Dispersion of the odd magnetic resonant mode in near-optimally doped Bi₂Sr₂CaCu₂O_8+δ

We report a neutron scattering study of the spin excitation spectrum in the superconducting state of the slightly overdoped Bi₂Sr₂CaCu₂O_8+δ system (T_c=87 K). We focus on the dispersion of the resonance peak in the superconducting state that is due to a S=1 collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the YBa₂Cu₃O_6+x system for a similar doping level (i.e., x∼0.95−1), which can be described as intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, known from angle resolved photoemission measurements in the same system, indicates that the magnetic response in the superconducting state is confined, in both energy and momentum, below the gapped Stoner continuum. In contrast to YBa₂Cu₃O_6+x, the spin excitation spectrum is broader than the experimental resolution. In the framework of an itinerant-electron model, we quantitatively relate this intrinsic energy width to the superconducting gap distribution observed in scanning tunneling microscopy experiments. Our study further suggests a significant in-plane anisotropy of the magnetic response.