In a classic Mott system, the transition from the insulating to the metallic state occurs when the lattice spacing is reduced such that the increase in bandwidth W overcomes the local Coulomb repulsion U. In this picture, both W and the ratio W/U become larger with decreasing the distance between correlated sites. Here we show that, in transition-metal compounds, there is another path to metallization. It is associated with an expansion (instead of a compression) of the lattice and thus with a decrease in W. In this scenario W/U grows with increasing distance-the opposite of the classical Mott case. Such a surprising inversion can be obtained by decoupling the main factors controlling W and screening. This mechanism explains the electronic behavior of the t22g triangular lattice series LiVX2 (X = O, S, and Se) with increasing anionic size.

In correlated transition-metal oxides, orbital-ordering appears to always precede magnetic ordering (TN

At ambient pressure, the t52g layered perovskite Sr2IrO4 is a correlated small-gap insulator. In the Mott picture, applying uniform pressure should therefore quickly close the gap; experimentally, however, the insulating state persists even under extreme pressures, suggesting that a mechanism other than Mott is at work. Yet, given the complexity of the system, it is unclear to what extent the Mott picture can be really excluded. Here, we thus reexamine the problem. We show that, surprisingly, the pressure-induced enhancement of the screened Coulomb interaction-combined with lattice distortions and spin-orbit driven jeff = 1/2 orbital ordering-can hold the system close to the metal-insulator transition up to very high pressure.

A central challenge in water electrolysis lies with the oxygen evolution reaction (OER) where the formation of molecular oxygen (O 2 ) is hindered by the constraint of angular momentum conservation. While the reactants OH − or H 2 O are diamagnetic (DM), the O 2 product has a paramagnetic (PM) triplet ground state, requiring a change in spin configuration when being formed. This constraint has prompted interest in spin‐selective catalysts as a means to facilitate OER. In this context, the roles of magnetism and chirality‐induced spin selectivity (CISS) in promoting the OER reaction have recently been investigated through both theoretical and experimental studies. However, pinpointing the key principles and their relative contribution in mediating spin‐enhancement remains a significant challenge. This roadmap offers a forward‐looking perspective on current experimental trends and theoretical developments in spin‐enhanced OER electrocatalysis and outlines strategic directions for integrating incisive experiments and operando approaches with computational modeling to disentangle key mechanisms. By providing a conceptual framework and identifying critical knowledge gaps, this perspective aims to guide researchers toward dedicated experimental and computational studies that will deepen the understanding of spin‐induced OER enhancement and accelerate the development of next‐generation catalysts.

Correlated metallic layered t_{2g}^{n} perovskites are intensively studied and yet their low-energy electronic properties remain hotly debated. Important elements of the puzzle, beside the on-site Coulomb repulsion, are the tetragonal crystal-field splitting and the spin-orbit interaction. Here, we show that they control the electronic properties principally via form and occupations of natural orbitals. We discuss consequences for shape and topology of the Fermi surface, effective masses, and metal-insulator transition, building a map of crystal-field effects. The emerging picture captures electronic-structure trends in this family of systems within a single framework.

The surprising inversion of the orbital- and magnetic-order transition temperatures in the RVO3 series with increasing the rare-earth radius makes the series unique among orbitally-ordered materials. Here, augmenting dynamical mean-field theory with a decomposition of the order parameter into irreducible tensors, we show that this anomalous behavior emerges from an unusual hierarchy of interactions. First, increasing the rare-earth radius, orbital physics comes to be controlled by xz-xz quadrupolar super-exchange rather than by lattice distortion. Next, for antiferromagnetic spin order, orbital super-exchange terms with different spin rank compete, so that the dipolar spin-spin interaction dominates. Eventually, G-type magnetic order (anti-ferro in all directions) can appear already above the orbital ordering transition, and C-type order (anti-ferro in the ab plane) right around it. The strict constraints we found explain why the inversion is rare, giving at the same time criteria to look for similar behavior in other materials.

