Spin ice
From Wikipedia, the free encyclopedia
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.
In 1935, Linus Pauling noted that the structure of ice (i.e. the solid phase of water), exhibited degrees of freedom that would be expected to exist even at absolute zero. That is, even upon cooling to absolute zero, water ice is expected to have residual entropy (i.e. intrinsic randomness). This is a result of the fact that the structure of ice contains oxygen atoms with four neighboring hydrogen atoms. For each oxygen atom, two of the neighboring hydrogen atoms are near (forming the traditional H2O molecule), and two are further away (being the hydrogen atoms of neighboring water molecules). What Pauling noted was that the number of configurations that conformed to this "two-in two-out" rule was non-trivial, and therefore that the entropy of ice was expected to be non-trivial. [1]
Pauling's findings were confirmed by experiment, though pure crystals of water ice are particularly hard to create.
Spin ices are materials consisting of tetrahedra of ions, each of which has a non-zero spin, 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 [2] 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. [3] 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 measurements find evidence for a dynamical freezing of the magnetic moments as the temperature is 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 ices are frustrated ferromagnets. It is the local nature of the strong crystal field forcing the magnetic moments to point either in or out of a tetrahedron that renders ferromagnetic interactions frustrated in spin ices. Interestingly, it is the long range magnetic dipolar interaction and not 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. [4] [5]
[edit] References
- ^ 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).
- ^ P.W. Anderson, Phys. Rev., Vol. 102, p. 1008 (1956).
- ^ M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske and K. W. Godfrey, Phys. Rev. Lett., Vol. 79, p. 2554 (1997).
- ^ 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).
