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Raman spectroscopy together with density functional calculations were used to study lattice dynamics in a layered honeycomb cobaltite Na$_3$Co$_2$SbO$_6$, which can host a field-induced phase related with the Kitaev physics. We show that there develops an additional mode well above Neel temperature (at $\approx 200$K) at 525 cm$^{-1}$, which origin can be related to an electronic excitation to one of $j_{3/2}$ doublets. Moreover, our theoretical calculations demonstrate that the highest frequency intensive mode related to the oxygen vibrations is very sensitive to type of the magnetic order. Thus, we propose to use the softening of this mode as a hallmark of the transition to a fully polarized regime, which is stabilized in Kitaev materials in strong magnetic fields., Comment: To be published in JETP Letters

Rattling phonon modes are known to be origin of various anomalous physical properties such as superconductivity, suppression of thermal conductivity, enhancement of specific heat etc. By means of DFT+$U$ calculations we directly show presence of the rattling mode in the quadruple perovskites CuCu$_3$V$_4$O$_{12}$ and CuCu$_3$Fe$_2$Re$_2$O$_{12}$ and argue that this can develop in others as well. It is demonstrated that Cu ions at $A$ sites vibrate in the center of the icosahedral oxygen O$_{12}$ cages and the corresponding potential has a complicated form with many local minima., Comment: 4 pages

In this article we give a general survey of the main properties of magnetic oxides - mostly the oxides of transition metals, but sometime also containing rare earths ions. This is a very rich class of materials, among which there are insulators and metals, systems with insulator-metal transitions, and there are among them even high-temperature superconductors. One of the main features of these compounds, which attract to them special attention and which serve as a basis of many applications, are their rich magnetic properties. In this article we discuss the main physical effects determining their behaviour, and describe in detail especially their magnetic properties, but not only. After shortly discussing the basic structure of isolated magnetic ions, we concentrate on the collective effects depending on the interaction between sites, especially exchange interaction, giving rise to different magnetic properties: different types of magnetic ordering in conventional systems, but also more exotic states such as spin liquid states in frustrated systems. We also cover related phenomena in magnetic oxides, such as magnetoelectric and multiferroic behaviour, and discuss at the end their diverse useful properties serving as a basis of many applications., Comment: Chapter to Encyclopedia of Condensed Matter Physics, 2nd edition

A survey of scientific and social activity of S. V. Vonsovsky is presented. His fundamental works on the theory of electronic properties and magnetism of transition and rare-earth metals and their compounds are reviewed. The historical development of the many-electron polar (preceding the famous Hubbard model) and $s-d(f)$ exchange (''Vonsovsky-Zener'', ''Kondo lattice'') models is considered., Comment: 6 pages, Kourovka Winter School of Theoretical Physics

Recent theoretical studies have suggested that Kitaev physics and such effects as formation of a mysterious spin-liquid state can be expected not only in RuCl3 and iridates, but also in conventional $3d$ transition metal compounds. Using DC and AC magnetometry, thermodynamic and $^{23}$Na nuclear magnetic resonance measurements (NMR) we studied such a candidate material Na3Co2SbO6. A full phase diagram of Na3Co2SbO6 in a wide range of magnetic fields and temperatures is presented. The results demonstrate transformation of the antiferromagnetic structure under the external magnetic field, gradual development of the saturation phase, as well as evidence of gapped behavior in certain parts of the phase diagram

Using {\it ab initio} band structure calculations we show that mineral cubanite, CuFe$_2$S$_3$, demonstrates an orbital-selective behavior with some of the electrons occupying molecular orbitals of $x^2-y^2$ symmetry and others localized at atomic orbitals. This is a rare situation for $3d$ transition metal compounds explains experimentally observed absence of charge disproportionation, anomalous M\"ossbauer data, and ferromagnetic ordering in between nearest neighbor Fe ions.

