New Approach to the Theory of Superexchange Interactions
TL;DR: In this article, the theory of indirect exchange in poor conductors is examined from a new viewpoint in which the $d$ (or $f$) shell electrons are placed in wave functions assumed to be exact solutions of the problem of a single $d-electron in the presence of the full diamagnetic lattice.
Abstract: The theory of indirect exchange in poor conductors is examined from a new viewpoint in which the $d$ (or $f$) shell electrons are placed in wave functions assumed to be exact solutions of the problem of a single $d$-electron in the presence of the full diamagnetic lattice. Inclusion of $d$-electron interactions leads to three spin-dependent effects which, in the usual order of their sizes, we call: superexchange per se, which is always antiferromagnetic; direct exchange, always ferromagnetic; and an indirect polarization effect analogous to nuclear indirect exchange. Superexchange itself is shown to be closely related to the poor conductivity, in agreement with experiment. By means of crystal field theory the parameters determining superexchange can be estimated, and in favorable cases (NiO, LaFe${\mathrm{O}}_{3}$) the exchange integrals can be evaluated with accuracy of several tens of percent. Qualitative understanding of the whole picture of exchange in iron group oxides and fluorides follows from these ideas.
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TL;DR: The oxide superconductors, particularly those recently discovered that are based on La2CuO4, have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties.
Abstract: The oxide superconductors, particularly those recently discovered that are based on La2CuO4have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties. This insulating phase is proposed to be the long-sought “resonating-valence-bond” state or “quantum spin liquid” hypothesized in 1973. This insulating magnetic phase is favored by low spin, low dimensionality, and magnetic frustration. The preexisting magnetic singlet pairs of the insulating state become charged superconducting pairs when the insulator is doped sufficiently strongly. The mechanism for superconductivity is hence predominantly electronic and magnetic, although weak phonon interactions may favor the state. Many unusual properties are predicted, especially of the insulating state.
5,409 citations
TL;DR: A review of the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds is presented in this article, with the purpose of providing an updated summary of the extensive literature.
Abstract: The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.
3,077 citations
Cites background from "New Approach to the Theory of Super..."
...13(a) and (b)] and suggests that the undoped parent compounds of the cuprate superconductors may belong to the class of the Mott-Hubbard insulators (Mott, 1949, 1956, 1974; Anderson, 1959; Hubbard, 1964a, 1964b)....
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TL;DR: In this paper, a single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer.
Abstract: A single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer. A state of mixed spin symmetry and lowered space symmetry is constructed which has both conceptual and practical computational value. Either unrestricted Hartree–Fock theory or spin polarized density functional theory, e.g., Xα theory, can be used to generate the mixed spin state wave function. The most important consequence of the theory is that the Heisenberg exchange coupling constant J can be calculated simply from the energies of the mixed spin state and the highest pure spin multiplet.
2,242 citations
TL;DR: In this article, a review of the basic ideas and techniques of spectral density functional theory which are currently used in electronic structure calculations of strongly correlated materials where the one-dimensional electron description breaks down is presented.
Abstract: We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly{correlated materials where the one{electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal{insulator transition, systems near volume collapse transition, and systems with local moments.
1,921 citations
TL;DR: The generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism, and the theorems hold in all dimensions without even the necessity of a periodic lattice structure.
Abstract: In the attractive Hubbard model (and some extended versions of it) the ground state is proved to have spin angular momentum S = 0 for every (even) electron filling. In the repulsive case, and with a bipartite lattice and a half filled band, the ground state has S = 1/2∥B∣ − ∣A∥, where ∣B∣ (resp. ∣A∣) is the number of sites in the B (resp. A) sublattice. In both cases the ground state is unique. These theorems hold for all values of U, the attraction or repulsion parameter. The second theorem confirms an old, unproved conjecture in the ∣B∣ = ∣A∣ case; the generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism. Since topology is irrelevant for the proofs, the theorems hold in all dimensions without even the necessity of a periodic lattice structure.
1,575 citations