Geometrically Frustrated Matter - Magnets to Molecules

Geometric frustration is a concept underlying many mysterious materials phenomena. Frustration and its various manifestations occur in ice, glass, liquid crystals, correlated metals, and antiferromagnets. Because frustration governs 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 immensely complex and anharmonic for Avogadro's number of particles. In fact, geometrically frustrated systems are so anharmonic that no theoretical framework exists to explain their collective behavior. Yet the states of matter that emerge from geometric frustration are so familiar that they transform a system indeed we will show an example of a liquid existing on a solid lattice. This article will explore the basic concepts of geometric frustration and illustrate these concepts with examples from magnetism, crystal structures, and molecular systems.