The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions., Comment: 6 pages, 4 figures

We study an interplay between the orbital degeneracy and spin-orbit coupling giving rise to spin-orbital entangled states. As a specific example, we analyze the interaction of electrons occupying triply degenerate single-ion $t_{2g}$ levels with trigonal vibronic modes (the $t\otimes T$ problem). A more general problem of the electron-lattice interaction involving both tetragonal and trigonal vibrations is also considered. It is shown that the result of such interaction crucially depends on the occupation of $t_{2g}$ levels leading to either the suppression or enhancement of the Jahn-Teller effect by the spin-orbit coupling., Comment: 11 pages, 10 figures

Based on the density functional theory, we examine the origin of ferromagnetism in the Weyl semimetal Co$_3$Sn$_2$S$_2$ using different types of response theories. We argue that the magnetism of Co$_3$Sn$_2$S$_2$ has a dual nature and bears certain aspects of both itineracy and localization. On the one hand, the magnetism is soft, where the local magnetic moments strongly depend on temperature and the angles formed by these moments at different Co sites of the kagome lattice, as expected for itinerant magnets. On the other hand, the picture of localized spins still remains adequate for the description of the local stability of the ferromagnetic (FM) order with respect to the transversal spin fluctuations. For the latter purposes, we employ two approaches, which provide quite different pictures for interatomic exchange interactions: the regular magnetic force theorem and a formally exact theory based on the calculation of the inverse response function. The exact theory predicts Co$_3$Sn$_2$S$_2$ to be a three-dimensional ferromagnet with the strongest interaction operating between next-nearest neighbors in the adjacent kagome planes. The ligand states are found to play a very important role by additionally stabilizing the FM order. When the local moments decrease, the interplane interactions sharply decrease, first causing the FM order to become quasi-two-dimensional, and then making it unstable with respect to the spin-spiral order propagating perpendicular to the kagome plane. The latter instability is partly contributed by the states at the Fermi surface and may be relevant to the magnetic behavior of Co$_3$Sn$_2$S$_2$ near the Curie temperature. Peculiarities of the half-metallic ferromagnetism in Co$_3$Sn$_2$S$_2$ are also discussed.

Recently the structural transition in Na2Ti3Cl8 at 200 K with the formation of triangular Ti3 clusters was studied by ab-initio calculations in PRL 124, 167203 (2020). It was concluded on the basis of the DFT+U results that the usual band effects are not sufficient to explain this transition. The authors then invoked magnetic mechanisms, including complicated factors such as biquadratic and ring exchanges. We point out that this overcomplicated description is unnecessary, and that the formation of trimers, or breathing kagome lattice in Na2Ti3Cl8, and in many other systems, has very simple, almost trivial explanation basing on the orbital-driven Peierls transition.

The recently discovered material Cs$_3$Fe$_2$Br$_9$ contains Fe$_2$Br$_9$ bi-octahedra forming triangular layers with hexagonal stacking along the $c$ axis. In contrast to isostructural Cr-based compounds, the zero-field ground state is not a nonmagnetic $S=0$ singlet-dimer state. Instead, the Fe$_2$Br$_9$ bi-octahedra host semiclassical $S=5/2$ Fe$^{3+}$ spins with a pronounced easy-axis anisotropy along $c$ and interestingly, the intra-dimer spins are ordered ferromagnetically. The high degree of magnetic frustration due to (various) competing intra- and inter-dimer couplings leads to a surprisingly rich magnetic phase diagram. Already the zero-field ground state is reached via an intermediate phase, and the high-field magnetization and thermal expansion data for $H\parallel c$ identify ten different ordered phases. Among them are phases with constant magnetization of 1/3, respectively 1/2 of the saturation value, and several transitions are strongly hysteretic with pronounced length changes reflecting strong magnetoelastic coupling., Comment: 11 pages, 12 figures (minor corrections and 3 additional have been included in V3)

We study physical properties of a potential candidate for the physical realization of the SU(4) spin-orbital model - layered alpha-ZrCl3. Both DFT and DFT+U+SOC calculations show that this material most probably dimerizes at normal conditions. Therefore it is unlikely that symmetric SU(4) model can be used for description of magnetic properties of alpha-ZrCl3 at low temperatures. In the dimerized structure electrons occupy molecular orbitals formed by the xy orbitals. One might expect a non-magnetic ground state in this case. Interestingly the energy difference between various dimers packings is rather small and thus dimers may start to flow over the lattice as they do in Li2RuO3.

