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In the study of frustrated quantum magnets, it is essential to be able to control the nature and degree of site disorder during the growth process, as many measurement techniques are incapable of distinguishing between site disorder and frustration-induced spin disorder. Pyrochlore-structured spinel oxides can serve as model systems of geometrically frustrated three-dimensional quantum magnets; however, the nature of the magnetism in one well-studied spinel, ZnFe 2 O 4 , remains unclear. Here, we demonstrate simultaneous control of both stoichiometry and inversion disorder in the growth of ZnFe 2 O 4 single crystals, directly yielding a revised understanding of both the collective spin behavior and lattice symmetry. Crystals grown in the stoichiometric limit with minimal site inversion disorder contravene all the previously suggested exotic spin phases in ZnFe 2 O 4 . Furthermore, the structure is confirmed on the F 4 ¯ 3 m space group with broken inversion symmetry that induces antiferroelectricity. The effective tuning of magnetic behavior by site disorder in the presence of robust antiferroelectricity makes ZnFe 2 O 4 of special interest to multiferroic devices.

The Jahn-Teller (JT) theorem constitutes one of the most fundamental concepts in chemistry. In transition-element chemistry, the 3d4 and 3d9 configurations in octahedral complexes are particularly illustrative, where a distortion in local geometry is associated with a reduction of the electronic energy. However, there has been a lasting debate about the fact that the octahedra are found to exclusively elongate. In contrast, for Na9 Bi5 Os3 O24 , the octahedron around Os6+ (5d2 ) is heavily compressed, lifting the degeneracy of the t2g set of 5d orbitals such that in the sense of a JT compression a diamagnetic ground state results. This effect is not forced by structural constraints, the structure offers sufficient space for osmium to shift the apical oxygen atoms to a standard distance. The relevance of these findings is far reaching, since they provide new insights in the hierarchy of perturbations defining ground states of open shell electronic systems.

This article presents a survey of many nontrivial effects connected with the coupling of electric and magnetic degrees of freedom in solids -- the field initiated by I.~E.~Dzyaloshinskii in 1959. I briefly consider the main physics of ultiferroic materials, and concentrate on different effects "beyond multiferroics", based on the same physical mechanisms which operate in multiferroics. In particular they lead to nontrivial electric properties of different magnetic textures -- such as the appearance of dipoles on magnetic monopoles in spin ice, dipoles on some domain walls in the usual ferromagnets, on skyrmions etc. The inverse effect, the appearance of magnetic monopoles on electric charges in magnetoelectrics, is also discussed. This nontrivial electric activity of different magnetic textures has manifestations in many experimental properties of these materials, and it can potentially lead to novel applications.

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

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.

We report x-ray and optical absorption spectroscopy as well as hard x-ray photoemission spectroscopy on hexagonal ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ in which a Cu $3d$ spin-orbital liquid state is suggested from absence of the Jahn-Teller distortion of ${\mathrm{Cu}}^{2+}{\mathrm{O}}_{6}$ octahedra and of the magnetic ordering. The experimental results and their cluster model analysis indicate that O $2p$ holes play a crucial role in realizing the spin-orbital liquid state of hexagonal ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$. These oxygen holes appear due to the ``reaction'' ${\mathrm{Sb}}^{5+}\ensuremath{\rightarrow}{\mathrm{Sb}}^{3+}\phantom{\rule{4pt}{0ex}}+$ two O $2p$ holes, with these holes being able to attach to Cu ions. The present work opens avenues towards spin-charge-orbital entangled liquid state in transition-metal oxides with small or negative charge transfer energy.

Spin ice systems display a variety of very nontrivial properties, the most striking being the existence in them of magnetic monopoles. Such monopole states can also have nontrivial electric properties: there exist electric dipoles attached to each monopole. A novel situation is encountered in the moment fragmentation (MF) state, in which monopoles and antimonopoles are perfectly ordered, whereas spins themselves remain disordered. We show that such partial ordering strongly modifies the electric activity of such systems: the electric dipoles, which are usually random and dynamic, become paired in the MF state in (d, −d) pairs, thus strongly reducing their electric activity. The electric currents existing in systems with noncoplanar spins are also strongly influenced by MF. We also consider modifications in dipole and current patterns in magnetic textures (domain walls, local defects) and at excitations with nontrivial dynamics in a MF state, which show very rich behaviour and which could in principle allow to control them by electric field., Spin-ices can exhibit a variety of remarkable phenomena, not least the appearance of emergent magnetic monopoles. In this theory paper, Daniel Khomskii shows that in the moment fragmentation state, the electric dipoles associated with magnetic monopoles become ordered, leading to a change in electrical activity.

