Zero-point entropy in 'spin ice'

Common water ice (ice I-h) is an unusual solid-the oxygen atoms form a peri odic structure but the hydrogen atoms are highly disordered due to there be ing two inequivalent O-H bond lengths'. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible groun d states(2,3), such that the system has finite entropy as the temperature t ends towards zero. The dynamics associated with this degeneracy are experim entally inaccessible, however, as ice melts and the hydrogen dynamics canno t be studied independently of oxygen motion(4). An analogous system(5) in w hich this degeneracy can be studied is a magnet with the pyrochlore structu re-termed 'spin ice'-where spin orientation plays a similar role to that of the hydrogen position in ice I-h. Here we present specific-heat data for o ne such system, Dy2Ti2O7, from which we infer a total spin entropy of 0.67R ln2. This is similar to the value, 0.71Rln2, determined for ice I-h, SO con firming the validity of the correspondence. We also find, through applicati on of a magnetic field, behaviour not accessible in water ice-restoration o f much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.