Magnetic systems with spins sitting on a lattice of corner sharing regular tetrahedra have been particularly prolific for the discovery of new magnetic states for the last two decades. The pyrochlore compounds have offered the playground for these studies, while little attention has been comparatively devoted to other compounds where the rare earth R occupies the same sub-lattice, e.g. the spinel chalcogenides CdR2X4 (X = S, Se). Here we report measurements performed on powder samples of this series with R = Yb using specific heat, magnetic susceptibility, neutron diffraction and muon-spin-relaxation measurements. The two compounds are found to be magnetically similar. They long-range order into structures described by the Gamma_5 irreducible representation. The magnitude of the magnetic moment at low temperature is 0.77 (1) and 0.62 (1) mu_B for X = S and Se, respectively. Persistent spin dynamics is present in the ordered states. The spontaneous field at the muon site is anomalously small, suggesting magnetic moment fragmentation. A double spin-flip tunneling relaxation mechanism is suggested in the cooperative paramagnetic state up to 10 K. The magnetic space groups into which magnetic moments of systems of corner-sharing regular tetrahedra order are provided for a number of insulating compounds characterized by null propagation wavevectors.
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