On the 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 YBa$_{2}$Cu$_{3}$O$_{6+x}$ and related materials, and use the results to interpret measurements of the optical magnon energy in YBa_{2}Cu_{3}O_{6.2} and of the NMR ``cross-relaxation" rate in Y_2Ba_{4}Cu_{7}O_{15}. We estimate $J_{\perp}\sim 14$ meV in both materials, and $\chi_{max}/\mu^2_{B} \sim 100$ {states}/{eV}-Cu in Y_2Ba_4Cu_7O_{15} at T=100K. 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 YBa_{2}Cu_{3}O_{7} 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 $J_{\perp}$. 
A. J. Millis, H. Monien