Spin ice

A spin ice is a magnetic substance that does not have a single minimal-energy state. It has magnetic moments (i.e. "spin") as elementary degrees of freedom which are subject to frustrated interactions. By their nature, these interactions prevent the moments from exhibiting a periodic pattern in their orientation down to a temperature much below the energy scale set by the said interactions. Spin ices show low-temperature properties, residual entropy in particular, closely related to those of common crystalline water ice. The most prominent compounds with such properties are dysprosium titanate (Dy₂Ti₂O₇) and holmium titanate (Ho₂Ti₂O₇). The orientation of the magnetic moments in spin ice resembles the positional organization of hydrogen atoms (more accurately, ionized hydrogen, or protons) in conventional water ice (see Figure 1).

Experiments have found evidence for the existence of deconfined magnetic monopoles in these materials, with properties reminding that of the hypothetical magnetic monopoles postulated to exist in vacuum.

In 1935, Linus Pauling noted that the hydrogen atoms in water ice 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 due to the fact that the hexagonal crystalline structure of common water ice contains oxygen atoms with four neighboring hydrogen atoms. In ice, 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 two neighboring water molecules). Pauling noted that the number of configurations conforming to this "two-near, two-far" ice rule grows exponentially with the system size, and, therefore, that the zero-temperature entropy of ice was expected to be extensive. Pauling's findings were confirmed by specific heat measurements, though pure crystals of water ice are particularly hard to create.

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