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.

Some frustrated pyrochlore antiferromagnets, such as Y2Mo2O7, show a spin-freezing transition and magnetic irreversibilities below a temperature T f similar to what is observed in randomly frustrated spin glasses. We present results of DC nonlinear magnetization measurements on Y2Mo2O7 that provide strong evidence that there is an underlying thermodynamic phase transition at T f , which is characterized by critical exponents γ ≈ 2.8 and β ≈ 0.8. These values are typical of those found in random spin glasses, despite the fact that the level of random disorder in Y2Mo2O7 is immeasurably small. The past five years have seen a resurgence of significant interest devoted to the systematic study of geometrically frustrated antiferromagnets [1][2][3][4]. Geometric frustration arises in materials containing antiferromagneticallycoupled magnetic moments which reside on geometrical units, such as triangles and tetrahedra, that inhibit the formation of a collinear magnetically-ordered state. The main motivation for the current interest in these systems stems from suggestions that (i) they may display critical phenomena belonging to a "new" chiral universality class different from the universality classes of collinear magnets [2,4], or (ii) the increased propensity of frustrated antiferromagnets for quantum zero-temperature spin fluctuations compared to collinear antiferromagnets might be sufficient to destroy Néel order and drive these systems into novel non-classical quantum disordered ground states [2,3].Systems of classical Heisenberg spins residing on lattices of corner-sharing triangles or tetrahedra and antiferromagnetically coupled via nearest-neighbor exchange constitute particularly interesting cases of highly frustrated antiferromagnets (see Fig. 1). Here, theory [5,6] and numerical work [7], show that these systems do not order and remain in a "collective paramagnetic state" [5] down to zero temperature. Since, even for classical spins, these systems have such a small tendency to order, they are excellent candidates to display exotic quantum disordered ground states [2,3,8]. However, and perhaps most interestingly, experiments show that some nominally perfect (i.e. disorder-free) [9] pyrochlore antiferromagnets [10] exhibit a spin-freezing transition at some temperature T f , below which they develop magnetic irreversibilities (see Fig. 1) and long-time magnetic relaxation similar to what is found in conventional randomly frustrated spin glasses such as CuMn, EuSrS, and CdMnTe [11].

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.