Magnetic excitations and their anisotropy in YBCO: slave-boson   mean-field analysis of 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. In the d-wave pairing state, the strongest magnetic spectral weight appears at q=Q=(pi,pi) and \omega=\omega_{Q}^{res}, and spreads into a diamond-shaped shell around Q in q space for \omega<\omega_{Q}^{res}. This weight is due to a collective mode, namely a particle-hole bound state, which has a downward \omega versus q dispersion around Q. Within the high intensity shell, the incommensurate (IC) signals at q=(pi,pi\pm 2pi\eta) and (pi\pm 2pi\eta,pi) tend to be stronger than the diagonal incommensurate (DIC) signals at q=(pi\pm 2pi\eta',pi\pm 2pi\eta'), especially for a large hole density \delta. For \omega \ll \omega_{Q}^{res} the IC signals completely disappear and the weight remains only around the DIC positions. For \omega > \omega_{Q}^{res} strong signals of Im\chi(q,\omega) tracing an upward dispersion are found and interpreted as an overdamped collective mode near \omega_{Q}^{res}. 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 (dFSD), 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. 
Hiroyuki Yamase and Walter Metzner