The LDA+DMFT (local density approximation combined with dynamical mean-field theory) computation scheme has been used to study spectral and magnetic properties of FeSi and Fe$_{1-x}$Co$_{x}$Si. Having compared different models we conclude that a correlated band insulator scenario in contrast to Kondo insulator model agrees with FeSi band structure as well as experimental data. Coulomb correlation effects lead to band narrowing of the states near the Fermi level with mass renormalization parameter $m^*\approx 2$ in agreement with the results of angle-resolved photoemission spectroscopy (ARPES). Temperature dependence of spectral functions and magnetic susceptibility calculated in DMFT reproduces transition from nonmagnetic semiconductor to metal with local magnetic moments observed experimentally. Cobalt doping leads to ferromagnetism that has itinerant nature and can be successfully described by LDA+DMFT method.
The possibilities to induce magnetism in the non-magnetic bulk alpha-FeSi2 by means of lattice distortions or intercalation with metal or non-metal ions of light elements is investigated theoretically by combined ab initio and model methods. We find that the distortions indeed can induce the formation of magnetic moment on iron atoms in certain local environments; however, the required strength of the distortions often is too large to be achieved in experiments. For this reason we suggest using "chemical pressure" that is, intercalating the alpha-FeSi2 films by light elements. We find that som…
A macroscopic single crystal of $γ_{\rm II}$-Li\(_2\)FeSiO\(_4\) has been grown by means of the high-pressure optical floating-zone technique. Static magnetic susceptibility $χ$ implies that the tetrahedrally-coordinated Fe$^{2+}$ ions are in the high-spin, $S=2$, state. While a sharp decrease in $χ$ implies long-range antiferromagnetic order below \tn\ = 17.0(5)~K, the presence of a broad maximum at $T_{\rm m} = 28$~K suggests quasi-low-dimensional magnetism. Applying magnetic fields along the easy magnetic $a$-axis yields additional contributions to the susceptibility $\partial M/\partial B$…
Recently, evidence for a conducting surface state below 19 K was reported for the correlated d-electron small gap semiconductor FeSi. In the work reported herein, the conducting surface state and the bulk phase of FeSi were probed via electrical resistivity measurements as a function of temperature T, magnetic field B to 60 T and pressure P to 7.6 GPa, and by means of a magnetic field modulated microwave spectroscopy (MFMMS) technique. The properties of FeSi were also compared to those of the Kondo insulator SmB6 to address the question of whether FeSi is a d-electron analogue of an f-electron…
A chiral compound FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band-structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although a signature of surface conduction was indicated according to size-dependent resistivity in bulk crystals, its existence and topological properties remain elusive. Here we demonstrate an inherent surface ferromagnetic-metal state of FeSi thin films and its strong spin-orbit-coupling (SOC) properties through multiple characterizations of the two-dimensiona…
The phase diagram of FeSi1-xGex, obtained from magnetic, thermal and transport measurements on single crystals, shows a first-order transition from a correlated electron semiconductor to a ferromagnetic metal at a critical concentration, x ~ 0.25. The gap of the insulating phase strongly decreases with x. The specific heat coefficient appears to track the density of states of a Kondo insulator. The phase diagram is consistent with a correlation induced insulator-metal transition in conjunction with disorder on the Si/Ge ligand site.
