Spin fluctuations ofd-wave superconductors

The dynamic spin correlation function near the commensurate point Q=(π,π) in the superconducting state is calculated within mean field theory. We take the generalized t-J model as used by Tanamoto et al. For d-wave superconductor at T=0 K, we find that there will be no energy gap at incommensurate point, while the energy gap ${\mathit{E}}_{\mathit{g}}$=2μ develops at commensurate point in the particle-hole channel. On the other hand for s-wave superconductor a large energy gap develops irrespective of the nature of antiferromagnetic fluctuations. Therefore the d-wave model describes the neutron scattering data from both ${\mathrm{La}}_{1.86}$ ${\mathrm{Sr}}_{0.14}$ ${\mathrm{CuO}}_4$ by Mason et al. and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ by Rossat-Mignod et al. quite well, while the s-wave model is incompatible with these experimental results.