The discovery of the spin-ice phase in Dy 2 Ti 2 O 7 numbers among the most significant findings in magnetic materials in over a decade 1-3. Spin ice has since been associated with the manifestation of magnetic monopoles 4,5 and may even inform our understanding of emergent quantum electrodynamics 6. The spin-ice model is based on an elegant analogy to Pauling's model of geometrical frustration in water ice, and predicts the same residual entropy, as confirmed by numerous measurements 1,2,7-11. Here we present results for the specific heat of Dy 2 Ti 2 O 7 , demonstrating why previous measurements were unable to correctly capture its lowtemperature behaviour. By carefully tracking the flow of heat into and out of the material, we observe a non-vanishing specific heat that has not previously been detected. This behaviour is confirmed in two samples of Dy 2 Ti 2 O 7 , in which cooling below 0.6 K reveals a deviation from Pauling's residual entropy, calling into question the true magnetic ground state of spin ice. Although the simple spin-ice model does account for most observed properties of the pyrochlore oxides Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , unsolved puzzles remain. Simulations have demonstrated that longrange dipolar interactions should lift the degeneracy of the spin-ice manifold of states, and give rise to a unique, ordered ground state 12. The Melko-den Hertog-Gingras (MDG) phase (Fig. 1) was the first theoretical prediction of an ordered state in spin ice; discovered through a numerical loop algorithm 12,13. So far, however, experimental work has been unsuccessful in observing the MDG phase, concluding that the large energy barrier for fluctuations out of the ice-rules manifold does not allow ordering to occur 2,8-11. Recent low-temperature measurements have determined that the spin relaxation time markedly increases as temperature is lowered. For example, magnetization 14,15 and a.c.-susceptibility 16 measurements show that the spin relaxation time in Dy 2 Ti 2 O 7 is greater than 10 4 s below 0.45 K. Ref. 16 also reported Arrhenius behaviour with a barrier to relaxation of 9.79 K, much larger than the cost of a single spin flip of 4J eff = 4.44 K, where J eff is the nearestneighbour effective exchange energy 17. This difference could be due to monopole effects 15 , or many-body phenomena such as screening, but remains as a major open question 18-21. Consequently, we would expect that thermal relaxation is dominated by this slow magnetic system in the spin-ice regime. These spin dynamics motivated us to re-measure the specific heat in a way that allows for extremely slow thermal equilibration.

The pyrochlore material Yb2Ti2O7 displays unexpected quasi-two-dimensional (2D) magnetic correlations within a cubic lattice environment at low temperatures, before entering an exotic disordered ground state below T=265mK. We report neutron scattering measurements of the thermal evolution of the 2D spin correlations in space and time. Short range three dimensional (3D) spin correlations develop below 400 mK, accompanied by a suppression in the quasi-elastic (QE) scattering below ∼ 0.2 meV. These show a slowly fluctuating ground state with spins correlated over short distances within a kagome-triangular-kagome (KTK) stack along [111], which evolves to isolated kagome spin-stars at higher temperatures. Furthermore, low-temperature specific heat results indicate a sample dependence to the putative transition temperature that is bounded by 265mK, which we discuss in the context of recent mean field theoretical analysis.

Low-temperature magnetic ac susceptibility measurements of single-crystal dipolar spin ice Dy 2 Ti 2 O 7 are presented. The relaxation is found to exhibit thermally activated Arrhenius behavior with an activation energy of 9.79 K (∼9J eff), which is not consistent with a simple scaling of 6J eff , as previously found for Ho 2 Ti 2 O 7. There are distinct quantifiable differences between Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 absorption spectra. The measured dynamics does not agree with simulations based on current magnetic monopole theory nor thermal relaxation measurements, but instead freezes out at a faster rate.

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