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How particular bonds form in quantum materials has been a long-standing puzzle. Two key concepts dealing with charge degrees of freedom are dimerization (forming metal-metal bonds) and charge ordering (CO). Since the 1930s, these two concepts have been frequently invoked to explain numerous exciting quantum materials, typically insulators. Here we report dimerization and CO within the dimers coexisting in metallic NaRu$_2$O$_4$. By combining high-resolution x-ray diffraction studies and theoretical calculations, we demonstrate that this unique phenomenon occurs through a new type of bonding, which we call Z-type ordering. The low-temperature superstructure has strong dimerization in legs of zigzag ladders, with short dimers in legs connected by short zigzag bonds, forming Z-shape clusters: simultaneously, site-centered charge ordering also appears. Our results demonstrate the yet unknown flexibility of quantum materials with the intricate interplay among orbital, charge, and lattice degrees of freedom., 37 pages, 9 figures, 4 tables

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

Ferrotoroidal order, which represents a spontaneous arrangement of toroidal moments, has recently been found in a few linear magnetoelectric materials. However, tuning toroidal moments in these materials is challenging. Here, we report switching between ferritoroidal and ferrotoroidal phases by a small magnetic field, in a chiral triangular-lattice magnet BaCoSiO4 with tri-spin vortices. Upon applying a magnetic field, we observe multi-stair metamagnetic transitions, characterized by equidistant steps in the net magnetic and toroidal moments. This highly unusual ferri-ferroic order appears to come as a result of an unusual hierarchy of frustrated isotropic exchange couplings revealed by first principle calculations, and the antisymmetric exchange interactions driven by the structural chirality. In contrast to the previously known toroidal materials identified via a linear magnetoelectric effect, BaCoSiO4 is a qualitatively new multiferroic with an unusual coupling between several different orders, and opens up new avenues for realizing easily tunable toroidal orders. Toroidal moments arise from vortex like spin arrangements. These moments can then interact, giving rise to ferri- or ferro-toroidal order, though controlling such order is difficult. Here, the authors demonstrate a ferri-toroidal state in BaCoSiO4, which under an applied magnetic field exhibits multiple toroidal and metamagnetic transitions.

The spin-orbit entangled (SOE) ${J}_{\mathrm{eff}}$ state has been a fertile ground to study quantum phenomena. Contrary to the conventional weakly correlated ${J}_{\mathrm{eff}}=1/2$ state of $4d$ and $5d$ transition metal compounds, the ground state of $\mathrm{Cu}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ hosts a ${J}_{\mathrm{eff}}=1/2$ state with a strong correlation of Coulomb $U$. Here, we report that, surprisingly, ${\mathrm{Cu}}^{2+}$ ions of $\mathrm{Cu}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ overcome the otherwise usually strong Jahn-Teller distortion and instead stabilize the SOE state, although the cuprate has relatively small spin-orbit coupling. From the x-ray absorption spectroscopy and high-pressure x-ray diffraction studies, we obtained definite evidence of the ${J}_{\mathrm{eff}}=1/2$ state with a cubic lattice at ambient pressure. We also found the pressure-induced structural transition to a compressed tetragonal lattice consisting of the spin-only $S=1/2$ state for pressure ${P}_{c}g8\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$. This phase transition from the Mott insulating ${J}_{\mathrm{eff}}=1/2$ to the $S=1/2$ states is a unique phenomenon. Our study offers an example of the SOE ${J}_{\mathrm{eff}}$ state under strong electron correlation and its pressure-induced transition to the $S=1/2$ state.

Investigation of the recently synthesized series of isostructural compounds Ba4NbTM3O12 (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. © 2020 American Physical Society. We are grateful to R.J. Cava for introducing us to trimer-based hexagonal perovskites and for various fruitful discussions. This research was supported by the Russian Foundation for Basic Researches (Grants No. RFBR 20-32-70019 and RFBR 20-32-90073) and the Russian Ministry of Science and High Education via program “Quantum” (Grant No. AAAA-A18-118020190095-4) and Contract No. 02.A03.21.0006 and the Deutche Forschungsgemeinschaft (DFG, German Reseach Foundation), Project No. 277146847-CRC 1238.

