Dispersive excitations in the $S=1$ antiferromagnet Ba$_3$Mn$_2$O$_8$

We present powder inelastic neutron scattering measurements on the $S=1$ dimerized antiferromagnet Ba$_3$Mn$_2$O$_8$. The measured $T=1.4$~K magnetic spectrum exhibits a spin-gap of $\Delta = 0.99$~meV and a dispersive spectrum with a bandwidth of approximately $1.67$~meV. Comparison to a coupled dimer model of the dispersion and scattering intensity yields an accurate description of the exchange constants in Ba$_3$Mn$_2 $O$_8$. Interdimer exchange between the stacked triangular lattice dimer bilayers is found to be two orders of magnitude weaker than the intradimer exchange resulting in a quasi-two- dimensional frustrated bilayer triangular lattice. The wave- vector dependent scattering intensity also confirms the proposed $S=1$ dimer bond. Temperature dependent measurements of the magnetic excitations indicate the presence of both singlet- triplet and thermally activated triplet-quintet excitations, with temperature dependent damping and spin-gap consistent with current models for weakly coupled quantum spin-liquids.