The low-energy jeff = 1/2 band of Sr2IrO4 bears stark resemblances with the x2 - y2 band of La2CuO4, and yet no superconductivity has been found so far by doping Sr2IrO4. Behind such a behavior could be inherent failures of the jeff = 1/2 picture, in particular when electrons or holes are introduced in the IrO2 planes. In view of this, here we reanalyze the jeff = 1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective jeff = 1/2 state is surprisingly stable upon doping. This supports the jeff = 1/2 picture. We show that, nevertheless, Sr2IrO4 remains in essence a multiorbital system: The hybridization with the jeff = 3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the jeff = 3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the jeff = 3/2 states contribute both to the Drude peak and to relatively low-energy features.

Sr$_{2}$IrO$_{4}$ has often been described via a simple, one-band pseudo-spin 1/2 model, subject to electron-electron interactions, on a square lattice, fostering analogies with cuprate superconductors, believed to be well described by a similar model. In this work we argue - based on a detailed study of the low-energy electronic structure by circularly polarized spin and angle-resolved photoemission spectroscopy combined with dynamical mean-field theory calculations - that a pseudo-spin 1/2 model fails to capture the full complexity of the system. We show instead that a realistic multi-band Hubbard Hamiltonian, accounting for the full correlated $t_{2g}$ manifold, provides a detailed description of the interplay between spin-orbital entanglement and electron-electron interactions, and yields quantitative agreement with experiments. Our analysis establishes that the $j_{3/2}$ states make up a substantial percentage of the low energy spectral weight, i.e. approximately 74% as determined from the integration of the $j$-resolved spectral function in the $0$ to $-1.64$ eV energy range. The results in our work are not only of relevance to iridium based materials, but more generally to the study of multi-orbital materials with closely spaced energy scales.

Material-specific super-exchange Hamiltonians are the key to studying spin and orbital physics in strongly correlated materials. Recently, via an irreducible-tensor operator representation, we derived the orbital superexchange Hamiltonian for t12g perovskites and successfully used it, in combination with many-body approaches, to explain orbital physics in these systems. Here, we generalize our method to eng and tn2g systems at arbitrary integer filling n, including both spin and orbital interactions. The approach is suitable for numerical implementations based on ab initio hopping parameters and realistic screened Coulomb interactions and allows for a systematic exploration of superexchange energy surfaces in a realistic context.

We show that the $t_{2g}^2$ perovskite LaVO$_3$, in its orthorhombic phase, is a rare case of a system hosting an orbital-ordering Kugel-Khomskii phase transition, rather than being controlled by the Coulomb-enhanced crystal-field splitting. We find that, as a consequence of this, the magnetic transition is close to (and even above) the super-exchange driven orbital-ordering transition, whereas typically magnetism arises at much lower temperatures than orbital ordering. Our results support the experimental scenario of orbital-ordering and G-type spin correlations just above the monoclinic-to-orthorhombic structural change. To explore the effects of crystal-field splitting and filling, we compare to YVO$_3$ and $t_{2g}^1$ titanates. In all these materials the crystal-field is sufficiently large to suppress the Kugel-Khomskii phase transition.

Spin-density modulations point to inhomogeneous superconductivity in a perovskite

Sr$_{2}$IrO$_{4}$ has often been described via a simple, one-band pseudo-spin 1/2 model, subject to electron-electron interactions, on a square lattice, fostering analogies with cuprate superconductors, believed to be well described by a similar model. In this work we argue - based on a detailed study of the low-energy electronic structure by circularly polarized spin and angle-resolved photoemission spectroscopy combined with dynamical mean-field theory calculations - that a pseudo-spin 1/2 model fails to capture the full complexity of the system. We show instead that a realistic multi-band Hubbard Hamiltonian, accounting for the full correlated $t_{2g}$ manifold, provides a detailed description of the interplay between spin-orbital entanglement and electron-electron interactions, and yields quantitative agreement with experiments. Our analysis establishes that the $j_{3/2}$ states make up a substantial percentage of the low energy spectral weight, i.e. approximately 74% as determined from the integration of the $j$-resolved spectral function in the $0$ to $-1.64$ eV energy range. The results in our work are not only of relevance to iridium based materials, but more generally to the study of multi-orbital materials with closely spaced energy scales.