Recently synthesized Ba 4 NbMn 3 O 12 belong to cluster magnets that are systems with tightly bound groups of magnetic ions, in this case Mn 3 trimers. Such magnetic clusters can often be described by molecular orbitals, however strong electron correlations may invalidate this description. To understand the electronic and magnetic state of Ba 4 NbMn 3 O 12 we carried out ab initio calculations and show that this system is better described not in molecular orbitals picture, but as a system with electrons localized on the Mn ions, with strong intracluster and weaker inter-cluster exchange. The calculated spin of the Mn 3 trimer is S = 2, in agreement with the experiment. The predicted magnetic structure of Ba 4 NbMn 3 O 12 is that of ferromagnetic layers of Mn 3 trimers, stacked antiferromagnetically. © 2018, Pleiades Publishing, Inc.

Significance It is shown that the long-standing puzzle of incommensurate crystal structure of A u T e 2 can be solved, if this material is considered as a negative charge-transfer system. Using modern computational methods, we demonstrate that charge redistribution associated with incommensurate modulations of crystal structure occurs not so much on Au, but predominantly on Te sites. This substantially reduces Coulomb energy costs for creating such a unique crystal structure. The same mechanism also explains superconductivity of doped A u T e 2 . Exploring different Au–Te compositions, we also discovered a previously unknown compound AuTe, which theoretically is very stable, and we predict its crystal structure.

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 t2g2, t2g4, and t2g5), partially suppress (t2g1), or, in contrast, induce (t2g3) 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. © 2020 authors. We are grateful to G. Jackeli, L. Chibotaru, and G. Khaliullin for various stimulating discussions and to the UK consulate in Ekaterinburg for organizing the “Scientific cafe” at Institute of metal physics, where this work was initiated. This research was supported by the Russian Foundation for Basic Researches (RFBR 20-32-70019) and the Russian Ministry of Science via program “Quantum” (No. AAAA-A18-118020190095-4) and Contract No. 02.A03.21.0006 and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project No. 277146847-CRC 1238.

Spin crossover plays a central role in the structural instability, net magnetic moment modification, metallization, and even in superconductivity in corresponding materials. Most reports on the pressure-induced spin crossover with a large volume collapse have so far focused on compounds with a single transition metal. Here we report a comprehensive high-pressure investigation of a mixed Fe-Mn perovskite ${\mathrm{La}}_{2}{\mathrm{FeMnO}}_{6}$. Under pressure, the strong coupling between Fe and Mn leads to a combined valence/spin transition: $\mathrm{F}{\mathrm{e}}^{3+}(S=5/2)\ensuremath{\rightarrow}\mathrm{F}{\mathrm{e}}^{2+}(S=0)$ and $\mathrm{M}{\mathrm{n}}^{3+}(S=2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\mathrm{M}{\mathrm{n}}^{4+}(S=3/2)$, with an isostructural phase transition. The spin transitions of both Fe and Mn are offset by $\ensuremath{\sim}20$ GPa of the onset pressure, and the lattice collapse occurs in between. Interestingly, ${\mathrm{Fe}}^{3+}$ ion shows an abnormal behavior when it reaches a lower valence state (${\mathrm{Fe}}^{2+}$) accompanied by a +0.5 eV energy shift in the Fe K-absorption edge at 15 GPa. This process is associated with the charge-spin-orbital state transition from high spin ${\mathrm{Fe}}^{3+}$ to low spin ${\mathrm{Fe}}^{2+}$, caused by the significantly enhanced ${t}_{2g}\text{\ensuremath{-}}{e}_{g}$ crystal field splitting in the compressed lattice under high pressure. Density functional theory calculations confirm the energy preference of the high-pressure state with charge redistribution accompanied by spin state transition of Fe ions. Moreover, ${\mathrm{La}}_{2}{\mathrm{FeMnO}}_{6}$ maintains semiconductor behaviors even when the pressure reached 144.5 GPa as evidenced by the electrical transport measurements, despite the huge resistivity decreasing seven orders of magnitude compared with that at ambient pressure. The investigation carried out here demonstrates high flexibility of double perovskites and their good potentials for optimizing the functionality of these materials.

RIXS interferometry is a promising new tool for studying the symmetry and character of excited states in complex materials., 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.

