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Recent inelastic neutron diffraction measurements on Cr$_2$(Te, W, Mo)O$_6$have revealed that these systems consist of bilayers of spin-3/2 Cr$^{3+}$ ionswith strong antiferromagnetic inter-bilayer coupling and tuneable intra-bilayercoupling from ferro (for W and Mo) to antiferro (for Te). These measurementshave determined the ground state spin structure and the values of sublatticemagnetization, which shows significant reduction of sublattice magnetizationfrom the atomic spin value of 3.0$\mu_B$ for Cr$^{3+}$ atoms. In an earlierpaper we theoretically investigated the low temperature spin dynamics ofCr$_2$TeO$_6$ bilayer system where both the intra and inter-bilayer couplingsare antiferromagnetic. In this paper we investigate Cr$_2$WO$_6$ andCr$_2$MoO$_6$ systems where intra-bilayer exchange couplings are ferromagneticbut the inter-bilayer exchange couplings are antiferromagnetic. We obtain themagnon dispersion, sublattice magnetization, two-magnon density of states,longitudinal spin-spin correlation function, and its powder average and comparethe results for these systems with results for Cr$_2$TeO$_6$.

Spin dynamics of antiferromagnetically coupled ferromagnetic bilayers -- the case of Cr$_2$WO$_6$ and Cr$_2$MoO$_6$