Magnetic excitations and their anisotropy in YBa2Cu3O6+x:: Slave-boson mean-field analysis of the bilayer t-J model

We perform a comprehensive analysis of the dynamical magnetic susceptibility chi(q,omega) in the slave-boson mean-field scheme of the bilayer t-J model. We use model parameters appropriate for YBa2Cu3O6+x (YBCO), a typical bilayer high-T-c cuprate compound well studied by neutron scattering experiments. In the d-wave pairing state, the strongest magnetic spectral weight appears at q=Q equivalent to(pi,pi) and omega=omega(res)(Q), and spreads into a diamond-shaped shell around Q in q space for omega omega(res)(Q) strong signals of Im chi(q,omega) tracing an upward dispersion are found and interpreted as an overdamped collective excitation near omega(res)(Q). In the normal state, Im chi(q,omega) has a broad peak at q=Q. That is, the IC and DIC signals appear only in the d-wave pairing state. We also study effects of a small orthorhombic anisotropy, which is intrinsic in untwinned YBCO crystals. Because of electron-electron correlations favoring d-wave shaped Fermi surface deformations, we expect an enhanced anisotropy of magnetic excitation spectra. This effect is particularly pronounced for low delta and at relatively high temperature. The present theory provides a rather detailed microscopic explanation of the most salient properties of magnetic excitations observed in YBCO.