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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.

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Figure 1: Schematic representation of frustration in water ice and spin ice.
Figure 2: Temperature dependence of the magnetic susceptibility in the absence of a d.c. magnetic field.
Figure 3: Real part of the a.c. magnetic susceptibility of Dy2Ti2O7 versus temperature for several different fields at 100 Hz.
Figure 4: The imaginary part of the magnetic susceptibility scaled to peak amplitude and frequency for Dy2Ti2O7 at several temperatures and in the absence of a d.c. magnetic field.
Figure 5: The real part of the a.c. magnetic susceptibility of Dy2-xYxTi2O7 as a function of temperature in the absence of a d.c. magnetic field.

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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.

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Correspondence to P. Schiffer.

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

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