# Microscopic Models for Spin Dynamics in the CuO_{2}-planes with application to NMR

## Abstract

Although the general form of the electronic structure of the *CuO* _{ 2 }-planes on the larger energy scale (∼1 *eV*) is generally agreed upon, the reduced model on the relevant energy scale for superconductivity (∼10^{-1} *e V*) continues to be debated. The key issue is usually represented in terms of the adequacy of a one-band model to describe this low energy region. Such a model was proposed at the outset of the high-T_{c} problem by Anderson^{(1)} and derived from a more general starting model with *Cu d*-states and *O p*-states by Zhang and Rice^{(2)}. In this derivation only the leading *d p* *σ* hybridization and Coulomb repulsion on *Cu* sites were kept and terms such as the direct *p — p* hybridization between *O* orbitals or Coulomb repulsion on the *O* sites were ignored. These latter terms are not small and could result in important changes in the model. Recently, these questions have been examined in some detail by a number of groups^{(3),(4)} who solved for the eigenstates, wavefunctions and response functions of small clusters, starting from the full model with all *Cu*- and *O*-orbitals and interactions. As an example, Hybertsen, Stechel, Schlüter and Jen- nison^{(4)} exactly diagonalized small clusters up to *Cu* _{ 5 } *O* _{ 16 } and found the low lying energy spectrum and wavefunctions. For the case of *Cu* ^{2+}-valence the low energy spectrum has spin degrees of freedom only and is well described by an antiferromag- netic Heisenberg model with nearest neighbor (n.n.) coupling only. The strength J is also in good agreement with experimental values. Introducing an extra hole or electron on the cluster allows charge degrees of freedom at low energy. These in turn are well represented by assuming that the extra hole (or electron) is tightly bound to a *Cu* ^{2+}-spin to form a spin singlet which however can hop with n.n. and n.n.n. matrix elements t and t′ respectively. Hybertsen et al. find relatively small values for the ratio ∣ *t′/t* ∣ (≈ 1/6). However Eskes, Tjeng and Sawatzky ^{(5)} report larger Dynamics of Magnetic Fluctuations in High-Temperature Superconductors Edited by G. Reiter et al., Plenum Press, New York, 1991 value for this ratio. The one-band *t — J* model with a possible n.n.n. *t′*-correction is then the most plausible reduced model to describe the low energy electronic structure of the doped *CuO* _{2}-planes.

## Keywords

Coulomb Repulsion Hyperfine Coupling Spin Dynamics Knight Shift Spin Degree## Preview

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## References

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