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 ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ and related materials, and use the results to interpret measurements of the optical magnon energy in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.2}$ and of the NMR ‘‘cross-relaxation’’ rate in ${\mathrm{Y}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_7$ ${\mathrm{O}}_{15}$. We estimate ${\mathit{J}}_{\mathrm{\perp }}$∼14 meV in both materials, and ${\mathrm{\chi }}_{\max }$/${\mathrm{\mu }}_{\mathit{B}}^2$∼100 states/eV Cu in ${\mathrm{Y}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_7$ ${\mathrm{O}}_{15}$ 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 ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ 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 ${\mathit{J}}_{\mathrm{\perp }}$. © 1996 The American Physical Society.