This note is dedicated to Professor B.Z. Malkin on the occasion of his 80th jubilee.

New measurements of EPR spectra in single crystals CsCdBr₃:Yb³⁺ are presented. The lines due to pairs of Yb³⁺ ions and single Yb³⁺ ions are observed. The spectra indicate the existence of several types of single Yb³⁺ paramagnetic centers. Resolved superhyperfine structure of some lines of these centers is observed for the first time.

Paramagnetic centers formed by isotopically pure impurity ⁵³Cr ions in synthetic forsterite (Mg₂SiO₄) are studied by continuous wave electron paramagnetic resonance. It is shown that chromium ions substitute magnesium ions as single ion with nonlocal charge compensation and dimer associate formed by two closely spaced Cr³⁺ ions. It is found that the integral intensity of resonance transitions belonging to the dimer associates is much higher than that to be expected for the statistical distribution of the impurity Cr³⁺ ions in the forsterite host. Therefore, there is a mechanism favoring the self-organization of the Cr³⁺ ions in dimer associates during the crystal growth.

Using an X-band EPR spectrometer and a submillimeter EPR spectrometer, Y₃Al₅O₁₂ (YAG), (Y_0.9Lu_0.1)₃Al₅O₁₂ (YLuAG) crystals with erbium and YAG with iron were investigated. In YAG:Er crystals the resonance transitions between ground and the first excited doublets in the frequency range 580-750 GHz were observed. The energy interval to the first excited Stark level is measured and the direction of the axes of the g-tensor of the excited doublet is specified. The field-frequency and angular dependences of these transitions are measured and theoretically calculated. In the YAG:Fe crystal a non-Kramers ion was detected in the frequency range 112-150 GHz. It was concluded that resonant transitions between the |+2⟩ ↔ |−2⟩ states of the Fe²⁺ ion in the tetrahedral environment are observed.

This paper is a short overview of the works performed with Boris Malkin in a friendly and fruitful collaboration which started fifteen years ago and will, hopefully, be continuing for as many years as possible. Dealing with quantum tunnelling and coherence in non-cooperative magnetic systems such as 3d-based single-molecules or 4f-based diluted alloys, those works also involved our respective students, post-docs and colleagues of the time who all appear in the reference list. If most of those papers were published in usual physics journals, some of them were also published in the proceedings of conferences organized or co-organized by Boris or myself in Kazan, St. Petersburg or Les Houches.

A short overview of the exchange charge model of crystal field is given. Several most important applications of the model to the calculations of the crystal field parameters, energy levels of impurity ions, parameters of the electron-vibrational interaction and transition intensities supported by the recent literature publications are discussed.

Crystal structure and phonon spectrum of rare-earth pyroclore oxide Nd₂Zr₂O₇ were studied within the framework of density functional theory and MO LKAO approach. The calculations were performed by using hybrid functionals that take into account both local and nonlocal (at the Hartree-Fock formalism) exchanges. Calculations were performed with the functionals PBESOL0 and PBE0. The fundamental vibration frequencies of Nd₂Zr₂O₇ were calculated. The calculations were performed in the CRYSTAL17 program designed to simulate periodic structures.

The paper reports on the ferromagnetic resonance (FMR) and magnetometry studies of the epitaxial superconductor/ferromagnet-type thin film heterostructure of VN/Pd_0.96Fe_0.04 on the (001)-oriented MgO substrate. Vanadium nitride layer was deposited by dc reactive magnetron sputtering of the V-target in the mixture of the Ar and N₂-gases. Pd-Fe layer was grown by molecular beam deposition in the ultrahigh vacuum conditions. LEED patterns and XRD analysis revealed the "cube-on-cube" epitaxy at both the MgO/VN and VN/Pd_0.96Fe_0.04 interfaces and single crystalline structure of both layers. Ferromagnetic resonance spectra revealed a single absorption line with strong orientation dependence and manifestations of superconductivity of the VN-layer at a temperature of 4.2 K. Magnetic anisotropy constants for the Pd_0.96Fe_0.04 layer were found from the analysis of the orientation dependence of the FMR resonance field and were compared with that of the film of the same composition grown directly on MgO. We find that the tetragonal distortion for Pd_0.96Fe_0.04 on the VN layer is reduced due to a relaxed lattice mismatch with respect to MgO.