The two-band Hubbard model with the density of states obtained from the band calculation is applied for FeSi, which is suggested to be a Kondo insulator or a correlated band insulator. Using this model, the correlation effects on FeSi are investigated in terms of the self-consistent second-order perturbation theory combined with the local approximation. The calculated optical conductivity spectrum reproduces the experiments by Damascelli et al. semiquantitatively and the specific heat explains the anomalous contribution at about 250 K observed in FeSi. Inclusion of the spin fluctuation and the…
Motivated by the peculiar behavior of FeSi and FeSb2 we study the effect of local electronic correlations on magnetic, transport and optical properties in a specific type of band insulator, namely a covalent insulator. Investigating a minimum model of covalent insulator within a single-site dynamical mean-field approximation we are able to obtain the crossover from low temperature non-magnetic insulator to high-temperature paramagnetic metal with parameters realistic for FeSi and FeSb2 systems. Our results show that the behavior of FeSi does not imply microscopic description in terms of Kondo …
We study the two-band Hubbard model introduced by Fu and Doniach as a model for FeSi which is suggested to be a Kondo insulator. Using the self-consistent second-order perturbation theory combined with the local approximation which becomes exact in the limit of infinite dimensions, we calculate the specific heat, the spin susceptibility and the dynamical conductivity and point out that the reduction of the energy gap due to correlation is not significant in contrast to the previous calculation. It is also demonstrated that the gap at low temperatures in the optical conductivity is filled up at…
Electronic structures of FeSi and Fe$_{1.02}$Si$_{0.98}$ under pressure (achieved through volume compression) have been investigated by using DFT+DMFT and KKR-CPA methods, respectively. The widening of band-gap with increasing pressure suggests that the experimentally observed insulator to metal transition temperature should shift towards the higher temperature for FeSi. KKR-CPA calculations have shown the presence of impurity states in the gapped region which predicts the half-metallic nature. The closure of gap (in one spin channel) with pressure increment appears to be responsible for exper…
Analysis on very detailed measurements of resistivity ($ ρ$) and thermoelectric power (S) of magnetic impurity (Co) substituted iron silicide (FeSi) has been presented in this report. The impurity valence electrons of Co dominate the whole physical properties at low temperatures below 35 K, below the critical concentration x$_{c}$. The negative thermopower and the positive slope in the resistivity at low temperatures are exotic and show that the system is not entirely insulator below the critical concentration of MIT (x$_{c}$). So, due to the external impurity electrons, the system's magnetic …
Iron based narrow gap semiconductors such as FeSi, FeSb2, or FeGa3 have received a lot of attention because they exhibit a large thermopower, as well as striking similarities to heavy fermion Kondo insulators. Many proposals have been advanced, however, lacking quantitative methodologies applied to this problem, a consensus remained elusive to date. Here, we employ realistic many-body calculations to elucidate the impact of electronic correlation effects on FeSi. Our methodology accounts for all substantial anomalies observed in FeSi: the metallization, the lack of conservation of spectral wei…
The physical properties of the semiconductor FeSi with very narrow band gap, anomalous behavior of the magnetic susceptibility and metal-insulator transition at elevated temperatures attract gross interest due to the still controversial theoretical understanding of their origin. On one side the purely band like mechanism of the gap formation in FeSi at low temperature is well established, on other side a number of experiments and their theoretical interpretation suggest a rich physics of strong correlations at finite temperature. In this work we use an ab-initio scheme based on the Random Phas…
We show that the interplay of a high density two-dimensional electron gas and localized electrons in a neighboring Mott insulator leads to kinetic magnetism unique to the Mott/band insulator interface. Our study is based upon a bilayer Hubbard model at $U=\infty$ with a potential difference between the two layers. We combine analytic results with DMRG simulations to show that magnetism, and especially ferromagnetism, is greatly enhanced relative by the proximity of the two subsystems. The results are potentially relevant to recent experiments suggesting magnetism in $R$TiO$_3$/SrTiO$_3$ hetero…
The intermetallic FeSi exhibits an unusual temperature dependence in its electronic and magnetic degrees of freedom, epitomized by the crossover from a low temperature non-magnetic semiconductor to a high temperature paramagnetic metal with a Curie-Weiss like susceptibility. Many proposals for this unconventional behavior have been advanced, yet a consensus remains elusive. Using realistic many-body calculations, we here reproduce the signatures of the metal-insulator crossover in various observables: the spectral function, the optical conductivity, the spin susceptibility, and the Seebeck coe…