We report on the synthesis and physical properties of cm-sized CoGeO3 single crystals grown in a high pressure mirror furnace at pressures of 80 bar. Direction dependent magnetic susceptibility measurements on our single crystals reveal highly anisotropic magnetic properties that we attribute to the impact of strong single ion anisotropy appearing in this system with TN∼33.5 K. Furthermore, we observe effective magnetic moments that are exceeding the spin only values of the Co ions, which reveals the presence of sizable orbital moments in CoGeO3.

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.

Electronic properties of ${\mathrm{V}}_{2}{\mathrm{OPO}}_{4}$ have been investigated by means of hard x-ray photoemission spectroscopy (HAXPES) and subsequent theoretical calculations. The V $1s$ and $2p$ HAXPES spectra are consistent with the charge ordering of ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$. The binding energy difference between the ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$ components is unexpectedly large, indicating large bonding-antibonding splitting between them in the final states of core level photoemission. The V $1s$ HAXPES spectrum exhibits a charge transfer satellite which can be analyzed by configuration interaction calculations on a ${\mathrm{V}}_{2}{\mathrm{O}}_{9}$ cluster. The V $3d$ spectral weight near the Fermi level is assigned to the $3d\phantom{\rule{4pt}{0ex}}{t}_{2g}$ orbitals of the ${\mathrm{V}}^{2+}$ site. The broad V $3d$ spectral distribution is consistent with the strong hybridization between ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$ in the ground state. The core level and valence band HAXPES results indicate substantial charge transfer from the ${\mathrm{V}}^{2+}$ site to the ${\mathrm{V}}^{3+}$ site.

V $3d$ charge and orbital states in ${\mathrm{V}}_{2}{\mathrm{OPO}}_{4}$ have been investigated by means of x-ray absorption spectroscopy (XAS). The electronic structure of ${\mathrm{V}}_{2}{\mathrm{OPO}}_{4}$ is very unique in that the charge transfer between ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$ in face-sharing ${\mathrm{VO}}_{6}$ chains provides negative thermal expansion as reported by E. Pachoud et al. [J. Am. Chem. Soc. 140, 636 (2018)]. The near-edge region of O $1s$ XAS exhibits the three features which can be assigned to transitions to O $2p$ mixed into the unoccupied V $3d\phantom{\rule{4pt}{0ex}}{t}_{2g}$ and ${e}_{g}$ orbitals of ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$. The V $2p$ XAS line shape can be reproduced by multiplet calculations for a mixed-valence state with ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$. The polarization dependence of the O $1s$ and V $2p$ XAS spectra indicates V $3d$ orbital order in which $xy$ and $yz$ (or $zx$) orbitals are occupied at the ${\mathrm{V}}^{3+}$ site in the face-sharing chains. The occupied $xy$ orbital is essential for the antiferromagnetic coupling between the ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$ sites along the chains, while the occupied $yz$ (or $zx$) orbital provides the antiferromagnetic coupling between the ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$ sites between the chains.

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 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

In the present paper, the electronic, magnetic, and structural properties of a novel system FeZnMo3O8 with a polar crystal structure are investigated using GGA + U (Generalized gradient approximation taking into account Coulomb correlations) 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. © 2019, Pleiades Publishing, Inc.

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

Recent discovery of the pyrite FeO2, 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 - FeS2. Doping, which is most likely to occur in the Earth’s mantle, makes FeO2 much more magnetic. In addition we show that unique electronic structure places FeO2 “in between” the usual dioxides and peroxides making this system interesting both for physics and solid state chemistry.

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 the pyrite FeO2, 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 - FeS2. Doping, which is most likely to occur in the Earth’s mantle, makes FeO2 much more magnetic. In addition we show that unique electronic structure places FeO2 “in between” the usual dioxides and peroxides making this system interesting both for physics and solid state chemistry.

