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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

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

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