We present a comprehensive optical study of the narrow gap $FeSb_2$ semiconductor. From the optical reflectivity, measured from the far infrared up to the ultraviolet spectral range, we extract the complete absorption spectrum, represented by the real part $σ_1(ω)$ of the complex optical conductivity. With decreasing temperature below 80 K, we find a progressive depletion of $σ_1(ω)$ below $E_g\sim 280$ cm$^{-1}$, the semiconducting optical gap. The suppressed (Drude) spectral weight within the gap is transferred at energies $ω>E_g$ and also partially piles up over a continuum of excitations e…
We study topological crystalline insulators doped with magnetic impurities, in which ferromagnetism at the surface lowers the electronic energy by spontaneous breaking of a crystalline symmetry. The number of energetically equivalent ground states is sensitive to the crystalline symmetry of the surface, as well as the precise density of electrons at the surface. We show that for a SnTe model in the topological state, magnetic states can have twofold symmetry, sixfold symmetry, or eightfold degenerate minima. We compute spin stiffnesses within the model to demonstrate the stability of ferromagn…
Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondo-insulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an anti…
Experiments demonstrating the controlled growth of oxide heterostructures have raised the prospect of realizing topologically nontrivial states of correlated electrons in low dimensions. Here, we study heterostructures consisting of {111}-bilayers of double perovskites separated by inert band insulators. In bulk, these double perovskites have well-defined local moments interacting with itinerant electrons leading to high temperature ferromagnetism. Incorporating spin-orbit coupling in the two-dimensional honeycomb geometry of a {111}-bilayer, we find a rich phase diagram with tunable ferromagn…
We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of st…
Electronic and magnetic structures of the newly synthesized cobalt oxyselenide La2Co2Se2O3 (structurally similar to the superconducting iron pnictides) are studied through density functional calculations. The obtained results show that this material is a Mott insulator, and that it has a very stable Co2+ high-spin ground state with a t2g-like orbital ordering, which is substantiated by the calculated crystal-field excitation energies. The square lattice of the Co2+ spins is found to have a strong antiferro (a weak ferro) magnetic coupling for the second nearest neighbors (2nn) via O (Se2) and …
We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality $\hatχ_{jkl}= \mathbf{S}_l\cdot\left(\mathbf{S}_j\times \mathbf{S}_k\right)$. This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. …
We review many-body effects, their microscopic origin, as well as their impact onto thermoelectricity in correlated narrow-gap semiconductors. Members of this class---such as FeSi and FeSb$_2$---display an unusual temperature dependence in various observables: insulating with large thermopowers at low temperatures, they turn bad metals at temperatures much smaller than the size of their gaps. This insulator-to-metal crossover is accompanied by spectral weight-transfers over large energies in the optical conductivity and by a gradual transition from activated to Curie-Weiss-like behaviour in th…
In Mott insulators with the t^4_{2g} electronic configuration such as of Re^{3+}, Ru^{4+}, Os^{4+}, and Ir^{5+} ions, spin-orbit coupling dictates a Van Vleck-type nonmagnetic ground state with angular momentum J=0, and the magnetic response is governed by gapped singlet-triplet excitations. We derive the exchange interactions between these excitons and study their collective behavior on different lattices. In perovskites, a conventional Bose condensation of excitons into a magnetic state is found, while an unexpected one-dimensional behavior supporting spin-liquid states emerges in honeycomb …
The magnetism of Sr$_2$F$_2$Fe$_2$OS$_2$ was examined through neutron powder diffraction and thermodynamic and transport measurements. Quasi-two-dimensional magnetic order develops below $T_N$ = 106(2) K with an in-plane correlation length exceeding 310 Å and an out-of-plane correlation length of just 17(3) Å. The data are consistent with a two-k structure with $k_1$ = (1/2, 0, 1/2) and $k_2$ = (0, 1/2, 1/2) and an ordered moment of 3.3(1) $μ_B$ oriented along the in-plane components of k. This structure is composed of orthogonal AFM chains intersecting at super-exchange mediating O sites. Den…
We investigate the metal-insulator transition in the layered Ruddelsden Popper series of strontium iridates Srn+1IrnO3n+1. Tight-binding models of t2g orbitals for n = 1, 2, and infinity are constructed, and changes in band dispersion due to dimensionality and spin-orbit coupling are presented. Identifying the states near the Fermi level to be predominantly Jeff = 1/2, we use an effective Hubbard model to study the effect of correlations. Transitions from a metallic state to various magnetically ordered states at different critical interactions are obtained. A canted antiferromagnetic insulato…
We show, by means of low-energy muon spin rotation measurements, that few-unit-cells thick La(2)CuO(4) layers synthesized digitally by molecular beam epitaxy synthesis are antiferromagnetically ordered. Below a thickness of about 5 CuO(2) layers the long-range ordered state breaks down, and a magnetic state appears with enhanced quantum fluctuations and a reduced spin stiffness. This magnetic state can exist in close proximity (few Angstrom) to high-temperature superconducting layers, without transmitting supercurrents.
