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.

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7 and show that it decays with a stretched exponential followed by a very slow long-time tail. In a Monte Carlo simulation governed by Metropolis dynamics we show that surface effects and a very low level of stuffed spins (0.30%)-magnetic Dy ions substituted for non-magnetic Ti ions-cause these signatures in the relaxation. In addition, we find evidence that the rapidly diverging experimental timescale is due to a temperature-dependent attempt rate proportional to the monopole density.The exceptional physical properties of the spin-ice materials arise from the underlying pyrochlore lattice of corner-sharing tetrahedra and crystal-field effects, which constrain the magnetic moments of the rare-earth ions to point along the axis connecting the centres of the two neighbouring tetrahedra 1 . As a result, the spin-ice materials are highly frustrated and possess a ground state containing a large residual entropy similar to water ice 2 . The thermodynamic properties of the spin-ice materials have been very successfully modelled by the Hamiltonian for Ising spins interacting through dipolar and exchange interactions 3,4 ,where r nn = 3.5 Å, D = 1.41 K and J = 3.72 K, and the moments S, of unit length, are forced to point along the local 111 axes. Recently, it was realized that the fundamental excitations are magnetic charges, commonly referred to as monopoles 5,6 that are created by overturning a spin in the highly degenerate spin-ice ground state, where two spins point in and two point out of each tetrahedron. The motion of magnetic monopoles has been observed experimentally through the generation of monopole currents by the application of a magnetic field 7 , and muon spin rotation 8 , which is a subject of recent controversy 9 . Monte Carlo simulations of a Coulomb gas of monopoles 10 and the dipolar spin-ice model 11 , equation (1), agree well with experimental results down to 1 K, below which the observed dynamics become much slower in the experiments than in the simulations [11][12][13][14][15][16][17] . In this study we find that significant corrections to the ideal model in equation (1) are necessary to accurately model the motion of magnetic monopoles in the real material. Similarly to electrical conductors and semiconductors, in which local impurities can decrease the conductivity, or introduce new states in the bandgap, we find that a small amount of extra spins and surface effects change the flow of magnetic monopoles. Experimental access to the properties of the magnetic monopoles is provided through the dynamic correlation function C(t ) = M (0)M (t ) , where M (t ) is the time-dependent magnetization of the sample. To study these excitations we therefore scrutinize the low-temperature dynamics of Dy 2 Ti 2 O 7 . In particular, we measure C(t ) by two independent methods using custom designed superconducting quantum interference device (SQUID) circuits. In the direct field-quench measurement we apply a small field of 5 mOe to the sample and directly observe the decay of the magnetization. In the second met...

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.