Structural properties of CuAl$_{2}$O$_{4}$, which was recently argued to show unusual suppression of the Jahn-Teller distortions by the spin-orbit coupling, are investigated under pressures up to 6 GPa. Analysis of X-ray powder diffraction experiments shows that CuAl$_{2}$O$_{4}$ gets unstable and decomposes onto CuO and Al$_{2}$O$_{3}$ at pressures $\sim$ 6 GPa and temperature $\sim$ 1000 K. This finding is complemented by the DFT+U+SOC calculations, which demonstrate that this instability is partially driven by a (relatively) large compressibility of strongly Jahn-Teller distorted CuO., Comment: 6 pages, 6 figures, 2 tables

The magnetic contribution of the Co3+ ions in Co3BO5 has been investigated using the Co (K-edge) XMCD, dc magnetic susceptibility, and heat capacity measurements. The crystal structure of Co3BO5 single crystal has been solved in detail at the T range 296-703 K. The results have been supplemented by the GGA+U calculations., Comment: 38 pages, 15 figures

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, but also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. They result in the famous Jahn-Teller effect leading to a plethora of consequences, in static and in dynamic properties, including nontrivial quantum effects. In the present review we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarising the basic phenomena and their description, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to directional character of orbitals, with concomitant appearance of some instabilities leading in particular to the formation of dimers, trimers and similar clusters in a material. The properties of such cluster systems, largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field which acquired special significance relatively recently is the role of relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in details in the second part of the review. In discussing all these questions special attention is paid to novel quantum effects in those., Comment: published in Chemical Reviews

We measured the temperature dependence of low-frequency Raman spectra in Li$_2$RuO$_3$, and observed multipeak quasielastic scattering in the Ru honeycomb polarizations below and above the magnetostructural transition temperature. We attribute this scattering to the fluctuations of the energy density in the spin system. High-frequency electronic light scattering was observed at 2150 $cm^{-1}$. Its intensity increased significantly below the transition temperature, confirming substantial modification of electronic structure due to removal of degeneracy in $t_{2g}$-manifold of Ru$^{4+}$ ions.

The Jahn-Teller effect is one of the most fundamental phenomena important not only for physics, but also for chemistry and material science. Solving the Jahn-Teller problem and taking into account strong electron correlations we show that quantum entanglement of the spin and orbital degrees of freedom via spin--orbit coupling strongly affects this effect. Depending on the number of $d$ electrons it may quench (electronic configurations $t_{2g}^2$, $t_{2g}^4$, and $t_{2g}^5$), partially suppress ($t_{2g}^1$) or in contrast induce ($t_{2g}^3$) Jahn-Teller distortions. Moreover, in certain situations, interplay between the Jahn-Teller effect and spin--orbit coupling promotes formation of the "Mexican hat" energy surface facilitating various quantum phenomena.

We unveil the microscopic origin of largely debated magnetism in the Mo$_{3}$O$_{8}$ cluster systems. Upon considering an extended Hubbard model at 1/6 filling on the anisotropic kagom\'e lattice formed by the Mo atoms, we argue that its ground state is determined by the competition between kinetic energy and intersite Coulomb interactions, which is controlled by the trimerisation of the kagom\'e lattice into the Mo$_{3}$O$_{13}$ clusters. Based on first-principles calculations, we show that the strong interaction limit is realised in LiZn$_{2}$Mo$_{3}$O$_{8}$ revealing a plaquette charge order with unpaired spins at the resonating hexagons, whose origin is solely related to the opposite signs of intracluster and intercluster hoppings, in contrast to all previous scenarios. On the other hand, both Li$_{2}$InMo$_{3}$O$_{8}$ and Li$_{2}$ScMo$_{3}$O$_{8}$ are demonstrated to fall into the weak interaction limit where the electrons are well localised at the Mo$_{3}$O$_{13}$ clusters. While the former is found to exhibit long-range antiferromagnetic order, the latter is more likely to reveal short-range order with quantum spin liquid-like excitations. Our results not only reproduce most of the experimentally observed features of these unique materials, but will also help to describe various properties in other quantum cluster magnets.

