Diffuse spin waves and classical spin liquid behavior in the kagomé antiferromagnet chromium jarosite, KCr3(OD)6(SO4)2

The dynamics of the $S=3/2$ kagom\'e antiferromagnet chromium jarosite, ${\mathrm{KCr}}_{3}$(OD)${}_{6}$(${\mathrm{SO}}_{4}$)${}_{2}$, was studied using high-resolution neutron time-of-flight spectroscopy on a polycrystalline sample with a nearly stoichiometric magnetic lattice [$2.8(2)%$ Cr vacancies]. Neutron spectroscopy reveals diffuse spin wave excitations in the ordered phase with an incomplete gap and significant finite-lifetime broadening as well as a pronounced kagom\'e zero mode. Using linear spin wave theory, we estimate the exchange couplings. The system is highly two dimensional with the leading nearest-neighbor coupling being ${J}_{1}=0.881$ meV. Above ${T}_{N}$, diffuse excitations from the classical spin liquid regime dominate. We model the $Q$ response and energy response separately and show that in both the ordered phase and the classical spin liquid regime they are strongly coupled.