Search

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF3, K2NiF4, NiO, and La2CuO4. Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved.

Using low-energy projection of the one-band t-t′-t′′ Hubbard model we derive an effective spin Hamiltonian and its spin-wave expansion to order 1/S. We fit the spin-wave dispersion of several parent compounds to the high-temperature superconducting cuprates La2CuO4, Sr2CuO2Cl2, and Bi2Sr2YCu2O8. Our accurate quantitative determination of the one-band Hubbard model parameters allows prediction and comparison to experimental results. Among those we discuss the two-magnon Raman peak line shape, the K-edge resonant inelastic x-ray scattering 500-meV peak, and the high-energy kink in the angle-resolved photoemission spectroscopy quasiparticle dispersion, also known as the waterfall feature.

The relevance of different models, such as the one-band t-J model and the three-band Emery model, as a realistic description of the electronic structure of high-${\mathit{T}}_{\mathit{c}}$ materials is discussed. Starting from a multiband approach using cluster calculations and an impurity approach, the following questions are addressed: What is the stabilization energy of the Zhang-Rice singlet and triplet with respect to other symmetry levels (such as the ${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$, etc.)? How does the oxygen 2p-band width (${\mathit{t}}_{\mathit{p}\mathit{p}}$) influence the stability of the Zhang-Rice singlet? How large is the dispersion of the singlet state? It is argued that, if the one-band model does not give a satisfactory description of the low-energy physics, then the three-band model will be incomplete as well.