We present comprehensive measurements of the structural, magnetic and electronic properties of layered van-der-Waals ferromagnet VI$_3$ down to low temperatures. Despite belonging to a well studied family of transition metal trihalides, this material has received very little attention. We outline, from high-resolution powder x-ray diffraction measurements, a corrected room-temperature crystal structure to that previously proposed and uncover a structural transition at 79 K, also seen in the heat capacity. Magnetization measurements confirm VI$_3$ to be a hard ferromagnet (9.1 kOe coercive field at 2 K) with a high degree of anisotropy, and the pressure dependence of the magnetic properties provide evidence for the two-dimensional nature of the magnetic order. Optical and electrical transport measurements show this material to be an insulator with an optical band gap of 0.67 eV - the previous theoretical predictions of d-band metallicity then lead us to believe VI$_3$ to be a correlated Mott insulator. Our latest band structure calculations support this picture and show good agreement with the experimental data. We suggest VI$_3$ to host great potential in the thriving field of low-dimensional magnetism and functional materials, together with opportunities to study and make use of low-dimensional Mott physics., 9 pages, 11 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.

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.

In many quantum spin systems, especially in low-dimensional ones, there exist states with spins forming singlets and with spin gaps. I consider several situations in which one gets such a state, paying main attention to the role of orbital occupation and orbital ordering. In particular, orbital ordering can reduce the effective dimensionality of the system and can lead to a Peierls-like state with the spin gap. It can also strongly influence the features of insulator-metal transitions in transition metal compounds, and can effectively remove frustrations in geometrically frustrated systems.

The magnetic behavior of the Ca3Co2O6 spin chain compound is characterized by a large Ising-like character of its ferromagnetic chains, set on a triangular lattice, that are antiferromagnetically coupled. At low temperature, T < 7 K, the 3D antiferromagnetic state evolves towards a spin frozen state. In this temperature range, magnetic field driven magnetization of single crystals (H // chains) exhibits stepped variations. The occurrence of these steps at regular intervals of the applied magnetic field, Hstep = 1.2 T, is reminiscent of the quantum tunneling of the magnetization (QTM) of molecular based magnets. Magnetization relaxation experiments also strongly support the occurrence of this quantum phenomenon. This first observation of QTM in a magnetic oxide belonging to the large family of A3BB′O6 compounds opens new opportunities to study a quantum effect in a very different class of materials from molecular magnets.

In analyzing various phenomena in TM compounds in the previous chapter, we have already several times come across the situation when a material, depending on conditions, can be in an insulating or in a metallic state. Such metal–insulator transitions can be caused either by doping (a change in band filling) or by temperature, pressure, magnetic field, etc. The topic of metal–insulator transitions is one of the most interesting in the physics of systems with correlated electrons. Such metal–insulator transitions often lead to dramaticffects and a drastic change in all properties of the system; and the large sensitivity of materials close to such transitions to external perturbations can be used in many practical applications. In principle, metal–insulator transitions are not restricted to systems with correlated electrons. They are often observed in more conventional solids, well described by the one-electron picture and standard band theory. However the most interesting such transitions, often significantly different from those in “band” systems, are indeed met in systems with strongly correlated electrons, in particular in transition metal compounds – see for example Mott (1990) or Gebhard (1997). Different types of metal–insulator transitions One can divide all metal–insulator transitions into three big groups; these are discussed in the sections below. Metal–insulator transitions in the band picture The first group of metal–insulator transitions are transitions which can be understood on the one-electron level in the framework of band theory – although, of course, interactions of some type are always necessary for such transitions.

When dealing with transition metal compounds one has to look at the different degrees of freedom involved and their interplay. These degrees of freedom are charge, spin, and orbitals. And of course all electronic phenomena occur on the background of the lattice, that is one always has to think about the role of the interaction with the lattice, or with phonons. The electron spins are responsible for different types of magnetic ordering. The orbitals, especially in the case of orbital (or Jahn—Teller) degeneracy, also lead to a particular type of ordering, and the type of orbital occupation largely determines the character of magnetic exchange and of the resulting magnetic structures. As to charges, the first question to ask is whether the electrons have to be treated as localized or itinerant. We actually started this book by discussing two possible cases: a band description of electrons in solids, in which the electrons are treated as delocalized, and the picture of Mott insulators, with localized electrons. But even for localized electrons there still exists some freedom, which has to do with charges. In some systems charges may be disordered in one state, for example at high temperatures, and become ordered at low temperatures. This charge ordering (CO) will be the main topic of this chapter. But, to put it in perspective, we will start by discussing different possible types of ordering, connected with charge degrees of freedom.

