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The dynamics of the S = 3=2 kagome antiferromagnet chromium jarosite,KCr$_3$(OD)$_6$(SO$_4$)$_2$ was studied using high-resolution neutrontime-of-flight spectroscopy on a polycrystalline sample with a nearlystoichiometric magnetic lattice (2.8(2)% Cr vacancies). Neutron spectroscopyreveals diffuse spin wave excitations in the ordered phase with an incompletegap and significant finite life-time broadening as well as a pronounced zeromode. Using linear spin wave theory, we estimate the exchange couplings, withthe leading nearest neighbor value being $J_1$ = 0:884 meV. Above $T_N$ diffuseexcitations from cooperative paramagnetism dominate. A model fortwo-dimensional magnetic cluster excitations is shown to capture the essentialfeatures of the data in the cooperative paramagnetic phase.

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