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The parameters of the interaction of 3d electron states with an electromagnetic wave, as well as the probabilities of magnetic and electric dipole transitions between states of the ground term of an iron ion, which is split by the crystal field, exchange interaction, and spin–orbit coupling, have been calculated. The dependences of the absorption lines on the magnitude and direction of the applied magnetic field have been determined. It has been shown that the optical diode effect discovered in [Sh. Yu, B. Gao, J. W. Kim, S.-W. Cheong, M. K. L. Man, J. Madeo, K. M. Dani, and D. Talbayev, Phys. Rev. Lett. 120, 037601 (2018)] can be explained by the interference of magnetic and electric dipole transitions.

Regular dosed physical activity in all cases has a tonic and healing effect on a person. Feasible muscle activity helps to improve the function of the heart, lungs, blood vessels and the nervous system. In martial arts, the reactivity of the vestibular apparatus is of great importance, providing the flow of information about the current position of the body in space, the success of movement in it and maintaining the stability of the posture due to the effective redistribution of muscle tone. Purpose of the work: to find out the dependence of the reaction of the cardiovascular system to the arising vestibular irritation in different types of martial arts. Martial arts classes help to increase the degree of vestibular stability. The statokinetic stability is very pronounced and increases in the course of hand-to-hand combat, which has a lot of moments with different severity of angular accelerations. The peculiarities of motor activity in any kind of martial arts inevitably affect the peculiarities of the reaction to the test with a change in the position of the head.

The mechanism of the magnetoelectric coupling of spins of Ni2+ and Cu2+ ions with the applied electric field in (Ni, Cu)B2O4, caused by the coupling of 3d electrons with the electric field and by the spin–orbit coupling, is analyzed. It is shown that the ordering of spins in the ab crystallographic plane of the crystal induces the electric polarization along the c axis of the crystal, and this polarization is mainly related to nickel ions. To obtain the electric polarization in the CuB2O4 antiferromagnet, it turns out to be necessary to apply the magnetic field in the ab plane.

An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022350016

Analytical expressions are obtained for the interaction between orbitally doubly degenerate states of ions through the strain field in weak-anisotropy cubic crystals. The arrangement of interacting pairs may be arbitrary. The energy of cooperative orbital ordering of the states of Fe2+ ions in FeCr2O4 crystal is calculated with regard to the local Jahn–Teller and the quadrupole–quadrupole interactions. It is found that the main contribution to the cooperative Jahn–Teller effect is made by the interaction through the strain field. The estimated critical phase transition temperature corresponds in order of magnitude to experimental data.

A microscopic theory is proposed for coupling of copper spins with an external electric field in the magnetically ordered phase of LiCu2O2. The expressions are derived for the dipole moment components of exchange-coupled pairs of copper spins, as well as expressions for describing the macroscopic polarization in terms of the angles determining spatial orientations of spin rotation planes (helixes) in copper bichains. It is shown that zero electric polarization in isostructural compound NaCu2O2 can be explained by the difference in the spin structures in NaCu2O2 and LiCu2O2.

The possible crystal field parameters in the RPd3S4 compounds, where R = Ce, Pr, Nd, Dy, and Er, are discussed on the basis on the available experimental data on neutron scattering and field dependences of magnetic susceptibilities at various temperatures. The values of splittings of the lowest multiplets and wave functions of ground states are calculated.

The quantum-spin $S=1/2$ chain system ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$ is of high interest due to competing antiferromagnetic intrachain $J$ and interchain exchange ${J}^{\ensuremath{'}}$ interactions and represents a paramount example for Bose-Einstein condensation of magnons [R. Coldea et al., Phys. Rev. Lett. 88, 137202 (2002)]. Substitution of chlorine by bromine allows tuning the competing exchange interactions and corresponding magnetic frustration. Thereby, anisotropic exchange contributions may be decisive for the resulting ground state. Here we report on electron spin resonance (ESR) in single crystals of ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4\ensuremath{-}x}{\mathrm{Br}}_{x}$ with the aim to analyze the evolution of these anisotropic exchange contributions. The main source of the ESR linewidth is attributed to the uniform Dzyaloshinskii-Moriya interaction. The vector components of the Dzyaloshinskii-Moriya interaction are determined from the angular dependence of the ESR spectra using a high-temperature approximation. The obtained results support the site selectivity of the Br substitution suggested from the evolution of lattice parameters and magnetic susceptibility dependent on the Br concentration.

