A spin ice is a substance that does not have a single minimal-energy state. It has "spin" degrees of freedom (i.e., it is a magnet), with frustrated interactions which prevent it from completely freezing. Spin ices show low-temperature properties – in particular residual entropy – closely related to those of crystalline water ice.1 The most prominent compounds with such properties are dysprosium titanate and holmium titanate. The magnetic ordering of a spin ice resembles the positional ordering of hydrogen atoms in conventional water ice.
Recent experiments have found evidence for the existence of deconfined magnetic monopoles in these materials,23 with analogous properties to the hypothetical magnetic monopoles postulated to exist in the vacuum.
In 1935, Linus Pauling noted that the structure of water ice exhibited degrees of freedom that would be expected to remain disordered even at absolute zero. That is, even upon cooling to zero temperature, 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). Pauling noted that the number of configurations conforming to this "two-in two-out" rule grows exponentially with the system size, and therefore that the zero-temperature entropy of ice was expected to be extensive.4 Pauling's findings were confirmed by specific heat measurements, though pure crystals of water ice are particularly hard to create.citation needed
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 19565 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.6 The first materials identified as spin ices were the pyrochlores Dy2Ti2O7 (dysprosium titanate), Ho2Ti2O7 (holmium titanate) and Ho2Sn2O7 (holmium stannate). Very recently, compelling evidence has been reported that Dy2Sn2O7 (dysprosium stannate) is also a spin ice.citation needed
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 geometrically 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 the nearest-neighbor exchange coupling that causes the frustration and the consequential "two-in two-out" spin orientations and which leads to the spin ice phenomenology.78
In September 2009, researchers described the observation of quasiparticles resembling monopoles.2 A single crystal of dysprosium titanate in a highly frustrated pyrochlore lattice (Fd3m) was cooled to 0.6 to 2 K. Using neutron scattering, the magnetic moments were shown to align in the spin ice into interwoven tube-like bundles resembling Dirac strings. At the defect formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the heat capacity of the system from an effective gas of these quasiparticles is also described.910
The effective charge of a magnetic monopole in a spin ice has been measured as 5 μB·Å−1 (Bohr magnetons per angstrom).11 The elementary constituents of spin ice are magnetic dipoles, so the emergence of monopoles is an example of the phenomenon of fractionalization.
- Bramwell, S. T.; Gingras, M. J. P. (2001), "Spin Ice State in Frustrated Magnetic Pyrochlore Materials", Science 294 (5546): 1495–1501, arXiv:cond-mat/0201427, Bibcode:2001Sci...294.1495B, doi:10.1126/science.1064761
- "'Magnetricity' Observed And Measured For First Time". Science Daily. 2009-10-15. Retrieved 2010-06-10.
- Gingras, M.J.P. (2009), "Observing Monopoles in a Magnetic Analog of Ice", Science 326 (5951): 375–376, doi:10.1126/science.1181510
- 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).
- "Magnetic Monopoles Detected In A Real Magnet For The First Time". Science Daily. 2009-09-04. Retrieved 2009-09-04.
- D.J.P. Morris, D.A. Tennant, S.A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, K.C. Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, and R.S. Perry (2009-09-03). "Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7". Science 326 (5951): 411–4. arXiv:1011.1174. Bibcode:2009Sci...326..411M. doi:10.1126/science.1178868. PMID 19729617.
- "Measurement of the charge and current of magnetic monopoles in spin ice". Nature.