Interplay of quantum magnetic and potential scattering around Zn and Ni impurity ions in superconducting cuprates

To describe the scattering of superconducting quasiparticles from non-magnetic (Zn) or magnetic (Ni) impurities in optimally doped high-Tc cuprates, we propose an effective Anderson model Hamiltonian of a localized electron hybridizing with dx2-y2-wave BCS type superconducting quasiparticles with an attractive scalar potential at the impurity site. Due to the strong local antiferromagnetic couplings between the original Cu ions and their nearest neighbors, the localized electron in the Ni-doped materials is assumed to be on the impurity sites, while in the Zn-doped materials the localized electron is distributed over the four nearest neighbor sites of the impurities with a dominant dx2-y2 symmetric form of the wave function. Since both scatterings from the localized electron and the scalar potential are relevant, localized resonant states due to their interplay are formed below the maximal superconducting gap. With Ni impurities, two resonant states are formed above the Fermi level in the local density of states at the impurity site, while for Zn impurities a sharp resonant peak below the Fermi level dominates in the local density of states at the Zn site, accompanied by a small and broad resonant state above the Fermi level mainly induced by the potential scattering. This is exactly what has been observed in the scanning tunneling microscopy experiments. In both cases, there are no Kondo screening effects. From the calculated spin relaxation functions, we find that the 3d localized electron in both Ni and Zn doped materials displays a weak magnetic oscillation. This result is consistent with the signal of a spin-1/2 magnetic moment exhibited by nuclear magnetic resonance measurements in YBa2Cu3O6+δ doped with Zn or Ni impurities. The local density of states and their spatial distribution at the dominant resonant energy around the substituted impurities are calculated for both cases, and they are in good agreement with the experimental results of scanning tunneling microscopy in Bi2Sr2CaCu2O8+δ with Zn or Ni impurities, respectively. Thus the scanning tunneling and nuclear magnetic resonance experiments on Zn and Ni substituted cuprates are interpreted self-consistently in a unified fashion.