Inelastic Neutron Scattering Excitations for a Spin $\frac{3}{2}$ Tetramer: Application to Magnetic Excitations in Na$_3$RuO$_4$

We examine the magnetic properties and inelastic neutron scattering excitations for spin 3/2 tetramer using an isotropic Hamiltonian. Results on magnetic excitations observed in polycrystalline sodium ruthenate (Na$_3$RuO$_4$) are compared to the theoretical predictions. Previous work has suggested that this material consists of relatively isolated tetramers of S=3/2 Ru(V) ions, where a Heisenberg antiferromagnetic Hamiltonian was proposed. We determine that tetramer model (interacting dimers) may not be a good candidate for the magnetic structure of the system. Using three separate models, we compare parameters determined from magnetic susceptibility and inelastic neutron scattering structure factors, which suggest that separate dimers may be a more plausible model. However, future studies on single crystals are suggested to help clarify the apparent discrepancies between these model and our results.