Geometrical Frustration - Spin Ice

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.

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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)

    “The room’s very hot, with all this crowd,” the Professor said to Sylvie. “I wonder why they don’t put some lumps of ice in the grate? You fill it with lumps of coal in the winter, you know, and you sit round it and enjoy the warmth. How jolly it would be to fill it now with lumps of ice, and sit round it and enjoy the coolth!”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)