Zero-point entropy in stuffed spin-ice

The third law of thermodynamics dictates that the entropy of a system in thermal equilibrium goes to zero as its temperature approaches absolute zero. In ice, however, a ‘zero point’ or residual entropy can be measured—attributable to a high degeneracy in the energetically preferred positions of hydrogen ions associated with the so-called ‘ice rules’1,2. Remarkably, the spins in certain magnetic materials with the pyrochlore structure of corner-sharing tetrahedra, called ‘spin ice’, have an equivalent degeneracy of energetically preferred states, and also have a zero-point entropy3,4,5,6,7. Here, we chemically alter Ho2Ti2O7 spin ice by ‘stuffing’ extra Ho magnetic moments into otherwise non-magnetic Ti sites surrounding the Ho tetrahedra. The resulting series, Ho2(Ti2−xHox)O7−x/2, provides a unique opportunity to study the effects of increased connectivity between spins on a frustrated lattice. Surprisingly, the zero-point entropy per spin measured appears unchanged by these excess spins. The results suggest a chemical approach for studying ice-like frustration and other properties of the broad family of geometrically frustrated magnets based on the pyrochlore structure.