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Transition-metal ions with $5d^2$ electronic configuration in a cubic crystal field are prone to have a vanishing dipolar magnetic moment but finite higher-order multipolar moments, and they are expected to exhibit exotic physical properties. Through an investigation using resonant inelastic X-ray spectroscopy (RIXS), Raman spectroscopy, and theoretical ligand-field multiplet and $ab initio$ calculations, we fully characterized the electronic structure of Ba$_2$CaOsO$_6$, particularly, the crystal-field symmetry of the 5$d^2$ electrons in this anomalous material. The low-energy multiplet excitations from RIXS at the oxygen $K$ edge and Raman-active phonons both show no splitting, confirming the absence of Jahn-Teller distortion. These findings are consistent with the ground state with the 'hidden order' of magnetic octupoles. Obtained parameters pave the way for further realistic microscopic studies of this highly unusual class of materials, advancing our understanding of spin-orbit physics in systems with higher-order multipoles., Comment: Main: 9 pages, 5 figures. Supplement: 5 pages, 2 figures

The Re5+(5d2) compounds possess large spin-orbital interaction which urges for large anisotropy, non-collinear structures and other phenomena. Here we present ReCl5 composed by separate Re2Cl10 units formed by edge-shared chlorine octahedra. It demonstrates the formation of antiferromagnetically ordered state in two steps at TN1 = 35.5 K and TN2 = 13.2 K seen in dc-, ac-magnetic susceptibility and in specific heat. At 4K it can be transformed to the state with spontaneous magnetic moment by relatively weak magnetic field m0H = 0.5 T via metamagnetic phase transition. Ab initio calculations give anisotropic ferromagnetic exchange interactions J1 and J2 within and between rhenium pairs forming the zig-zag chains along the a-axis. Pairs of zig-zag chains are coupled by ferromagnetic interaction J3 along the c-axis into magnetic honeycomb ladders. The ladders are coupled by significantly weaker interaction J4., Comment: 11 pages, 8 figures

The electronic and magnetic properties of recently synthesized new perovskite phase of HgMnO$_3$ are studied. By means of $ab$ $initio$ DFT calculations this material was shown to be altermagnetic. We discuss features of its electronic structure and unveil the physical mechanism of anomalous suppression of antiferromagnetic exchange interaction in this material. While it is tempting to ascribe unexpectedly weak exchange interaction between nearest neighbors to crystal structure distortions, this is the indirect ferromagnetic exchange via Hg $6s$ states, which strongly affects the magnetic properties. This effect can be important not only for HgMnO$_3$, but also for many other transition metal compounds having empty $s$ states, placed not far above the Fermi level.

In this work, we explore the electronic properties and chemical bonding in the recently discovered mineral zaykovite, the first natural rhodium selenide Rh$_3$Se$_4$. We comprehensively studied the bulk electronic structure, hybridization of rhodium and selenium orbitals, and the influence of spin-orbit interaction on the electronic spectrum, as well as inspected its topological properties. Besides, we investigated the surface electronic structure of zaykovite and revealed the anisotropic Rashba-type spin splitting in the surface states. In addition, using calculations of the phonon spectra and enthalpy of formation we predicted the family of similar selenides based on other $4d$ and $5d$ transition metals such as Ir, Pd, and Pt. The structural and electronic properties of these materials are discussed., Comment: 10 pages, 8 figures, to be published in The Journal of Chemical Physics

The results of polarization-dependent Raman spectroscopy of single-crystalline LiVO$_2$ exhibiting transition to a diamagnetic state below $T_c \sim $500K are reported. Our measurements clearly detect additional peaks in the low-temperature phase, which disappear nearly completely when heated above $T_c$. Proposed $\sqrt{3}$a \times $\sqrt{3}$a lattice reconstruction explains these new Raman peaks by the Brillouin zone folding. The experiment, on the one hand, confirms that the symmetry of the non-magnetic phase is not lower than trigonal, but, on another hand, our thermal cycling study suggests possible stacking faults. This agrees with results of the density functional theory calculations, which show that the energy difference between different types of stacking does not exceed 1 K per formula unit.

