Spin ice cream
Under spin ice are materials in which the magnetic moments in the material similar to the protons in water ice behave.
In 1935 Linus Pauling determined that the structure of ice (i.e. the solid phase of water ) has degrees of freedom that should also exist at absolute zero . This means that a residual entropy (i.e. an intrinsic disorder) remains even when it cools down to absolute zero . This is a consequence of the fact that ice contains oxygen atoms with four neighboring hydrogen atoms . For each oxygen atom, two hydrogen atoms are closer (these form the traditional H 2 O molecule ) and two further away (these correspond to hydrogen atoms of molecules further away). Pauling found that the configuration that corresponds to this “two-near-two-far rule” is nontrivial and consequently also has nontrivial entropy. This is an example of geometric frustration .
Pauling's considerations have been verified experimentally, even if pure water ice crystals are difficult to produce.
In spin ice, there are tetrahedra made up of ions , all of which have non-zero spin . Due to the interactions between neighboring ions, these must also comply with a “two-near-two-far rule” analogous to the case of ice discussed above. Spin ice therefore shows the same residual entropies as water ice. Depending on the materials used for the spin ice, large, individual crystals are easier to produce than pure water ice crystals in this case. In addition, the interaction of the ion spins with a magnetic field ensures that these materials are better suited for studying the residual entropies.
While Philip Anderson recognized the connection between the frustrated Ising antiferromagnet on a tetrahedral lattice made of pyrochlore and Pauling's water ice problem as early as 1956, real spin ice materials were only discovered in 1997. The first materials identified as spin ice were the pyrochlores Ho 2 Ti 2 O 7 , Dy 2 Ti 2 O 7 and Ho 2 Sn 2 O 7 . Furthermore, clear indications were published that Dy 2 Sn 2 O 7 is also a spin ice.
Spin ice is characterized by a disorder of the magnetic ions even at very low temperatures. Measurements of the dynamic magnetic susceptibility provide evidence of a dynamic freezing of the magnetic moments below temperatures at which the specific heat has a maximum.
Spin-ice materials are frustrated magnetic systems. While frustration is usually associated with triangular or tetrahedral arrangements of magnetic moments coupled through antiferromagnetic exchange interactions, spin-ice materials are more complicated: they are frustrated ferromagnets . The locally acting, strong crystal field forces the magnetic moments in either the tetrahedral into or out of the tetrahedron addition to show what a antiferromagnetically interacting frustrated "exchange" system is equivalent. In reality, however, there is no antiferromagnetic interaction at all, rather the long-range magnetic dipole interactions are responsible for the frustration, and not the exchange interactions of the closest neighbors. The “two-in-two-out spin orientation” and thus the spin-ice state results from the frustration.
In 2008, magnetic quasi-monopoles were detected and measured for the first time in spin ice . They are sources of magnetization , but not magnetic flux ; this is still divergence-free.
Individual evidence
- ↑ 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).
- ↑ PW Anderson, Phys. Rev., Vol. 102 , p. 1008 (1956).
- ^ MJ Harris, ST Bramwell, DF McMorrow, T. Zeiske and KW Godfrey, Phys. Rev. Lett., Vol. 79 , p. 2554 (1997).
- ^ BC den Hertog and MJP Gingras, Phys. Rev. Lett., Vol. 84 , p. 3430 (2000).
- ^ SV Isakov, R. Moessner and SL Sondhi, Phys. Rev. Lett., Vol. 95 , p. 217201 (2005).
- ↑ R. Scharf, Magnetic Monopoles sighted in Spineis , Pro-Physik.de, September 4, 2009, accessed on October 23, 2009.
- ↑ M. Vojta, Frustriert zum Monopol, published in the Physik Journal November 2009, p. 22