MnSnTeO6, a new chiral antiferromagnet, was prepared both by topotactic transformation of the metastable rosiaite-type polymorph and by direct synthesis from coprecipitated hydroxides. Its structure, static and dynamic magnetic properties were studied comprehensively both experimentally (through X-ray and neutron powder diffraction, magnetization, specific heat, dielectric permittivity and ESR techniques) and theoretically (by means of ab initio density functional theory (DFT) calculations within the spin-polarized generalized gradient approximation). MnSnTeO6 is isostructural with MnSb2O6 (space group P321) and does not show any structural transition between 3 and 300 K. The magnetic susceptibility and specific heat exhibit an antiferromagnetic ordering at TN=9.8 K, which is confirmed by low-temperature neutron data. At the same time, the thermodynamic parameters demonstrate an additional anomaly on the temperature dependences of magnetic susceptibility chi(T), specific heat Cp(T) and dielectric permittivity epsilon(T) at T*=4.9 K, which is characterized by significant temperature hysteresis. Clear enhancement of the dielectric permittivity at T* is most likely to reflect the coupling of dielectric and magnetic subsystems leading to development of electric polarization. It was established that the ground state of MnSnTeO6 is stabilized by seven exchange parameters, and neutron diffraction revealed incommensurate magnetic structure with propagation vector k= (0, 0, 0.183) analogous to that of MnSb2O6. Ab initio DFT calculations demonstrate that the strongest exchange coupling occurs between planes along diagonals. All exchange parameters are antiferromagnetic and reveal moderate frustration.

The electronic and magnetic properties of clinopyroxene CaMnGe$_2$O$_6$ were studied using density function calculations within the GGA+U approximation. It is shown that anomalous ferromagnetic ordering of neighboring chains is due to a "common-enemy" mechanism. Two antiferromagnetic exchange couplings between nearest neighbours within the Mn-Mn chain and interchain coupling via two GeO$_4$ tetrahedra suppress antiferromagnetic exchange via single GeO$_4$ tetrahedron and stabilize ferromagnetic ordering of Mn chains., Comment: 5 pages, 4 figures. Accepted to JETP Letters

In the present paper electronic, magnetic, and structural properties of a novel system FeZnMo$_3$O$_8$ with a polar crystal structure are investigated using GGA+U calculations. It is shown that Fe ions preferably occupy octahedral and Zn ions tetrahedral positions. This structural feature is caused by different ionic radii of these ions and not by the exchange coupling. The calculated exchange constants naturally explain magnetic structure observed in this material.

The kamiokite, Fe$_2$Mo$_3$O$_8$, is regarded as a promising material exhibiting giant magnetoelectric (ME) effect at the relatively high temperature $T$. Here, we explore this phenomenon on the basis of first-principles electronic structure calculations. For this purpose we construct a realistic model describing the behavior of magnetic Fe $3d$ electrons and further map it onto the isotropic spin model. Our analysis suggests two possible scenaria for Fe$_2$Mo$_3$O$_8$. The first one is based on the homogeneous charge distribution of the Fe$^{2+}$ ions amongst tetrahedral ($t$) and octahedral ($o$) sites, which tends to low the crystallographic P6$_3$mc symmetry through the formation of an orbitally ordered state. Nevertheless, the effect of the orbital ordering on interatomic exchange interactions does not seem to be strong, so that the magnetic properties can be described reasonably well by averaged interactions obeying the P6$_3$mc symmetry. The second scenario, which is supported by obtained parameters of on-site Coulomb repulsion and respects the P6$_3$mc symmetry, implies the charge disproportionation involving somewhat exotic $1+$ ionization state of the $t$-Fe sites (and $3+$ state of the $o$-Fe sites). Somewhat surprisingly, these scenarios are practically indistinguishable from the viewpoint of exchange interactions, which are practically identical in these two cases. However, the spin-dependent properties of the electric polarization are expected to be different due to the strong difference in the polarity of the Fe$^{2+}$-Fe$^{2+}$ and Fe$^{1+}$-Fe$^{3+}$ bonds. Our analysis uncovers the basic aspects of the ME effect in Fe$_2$Mo$_3$O$_8$. Nevertheless, the quantitative description should involve other ingredients, apparently related to the lattice and orbitals degrees of freedom., Comment: 11 pages, 11 figures