Among the large class of $A$-site ordered perovskites of stoichiometry $A{C}_{3}{B}_{4}{\mathrm{O}}_{12}$, the rare-earth $(R)$ ruthenates $R{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ $(R=\mathrm{La}, \mathrm{Pr}, \mathrm{Nd})$ are interesting compounds due both to $\mathrm{Ru}\text{\ensuremath{-}}4d$-derived electronic correlations and to unconventional crystal-electric-field effects of the $R$ ions. Here we report on detailed investigations of these compounds utilizing x-ray diffraction, neutron scattering, magnetic susceptibility, and electrical resistivity measurements as well as heat capacity and nuclear resonance experiments. A broad range of external parameters is scanned and depending on the specific technique, temperatures range from 100 mK to 730 K in external magnetic fields up to 14 T. In this work ${\mathrm{LaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ serves as reference compound with a nonmagnetic $A$ site, characterized in detail recently [S. Riegg et al., Phys. Rev. B 93, 115149 (2016)]. All compounds investigated reveal heavy-fermion behavior with a ${T}^{2}$ dependence of the low-temperature electrical resistivity and significantly enhanced Sommerfeld coefficients. Toward low temperatures, the compounds with $R=\mathrm{Pr}$ and Nd are dominated by the magnetic moments of the $R$ ions, which occupy crystallographic positions with point-group symmetry ${T}_{h}$. The crystal-electric-field effects are clearly visible especially in heat capacity and inelastic neutron scattering data from which the crystal-electric-field parameters are derived. The ground state of the ${\mathrm{Pr}}^{3+}$ ion is identified as a triplet $({\mathrm{\ensuremath{\Gamma}}}_{4}^{(1)})$, whereas for ${\mathrm{Nd}}^{3+}$ it is a quartet $({\mathrm{\ensuremath{\Gamma}}}_{67})$. Evidence for lowering of the ${T}_{h}$ symmetry is observed at the Pr site at temperatures below 10 K, suggesting the formation of orbital order. Moreover, the spin-lattice relaxation derived from $^{63}\mathrm{Cu}$ nuclear quadrupole resonance indicates characteristic temperatures close to 7 K and 350 mK, probably related to orbital and magnetic order, respectively.

Within the framework of the quantum mechanical approach, the available experimental data are analyzed to identify the electronic structure of the multiferroic FeCr

We report on the low-frequency optical excitations in the multiferroic ground state of polycrystalline ${\mathrm{FeCr}}_{2}{\mathrm{S}}_{4}$ in the frequency range 0.3--3 THz and their changes upon applying external magnetic fields up to 7 T. In the ground state below the orbital-ordering temperature ${T}_{\mathrm{OO}}=9$ K we observe the appearance of several new modes. By applying the external magnetic field parallel and perpendicular to the propagation direction of the THz radiation, we can identify the strongest absorptions to be of predominantly electric-dipole origin. We discuss these modes as the low-energy electronic excitations of the ${\mathrm{Fe}}^{2+}$ ions ($3{d}^{6}, S\phantom{\rule{0.16em}{0ex}}=2$) in an tetrahedral ${\mathrm{S}}^{2\ensuremath{-}}$ environment. The eigenfrequencies and relative intensities of these absorption lines are satisfactorily reproduced by our calculation assuming an effective exchange field of $12.8\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ at the ${\mathrm{Fe}}^{2+}$-ions sites. The direction of the exchange field is found to be slightly tilted out of the $ab$ plane. With our approach we can also describe previously reported results from M\"ossbauer studies and the order of magnitude of the electric polarization induced by orbital and noncollinear spin ordering.

A microscopic theory of the interaction of Cr spins with electric and magnetic fields in ${\mathrm{DyCrO}}_{4}$ is described. The derived effective energy operator allows calculating the electric polarization vector using information about the magnetic structure. The calculated linear electric polarization in electric and magnetic fields at $Hl3\phantom{\rule{4.pt}{0ex}}\text{T}$ is consistent with the available experimental data. The electric field is induced by an odd crystalline field on chromium ions and the charge transfer process from the nearest oxygen ions. The enhancement of the magnetic field is associated with magnetic susceptibility, mainly due to dysprosium ions.