The effect of the spin-orbit coupling on the ground state properties of the square-lattice three-band Hubbard model with a single electron per site is studied by a generalized Hartree-Fock approximation. We calculate the full phase diagram and show that there appear additional orbital-entangled phases brought about by competition of various exchange channels or by the spin-orbit coupling in addition to conventional states stabilized by the Kugel-Khomskii mechanism. One of these phases previously proposed to explain magnetic properties of Sr$_2$VO$_4$ is characterized by vanishing dipolar magnetic moments and antiferro-octupolar ordering. We calculated microscopic parameters for this material and demonstrate that it is located near a phase boundary of two orbital-entangled and two conventional antiferromagnetic ferro-orbital states.

We investigated the spin-lattice coupling in orthorhombic pseudobrookite FeTi2O5 single crystal with highly ordered $ Fe^{2+} / Ti^{4+}$ occupation, which consists of quasi-1D S=2 chains running along a-axis. Both the magnetization and specific heat measurements confirm that the antiferromagnetic phase transition of FeTi2O5 occurs at TN = 42 K. The structural distortions were also observed around TN in the thermal expansion $ \Delta L / L (T)$ data. Moreover, the magnetic field was found to strongly affect the thermal expansion both along chains and in the perpendicular direction clearly signaling a substantial magnetoelastic coupling, which was recently proposed to be the origin of a rare spin Jahn-Teller effect, when frustration is lifted via additional lattice distortions. Experimentally observed change in the thermal conductivity slope around TN is usually associated with the orbital ordering, but DFT+U calculations do not detect modification of the orbital structure across the transition. However, the first-principles calculation results confirm that FeTi2O5 is a quasi-1D magnet with a ratio of frustrating inter-chain to intra-chain exchanges $ J' / J = 0 . 0 3$ and a substantial single-ion anisotropy (A = 4K) of easy-axis type making this material interesting for studying quantum criticality in transverse magnetic fields., Comment: 20 pages, 7 figures

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

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe$_2$O$_6$ using a combination of neutron scattering, {\it ab initio} methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co$^{2+}$ ions. The extended Kitaev-Heisenberg model, including a significant anisotropic bond-dependent exchange term with $K/|J|=0.96$, is identified as the key descriptor of the magnetic interactions in SrCoGe$_2$O$_6$. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13~T) which shifts the system from a fragile antiferromagnetic ordering with $T_{\mathrm{N}}=9$~K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended $p$ orbitals, emerge as a novel platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics., Comment: 11 + 2 pages, 7 + 3 figures

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

Gold is one of the most inert metals, forming very few compounds, some with rather interesting properties, and only two of them currently known to be superconducting under certain conditions (AuTe$_2$ and SrAuSi$_3$). Compounds of another noble element, Ag, are also relatively rare, and very few of them are superconducting. Finding new superconducting materials containing gold (and silver) is a challenge - especially having in mind that the best high-$T_c$ superconductors at normal conditions are based upon their rather close ''relative'', Cu. Here we report combined X-ray diffraction, Raman, and resistivity measurements, as well as first-principles calculations, to explore the effect of hydrostatic pressure on the properties of the sylvanite mineral, AuAgTe$_4$. Our experimental results, supported by density functional theory, reveal a structural phase transition at $\sim$5 GPa from a monoclinic $P2/c$ to $P2/m$ phase, resulting in almost identical coordinations of Au and Ag ions, with rather uniform interatomic distances. Further, resistivity measurements show the onset of superconductivity at $\sim$1.5 GPa in the $P2/c$ phase, followed by a linear increase of $T_c$ up to the phase transition, with a maximum in the $P2/m$ phase, and a gradual decrease afterwards. Our calculations indicate phonon-mediated superconductivity, with the electron-phonon coupling coming predominantly from the low-energy phonon modes. Thus, along with the discovery of a new superconducting compound of gold/silver, our results advance understanding of the mechanism of the superconductivity in Au-containing compounds, which may pave the way to the discovery of novel ones.