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: the elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double 'slits' in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures., Comment: 8 pages, 8 figures

We establish the double perovskite Ba$_2$CeIrO$_6$ as a nearly ideal model system for j=1/2 moments, with resonant inelastic x-ray scattering indicating a deviation of less than 1% from the ideally cubic j=1/2 state. The local j=1/2 moments form an fcc lattice and are found to order antiferromagnetically at $T_N$=14K, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, indicated by ab initio theory. Magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magneto-elastic effect - both effects are typically not expected for j=1/2 compounds making Ba2CeIrO6 a riveting example for the rich physics of spin-orbit entangled Mott insulators., Comment: published version, 10 pages, 7 figures

Gold is inert and forms very few compounds. One of the most interesting of those is calaverite AuTe2, which has incommensurate structure and which becomes superconducting when doped or under pressure. There exist a "sibling" of AuTe2 the mineral sylvanite AuAgTe4, which properties are almost unknown. In sylvanite Au and Ag ions are ordered in stripes, and Te6 octahedra around metals are distorted in such a way that Ag becomes linearly coordinated, what is typical for Ag^{1+}, whereas Au is square coordinated - it is typical for d^8 configurations, i.e. one can assign to Au the valence 3+. Our theoretical study shows that at pressure P_C ~ 5 GPa there should occur in it a structural transition such that above this critical pressure Te6 octahedra around Au and Ag become regular and practically identical. Simultaneously Te-Te dimers, existing at P = 0 GPa, disappear, and material from a bad metal becomes a usual metal with predominantly Te 5p states at the Fermi energy. We expect that, similar to AuTe2, AuAgTe4 should become superconducting above P_C., Comment: 8 pages, 4 figures

We report results of the Raman measurements for SrRu$_2$O$_6$ having extraordinary high N$\acute{\textrm{e}}$el temperature for a layered material. No additional phonon modes were detected at the temperature of magnetic transition thus excluding lowering of the symmetry in the magnetically ordered phase. An unusual increase in softening and damping of some phonons as the temperature approaches $T_N$ indicate the appearance of a continuum of interacting electronic excitations at $T\geq300K$. We also observe an intensive Raman response at 2050 cm$^{-1}$. Analysis of the polarization dependence and comparison with available theoretical data shows that this peak likely originates from the transitions between molecular orbitals previously proposed to explain the magnetic properties of SrRu$_2$O$_6$.

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-$\boldsymbol{q}$ spiral.

Recently synthesised Ba4NbMn3O12 belong to cluster magnets - systems with tightly bound groups of magnetism ions, in this case Mn3 trimers. Often such magnetic clusters can be described by molecular orbitals (MO), however strong electron correlations may invalidate this description. To understand the electronic and magnetic state of Ba4NbMn3O12 we carried out ab initio calculations and show that this system is better described not in MO picture, but as a system with electrons localized on the Mn ions, with strong intra-cluster and weaker inter-cluster exchange. The calculated spin of the Mn3 trimer is S=2, in agreement with the experiment. The predicted magnetic structure of Ba4NbMn3O12 is that of ferromagnetic layers of Mn3 trimers, stacked antiferromagnetically.