The solutions of the Bardeen–Cooper–Schrieffer equation are found within the model of the lower Hubbard subband taking into account three-site correlations and the superexchange, Coulomb, phonon, and spinfluctuation mechanisms of quasiparticle pairing. The Pr0.89LaCe0.11CuO4 compound is considered as an example. The dependence of the superconducting gap on the wave vector along the Fermi contour is approximated by the expression Δφ = Δ0 (B cos(2φ) + (1 − B) cos(6φ)) where the angle φ is measured from the edge of the Brillouin zone. The calculated parameters Δ0 and B correspond to the experimental data. The role of the phonon mechanism is relatively small. The competition of other specified mechanisms in the formation of Δ0 is quite strong. The effect of their interference is important and is different in different parts of the Fermi surface. The main contribution to the formation of the component proportional to cos(6φ) (the highest harmonic of the gap) is due to the spin-fluctuation and Coulomb interactions. It is numerically and analytically proved that the role of three-site correlations is reduced to weakening the superexchange mechanism.

An explicit expression for the energy of interaction between two spherically symmetric particles via the strain field in cubic crystals is obtained with an accuracy up to quadratic terms with respect to the anisotropy parameter d = c11 – c12 – 2c44. The diagrams depicting the regions of attraction and repulsion between particles projected onto the xy plane are drawn. It is found that at d 0, the directions preferable for the attraction in the linear approximation with respect to the anisotropy parameter d are diagonals. However, each such direction becomes “split” into two directions if the nonlinear corrections are taken into account. In passing, we reveal the errors and misprints in the earlier papers based on the isotropic medium approximation (d = 0) and on the linear approximation with respect of parameter d.

An explicit expression for the dynamic charge susceptibility for electron-doped cuprates has been derived. This expression accurately reproduces the wave vector dependence of the plasmon frequency observed in inelastic X-ray scattering experiments for Nd2 – xCexCuO4. The imaginary part of the charge susceptibility along the triangular path in the Brillouin zone is plotted. It is demonstrated that the spectral weight of the plasmon mode near q = 0 is negligibly low. The calculated frequencies of the plasmon mode for all wave vectors in the Brillouin zone turn out to lie outside the range of damping related to electron−hole excitations. A formula for the charge susceptibility is derived within the t−t′−t″−J model supplemented by the Coulomb interaction operator and three-site terms. The derivation is performed by the Green’s function technique employing the formalism of composite Hubbard operators and the Mori projection method, which have proved themselves in the analysis of collective spin excitations. The used Fourier transform of the Coulomb interaction corresponds to the monolayer model with a spatially periodic structure, which is embedded in a three-dimensional crystal lattice.

The role of focal infection as a possible risk factor for development of atherosclerotic cardiovascular diseases is discussed quite intensively now. Estimated some parameters of vascular stiffness in young men of military age with the features of their infectious-inflammatory medical history by the type of foci of chronic infection. It is established that in young men with foci of chronic infection such indicators of vascular stiffness, as peripheral augmentation index, augmentation index, normalized to heart rate, and augmentation index of the aorta were significantly higher than in their peers with a positive history. The differences in the first two indicators have reached a reliable level. It should be emphasized the presence of more low blood pressure in the presence of foci of chronic infection , which eliminates the distortion parameters of vascular status, influenced by the tensile effect from the blood pressure in the time of the study. The obtained data clearly indicate the higher rigidity of the walls of the aorta and large arteries in young men under the influence of their foci of chronic infection. Some tendency to development of left ventricular dysfunction in young people with presence of chronic tonsillitis and other infectious and inflammatory diseases was also revealed. This dysfunction is expressed in reducing the maximum rate of growth of blood pressure and increasing the period of expulsion of the left ventricle. The presented results confirm the concept of lifelong formation of «infectious-inflammatory load» in terms of increasing vascular rigidity and subclinical changes in the functioning of the myocardium at young age, subject to the presence of a focal chronic infection. These data allow us to regard foci of chronic infection as another risk factor of atherosclerosis, which in turn requires consideration when carrying out the relevant preventive measures among young population in the process of health checkups.

