Neutron-scattering study of antiferromagnetism in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.15}$

Both the static and dynamic properties of the antiferromagnetic state in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{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 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ state. The form-factor anisotropy can explain much of the Q dependence of the inelastic magnetic cross section that has been observed in superconducting ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{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 ${\mathit{J}}_{\mathrm{\parallel }}$ of 120±20 meV (without correction for quantum renormalization) with an anisotropy ${\mathrm{\alpha }}_{\mathit{x}\mathit{y}}$=(7±1)×${10}^{\mathrm{-}4}$, and an effective next-nearest-layer exchange ${\mathit{J}}_{\mathrm{\perp }2}$ of 0.04±0.01 meV. A lower limit for the intrabilayer exchange, ${\mathit{J}}_{\mathrm{\perp }1}$, 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 ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{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.