The fine control of magnetism and electronic structure is crucial since the interplay between magnetism and band topology can lead to various novel magnetic topological states including axion insulators, magnetic Weyl semimetals and Chern insulators etc. Through crystal growth, transport, thermodynamic, neutron diffraction measurements, we show that with Sb-doping, the newly-discovered intrinsic antiferromagnetic topological insulator MnBi4Te7 evolves from antiferro-magnetic to ferromagnetic and then ferrimagnetic. We attribute this to the formation of Mn(Bi,Sb) antisites upon doping, which re…
The nature of metal-insulator and magnetic transitions is still a subject under intense debate in condensed matter physics. Amongst the many possible mechanisms, the interplay between electronic correlations and spin-orbit couplings is an issue of a great deal of interest, in particular when dealing with quasi-2D compounds. In view of this, here we use a Hartree-Fock approach to investigate how the Rashba spin-orbit coupling, $V_\text{SO}$, affects the magnetic ordering provided by a Hubbard interaction, $U$, on a square lattice. At half-filling, we have found a sequence of transitions for inc…
The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, bu…
Magnetic semiconductors have attracted interest because of the question of how a magnetic metal can be derived from a paramagnetic insulator. Here our approach is to carrier dope insulating FeSi and we show that the magnetic half-metal which emerges has unprecedented optical properties, unlike those of other low carrier density magnetic metals. All traces of the semiconducting gap of FeSi are obliterated and the material is unique in being less reflective in the ferromagnetic than in the paramagnetic state, corresponding to larger rather than smaller electron scattering in the ordered phase.
Magnetic properties of stechiometric Cs2AgF4 have been calculated within a very strong correlation limit taking into account a low-symmetry crystal field and the intra-atomic spin-orbit coupling of the Ag2+ ion. We consistently explain the insulating ground state and the magnetic state revealing the spin gap of 2.6 meV below Tc of 14.9 K. A d-d excitation of 2.0-2.3 eV related to the t2g-eg promotion energy (=10Dq) is a reason for the lilac colour of Cs2AgF4. Our approach can be experimentally verified by the measurement of the g factor (gz =2.12 and gy =2.52) and the absorption energy at 2.0-…
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
CrI3 is a two-dimensional ferromagnetic van der Waals material with a charge gap of 1.1-1.2 eV. In this study, the electronic structure and magnetism of CrI3 are investigated by using density functional theory and dynamical mean-field theory. Our calculations successfully reproduce a charge gap of 1.1 eV in the paramagnetic state when a Hund coupling JH = 0.7 eV is included with an on-site Hubbard U = 5 eV. In contrast, with a large U value of 8 eV and negligible Hund coupling JH, CrI3 is predicted to be a moderately correlated metal in the paramagnetic state. We conclude that CrI3 is a Mott-H…
We study the behaviour of electrons interacting with a classical magnetic background via a strong Hund coupling. The magnetic background results from a Hamiltonian which favours at low temperature the emergence of a phase with non-zero scalar chirality. The strong Hund's coupling combined with the total chirality of the classical spins induces in the electrons an effective flux which results in the realisation of a band structure with non zero Chern number. First, we consider as a magnetic background a classical spin system with spontaneous net chirality. We study the Density of States (DoS) a…
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-fill…
Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba$_2$NaOsO$_6$. Experimental tests of such theories by local probe…
Ground state properties of the spin$-1/2$ Falicov-Kimball model on a triangular lattice in the presence of uniform external magnetic field are explored. Both the orbital and the Zeeman field-induced effects are taken into account and in each unit cell only rational flux fractions are considered. Numerical results, obtained with the help of Monte Carlo simulation algorithm, reveal that the ground state properties strongly depend on the onsite Coulomb correlation between itinerant and localized electrons, orbital magnetic field as well as the Zeeman splitting. Strikingly, for the on-site Coulomb…
We study experimentally and theoretically the electronic and magnetic properties of two insulating double perovskites that show similar atomic and electronic structure, but different magnetic properties. In magnetization measurements, La2ZnIrO6 displays weak ferromagnetic behavior below 7.5 K whereas La2MgIrO6 shows antiferromagnetic behavior (AFM) below TN = 12 K. Electronic structure calculations find that the weak ferromagnetic behavior observed in La2ZnIrO6 is in fact due to canted antiferromagnetism. The calculations also predict canted antiferromagnetic behavior in La2MgIrO6, but intrigu…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
We have carried out a detailed first-principles study of a d$^{4.5}$ quaternary iridate Ba$_3$YIr$_2$O$_9$ both in its 6H-perovskite-type ambient pressure (AP) phase and also for the high pressure (HP) cubic phase. Our analysis reveals that the AP phase belongs to the intermediate spin-orbit coupling (SOC) regime. This is further supported by the identification of the spin moment as the primary order parameter (POP) obtained from a magnetic multipolar analysis. The large $t_{2g}$ band width renormalizes the strength of SOC and the Ir intersite exchange interaction dominates resulting in long r…