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.

In recent years, A-site ordered half-doped double-perovskite manganites $\rm RBaMn_2O_6$ (R=rare earth) have attracted much attention due to their remarkable physical properties and a prospect of application as magnetoresistance, multiferroic, and oxygen storage materials. The nature of the ground state in ${\rm RBaMn_2O_6}$ as well as sequence of phase transitions taking place at cooling are not yet well understood due to complexity in both experimental and theoretical studies. Here we address the origin of the ground-state structure in PrBaMn$_2$O$_6$ as well as its electronic and magnetic properties. Utilizing GGA+U approach and specially designed strategy to perform structural optimization, we show that the system has two competing AFM-A and AFM-CE magnetic structures with very close energies. The AFM-A structure is a metal, while AFM-CE is an insulator and the transition to the insulating state is accompanied by the charge Mn$^{3+}$/Mn$^{4+}$, and orbital $3x^2-r^2$/$3y^2-r^2$ orderings. This orbital ordering results in strong cooperative Jahn-Teller (JT) distortions, which lower the crystal symmetry. Our findings give a key to understanding contradictions in available experimental data on ${\rm PrBaMn_2O_6}$ and opens up the prospects to theoretical refinements of ground-state structures in other ${\rm RBaMn_2O_6}$ compounds.

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

By considering two {\it ab initio}-based complementary approaches, we analyze the electronic structure and extract effective spin models of BaCo$_2$(AsO$_4$)$_2$, a honeycomb material which has been proposed as a candidate for Kitaev physics. Both methods show that the dominant direct hopping makes the bond-dependent Kitaev term negligible averting the material away from the sought-after spin-liquid regime. As a result, we present a simple three-parameter exchange model to describe the interactions of the lowest doublet of the honeycomb cobaltate BaCo$_2$(AsO$_4$)$_2$. Remarkably, it is the third-neighbor interactions, both isotropic and anisotropic, that are responsible for the standout double-zigzag ground state of BaCo$_2$(AsO$_4$)$_2$, stabilized by quantum fluctuations. A significantly large third-nearest neighbor hopping, observed in {\it ab initio}, supports the importance of the third-neighbor interactions in the stabilization of the unique ground state of BaCo$_2$(AsO$_4$)$_2$., Comment: 8 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.

The importance of many-body effects on electronic and magnetic properties and stability of different structural phases was studied in novel iron oxide - Fe$_2$O. It was found that while Hubbard repulsion hardly affects the electronic spectrum of this material ($m^*/m \sim 1.2$), but it strongly changes its phase diagram shifting critical pressures of structural transitions to much lower values. Moreover, one of the previously obtained in the density functional theory (DFT) structures (P$\bar 3$m1) becomes energetically unstable if many-body effects are taken into consideration. It is shown that this is an account of magnetic moment fluctuations in the DFT+DMFT approach, which strongly contributes to modification of the phase diagram of Fe$_2$O., Comment: Main article: 6 pages, 7 figures, Supplementary information: 5 figures

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)

The Jahn-Teller theorem constitutes one of the most popular and stringent concepts, applicable to all fields of chemistry. In open shell transition elements chemistry and physics, 3d4, 3d9, and 3d7(low-spin) configurations in octahedral complexes serve as particular illustrative and firm examples, where a striking change (distortion) in local geometry is associated to a substantial reduction of electronic energy. However, there has been a lasting debate, about the fact that the octahedra are found to exclusively elongate, (at least for eg electrons). Against this background, the title compound displays two marked features, (1) the octahedron of oxygen atoms around Os6+ (d2) is drastically compressed, in contrast to the standard JT expectations, and (2) the splitting of the t2g set induced by this compression is extreme, such that a diamagnetic ground state results. What we see is obviously a Jahn-Teller distortion resulting in a compression of the respective octahedron and acting on the t2g set of orbitals. Both these issues are unprecedented. Noteworthy, the splitting into a lower dxy (hosting two d electrons with opposite spin) and two higher dxz and dyz orbitals is so large that for the first time ever the Hund's coupling for t2g electrons is overcome. We show that these effects are not forced by structural frustration, the structure offers sufficient space for Os to shift the apical oxygen atoms to a standard distance. Local electronic effects appear to be responsible, instead. The relevance of these findings is far reaching, since they provide insights in the hierarchy of perturbations defining ground states of open shell electronic systems. The system studied here, offers substantially more structural and compositional degrees of freedom, such that a configuration could form that enables Os6+ to adopt its apparently genuine diamagnetic ground state., Comment: 8 pages, 6 figures + supplementary information (7 pages)