The structural properties of Na2RuO3 under pressure are studied using density functional theory within the generalized gradient approximation (GGA). We found that one may expect a structural transition at ~ 3 GPa. This structure at the high-pressure phase is exactly the same as the low-temperature structure of Li2RuO3 (at ambient pressure) and is characterized by the P21/m space group. Ru ions form dimers in this phase and one may expect strong modification of the electronic and magnetic properties in Na2RuO3 at pressure higher than 3 GPa., Comment: 5 pages, 4 figures

In the present review different effects related to the orbital degrees of freedom are discussed. Leaving aside such aspects as the superexchange mechanism of the cooperative Jahn-Teller distortions and different properties of "Kugel-Khomskii"-like models, we mostly concentrate on other phenomena, which are in the focus of the modern condensed matter physics. After a general introduction we start with the discussion of the concept of effective reduction of dimensionality due to orbital degrees of freedom and consider such phenomena as the orbitally-driven Peierls effect and the formation of small clusters of ions in the vicinity of a Mott transition, which behave like "molecules" embedded in a solid. The second large section is devoted to the orbital-selective effects such as the orbital-selective Mott transition and the suppression of magnetism due to the fact that part of the orbitals start to form singlet molecular orbitals. At the end the rapidly growing field of the so-called "spin-orbit-dominated" transition metal compounds is briefly reviewed including such topics as the interplay between the spin-orbit coupling and the Jahn-Teller effect, the formation of the spin-orbit driven Mott and Peierls states, the role of orbital degrees of freedom in generation of the Kitaev exchange coupling, and the singlet (excitonic) magnetism in $4d$ and $5d$ transition metal compounds., Comment: Russian version of Physics-Uspekhi is available; https://ufn.ru/ru/articles/2017/11/d/

To sum up, we show in the present paper that magnetic response in Nb$_2$O$_2$F$_3$ at the high-temperatures ($T>$90 K) is related to the orbital selective regime, when part of the electrons form molecular orbitals while other electrons have local magnetic moments. The charge disproportionation, which occurs at $T\sim$90 K is seen in the GGA calculations, but its degree ($\delta n \sim 0.1$ electron) is far from what one would expect from naive expectations based on the formal ionic valences. The mechanism of the charge ordering is argued to be related with a sizable kinetic energy gain due to formation of two molecular orbitals in short Nb$^{3+}$-Nb$^{3+}$ dimers caused by a strong nonlinearity of the distance dependence on electron hopping. We think that this mechanism of charge ordering, stabilized not by decrease of interaction energy, but rather by the gain in kinetic energy, may be operative in many other systems, especially consisting of structural dimers.

Recent discovery of pyrite FeO$_2$, which can be an important ingredient of the Earth's lower mantle and which in particular may serve as an extra source of water in the Earth's interior, opens new perspectives for geophysics and geochemistry, but this is also an extremely interesting material from physical point of view. We found that in contrast to naive expectations Fe is nearly 3+ in this material, which strongly affects its magnetic properties and makes it qualitatively different from well known sulfide analogue - FeS$_2$. Doping, which is most likely to occur in the Earth's mantle, makes FeO$_2$ much more magnetic. In addition we show that unique electronic structure places FeO$_2$ "in between" the usual dioxides and peroxides making this system interesting both for physics and solid state chemistry.

The magnon dispersion of Ca$_2$RuO$_4$ has been studied by polarized and unpolarized neutron scattering experiments on crystals containing 0, 1 and 10 % of Ti. The entire dispersion of transverse magnons can be well described by a conventional spin-wave model with interaction and anisotropy parameters that agree with density functional theory calculations. Spin-orbit coupling strongly influences the magnetic excitations, which is most visible in large energies of the magnetic zone-center modes arising from magnetic anisotropy. We find evidence for a low-lying additional mode that exhibits strongest scattering intensity near the antiferromagnetic zone center. This extra signal can be explained by a sizable magnetic moment of 0.11 Bohr magnetons on the apical oxygens parallel to the Ru moment, which is found in the density functional theory calculations. The energy and the signal strength of the additional branch are well described by taking into account this oxygen moment with weak ferromagnetic coupling between Ru and O moments., Comment: 14 pages, 11 figures

We report a Raman study of the effect of temperature on the self-energies of optical phonons in a number of transition metals with hexagonal-close-packed structure. Anisotropic softening of phonon energies and narrowing of phonon linewidths with increasing temperature are observed. These effects are reproduced in the calculations of phonon spectral functions based on \textit{ab initio} electronic structures and with carrier scattering by phonons taken into account. The combined observations and results of simulations indicate a relation between observed anomalies and the renormalization of the electron spectrum due to electron-phonon interaction. It is emphasized that the temperature dependence of the phonon energies resembles anharmonic behavior but is actually an electron-induced effect.

