F_B, decreases. The condensate current decreases F_N, but increases the total free energy making the current-carrying state of the S/N system energetically unfavorable.