Pauling entropy, metastability and equilibrium in Dy$_2$Ti$_2$O$_7$ spin ice

TL;DR

This study investigates the fate of Pauling entropy in Dy$_2$Ti$_2$O$_7$ spin ice, using neutron scattering and specific heat measurements, finding no evidence of entropy recovery or deviation from the dipolar spin ice model predictions.

Contribution

The paper provides experimental and simulation evidence that the Pauling entropy in Dy$_2$Ti$_2$O$_7$ remains stable at low temperatures, supporting the dipolar spin ice model and validating previous entropy measurements.

Findings

No entropy reduction observed at low temperatures.

Spin correlations remain consistent with the dipolar spin ice model.

Original entropy measurements are validated as accurate.

Abstract

Determining the fate of the Pauling entropy in the classical spin ice material Dy$_2$Ti$_2$O$_7$ with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice - the dipolar spin ice model - predicts an ordering transition at $T\approx 0.15$ K, but recent experiments by Pomaranski $et\ al.$ suggest an entropy recovery over long time scales at temperatures as high as $0.5$ K, much too high to be compatible with theory. Using neutron scattering and specific heat measurements at low temperatures and with long time scales ($0.35$ K$/10^6$ s and $0.5$ K$/10^5$ s respectively) on several isotopically enriched samples we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Further, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez $et\ al.$ are, after all, essentially correct: the short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions.