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The origin of the magnetic resonance structure observed in the
superconducting (SC) state of YBa2Cu3O6+x(YBCO), and Bi2Sr2CaCu2O8+x, is
one of the most controversial topics in today's high-Tc superconductor
(HTSC) physics. Existing theories waver between the itinerant magnetism
resulting from the fermiology and the local spins pictures (such as static
and fluctuating stripes, coupled spin ladders, or spiral spin phase
models), as it appears that both approaches can qualitatively reproduce
the main features of the magnetic spectra in the neighborhood of the
optimal doping.
Here, starting on fermiology like treatment, we study the momentum and frequency dependence of the dynamical spin susceptibility in the superconducting state of bilayer cuprate superconductors. We show that there exists a resonance mode in the odd as well as the even channel of the spin susceptibility, with the even mode being located at higher energies than the odd mode. We demonstrate that this energy splitting between the two modes arises not only from a difference in the interaction, but also from a difference in the free-fermion susceptibilities of the even and odd channels. In addition, we demonstrate that there exists a second branch of the even resonance, similar to the recently observed second branch (the Q*-mode) of the odd resonance. Finally, we identify the origin of the qualitatively different doping dependence of the even and odd resonance. We further estimate the dynamic spin susceptibility in the odd (o) and even (e) channels within the random phase approximation (RPA) from the single-particle spectral function obtained by ARPES, and compare the resulting spectrum calculated for optimally doped BSCCO with the available INS measurements on both BSCCO and YBCO. |
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