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In an electron-phonon system the electron-phonon interaction spectral density, α²F(ω), is approximately equal to W(ω) defined as:

                           α²F(ω)≈W(ω)=(1/2π)d²[ωRe(σ^-1(ω))]/dω²   (1)

Where, Re(σ(ω)) is the real part of the optical conductivity. For the electron-spin interaction systems this relation could be converted to I²χ(ω)≈W(ω), where I is the coupling constant of electron-spin interaction and χ(ω) is the imaginary part of spin susceptibility. So, comparison of the W(ω) extracted from the experimental or computational study with the phonon or spin spectral density, gives suitable information about the type and coupling strength of the interaction with the carriers. Recently, the ~41 meV resonance magnetic mode has been observed in the spin spectral of the optimal doped YBCO and Bi2212 in the superconducting state. A group of scientist from Canada, Austria, and the USA has applied this method for both YBCO and Bi2212 systems to indicate the importance of the spin fluctuations in the superconducting state of HTSCs systems.  

Results:

• The calculated W(ω+Δ₀) from Eq. 1 for optimal doped YBCO (with the gap amplitude Δ₀~27 meV) traces the resonance pattern of the magnetic susceptibility and is in good agreement with the experimental I²χ(ω) data (Fig. 2a). The χ(ω) have been taken from the spin-polarized inelastic neutron experiment (integrated over momentum space), and W(ω+Δ₀) function has been derived (by Eq. 1) from the calculated σ(ω) in superconducting state considering d-wave gap.
• The W(ω+Δ₀) function has a peak in 68 meV (=ω_res+Δ₀=41+27 meV) and the coupling constant λ~2.6 (twice the first inverse moment of I²χ(ω)) is high enough to get T_c~100 K. The negative wiggles in W(ω) above the resonance peak is not consistent with the I²χ(ω), because the I²χ(ω) is not exactly equal to W(ω), i.e. the correspondence is expectable just near the resonance peak.  
• The experimental W(ω) for YBCO_x with x=6.95 and 6.6 have been derived from the experimental a-axis σ(ω) by Eq. 1 (Fig. 2b). The lower energy peak in x=6.6 sample could be related to the smaller ω_res in x=0.6 sample relative to x=6.95, and the lower amplitude of the peak (~smaller λ) could be calculated to lower T_c in x=0.6 sample.  
• The similarity of the experimental W(ω) pattern with the calculated W(ω+Δ₀) and experimental I²χ(ω) indicates that the σ(ω) has a trace of spin fluctuation in superconducting state rather than phonon.The similar behavior has been obtained in Bi-2212 system, which shows a magnetic resonance peak at ~43 meV.   

Finally, this study indicates the important role of the spin fluctuation in the superconducting state of HTSCs, and the strength of the electron-spin interaction is high enough to account for high T_c (~100 K) in these systems.

Ref.: J.P. Carbotte, E. Schachinger, and D.N. Basov, Nature 401 (1999) 354.