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# How ‘spin ice’ freezes

## Abstract

The large degeneracy of states resulting from the geometrical frustration of competing interactions is an essential ingredient of important problems in fields as diverse as magnetism1, protein folding2 and neural networks3. As first explained by Pauling4, geometrical frustration of proton positions is also responsible for the unusual low-temperature thermodynamics of ice and its measured ‘ground state’ entropy5. Recent work has shown that the geometrical frustration of ice is mimicked by Dy2Ti2O7, a site-ordered magnetic material in which the spins reside on a lattice of corner-sharing tetrahedra where they form an unusual magnetic ground state known as ‘spin ice’6,7,8,9,10,11,12,13. Here we identify a cooperative spin-freezing transition leading to the spin-ice ground state in Dy2Ti2O7. This transition is associated with a very narrow range of relaxation times, and represents a new form of spin-freezing. The dynamics are analogous to those associated with the freezing of protons in ice, and they provide a means through which to study glass-like behaviour and the consequences of frustration in the limit of low disorder.

## Relevant articles

• ### Evolution﻿ of spin freezing transition and structural, magnetic phase diagram of Dy$$_{2-\textit{x}}$$La$$_\textit{x}$$Zr$$_{2}$$O$$_{7}$$ (0 $$\le$$ $$\textit{x}$$ $$\le$$ 2.0)

Scientific Reports Open Access 06 October 2021

• ### Monopole matter from magnetoelastic coupling in the Ising pyrochlore

Communications Physics Open Access 19 March 2021

• ### Machine-learning-assisted insight into spin ice Dy2Ti2O7

Nature Communications Open Access 14 February 2020

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## References

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## Acknowledgements

We thank D.A. Huse, T. Rosenbaum and J. Banavar for discussions. This work was supported by the Army Research Office.

## Author information

Authors

### Corresponding author

Correspondence to P. Schiffer.

## Rights and permissions

Reprints and Permissions

Snyder, J., Slusky, J., Cava, R. et al. How ‘spin ice’ freezes. Nature 413, 48–51 (2001). https://doi.org/10.1038/35092516

• Accepted:

• Issue Date:

• DOI: https://doi.org/10.1038/35092516

• ### Monopole matter from magnetoelastic coupling in the Ising pyrochlore

• D. Slobinsky
• L. Pili
• R. A. Borzi

Communications Physics (2021)

• ### Evolution﻿ of spin freezing transition and structural, magnetic phase diagram of Dy$$_{2-\textit{x}}$$La$$_\textit{x}$$Zr$$_{2}$$O$$_{7}$$ (0 $$\le$$ $$\textit{x}$$ $$\le$$ 2.0)

• Sheetal

Scientific Reports (2021)

• ### Machine-learning-assisted insight into spin ice Dy2Ti2O7

• Anjana M. Samarakoon
• Kipton Barros
• D. Alan Tennant

Nature Communications (2020)

• ### Magnetodielectric Relaxation in Ho2Ti2O7 and Dy2Ti2O7 Spin Ice

Journal of Superconductivity and Novel Magnetism (2019)

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