An unusual effect was discovered in Li et al (2010 J. Solid State Chem. 183 1388): the substitution of nonmagnetic low-spin Co(3+) in LaCoO3 by the formally isoelectronic and also nonmagnetic Rh(3+) led, surprisingly, to a rapid appearance of magnetism in LaCo(1-x)Rh(x)O3, even for small amounts of doping. Different explanations for this effect were proposed in the literature. To clarify the situation we carried out unbiased ab initio calculations of this system. We concluded that, in agreement with the original assumption of Li et al, but in contrast with later statements (Knizek et al 2012 Phys. Rev. B 85 134401), this effect is caused by the valence change ('redox reaction') Co(3+) + Rh(3+) → Co(2+) + Rh(4+), which creates magnetic Co(2+) and Rh(4+) ions. For the half-filled case LaCo1/2Rh1/2O3 we obtained the state with charge ordering of Co(2+) and Rh(4+) ions, which according to our calculations are antiferromagnetically coupled. The obtained results reasonably explain the observed behavior of the magnetic susceptibility of LaCo(1-x)Rh(x)O3, and the novel state predicted at half-doping could be verified experimentally by detailed structural and magnetic studies and by x-ray absorption spectroscopy.

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.

Crystal field splitting When we put a transition metal ion in a crystal, the systematics of the corresponding electron states changes. For isolated atoms or ions we have spherical symmetry, and the corresponding states are characterized by the principal quantum number n , by orbital moment l and, with spin–orbit coupling included, by the total angular momentum J . When the atom or ion is in a crystal, the spherical symmetry is violated; the resulting symmetry is the local (point) symmetry determined by the structure of the crystal. Thus, if a transition metal ion is surrounded by a regular octahedron of anions such as O 2− (Fig. 3.1) (this is a typical situation in many TM compounds, e.g. in oxides such as NiO or LaMnO 3 ), the d levels which were fivefold degenerate in the isolated ion ( l = 2; l z = 2, 1, 0, −1, −2) are split into a lower triplet, t 2 g , and an upper doublet, e g (Fig. 3.2). The corresponding splitting is caused by the interaction of d -electrons with the surrounding ions in the crystal, and is called crystal field (CF) splitting. The type of splitting and the character of the corresponding levels is determined by the corresponding symmetry. The detailed study of such splittings is a major field in itself, and is mostly treated using group-theoretical methods.

As discussed at the beginning of Chapter 7, there can exist different types of ordering phenomena connected with charge degrees of freedom. Examples are ordering of charges themselves (charge “monopoles”); ordering of electric dipoles, giving ferroelectricity (FE); or ordering of electric quadrupoles, which happens in orbital ordering. We have already discussed the first and third possibilities; we now turn to the second. Ferroelectricity is a broad phenomenon, in no way restricted to TM compounds. There are ferroelectrics among organic compounds, in some molecular crystals, in systems with hydrogen bonds. But the best, and most important in practice, are ferroelectrics on the basis of TM compounds such as the famous BaTiO 3 , or the widely used Pb(ZrTi)O 3 (“PZT”). And it is in these compounds that one also sometimes meets a very interesting interplay of ferroelectricity and magnetism – the field now known mostly as multiferroicity. By multiferroics (Schmid, 1994) we refer to materials which are simultaneously ferroelectric and magnetic – possibly ferro- or ferrimagnetic, although such cases are rather rare, most of the known multiferroics being antiferromagnetic. (Sometimes ferroelastic systems are alsoincluded in this class.) In this chapter we discuss these classes of compounds, paying attention mostly to the microscopic mechanisms of ferroelectricity and its eventual coupling to magnetism. A general treatment of ferroelectricity, dealing mainly with the macroscopic aspects of ferroelectrics and their phenomenological description, with special attention paid to practical applications, may be found in many books, for example Megaw (1957), Lines and Glass (1977), Scott (2000), Gonzalo (2006), Blinc (2011).

Describing all aspects of the physics of transition metal compounds, this book provides a comprehensive overview of this unique and diverse class of solids. Beginning with the basic concepts of the physics of strongly correlated electron systems, the structure of transition metal ions, and the behaviours of transition metal ions in crystals, it goes on to cover more advanced topics such as metal-insulator transitions, orbital ordering, and novel phenomena such as multiferroics, systems with oxygen holes, and high-Tc superconductivity. Each chapter concludes with a summary of key facts and concepts, presenting all the most important information in a consistent and concise manner. Set within a modern conceptual framework, and providing a complete treatment of the fundamental factors and mechanisms that determine the properties of transition metal compounds, this is an invaluable resource for graduate students, researchers and industrial practitioners in solid state physics and chemistry, materials science, and inorganic chemistry.

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.