The spin excitation spectrum in striped bilayer compounds

The spin dynamics of bilayer cuprate compounds are studied in a basic model. The magnetic spectral properties are calculated in linear spin-wave theory for several stripe configurations which differ by the relative location of the stripes in the layers. We focus on the bilayer splitting of the magnon bands near the incommensurate low energy peaks as well as near the $\pi$ resonance, distinguishing between the odd and even channel. We find that a x-shaped dispersion near the $\pi$ resonance is generic for stripes. By comparison of our results to neutron scattering data for $\mathrm{Y}\mathrm{B}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\mathrm{x}}$ we conclude that the stripe model is consistent with characteristic features of bilayer high-$T_c$ compounds.