Quantum Spin Fluctuations and magnons in antiferromagnetically coupled bilayers with tuneable intra-bilayer exchange - the case of Cr$_2$W(Te)O$_6$

Recent neutron diffraction studies have shown that in Cr$_2$(W,Te)O$_6$ systems, which consist of bilayers with strong antiferromagnetic inter-bilayer coupling between Cr moments, the intra-bilayer coupling between the Cr moments can be tuned from ferro (for W) to antiferro (for Te). Ab initio density functional calculations provide a microscopic understanding of the magnetic structure but cannot explain the magnitude of the ordered Cr$^{3+}$ moments. In order to understand the reduction of the ordered moment (ROM) caused by quantum spin fluctuations we have studied the magnon dispersion and ROM using a two parameter quantum Heisenberg spin Hamiltonian with tunable intra-($j$) and antiferromagnetic inter- ($J$) bilayer couplings. The magnon dispersion and sublattice magnetization have been calculated using non-linear spin wave theory up to second-order corrections in spin $S$.