Neutron scattering study of magnetic excitations in YBa₂Cu₃O_6+x

Inelastic neutron scattering has been used to study magnetic excitations in several single crystals of YBa₂Cu₃O_6+x. In particular, an extensive study of spin waves in a large crystal with x=0.3 has been performed. As in La₂CuO₄, a very large superexchange is found within the CuO₂ layers, with J_?=80_-30⁺⁶⁰ meV. The optical-mode spin-wave energies are higher than 30 meV, indicating that J_⊥1, the coupling between nearest-neighbor CuO₂ planes, is ≳2 meV. From the dispersion and splitting of the acoustic modes, we obtain values of 0.020±0.005 meV for the effective exchange between next-nearest-neighbor layers, J_⊥2, and 0.035±0.005 meV for the anisotropy parameter D. The weak anisotropy gives the planes an XY-like symmetry; no evidence has been found for any in-plane anisotropy. The CuO₂ bilayers remain strongly correlated well above T_N, and dispersion of the acoustic modes appears 30 K above T_N. The decrease of the magnetic order parameter below 30 K in the x=0.3 crystal is interpreted as the onset of an incoherent ordering of Cu moments in the oxygen-deficient CuO_x layers. Low-energy inelastic scattering associated with the transition is also observed. Searches for low-energy magnetic fluctuations in several superconducting single crystals have so far been unsuccessful.