We report thermodynamic measurements on the cooperative paramagnet Tb ₂Ti₂O₇ and the stuffed spin ices Ho₂(Ho _xTi_2-x)O_7-x/2 and Dy₂(Dy_xTi _2-x)O_7-x/2, where 0 ≤ x ≤ 0.67. For Tb₂Ti ₂O₇, AC susceptibility data taken down to T = 1.8 K and in applied magnetic fields up to H = 9 T show the expected saturation maximum in χ(T) and also an unexpected low frequency dependence (< 1 Hz) of this peak, suggesting very slow spin relaxations are occurring. Measurements on samples diluted with nonmagnetic Y³⁺ or Lu ³⁺ and complementary measurements on pure and diluted Dy₂Ti ₂O₇ strongly suggest that the relaxation is associated with dipolar spin correlations, representing unusual cooperative behavior in a paramagnetic system.

For the stuffed spin ices Ho₂(Ho_xTi_2-x)O _7-x/2 and Dy₂(Dy_xTi_2-x)O_7-x/2 , 0 ≤ x ≤ 0.67, magnetization data show an increasingly antiferromagnetic effective interaction with increased stuffing x, with Ising like single spin ground states. Although heat capacity measurements down to T = 0.4 K yield the expected residual entropy for x = 0, surprisingly, despite the changing magnetic interactions, the total entropy per spin in (Ho_xTi _2-x)O_7-x/2 remains at the spin ice value for all x, while the entropy per spin in Dy₂(Dy_xTi_2-x)O _7-x/2 approaches the Ising value of S = Rln2 for x ≥ 0.3. AC susceptibility measurements confirm different low temperature states in Ho_2.67Ti _1.33O_6.67 and Dy_2.67Ti_1.33O_6.67 , showing a disordered spin freezing in Ho_2.67Ti_1.33 O_6.67, and a partial freezing in Dy_2.67Ti _1.33O_6.67 coexisting with behavior seen in some cooperative paramagnets and spin liquids.