Neutron-scattering study of antiferromagnetism in YBa₂Cu₃O_6.15

Both the static and dynamic properties of the antiferromagnetic state in YBa₂Cu₃O_6.15 have been reinvestigated by neutron scattering. The crystal studied exhibited a Néel temperature of 410±3 K, with a continuous transition below 15 K to a magnetic structure with a doubled unit cell along the c axis. The Cu magnetic form factor has been extracted from magnetic Bragg peak intensities measured at 15 K, and it is shown to have the large anisotropy expected for a Cu 3d_x²-y² state. The form-factor anisotropy can explain much of the Q dependence of the inelastic magnetic cross section that has been observed in superconducting YBa₂Cu₃O_6+x. A search for the optical spin-wave modes at excitation energies up to 60 meV was unsuccessful. Analysis of acoustic spin-wave measurements yields an intralayer superexchange energy J_∥ of 120±20 meV (without correction for quantum renormalization) with an anisotropy α_xy=(7±1)×10^-4, and an effective next-nearest-layer exchange J_⊥2 of 0.04±0.01 meV. A lower limit for the intrabilayer exchange, J_⊥1, of 8 meV is established. Use of theoretical and experimental results for Q-integrated spin-wave intensities in the antiferromagnet, together with a crystal volume normalization based on phonon measurements, allows us to put previous measurements of spin fluctuations in superconducting YBa₂Cu₃O_6.6 on an absolute scale. The results for the superconductor are shown to be consistent with the relaxation rates determined by nuclear magnetic resonance.