Spin Ice
A mathematically analogous situation to the degeneracy in water ice is found in the spin ices. A common spin ice structure is shown in Figure 6 in the cubic pyrochlore structure with one magnetic atom or ion residing on each of the four corners. Due to the strong crystal field in the material, each of the magnetic ions can be represented by an Ising ground state doublet with a large moment. This suggests a picture of Ising spins residing on the corner-sharing tetrahedral lattice with spins fixed along the local quantization axis, the <111> cubic axes, which coincide with the lines connecting each tetrahedral vertex to the center. Every tetrahedral cell must have two spins pointing in and two pointing out in order to minimize the energy. Currently the spin ice model has been approximately realized by real materials, most notably the rare earth pyrochlores Ho2Ti2O7, Dy2Ti2O7, and Ho2Sn2O7. These materials all show nonzero residual entropy at low temperature.
Read more about this topic: Geometrical Frustration
Famous quotes containing the words spin and/or ice:
“In tragic life, God wot,
No villain need be! Passions spin the plot:
We are betrayed by what is false within.”
—George Meredith (1828–1909)
“I also heard the whooping of the ice in the pond, my great bed-fellow in that part of Concord, as if it were restless in its bed and would fain turn over, were troubled with flatulency and bad dreams; or I was waked by the cracking of the ground by the frost, as if some one had driven a team against my door, and in the morning would find a crack in the earth a quarter of a mile long and a third of an inch wide.”
—Henry David Thoreau (1817–1862)