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Geometrically Frustrated Matter—Magnets to Molecules

Published online by Cambridge University Press:  31 January 2011

A. P. Ramirez
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Abstract

Geometric frustration occurs when a set of degrees of freedom is incompatible with the space it occupies. A purely geometric example is the impossibility of close-packing pentagons in two dimensions. Another simple example is atomic magnetic moments with antiferromagnetic interactions. These moments lower their interaction energy by pointing antiparallel to their neighbors, an arrangement incompatible with the occupation of a crystal lattice of triangular symmetry. Other manifestations of frustration occur in ice, glass, liquid crystals, and correlated metals. Because frustration governs the rules of packing, examples are also found in biological materials, as in the self-assembly of liposomes that form nanotubules. Geometric frustration is essentially “many-body” in nature: the basic concept is trivial on the scale of three particles, but complex and anharmonic for an Avogadro's number of particles. In fact, geometrically frustrated systems are so anharmonic that no general theoretical framework exists to explain their collective behavior. This article will explore the basic concepts of geometric frustration and illustrate these concepts with examples from magnetism, crystal structures, and molecular systems.

Keywords

complex adaptive matteremergent behaviorgeometric frustration

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Type
Research Article
Information
MRS Bulletin , Volume 30 , Issue 6: Complex Adaptive Matter: Emergent Phenomena in Materials , June 2005, pp. 447 - 451
Copyright
Copyright © Materials Research Society 2005

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References

1.Wannier, G.H., Phys. Rev. 79 (1950) p. 397.CrossRefGoogle Scholar
2.Houtappel, R.M.F., Physica 16 (1950) p. 425.CrossRefGoogle Scholar
3.Anderson, P.W., Phys. Rev. 102 (1956) p. 1008.CrossRefGoogle Scholar
4.Liebmann, R., Statistical Mechanics of Periodic Frustrated Ising Systems (Springer-Verlag, Berlin, 1986).Google Scholar
5.Binder, K. and Young, A.P., Rev. Mod. Phys. 58 (1986) p. 801.CrossRefGoogle Scholar
6.Mydosh, J.A., Spin Glasses (Taylor and Francis, London, 1993).Google Scholar
7.Obradors, X., Labarta, A., Isalgue, A., Tejada, J., Rodriguez, J., and Pernet, M., Solid State Commun. 65 (1988) p. 189.Google Scholar
8.Ramirez, A.P., Espinosa, G.P., and Cooper, A.S., Phys. Rev. Lett. 64 (1990) p. 2070.Google Scholar
9.Ramirez, A.P., Annu. Rev. Mater. Sci. 24 (1994) p. 453.CrossRefGoogle Scholar
10.Schiffer, P. and Ramirez, A.P., Comments Condens. Mat. Phys. 18 (1996) p. 21.Google Scholar
11.Greedan, J.E., Sato, M., Yan, X., Razavi, F.S., Solid State Commun. 59 (1986) p. 895.CrossRefGoogle Scholar
12.Ramirez, A.P., in Handbook of Magnetic Materials Vol. 13 (Elsevier, Amsterdam, 2001) p. 423.Google Scholar
13.Moessner, R. and Chalker, J.T., Phys. Rev. B 58 (1998) p. 12049.CrossRefGoogle Scholar
14.Broholm, C., Aeppli, G., Espinosa, G.P., and Cooper, A.S., Phys. Rev. Lett. 65 (1990) p. 3173.Google Scholar
15.Sindzingre, P., Misguich, G., Lhuillier, C., Bernu, B., Pierre, L., Waldtmann, Ch., and Everts, H.U., Phys. Rev. Lett. 84 (2000) p. 2953.CrossRefGoogle Scholar
16.Lee, S.H., Broholm, C., Ratcliff, W., Gasparovic, G., Huang, Q., Kim, T.H., and Cheong, S.W., Nature 418 (2002) p. 856.Google Scholar
17.Pauling, L.C., The Nature of the Chemical Bond (Cornell University Press, Ithaca, NY, 1945).Google Scholar
18.Harris, M.J., Bramwell, S.T., McMorrow, D.F., Zeiske, T., and Godfrey, K.W., Phys. Rev. Lett. 79 (1997) p. 2554.CrossRefGoogle Scholar
19.Bramwell, S.T. and Gingras, M.J.P., Science 294 (2001) p. 1495.CrossRefGoogle Scholar
20.Ramirez, A.P., Hayashi, A., Cava, R.J., Siddharthan, R., and Shastry, B.S., Nature 399 (1999) p. 333.Google Scholar
21.Schiffer, P., Ramirez, A.P., Huse, D.A., and Valentino, A.J., Phys. Rev. Lett. 73 (1994) p. 2500.Google Scholar
22.Snyder, J., Ueland, B.G., Slusky, J.S., Karunadasa, H., Cava, R.J., Mizel, A., and Schiffer, P., Phys. Rev. Lett. 91 107201(2003).CrossRefGoogle Scholar
23.den Hertog, B.C. and Gingras, M.J.P., Phys. Rev. Lett. 84 (2000) p. 3430.CrossRefGoogle Scholar
24.Mary, T.A., Evans, J.S.O., Vogt, T., and Sleight, A.W., Science 272 (1996) p. 90.CrossRefGoogle Scholar
25.Dove, M.T., Heine, V., and Hammonds, K.D., Mineral. Mag. 59 (1995) p. 629.CrossRefGoogle Scholar
26.Ernst, G., Broholm, C., Kowach, G.R., and Ramirez, A.P., Nature 396 (1998) p. 147.CrossRefGoogle Scholar
27.Handcock, J.N., Turpen, C., Schlesinger, Z., Kowach, G.R., and Ramirez, A.P., Phys. Rev. Lett. 93 225501(2004).Google Scholar
28.Kumar, B. and Shastry, B.S., Phys. Rev. B 68 (2003).Google Scholar
29.Wang, Y.Y., Rogado, N.S., Cava, R.J., and Ong, N.P., Nature 423 (2003) p. 425.Google Scholar
30.Kondo, S., Johnston, D.C., Swenson, C.A., Borsa, F., Mahajan, A.V., Miller, L.L., Gu, T., Goldman, A.I., Maple, M.B., Gajewski, D.A., Freeman, E.J., Dilley, N.R., Dickey, R.P., Merrin, J., Kojima, K., Luke, G.M., Uemura, Y.J., Chmaissem, O., and Jorgensen, J.D., Phys. Rev. Lett. 78 (1997) p. 3729.CrossRefGoogle Scholar
31.Urano, C., Nohara, M., Kondo, S., Sakai, F., Takagi, H., Shiraki, T., and Okubo, T., Phys. Rev. Lett. 85 (2000) p. 1052.CrossRefGoogle Scholar
32.Kimura, T., Goto, T., Shintani, H., Ishizaka, K., Arima, T., and Tokura, Y., Nature 426 (2003) p. 55.CrossRefGoogle Scholar
33.Hemberger, J., Lunkenheimer, P, Fichtl, R., von Nidda, H.A.K., Tsurkan, V., and Loidl, A., Nature 434 (2005) p. 364.Google Scholar
34.Meiboom, S. and Sammon, M., Phys. Rev. Lett. 44 (1980) p. 882.CrossRefGoogle Scholar
35.Nelson, D.R., Phys. Rev. B 28 (1983) p. 5515.CrossRefGoogle Scholar
36.Wong, G.C.L., Tang, J.X., Lin, A., Li, Y.L., Janmey, P.A., and Safinya, C.R., Science 288 (2000) p. 2035.CrossRefGoogle Scholar