The mechanism of the linear electric polarization in FeCr2O4 ferrimagnet is suggested. The polarization is induced by the odd crystal field acting on 3d electrons of Fe2+, as well as by the spin–orbit interaction, exchange field, and orbital ordering. The calculated polarization is directed along the c axis of the crystal.

A mechanism underlying the magnetoelectric effect is discussed. This mechanism is related to the combined action of an odd crystal field, spin−orbit coupling, and the interaction of the orbital angular momentum with an applied magnetic field. The effective operator describing the spin states of Fe2+ ions is obtained. Such operator allows one to interpret the terahertz spectroscopy data and to calculate both the electric field effect on the magnetization and the magnetic field effect on the electric polarization of the sample. It is demonstrated that the magnetoelectric effect is enhanced with a decrease in the energy corresponding to the tetragonal distortion of ligand tetrahedra.

Solutions of the equation for the superconducting gap including superexchange, spin–fluctuation, plasmon, and phonon pairing mechanisms are obtained. Solutions of the Bardeen–Cooper–Schrieffer equation are approximated by the expression Δk = Δ0(B cos(2ϕ) + (1 − B)cos(6ϕ) at a carrier concentration close to optimal. It is found that the dependence proportional to cos(6ϕ) is due to the spin–fluctuation and phononmediated interactions.

Within the framework of the quantum mechanical approach, the available experimental data are analyzed to identify the electronic structure of the multiferroic FeCr2O4. The relative values of the key contributions to the parameters of even and odd crystal fields acting on the 3d electrons of the Fe2+ ion are determined. Data on local lattice distortions are systematized. The parameter of the electron-deformation interaction of the ground term Fe2+ (5 E) is determined considering lattice distortions, and the parameters of binding of the spins of Fe2+ and Cr3+ to the electric field are estimated. The calculation results are compared with the available experimental data on the magnetic and structural characteristics of FeCr2O4, the critical temperature of the transition to an orbitally ordered state, optical conductivity data, the Mössbauer effect study, and measurements of spontaneous electric polarization.

An analytical formula with three-center terms has been proposed for the calculation of the dynamic spin susceptibility of electron-doped cuprates. The results of the calculation of the imaginary part of the susceptibility reproduce the main features of inelastic neutron scattering and resonant inelastic X-ray scattering. It has been shown that the high-frequency behavior of the dispersion of collective spin excitations is mainly determined by the parameters of the conduction band and hardly depends on the exchange coupling of copper spins. The spin and superconducting gap parameters, as well as correlation effects associated with the three-center terms, play the determining role in the formation of the spin response in the region Q ≈ (π, π).

A formula for computing the temperature dependence of the London penetration depth of a magnetic field in the regime of coexistence of charge density waves and superconductivity has been proposed taking into account the dependence of both order parameters on the wave vector. It has been shown that an anomalously high diamagnetic response of the system and a finite value of the superconducting current persist even at Tc ≤ T ≤ TCDW.

An analytical expression for the temperature dependence of the superfluid density in the regime of the coexistence of charge density waves (CDW) and superconductivity has been derived beyond the effective mass approximation. In contrast to the previous research on this subject, possible dispersions of both order parameters have been taken into account. In particular, it was found that when the CDW gap parameter depends on the wave vector, London’s type current is nonzero even above \(T_\mathrm{c}\), i.e., in the interval \(T_\mathrm{c}

Introduction. The best diagnostic approach for early detection of vascular remodeling in prenosological stage of development the main cardiovascular (CV) diseases has not yet been determined, which inhibits effective vascular screening in the youth population. Objective of the present study was to assess the possible impact of risk factors (RF) on central aortic pressure (CAP) and its augmentation index in young age. Materials and Methods. A total of 80 students (38 girls, 42 boys) were examined in University Center of Student's Health for the presence of major cardiovascular RF and evaluation of CAP in the office format using diagnostic complex BPLab (company «Peter Telegin», Nizhny Novgorod, Russia) on technology Vasotens. In addition to BP in the brachial arterial (BA), the systolic aortic BP (SYSao), diastolic aortic BP (DIAao), index of augmentation in aorta (AIxao), pulse pressure amplification (PPA) and other parameters were analyzed. Surveyed persons were divided into two groups, taking into account the lack of RF ( 26 persons ) and their presence (54 persons). Results. Statistically significant increase in systolic, pulse, average pressure in the aorta and index of augmentation of pulse pressure was revealed in persons with cardiovascular RFs in comparison with those without the specified RFs. Among peripheral hemodynamic parameters, significant difference between the groups was is noted in the value of average pressure. The profile of various options of increase CAP in students as systemic, hidden and false prehypertension / hypertension substantially depends on presence of RF. Conclusion. Obtained data have confirmed the idea about valuability of using the assessment of CAP in Centers of youth's health and Student's policlinics when carrying checkups for the purpose of early detection of CV risk among young people and timely conduct personalized measures for prevention.

