Bilayer coupling in the yttrium-barium family of high-temperature superconductors

We derive the expressions needed to interpret experiments relating to interplane magnetic coupling in YBa₂{Cu}₃O₆₊ₓ and related materials, and use the results to interpret measurements of the optical magnon energy in YBa₂{Cu}₃O6.2 and of the NMR ``cross-relaxation'' rate in Y₂{Ba}₄Cu₇{O}₁₅$. We estimate ${J}_{{{⊥}}}~14 meV in both materials, and{{{χ}}}ₘₐₓ$/${{{μ}}}B²~100 states/eV Cu in{Y}₂Ba₄{Cu}₇O₁₅ at T=100 K. We show that there is at present no obvious contradiction between the results of a widely used analysis of NMR experiments and the results of neutron scattering experiments in the Y-Ba system. We argue that the 41 meV excitation observed in superconducting YBa₂{Cu}₃O₇ is a collective mode pulled down below the superconducting gap by interactions, and that the observed antisymmetry under interchange of planes follows from the non-negligible value of J_⊥. {} 1996 The American Physical Society.