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A complete theoretical analysis using first the simple Hückel model followed by more sophisticated multi-reference calculations on a trinuclear Ni(II) complex (Tp#Ni3HHTP), bearing the non-innocent bridging ligand HHTP3−, is carried out. The three semiquinone moieties of HHTP3− couple antiferromagnetically and lead to a single unpaired electron localized on one of the moieties. The calculated exchange coupling integrals together with the zero-field parameters allow, when varied within a certain range, reproducing the experimental data. These results are generalized for two similar other trinuclear complexes containing Ni(II) and Cu(II). The electronic structure of HHTP3− turns out to be independent of both the chemical nature and the geometry of the metal ions. We also establish a direct correlation between the geometrical and the electronic structures of the non-innocent ligand that is consistent with the results of calculations. It allows experimentalists to get insight into the magnetic behavior of this type of complexes by an analysis of their X-ray structure.

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In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the $j_{\mathrm{eff}}$ states is key. However, in particular for its structurally simple member Ba$_2$IrO$_4$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-$j_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling and Coulomb interactions, we map out a rich phase diagram and identify a region of effective one-band metal-insulator transition relevant to Ba$_2$IrO$_4$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba$_2$IrO$_4$ and to clarify further the similarities and differences with cuprates.

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Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.

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This chapter is dedicated to the rationalization of magnetic anisotropy in metal complexes. Analytical derivations allow one to predict the nature and magnitude of both the zero-field-splitting and the anisotropies of magnetic exchange. The first section is devoted to mononuclear complexes. It addresses the effect of spin–orbit coupling (SOC) in two different cases: (i) when the ground state is non-degenerate and a second-order SOC applies. The effect of the SOC can then be modeled by an energy splitting of the MS components of the ground spin state. Illustrations of the power of these analytical derivations for the rationalization of the ZFS of various complexes are presented; (ii) when the ground state is (almost) degenerate, a first-order SOC applies. A more sophisticated model is here derived which rationalizes the obtaining of a giant value of the ZFS in a Ni(II) complex. The second section is devoted to the derivation of multi-spin models for binuclear complexes. We will determine the physical content of both the symmetric and the antisymmetric exchange tensors in the case of two centers with spin S = 1/2. A peculiar derivation concerns the Dzyaloshinskii–Moriya (antisymmetric exchange) interaction in case of a local degeneracy of the orbitals and shows how the first-order SOC can generate giant values of this anisotropy of exchange. In the last subsection, we will show that the usual multi-spin model for spin S = 1 centers is not valid and derive an appropriate model involving a four-rank exchange tensor. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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This chapter is devoted to theoretical calculations aimed at determining the electronic structure of binuclear complexes, including isotropic and anisotropic interactions in both the strong and in the weak-exchange coupling limits. The theory of effective Hamiltonians is used to extract magnetic anisotropy terms in various regimes and in particular those for which the giant-spin approximation holds. While only a second-rank symmetric tensor is necessary to describe the zero-field splitting in centrosymmetric compounds with a single electron on each metal ion, a 4-rank tensor must also be introduced to describe the anisotropic exchange in the case of two unpaired electrons per metal ion. The magnitude of these additional interactions was found to be larger than those of the well admitted 2-rank tensor. Even though, the magnetic anisotropy of binuclear complexes can often be predicted from the knowledge of the local anisotropy of its mononuclear constituents, the large magnitude of the 4-rank tensor makes theoretical calculations important if not mandatory to rationalize experimental results on firm grounds in systems where anisotropic binuclear interactions are important.

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Sujets

Magneto-resistive effects Electron g-factor Magnetic properties Anisotropy Crystal-field theory and spin Hamiltonians Model Hamiltonian derivation Hyperfine coupling Déplacements chimiques paramagnétiques Relativistic corrections Dynamical mean field theory Diagonalisations exactes Metal-insulator transition Dzyaloshinskii–Moriya interaction Luminescence Hamiltonien modèle FOS Physical sciences Anisotropie magnétique Complexes de métaux de transition Calcul ab initio Cooperative effect Ab initio calculations Dzyaloshinskii-Moriya interaction Iridates MACROCYCLIC POLYARYLMETHYL POLYRADICALS Modèle de double échange Disordered Systems and Neural Networks cond-matdis-nn Electron paramagnetic resonance Electronic structure Crystal field theory Coupled cluster calculations Density functional theory Configuration interaction Exchange and superexchange interactions Correlated relativistic ab initio calculations Exact diagonalization Spin-orbit coupling Imidazolium salt Binuclear compounds Calculs ab initio relativistes et corrélés Ab initio calculation Bleaney Anderson mechanism Wave functions Ligand-field theory Magnétisme dans les systèmes organiques Lanthanide Actinide Electronic correlation Manganites Molecular electronic states Modèle de Bleaney CLUSTERS Determinants Bleaney's model Magnetism Hyperfine structure Molecular magnetism Finite nucleus effects Magnétisme moléculaire Covalency Molécules aimants Lanthanides Iodine Ground states Ionic liquid Excitation energies Bleaney's theory Iridate Heavy fermions HIGH-SPIN Molecular magnet Décontamination de spin Configuration interactions MOLECULAR MAGNETIC-MATERIALS Actinides Free radicals Crystal field parameters First-order spin–orbit coupling Double exchange model Divalent cobalt Spin-orbit interactions Effets magnéto-résistifs High pressure AB-INITIO Effective Hamiltonian theory Calculs ab initio Dynamical mean-field theory Model Hamiltonians Perturbation theory Magnetic anisotropy Magnetism in organic systems Heptacoordination Isotropic and anisotropic exchange Excited states MECHANISM Electron paramagnetism Electron spin Basis sets Molecule-photon collisions Model hamiltonian

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