Zero-point entropy in ‘spin ice’

Common water ice (ice Ih) is an unusual solid—the oxygen atoms form a periodic structure but the hydrogen atoms are highly disordered due to there being two inequivalent O–H bond lengths1. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible ground states2,3, such that the system has finite entropy as the temperature tends towards zero. The dynamics associated with this degeneracy are experimentally inaccessible, however, as ice melts and the hydrogen dynamics cannot be studied independently of oxygen motion4. An analogous system5 in which this degeneracy can be studied is a magnet with the pyrochlore structure—termed ‘spin ice’—where spin orientation plays a similar role to that of the hydrogen position in ice Ih. Here we present specific-heat data forone such system, Dy2Ti2O7, from which we infer a total spinentropy of 0.67R ln2. This is similar to the value, 0.71R ln2, determined for ice Ih, so confirming the validity of the correspondence. We also find, through application of a magnetic field, behaviour not accessible in water ice—restoration of much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.