We show that in transition metal compounds containing structural metal dimers there may exist in the presence of different orbitals a special state with partial formation of singlets by electrons on one orbital, while others are effectively decoupled and may give e.g. long-range magnetic order or stay paramagnetic. Similar situation can be realized in dimers spontaneously formed at structural phase transitions, which can be called orbital-selective Peierls transition. This can occur in case of strongly nonuniform hopping integrals for different orbitals and small intra-atomic Hund's rule coupling JH. Yet another consequence of this picture is that for odd number of electrons per dimer there exist competition between double exchange mechanism of ferromagnetism, and the formation of singlet dimer by electron on one orbital, with remaining electrons giving a net spin of a dimer. The first case is realized for strong Hund's rule coupling, typical for 3d compounds, whereas the second is more plausible for 4d-5d compounds. We discuss some implications of these phenomena, and consider examples of real systems, in which orbital-selective phase seems to be realized., to be published in PRB Rapid Com

The honeycomb lattice material Li2RuO3 undergoes a dimerization of Ru4+ cations on cooling below 270 degrees C, where the magnetic susceptibility vanishes. We use density functional theory calculations to show that this reflects the formation of a valence bond crystal, with a strong structural bond disproportionation. On warming, x-ray diffraction shows that discrete threefold symmetry is regained on average, and the dimerization apparently disappears. In contrast, local structural measurements using high-energy x rays show that disordered dimers survive at the nanoscale up to at least 650 degrees C. The high-temperature phase of Li2RuO3 is thus an example of a valence bond liquid, where thermal fluctuations drive resonance between different dimer coverages, a classic analog of the resonating valence bond state often discussed in connection with high-T-c cuprates. (Less)

The effect of oxygen isotope substitution on the alternating-current magnetic susceptibility for (La1-yPry)0.7Ca0.3MnO3 ceramics (y = 0, 0.25, 0.5, 0.75, 1) was studied in the temperature range 4.2-300 K. At y < 0.75, the low-temperature behaviour of these manganites is typical for a ferromagnetic metal, whereas at y close to 1, the system behaves as an antiferromagnetic charge-ordered insulator. The 16O18O isotope substitution significantly shifts the Curie point TC, but has a smaller effect on the Neel temperature TN. At the crossover concentration y = 0.75, the exchange of 16O with 18O gives rise to a metal-insulator transition. The temperature dependence of the magnetic susceptibility is characterized by a pronounced hysteresis at y0 or 1, and the width of the hysteresis loops is strongly affected by the 16O18O exchange. The behaviour of the susceptibility in the paramagnetic phase gives an indication of the phase separation over quite a wide temperature range near the transition point. The phase diagram in the T-y plane is obtained and its modification with isotope substitution is discussed.

We discuss a novel mechanism for obtaining a spin-gap state through the creation of a coherent spin-orbital structure in systems with orbital degeneracy. Using the density matrix renormalization group, we calculate the phase diagram for a coupled spin-orbital model. We find that, in addition to ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The relevance to several recently discovered materials is discussed.

We show that in manganites close to half-doping, novel non-bipartite magnetic phases appear due to the interplay between double exchange, superexchange and orbital ordering. In considerable part of the phase diagram the ground state has a magnetic order that is intermediate between the canonical magnetic CE phase and a state that we identify as the recently observed Zener polaron state. The intermediate phase shows a type of charge ordering that breaks inversion symmetry and is therefore predicted to be ferroelectric.

We report a novel soft x-ray nanodiffraction study of antiferromagnetic domains in the strongly correlated bylayer manganite La$_{0.96}$Sr$_{2.04}$Mn$_{2}$O$_{7}$. We find that the antiferromagnetic domains are quenched, forming a unique domain pattern with each domain having an intrinsic memory of its spin direction, and with associated domain walls running along crystallographic directions. This can be explained by the presence of crystallographic or magnetic imperfections locked in during the crystal growth process which pin the antiferromagnetic domains. The antiferromagnetic domain pattern shows two distinct types of domain. We observe, in one type only, a periodic ripple in the manganese spin direction with a period of approximately 4 \micro\meter. We propose that the loss of inversion symmetry within a bilayer is responsible for this ripple structure through a Dzyaloshinskii-Moriya-type interaction., 4 figures, 5 pages