The silver ruthenium oxide AgRuO$_3$ consists of honeycomb [Ru$_2^{5+}$O$_6^{2-}$] layers, and can be considered an analogue of SrRu$_2$O$_6$ with a different intercalation stage. We present measurements of magnetic susceptibility and specific heat on AgRuO$_3$ single crystals which reveal a sharp antiferromagnetic transition at 342(3)K. The electrical transport in single crystals of AgRuO$_3$ is determined by a combination of activated conduction over an intrinsic semiconducting gap of $\approx$ 100 meV and carriers trapped and thermally released from defects. From powder neutron diffraction data a N\'eel-type antiferromagnetic structure with the Ru moments along the $c$ axis is derived. Raman and muon spin rotation spectroscopy measurements on AgRuO$_3$ powder samples indicate a further weak phase transition or a crossover in the temperature range 125-200 K. The transition does not show up in magnetic susceptibility and its origin is argued to be related to defects but cannot be fully clarified. The experimental findings are complemented by DFT-based electronic structure calculations. It is found that the magnetism in AgRuO$_3$ is similar to that of SrRu$_2$O$_6$, however with stronger intralayer and weaker interlayer magnetic exchange interactions., Comment: 13 pages, 16 figures, includes supplement 3 pages, 3 figures

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

A recently synthesised series of isostructural compounds Ba$_4$NbTM$_3$O$_{12}$ (TM = Mn, Rh and Ir) with transition-metal trimers in a face-sharing geometry makes it possible to examine a tendency to the molecular orbitals (MO) formation going from $3d$ to $5d$ transition metal ions. Our $ab$ $initio$ calculations of electronic and magnetic properties describe the experimental findings and demonstrate gradual transition from the picture of localized electrons for Mn to the MO picture for Rh and especially for Ir. We also show that the often used criterion, according to which the metal-metal distance in a compound shorter than in a respective metal always gives MO, may break down in some cases.

First-principles calculations and a model consideration of magnetically frustrated layered material PdCrO$_2$ are performed. The results on the exchange parameters are in agreement with the experimental data on the Curie-Weiss temperature ($\theta$). We show that experimentally observed strong suppression of the N\'eel temperature ($T_N$) in comparison with the Curie-Weiss temperature is due to three main factors. First, as expected, this is connected with the layered structure and relatively small exchange interaction along the $c$ axis. Second, deformation of the ideal in-plane 120$^{\circ}$ magnetic structure is crucial to provide finite $T_N$ value. However, these two factors are still insufficient to explain low $T_N$ and the large frustration factor $|\theta|/T_N$. Thus, we suggest a scenario of an exotic non-Fermi-liquid state in PdCrO$_2$ above $T_N$ within the frameworks of the Anderson lattice model, which seems to explain qualitatively all its main peculiarities.

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.

Uniaxial pressure applied along an Ru-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr$_2$RuO$_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report new measurements, employing new uniaxial stress apparatus and new measurements of the low-temperature elastic moduli, of the strain at which this Lifshitz transition occurs: a longitudinal strain $\varepsilon_{xx}$ of $(-0.44\pm0.06)\cdot10^{-2}$, which corresponds to a B$_{1g}$ strain $\varepsilon_{xx} - \varepsilon_{yy}$ of $(-0.66\pm0.09)\cdot10^{-2}$. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is furthermore important to bring this critical strain close to the experimental number, and thus well into the experimentally accessible range of strains.

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