We show that the interplay of strong Hubbard interaction $U$ and spin-orbit coupling $λ$ in systems with $d^4$ electronic configuration leads to several unusual magnetic phases. Most notably, we find that competition between superexchange and spin-orbit coupling leads to a phase transition from a non-magnetic state predicted by atomic physics to a novel magnetic state in the large $U$ limit. We show that the local moment changes dramatically across this phase transition, challenging the conventional wisdom that local moments are robust against small perturbations in a Mott insulator. The Hund'…
We use synchrotron x-ray diffraction and electrical transport under pressure to probe both the magnetism and the structure of single crystal NiS2 across its Mott-Hubbard transition. In the insulator, the low-temperature antiferromagnetic order results from superexchange among correlated electrons and couples to a (1/2, 1/2, 1/2) superlattice distortion. Applying pressure suppresses the insulating state, but enhances the magnetism as the superexchange increases with decreasing lattice constant. By comparing our results under pressure to previous studies of doped crystals we show that this depen…
This article reviews recent results of magnetotransport and magnetization measurements performed on highly oriented pyrolitic graphite (HOPG) and single crystalline Kish graphite samples. Both metal-insulator and insulator-metal transitions driven by magnetic field applied perpendicular to the basal planes of graphite were found and discussed in the light of relevant theories. The results provide evidence for the existence of localized superconducting domains in HOPG even at room temperature, as well as an interplay between superconducting and ferromagnetic correlations. We also present experi…
An intriguing idea of spin-orbit Mott insulator has been proposed to explain magnetic insulating behavior in various iridates. This scenario relies on the strength of the spin-orbit coupling being comparable to electronic correlations, and it is not a priori obvious whether this picture is valid for all iridates. In particular, Sr3Ir2O7 exhibits a small charge gap and magnetic moment compared to Sr2IrO4, questioning the validity of such hypothesis. To understand the microscopic mechanism for magnetism in Sr3Ir2O7, we construct a tight binding model taking into account the full t2g- orbitals, t…
We theoretically study the magnetic phase diagram of a three-dimensional topological Kondo insulator by means of real-space dynamical mean field theory. We find that ferromagnetically ordered states become stable upon hole doping. Besides a wide ferromagnetic phase, we observe surface magnetism close to half-filling, which corresponds to an A-type antiferromagnetic state. We further study the impact of the magnetism on the symmetry protected surface states and find that depending on the surface and the magnetization direction, surface states are still protected by reflection symmetry present i…
We report a study of electronic transport in van der Waals heterostructures composed of flakes of the antiferromagnetic Mott insulator a-RuCl_3 placed on top of monolayer graphene Hall bars. While the zero-field transport shows a strong resemblance to that of isolated graphene, we find a consistently $p$-type Hall effect suggestive of multiband conduction, along with a non-monotonic and gate-voltage-dependent excursion of the resistivity at low temperatures that is reminiscent of transport in the presence of a magnetic phase transition. We interpret these data as evidence for charge transfer f…
By bosonizing the electronic t-J model exactly on any two-dimensional (2D) lattices, and integrating out the gauge fluctuations combined to slave particles beyond mean fields, we get a theory in terms of physical Cooper pair and spin condensates. In the sense of mutual Berry phase they turns out to be dual to each other. The mutual-duality is the missing key in the resonant-valance-bond idea\cite{rvb} to work as a paradigm of doped 2D Mott insulators. We argue that essential aspects of high-$T_c$ phenomenology find natural solutions in the theory. We also provide interesting predictions for sy…
Recent thermodynamic measurements on two-dimensional (2D) electron systems have found diverging behavior in the magnetic susceptibility and appearance of ferromagnetism with decreasing electron density. The critical densities for these phenomena coincide with the metal-insulator transition recorded in transport measurements. Based on density functional calculations within the local spin-density approximation, we have investigated the compressibility and magnetic susceptibility of a 2D electron gas in the presence of remote impurities. A correlation between the minimum in the inverse capacitanc…
The physical properties of rare-earth (RE) dodecaborides, characterized by a cage-glass crystal structure with loosely bound RE ions, are reviewed. These compounds are strongly correlated electron systems with simultaneously active charge, spin, orbital, and lattice degrees of freedom, which explains the complexity of all $R\mathrm{B}_{12}$ compounds including antiferromagnetic (TbB$_{12}$-TmB$_{12}$) and nonmagnetic (LuB$_{12}$) metals, on one side, and the so-called Kondo insulator compound YbB$_{12}$ and Yb-based Yb$_{x}R_{1-x}$B$_{12}$ solid solutions, on the other. The development of the …
