Spin ice

A spin ice is a material where the behavior of the magnetic moments in the material is analogous to the behavior of the protons in water ice.

of ice was expected to be non-trivial. [L. Pauling, "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society, Vol. 57, p. 2680 (1935).]

Pauling's findings were confirmed by experiment, though pure crystals of water ice are particularly hard to create.

, which must satisfy some two-in, two-out rule analogous to water ice because of the interactions between neighbouring ions. Spin ice materials therefore exhibit the same residual entropy properties as water ice. However, depending on the material used in a spin ice, it is generally much easier to create large single crystals of spin ice materials than the corresponding water ice materials. Additionally, the interaction of a magnetic field with the spins in a spin ice material make spin ice materials much better materials for examining residual entropy than water ice.

While Philip Anderson had already noted in 1956 [P.W. Anderson, Phys. Rev., Vol. 102, p. 1008 (1956).] the connection between the problem of the frustrated Ising antiferromagnet on a (pyrochlore) lattice of corner-shared tetrahedra and Pauling's water ice problem,real spin ice materials were only discovered quite recently. [M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske and K. W. Godfrey, Phys. Rev. Lett., Vol. 79, p. 2554 (1997).] The first materials identified as spin ices were the pyrochlores Ho₂Ti₂O₇,
Dy₂Ti₂O₇, and Ho₂Sn₂O₇. Very recently, compelling evidence has been reported that Dy₂Sn₂O₇ is also a spin ice.

Spin ice materials are characterized by disorder of magnetic ions even when said ions are at very low temperatures. AC
magnetic susceptibility measurementsfind evidence for a dynamical freezing of the magnetic moments as the temperatureis lowered somewhat below the temperature at which the specific heat displays a maximum.

Spin ices are frustrated magnetic systems. While frustration is usually associated with triangular or tetrahedral arrangements of magnetic moments coupled via antiferromagnetic exchange interactions, spin icesare frustrated ferromagnets. It is the local nature of the strong crystal field forcingthe magnetic moments to point either in or out of a tetrahedron that renders ferromagneticinteractions frustrated in spin ices. Interestingly, it is the long range magnetic dipolar interaction andnot nearest-neighbor exchange coupling that causes the frustration and the consequential"two-in two-out" spin orientations and which lead to the spin ice phenomenology. [B. C. den Hertog and M. J. P. Gingras, Phys. Rev. Lett., Vol. 84, p. 3430 (2000).] [S. V. Isakov, R. Moessner and S. L. Sondhi, Phys. Rev. Lett., Vol. 95, p. 217201 (2005).]

References

See also

* Geometrically frustrated magnet
* Spin glass