This corrects the article DOI: 10.1103/PhysRevLett.110.157204.

We perform a systematic study of static and dynamical magnetic properties of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model in a parameter regime relevant for high-temperature superconducting cuprates. We adopt as solution method the dynamical mean-field theory approximation and its real-space cluster extension. Our results show that large ${t}^{\ensuremath{'}}/t$ suppresses incommensurate features and eventually leads to ferromagnetic instabilities for sufficiently large hole doping $x$. We identify isosbestic points which separate parts of the Brillouin zone with different scaling behaviors. Calculations are compared to available nuclear magnetic resonance, nuclear quadrupole resonance, inelastic neutron scattering, and resonant inelastic x-ray scattering experiments. We show that while many trends are correctly described, e.g., the evolution with $x$, some aspects of the spin-lattice relaxation rates can apparently only be explained invoking accidental cancellations. In order to capture the material dependence of magnetic properties in full, it may be necessary to add further degrees of freedom.

This article is a short introduction to the modern computational techniques used to tackle the many-body problem in materials. The aim is to present the basic ideas, using simple examples to illustrate strengths and weaknesses of each method. We will start from density-functional theory (DFT) and the Kohn–Sham construction—the standard computational tools for performing electronic structure calculations. Leaving the realm of rigorous density-functional theory, we will discuss the established practice of adopting the Kohn–Sham Hamiltonian as approximate model. After recalling the triumphs of the Kohn–Sham description, we will stress the fundamental reasons of its failure for strongly-correlated compounds, and discuss the strategies adopted to overcome the problem. The article will then focus on the most effective method so far, the DFT+DMFT technique and its extensions. Achievements, open issues and possible future developments will be reviewed. The key differences between dynamical (DFT+DMFT) and static (DFT+ U ) mean-field methods will be elucidated. In the conclusion, we will assess the apparent dichotomy between first-principles and model-based techniques, emphasizing the common ground that in fact they share.

We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

We investigate the magnetic couplings in Sr2IrO4 in the Mott-insulating picture, combining density-functional theory, dynamical mean-field theory, and many-body perturbation theory. We first determine the form of the j(eff) = 1/2 pseudospin via the local-density-approximation + dynamical mean-field theory approach. Next we study the magnetic interactions in the strong-to-intermediate coupling regime. To this end, we calculate the superexchange pseudospin tensors Gamma(1) , Gamma(2) , and Gamma(3) up to fourth order and analyze their dependence on the screened Coulomb interaction integrals U and J. We show that, due to term cancellations, the experimental nearestneighbor coupling Gamma(1) is reasonably well reproduced for a whole range of realistic (U, J) values. We show that increasing the Hund's rule coupling J (within the window of realistic values) can lead to large fourth-order contributions, which could explain the ferromagnetic next-nearest-neighbor coupling Gamma(2) extracted from the spinwave dispersion. This regime is characterized by a sizable ring exchange K. For (U, J) values that yield a Mott insulator with a half-filled j(eff) = 1/2 state, however, fourth-order terms remain minor even if the gap is small. For no realistic parameters, we find a sizable next-next-nearest-neighbor coupling Gamma(3) similar to vertical bar Gamma(2)vertical bar. Possible implications are discussed.

2 From DMFT to LDA+DMFT 4 2.1 DMFT for a toy model: The Hubbard dimer . . . . . . . . . . . . . . . . . . . 4 2.2 Non-local Coulomb interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Quantum-impurity solvers: Continuous-time quantum Monte Carlo . . . . . . 12 2.4 DMFT for the one-band Hubbard model . . . . . . . . . . . . . . . . . . . . . 17 2.5 DMFT for multi-orbital models . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6 LDA+DMFT: Model building . . . . . . . . . . . . . . . . . . . . . . . . . . 22