Theoretical Investigations of the Knight Shifts and the Hyperfine Structure Constants for the Tetragonal Cu2+ Sites in the Bismuth- and Thallium-Based High-Tc Superconductors

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The Knight shifts and hyperfine structure constants for the tetragonal Cu2+ sites in bismuth- and thallium-based high-Tc uperconductors ( Bi1:6Pb0:4Sr2Ca2Cu3O10, TlSr2CaCu2O7-y, and Tl2Ba2CuOy) are theoretically investigated from the high-order perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated octahedra in a unified way. The calculation results show good agreement with the observed values. The significant anisotropies of the Knight shifts are attributed to the local tetragonal elongation distortions of the five-(or six-)coordinated Cu2+ sites in these systems. The present studies would be beneficial to establish a complete physical scheme for unified understandings of electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) spectral behaviours of Cu2+ (or other similar 3d9 ions) in the high-Tc superconductors.