Detailed Structure of the Magnetic Excitation Spectra of YBa ₂Cu ₃O _y and Its Implication on the Physical Characteristics of the Electron System

Detailed structure of the magnetic excitation spectra χ″(q, ω) of the superconducting oxide YBa ₂Cu ₃O _6.5 (the transition temperature T _c ≅ 52K) in the wave vector (q)- and the energy(ω)-space, and its temperature (T) dependence have been studied. By adopting an effective energy dispersion of the quasi particles which can reproduce the shape of the Fermi surface and by introducing the exchange interaction between the Cu spins, a rather satisfactory agreement between the calculation and the experimentally observed data can be obtained. In the study, it has been found that the effects of the quasi particle-energy broadening on the excitation spectra χ″ (q,ω) is important. The sharp resonance peak observed at w ∼ 40 meV for the optimally doped system of YBa ₂Cu ₃O _y can be naturally reproduced by the present model.