Diffuse spin waves, zero modes and cluster excitations in the spin-3/2 kagomé antiferromagnet chromium jarosite, KCr${}_3$(OD)${}_6$(SO${}_4$)${}_2$

The dynamics of the S = 3=2 kagome antiferromagnet chromium jarosite, KCr${}_3$(OD)${}_6$(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 life-time broadening as well as a pronounced zero mode. Using linear spin wave theory, we estimate the exchange couplings, with the leading nearest neighbor value being $J_1$ = 0:884 meV. Above $T_N$ diffuse excitations from cooperative paramagnetism dominate. A model for two-dimensional magnetic cluster excitations is shown to capture the essential features of the data in the cooperative paramagnetic phase.