Electronic Raman scattering and optical phonon self-energies are studied on single crystals of $LuB_{12}$ with different isotopic composition in the temperature region 10-650K and at pressures up to 10 GPa. The shape and energy position of the spectral peaks depend on the magnitude of the probed wave vector, temperature, and symmetry of excitations. We simulated experimental spectra using electronic structure obtained in the density function theory and taking into account the electron-phonon scattering. The emergence of a broad continuum in the spectra is identified with the inelastic scattering of light from the electronic intraband excitations. Their coupling to non-fully symmetric phonon modes is the source of both the Fano interference and temperature-dependent phonon self-energies. In addition, long wavelength vibrations of the boron atoms are in nonadiabatic regime, so the electronic contribution to their self-energies provides a temperature dependence that is similar to the anharmonic contribution. Comparison of calculation and experiment allowed us to determine the coupling constant $\lambda_{ep}$=0.32, which gives correct critical temperature of the transition to the superconducting state.

We show that evolution of magnetic properties in FeS under pressure cannot be explained only in terms of a spin state transition. While uniform compression does show substantial suppression of the local magnetic moment and increase of the weights of configurations with low spin, analysis of the local spin-spin correlation function demonstrates increase of the spin itinerancy. This is related to a strong modification of the electronic structure under pressure: in the high-pressure phase FeS is in the Fermi-liquid state, while decrease of the pressure moves the system to an orbital-selective regime.

Magnetic properties of Li$_x$CoO$_2$ for $x = 0.94, 0.75, 0.66$ and $0.51$ were investigated in frames of method combining Generalized Gradient Approximation with Dynamical Mean--Field Theory (GGA+DMFT). We found that a delicate interplay between Hund's exchange energy and $t_{2g}-e_g$ crystal field splitting is responsible for the high spin to low spin state transition for Co$^{4+}$ ions. The GGA+DMFT calculations show that at small doping level the Co$^{4+}$ ions adopt high spin state, while delithiation results in increase of the crystal field splitting and low spin state becomes preferable. The Co$^{3+}$ ions were found to stays in the low spin configuration for any $x$.

A tendency to form benzene-like molecular orbitals has been recently shown to be a common feature of the $4d$ and $5d$ transition metal oxides with a honeycomb lattice. This tendency competes with other interactions such as the spin-orbit coupling and Hubbard correlations, and can be partially or completely suppressed. In the calculations, SrRu$_{2}$O$_{6}$ presents the cleanest, so far, case of well-formed molecular orbitals, however, direct experimental evidence for or against this proposition has been missing. In this paper, we show that combined photoemission and optical studies can be used to identify molecular orbitals in SrRu$_{2}$O$_{6}$. Symmetry-driven election selection rules suppress optical transitions between certain molecular orbitals, while photoemission and inverse photoemission measurements are insensitive to them. Comparing the photoemission and optical conductivity spectra one should be able to observe clear signatures of molecular orbitals.

We study \textit{ab initio} a pyrochlore compound, CsW$_{2}$O$_{6}$, which exhibits a yet unexplained metal-insulator transition. We find that (1) the reported low-$T$ structure is likely inaccurate and the correct structure has a twice larger cell; (2) the insulating phase is not of a Mott or dimer-singlet nature, but a rare example of a 3D Peierls transition, with a simultaneous condensation of three density waves; (3) spin-orbit interaction plays a crucial role, forming well-nested bands. The high-$T$ (HT) phase, if stabilized, could harbor a unique $e_{g}+ie_{g}$ superconducting state that breaks the time reversal symmetry, but is not chiral. This state was predicted in 1999, but never observed. We speculate about possible ways to stabilize the HT phase while keeping the conditions for superconductivity.