The dynamic charge susceptibility as a function of the wave vector and the frequency has been analyzed in the context of the existing experimental data on the plasmon frequencies, softening of the longitudinal phonon modes, and charge density waves in the electron subsystem of the high-temperature superconducting cuprates. It is emphasized that a set of all experimental data can be explained only under the assumption that the interaction via the phonon field plays an important role and differs in different regions of the Fermi surface; i.e., the parameters of the electron-phonon coupling depend not only on the value of the momentum transfer q but also on the wave vector k.

Analytical expressions for the charge susceptibility and permittivity of cuprates are obtained using the singlet-correlated conduction band model. The screening parameter caused by interband transitions is refined using experimental plasmon frequencies. A new branch of acoustic plasmons is predicted. The range of values in which acoustic plasmons do not experience Landau damping is determined for wave vectors in the Brillouin zone. Fourier images of the effective Coulomb interaction among charge carriers is calculated for different wave vectors.

The interaction of orbital momenta of copper in KCuF3 via the field of elastic deformations is analyzed taking into account the local rotations of electron density on copper ions. It is found that the interaction energy related to local rotations of copper ions is comparable in order of magnitude with the Dzyaloshinskii-Moriya interaction energy. The calculated interaction energy of copper orbitals in the ab plane of the crystal exceeds the energy of their interaction along the c axis. This circumstance explains recently found specific features of orbital melting in LaMnO3 with increasing temperature.

Zero-phonon lines of a pair center of Mn4+ ions are observed in the luminescence and luminescence-excitation spectra of SrTiO3:Mn crystal. Based on the experimental data, the energy-level structure of the ground state ∣4A2g,4A2g〉 and excited state ∣4A2g,2Eg〉 of the Mn4+-Mn4+ pair center is constructed. It is shown that the exchange interaction in the ground state of the Mn4+-Mn4+ pair is antiferromagnetic. Energies of the levels are calculated assuming that the pair is formed by Mn4+ ions occupying neighboring octahedral positions of Ti4+ ions along the [110] axis. Experimental values of the exchange integral in the ground state ∣4A2g,4A2g〉 and energies of spin multiplets in the excited state ∣4A2g,2Eg〉 agree well with calculation of the exchange interaction carried out within the framework of the channel model with the parameters Jξη = 32 cm4-1 and Jζζ = −45.5 cm4-1. Experimental data and calculations unambiguously demonstrate that zero-phonon lines in the luminescence and luminescence-excitation spectra have magnetic-dipole nature.

A simple description has been proposed for the renormalization of the conduction band parameters in cuprates owing to the interaction of the current carriers with phonons. Kinks in the quasiparticle dispersion law in the optical phonon mode region (70 meV, compound Bi2Sr2CaCu2O8 − x ) and data on the temperature dependence of the superconducting current density in YBa2Cu3O7 have been analyzed. Ideas of new experiments have been discussed.

Using modern concepts of the crystal field in ion-covalent compounds, we calculate the energy level diagram, wavefunctions, and probabilities of optical transitions in the orbital ordering phase of KCuF3. On this basis, we discuss the possible mechanisms by which an optical absorption sideband structure forms, accompanied by the creation of magnons.

New designs of bolted joints with bolt countersunk heads having high longevity in comparison with the used ones were proposed. One type of joint has the bolt heads with the reduced surface taper of the bolt head and in a joined part. Two other types have a spherical head surface, which is in contact with a tapered countersink surface. The rise in the fatigue life is achieved owing to the balance of the radial tension along the contact surfaces of the head and the countersink. Designs of a washer from the direction of a nut are proposed. These washers have ring bulges of wedge-shaped cross section that form areas of plastic deformations around a bolt body during the bolt tightening and reduce the concentration of contact stresses close to an edge of the contact surfaces of the bolt and joined parts. Procedures of fatigue tests were developed. Results of tests of the proposed bolted joints supporting their high longevity are presented. Findings of experimental investigations verify the efficiency of the application of proposed types of bolted joints in the designs of aircrafts.

