Geometrical frustration is a condition that occurs when a material’s lattice geometry precludes minimizing the energy of all the interactions among pairs of neighbors simultaneously. The simplest example is three antiferromagnetically coupled Ising spins, pointing up or down, on the corners of an equilateral triangle: It is impossible to arrange the spins so that each pair is antiparallel. In more complex magnetic lattices, the frustrated state can arise from the combination of lattice geometry and the strength and sign of the interactions among the magnetic dipole moments.1 (See the article by Roderich Moessner and Art Ramirez, Physics Today, February 2006, page 24.) A wide variety of exotic and collective phenomena sometimes arises from the competing interactions. A prime example is spin liquids, materials in which the local atomic moments fluctuate down to the lowest accessible temperatures and never settle into a static ground-state configuration.
Among the most...