When an electronic system has strong correlations and a large spin-orbit interaction, it often exhibits a plethora of mutually competing quantum phases. How a particular quantum ground state is selected out of several possibilities is a very interesting question. However, equally fascinating is how such a quantum entangled state breaks up due to perturbation. This important question has relevance in very diverse fields of science from strongly correlated electron physics to quantum information. Here we report that a quantum entangled dimerized state or valence bond crystal (VBC) phase of Li2RuO3 shows nontrivial doping dependence as we perturb the Ru honeycomb lattice by replacing Ru with Li. Through extensive experimental studies, we demonstrate that the VBC phase melts into a valence bond liquid phase of the RVB (resonating valence bond) type. This system offers an interesting playground where one can test and refine our current understanding of the quantum competing phases in a single compound., Comment: Scientific Reports (in press)

Magnetism in transition metal compounds is usually considered starting from a description of isolated ions, as exact as possible, and treating their (exchange) interaction at a later stage. We show that this standard approach may break down in many cases, especially in $4d$ and $5d$ compounds. We argue that there is an important intersite effect -- an orbital-selective formation of covalent metal-metal bonds, which leads to an "exclusion" of corresponding electrons from the magnetic subsystem, and thus strongly affects magnetic properties of the system. This effect is especially prominent for noninteger electron number, when it results in suppression of the famous double exchange, the main mechanism of ferromagnetism in transition metal compounds. We study this novel mechanism analytically and numerically and show that it explains magnetic properties of not only several $4d-5d$ materials, including Nb$_2$O$_2$F$_3$ and Ba$_5$AlIr$_2$O$_{11}$, but can also be operative in $3d$ transition metal oxides, e.g. in CrO$_2$ under pressure. We also discuss the role of spin-orbit coupling on the competition between covalency and magnetism. Our results demonstrate that strong intersite coupling may invalidate the standard single-site starting point for considering magnetism, and can lead to a qualitatively new behaviour.

We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with N\'eel temperature TN ~ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-flop type) transition below TN in moderate magnetic fields. The GGA+U calculations show the importance of the orbital degrees of freedom, which maintain a hierarchy of exchange interaction in the system. The strongest antiferromagnetic exchange coupling was found in the shortest Co-Co pairs and is due to direct and superexchange interactions between the half-filled xz+yz orbitals pointing directly to each other. The other four out of six nearest neighbor exchanges within the cobalt hexagon are suppressed, since for these bonds active half-filled orbitals turned out to be parallel and do not overlap. The electron spin resonance (ESR) spectra reveal a Gaussian shape line attributed to Co2+ ion in octahedral coordination with average effective g-factor g=2.3+/-0.1 at room temperature and shows strong divergence of ESR parameters below 120 K, which imply an extended region of short-range correlations. Based on the results of magnetic and thermodynamic studies in applied fields, we propose the magnetic phase diagram for the new honeycomb-lattice delafossite.

We analyze the role of local geometry in the spin and orbital interaction in transition metal compounds with orbital degeneracy. We stress that the tendency observed for the most studied case (transition metals in O$_6$ octahedra with one common oxygen -- common corner of neighboring octahedra and with $\sim 180^{\circ}$ metal--oxygen--metal bonds), that ferro-orbital ordering renders antiferro-spin coupling, and, {\it vice versa}, antiferro-orbitals give ferro-spin ordering, is not valid in general case, in particular for octahedra with common edge and with $\sim 90^{\circ}$ M--O--M bonds. Special attention is paid to the ``third case'', neighboring octahedra with common face (three common oxygens) -- the case practically not considered until now, although there are many real systems with this geometry. Interestingly enough, the spin--orbital exchange in this case turns out to be to be simpler and more symmetric than in the first two cases. We also consider, which form the effective exchange takes for different geometries in case of strong spin--orbit coupling., Comment: 31 pages, 9 figures, submitted to JETP