Spin dynamics of antiferromagnetically coupled bilayers - the case of Cr_2TeO_6

Understanding the dynamics of interacting quantum spins has been one of the active areas of condensed matter physics research. Recently, extensive inelastic neutron scattering measurements have been carried out in an interesting class of systems, Cr_2(W, Te, Mo)O_6. These systems consist of bilayers of Cr^{3+} spins (S=3/2) with strong antiferromagnetic inter-bilayer coupling (J) and tuneable intra-bilayer coupling (j) from ferro (for W and Mo) to antiferro (for Te). In the limit when J>|j|, the system reduces to weakly interacting quantum spin-3/2 dimers. In this paper we discuss the low-temperature magnetic properties of Cr_2TeO_6 systems where both intra-layer and inter-layer exchange couplings are antiferromagnetic, i.e. J,j>0. Using linear spin-wave theory we obtain the magnon dispersion, sublattice magnetization, two-magnon density of states, and longitudinal spin-spin correlation function.