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Condensed-matter physics

Taking the frustration out of ice

Nature volume 399, pages 311–312 (1999)Cite this article

Ferromagnetism — the ability of solids such as iron to be magnetized permanently — is the most familiar manifestation of magnetic order. It arises from a spontaneous alignment of the atomic magnetic dipoles (spins), driven by magnetic interactions between the atoms. But some magnetic solids display far more spectacular consequences of these interactions, particularly those that are geometrically frustrated. Put simply, this is the inability of magnets with certain crystal structures to attain magnetic order, solely by virtue of the geometrical arrangement of the magnetic atoms. The resulting behaviour is complex and rich in subtleties, pushing at the boundaries of our understanding of what constitutes crystalline order. It has implications far beyond magnetism — uniting many diverse problems, from the origin of freezing and glassiness to neural networks. Indeed, high-temperature superconductivity is believed by some to be due to a kind of frustrated magnetic state1. But progress in the field has been slow, hampered by the experimental difficulties of isolating the frustration from other perturbations, such as defects, which are present in all real materials. On page 333 of this issue, Ramirez and co-workers2 present convincing evidence that the pyrochlore compound Dy2Ti2O7corresponds to a new class of frustrated magnet called ‘spin ice’, which appears to be the cleanest laboratory yet for studying frustration.

It was discovered that anisotropy (a further constraint on each spin's alignment, and present to varying degrees in all magnetic materials) changes the accepted picture of frustration3, and in some cases turns it completely on its head. That is, even with the pyrochlore lattice, antiferromagnetic interactions can become unfrustrated and produce a conventionally ordered magnet, whereas ferromagnetic interactions can become strongly frustrated. This anisotropy is particularly strong in pyrochlores where the magnetic atom is a rare earth, notably Ho (holmium) and Dy (dysprosium). Here the anisotropy constrains each spin to point either directly into or away from the centre of each tetrahedron. With ferromagnetic interactions, the four spins on each tetrahedron align so that there are two pointing in and two out. One of the six possible ways of achieving this on a tetrahedron is shown in Fig. 1d. When tetrahedra are linked to form a pyrochlore lattice, the large number of ways of satisfying the ‘two spins in, two spins out’ rule means that no single, ordered pattern is more favourable than any other. This is another definition of frustration. In fact, it can be shown4 that such a lattice is every bit as frustrated as any possible antiferromagnet, which came as a big surprise to those who had always blithely assumed that ferromagnetism had no surprises left.

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Figure 1: Three common crystal- structure building blocks (square, triangle and tetrahedron).

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  1. the ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, Oxfordshire, UK

    Mark Harris

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Harris, M. Taking the frustration out of ice. Nature 399, 311–312 (1999). https://doi.org/10.1038/20562

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