In the previous chapter we have considered the properties of strongly correlated electrons. The systems we mostly had in mind were the compounds of transition metal and maybe rare earth elements with partially filled inner d or f shells. We have discussed only the correlated electrons themselves, the prototype model being the Hubbard model (12.1). When turning to real materials, several extra factors missing in the model (12.1) are important. One of them is the possible influence of orbital degrees of freedom, especially in cases with orbital degeneracy, treated in Section 12.9. In many situations there is yet another very important factor. There may exist in a system, besides correlated electrons, also electrons of other bands, e.g. electrons in wide conduction bands, responsible for ordinary metallic conductivity. Such is for instance the situation for magnetic impurities in metals, or in the concentrated systems like rare earth metals and compounds in which localized f electrons coexist with the metallic electrons in broad spd bands. The interplay between localized, or, better, strongly correlated electrons and itinerant electrons of the wide bands can lead to a number of very interesting consequences; these will be discussed in this chapter. Localized magnetic moments in metals When we put transition metal impurities in ordinary metals (e.g. Mn or Fe in Cu, Au), the result may be two-fold. In certain cases the impurities retain their magnetic moment, but in others they lose it.

We discuss the ground state of the spin-orbital model for spin-one ions with partially filled $t_{2g}$ levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into nonmagnetic manifold spanned by hard-core dimer (spin-singlet) coverings of the lattice. The cooperative ``dimer Jahn-Teller'' effect is introduced through a magnetoelastic coupling and is shown to lift the orientational degeneracy of dimers leading to a peculiar valence bond crystal pattern. The present theory provides a theoretical explanation of nonmagnetic dimerized superstructure experimentally seen in Li$_2$RuO$_3$ compound at low temperatures., to appear in Phys. Rev. Lett

We show that the Mott transition in orbitally degenerate systems can, and often does, proceed not in the standard ``Mott insulator---weakly correlated metal'' sequence, but via a novel intermediate phase with a charge (rather than orbital) ordering. Lifting an orbital degeneracy this way can be viewed as an alternative to a Jahn-Teller distortion. This may occur in a crossover between localized and itinerant regimes, if Hund's rule coupling overcomes the on site Coulomb repulsion. We show both by calculations and by experiment that this scenario is realized in rare-earth nickelates, and argue that the same phenomenon takes place in many other systems.

We review some aspects related to orbital degrees of freedom in manganites. The Mn$^{3+}$ ions in these compounds have double orbital degeneracy and are strong Jahn-Teller ions, causing structural distortions and orbital ordering. We discuss ordering mechanisms and the consequences of orbital order. The additional degeneracy of low-energy states and the extreme sensitivity of the chemical bonds to the spatial orientation of the orbitals result in a variety of competing interactions. This quite often leads to frustration of classical ordered states and to the enhancement of quantum effects. Quantum fluctuations and related theoretical models are briefly discussed, including the occurence of resonating orbital bonds in the metallic phase of the colossal magnetoresistance manganites., Comment: 46 pages, 22 figures. To appear as chapter in: Colossal Magnetoresistive Manganites, ed. T. Chatterji, Kluwer Academic Publishers, Dordrecht, Netherlands (2002)

Transition metal oxides with a perovskite-type structure constitute a large group of compounds with interesting properties. Among them are materials such as the prototypical ferroelectric system BaTiO(3), colossal magnetoresistance manganites and the high-T(c) superconductors. Hundreds of these compounds are magnetic, and hundreds of others are ferroelectric, but these properties very seldom coexist. Compounds with an interdependence of magnetism and ferroelectricity could be very useful: they would open up a plethora of new applications, such as switching of magnetic memory elements by electric fields. Here, we report on a possible way to avoid this incompatibility, and show that in charge-ordered and orbitally ordered perovskites it is possible to make use of the coupling between magnetic and charge ordering to obtain ferroelectric magnets. In particular, in manganites that are less than half doped there is a type of charge ordering that is intermediate between site-centred and bond-centred. Such a state breaks inversion symmetry and is predicted to be magnetic and ferroelectric.

We show that superexchange interactions in frustrated Jahn-Teller systems with transition metal ions connected by the 90° metal-oxygen-metal bonds (e.g., NaNiO2, LiNiO2, and ZnMn2O4) are much different from those in materials with the 180° bonds. In the 90°-exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Though the mean-field orbital ground state is strongly degenerate, quantum orbital fluctuations select particular ferro-orbital states. We explain the orbital and magnetic ordering observed in NaNiO2 and show that LiNiO2 is not a spin-orbital liquid.