EPR and optical spectra are used for the analysis of distortions of a crystal lattice in the vicinity of an impurity ion Yb³⁺ of trigonal symmetry in RbMgF₃ crystal. Within the framework of the superposition model, it is established that three F⁻ ions of the nearest-neighboring octahedron, located symmetrically along the threefold axis of the trigonal center, move away from the impurity ion and have considerable angular deviations from the symmetry axis of the center. The next three F⁻ ions, which enter the other octahedra, shift towards the paramagnetic ion and, on the contrary, come a bit closer to the axis.

The Löwdin orthogonalization procedure being the well-known technique, particularly in quantum chemistry, however, gives rise to novel effects missed in earlier studies. Making use of the technique of irreducible tensorial operators, we have developed a regular procedure for the account of the orthogonalization effects. For illustration, we address the emergence of a specific magnetoelectric coupling for noncentrosymmetric 3d or 4f ions.

A brief review is presented of high-resolution optical Fourier spectroscopy and EPR research on crystals containing 4f or/and 3d transition-metal ions, performed in the Institute of Spectroscopy RAS, in collaboration with the Kazan Federal University, the E.K. Zavoisky Kazan PhysicalTechnical Institute RAS, and many other institutions in Russia and abroad. The theoretical basis of these studies was developed by Boris Malkin.

 An EPR technique and optical measurements have been applied to study LaF₃ nanoparticles doped with 7% of Pr³⁺ ions. It has been found that vacuum annealing of the studied samples leads to the appearance of paramagnetic defects with g-factor close to the value which is typical for the electron trapped in a fluorine vacancy. The concentration of paramagnetic defects was reduced after fluorination of initial nanoparticles. The possible origin of surface defects due to vacuum annealing is discussed. The results of study can help to improve the performance of fluoride nanoparticles for biomedical applications.

We review the magnetic and magnetoelastic properties of rare earth tetrafluorides LiLnF₄ recently studied at Kazan Federal University in collaboration with the Laboratory of Low Temperatures, Kanazawa University, Japan.

The Lu³⁺ 4f ¹³5d‐4f ¹⁴ VUV luminescence in CaF₂:Lu³⁺ crystal at 8 K was studied with a high spectral resolution using synchrotron radiation excitation. Absence of a zero-phonon line in the recorded spectrum was explained and features in the recorded spectrum were reproduced by simulation based on the microscopic model of electron-phonon interaction and the developed theory of non-Condon spectra.

The article is devoted to the theoretical study of the four-site cells as the basic units in the architecture of quantum-dot or molecular cellular automata. The functional characteristics of two possible compositions of square cells for quantum cellular automata are compared. We analyze the properties of the tetrameric cells composed of two isolated one-electron dimers (half-cells) and the cells based on the bi-electron tetramers (full cells). The inter-site Coulomb interactions and the electron transfer processes are taken into account as well as the external field of the neighboring cell. The difference in the transfer pathways is shown to result in a more abrupt nonlinear cell-cell response function for the double-dimer arrangement of the charge containers. This result shows that the double-dimeric cell is preferable to design quantum cellular automata devices.

In the spectra of the electron paramagnetic resonance of YAlO₃:¹⁵¹Eu single crystals, the signals of the Eu²⁺, Gd³⁺, Cr³⁺, and Mo³⁺ paramagnetic centers were observed. Using high-frequency EPR, it was shown that the signals of Mo³⁺ ions observed in the X-range belong to two intradoublet transitions of the same center with S = 3/2.