We propose a new mechanism of exciton-magnon absorption in the 1D Heisenberg antiferromagnet KCuF3. It yields the correct description of the relative intensity of the spectral lines in both polarizations E c and E‖c. The magnon density of states has been calculated. The origin of the fine sideband structure in KCuF3 can be explained. The sharp magnon lines, observed in Ref. [1], correspond to the low energy singularities in the magnon density of states.

We report detailed optical experiments on the layered compound α-RuCl3 focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of THz and spin-orbital excitations via a study of temperature and symmetry-induced changes. The optical studies are complemented by thermal expansion experiments. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. A complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Orbital excitations, which cannot be explained based on recent models, and an electronic excitation, which appears in a narrow temperature range just across the structural phase transition. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition and a change of the stacking sequence, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of a single molecular layer determines the eigenfrequencies of most of these excitations. Only one mode at THz frequencies, which becomes suppressed in the high-temperature monoclinic phase and one phonon mode experience changes in symmetry and stacking. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (

The temperature dependences of the Knight shift at the Cu(2) site in YBa2Cu4O8 and Bi2Sr2CaCu2O8 + x compounds were analyzed based on the band structure parameter extracted from photoemission data. Different scenarios for the pseudogap state are discussed, and the densities of states of quasiparticle excitations are calculated.

The possibilities of obtaining information on the pseudogap parameter dependence on the wave vector in high-temperature superconductors based on layered cuprates by analyzing the temperature behavior of the line shift of the nuclear quadrupole resonance (NQR) on the Cu and O nuclei are discussed. As an example, the Cu NQR data available for YBa2Cu4O8 are analyzed.

A formula for the dynamical spin susceptibility of electron-doped high-temperature superconductors has been derived with the inclusion of strong correlation between localized and itinerant electrons. It provides an explanation of the basic features of inelastic neutron scattering in Pr0.88LaCe0.12CuO4−x with variation of the frequency and wave vector.

The energy level diagram and the wave functions for the Ti3+ ions (3d1) in LaTiO3 are calculated using modern crystal-field theory. The relative orbital ordering of these ions in the ground state is obtained. It turns out that the states of the ground triplet are considerably split and therefore the effect of the electronic-vibrational interaction is suppressed despite the fact that the distortions of the TiO6 building block seem to be small. The components of the electric field gradient tensor at the Ti3+ nuclei sites are calculated using the wave functions of the ground states obtained. The calculated asymmetry parameter agrees well with the experimental values, which demonstrates the adequacy of the proposed orbital-ordering pattern of the Ti3+ ions in the ground state.

Using high resolution X-Ray diffraction (XRD) on high purity powders, we resolved the structure and $ab$ symmetry of the intriguing compound \svo$ $ from room temperature down to 20 K to an unprecedented level of accuracy. Upon cooling, this new set of data unambiguously reveals a second order phase transition lowering the symmetry from tetragonal to orthorhombic at a temperature $T_{c2}=136$ K. The observation of an orthorhombic distortion of the $ab$-plane is attributed to nematic phase formation supported by local Jahn-Teller (JT) dynamical instability. At $T_{N}=105$ K, spins order and at $T_{c1}=100$ K the tetragonal structure is recovered with an elongated c-axis., 4 pages, 2 figures

In the framework of the singlet-correlated motion of holes over oxygen sites in CuO2 layers, a formula for the dynamic spin susceptibility has been derived taking into account the strong correlation between the magnetizations of the spins of the collective holes and localized moments on copper sites. The calculated behavior of the imaginary part of the susceptibility as a function of the frequency and wave vector is consistent with the available experimental data on the inelastic neutron scattering. The plot of the dispersion of the collective spin modes over the entire Brillouin zone is proposed.

An analytical expression for the EPR linewidth of an exchange-coupled 1/2-spin chain originating from uniform Dzyaloshinskii-Moriya interaction is derived using a quasi-classical approach. The expression successfully reproduces the results obtained by numerical quantum mechanical calculations based on Green’s function method at T > 2J/kB.