The effect of partial 16 O→ 18 O isotope substitution on electrical and thermal resistivity and AC magnetic susceptibility was studied for (La 0.25 Pr 0.75 ) 0.7 Ca 0.3 MnO 3 ceramic samples. The measurements were performed for 11 samples with the molar percentage of 18 O varying from zero to 90%. For 0–40% enrichment by 18 O, the low-temperature resistivity had a metallic behavior. At higher 18 O content, the samples exhibited a percolation-like transition to the insulating state. Magnetic measurements demonstrated that the behavior typical of antiferromagnets arose only at 18 O enrichment exceeding 60%, whereas at lower 18 O content, we obtain an appreciable ferromagnetic contribution. The experimental data are interpreted in the picture of a percolation-type phase-separated system with the regions of ferromagnetic metal and antiferromagnetic charge ordered insulator.

A simple model of charge ordering is considered. It is shown explicitly that at any deviation from half-filling ($n \neq 1/2$) the system is unstable with respect to phase separation into charge ordered regions with $n = 1/2$ and metallic regions with smaller electron or hole density. Possible structure of this phase-separated state (metallic droplets in a charge-ordered matrix)is discussed. The model is extended to account for the strong Hund-rule onsite coupling and the weaker intersite antiferromagnetic exchange. An analysis of this extended model allows us to determine the magnetic structure of the phase-separated state and to reveal the characteristic features of manganites and other substances with charge ordering., Comment: 9 pages, revtex

An explanation is given for the charge order, orbital order and insulating state observed in half-doped manganese oxides, such as Nd$_{1/2}$Sr$_{1/2}$MnO$_{3}$. The competition between the kinetic energy of the electrons and the magnetic exchange energy drives the formation of effectively one-dimensional ferromagnetic zig-zag chains. Due to a topological phase factor in the hopping, the chains are intrinsically insulating and orbital-ordered. Most surprisingly, the strong Coulomb interaction between electrons on the same Mn-ion leads to the experimentally observed charge ordering. For doping less than 1/2 the system is unstable towards phase separation into a ferromagnetic metallic and charge-ordered insulating phase., To appear in Phys. Rev. Lett., 4 pages, 4 figures

We study the competition between different possible ground states of the double-exchange model with strong ferromagnetic exchange interaction between itinerant electrons and local spins. Both for classical and quantum treatment of the local spins the homogeneous canted state is shown to be unstable against a phase separation. The conditions for the phase separation into the mixture of the antiferromagnetic and ferromagnetic/canted states are given. We also discuss another possible realization of the phase-separated state: ferromagnetic polarons embedded into an antiferromagnetic surrounding. The general picture of a percolated state, which emerges from these considerations, is discussed and compared with results of recent experiments on doped manganaties., 10 pages, revtex, modified text and 2 new figures

We construct a phase diagram for the materials with colossal magnetoresistance. The basic model which describes these materials is a double-exchange model. We rigorously prove that a ground state of this model corresponds to a phase-separated state with small ferromagnetic polarons inside an antiferromagnetic matrix. The general picture of a percolative state, which emerges from our calculations, is in good agreement with recent experiments on doped manganites.

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ƒ-holes and s -electrons, similar to that in excitonic insulators, the virtual ƒ-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ƒ-level, the width being the largest when the ƒ-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.

We discuss the characteristic properties of the Spin-Peierls (SP) transition which allow one to distinguish experimentally between such a transition and the ordinary structural instability. It is shown that commensurability effects cause the strong dependence of the transition temperature T c on magnetic field H as well as nonlinear dependence of magnetization on H . They also suppress the phase fluctuations for the SP transition. It is shown also that dimensionless coupling constant of spin-phonon interaction which drives SP transition may be large enough only when the relevant phonon frequencies are extremely small already in a high-temperature phase.

The cooperative ordering of degenerate d -orbitals in two-dimensional ferromagnets of K 2 CuF 4 type is considered by employing both the usual Jahn- Teller mechanism and the superexchange one. The orbital structure obtained differs from that usually assumed for K 2 CuF 4 ; the latter is shown to be incompatible with the observed ferromagnetic ordering.

Band structure calculations of CrO2 carried out in the LSDA+U approach reveal a clear picture of the physics behind the metallic ferromagnetic properties. Arguments are presented that the metallic ferromagnetic oxide CrO2 belongs to a class of materials in which magnetic ordering exists due to double exchange (in this respect CrO2 turns out to be similar to the CMR manganates). It is concluded that CrO2 has small or even negative charge transfer gap which can result in self-doping. Certain experiments to check the proposed picture are suggested., 4 pages, 4 Figures