Geometric frustration occurs to (Ba,Sr)TiO3 ferroelectrics

Both BT and ST are old systems and a lot, but still much to be unveiled, has been learned about their lattice dynamics. However, exotic phenomena might happen when these two compounds are mixed compositionally. According to this ab initio study [Nature, 470:513(2011)], some geometric frustration has been spotted in this BST system. And this gives rise to a number of new phases such as stripes. What this story suggests is that, much more can be lavished about these common systems, and only imagination can limit.

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry^{1, 2, 3, 4, 5, 6, 7}. Geometric frustration gives rise to new fundamental phenomena and is known to yield intriguing effects such as the formation of exotic states like spin ice, spin liquids and spin glasses^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. It has also led to interesting findings of fractional charge quantization and magnetic monopoles^{5, 6}. Mechanisms related to geometric frustration have been proposed to understand the origins of relaxor and multiferroic behaviour, colossal magnetocapacitive coupling, and unusual and novel mechanisms of high-transition-temperature superconductivity^{3, 4, 5, 12, 16}. Although geometric frustration has been particularly well studied in magnetic systems in the past 20 years or so, its manifestation in the important class formed by ferroelectric materials (which are compounds with electric rather than magnetic dipoles) is basically unknown. Here we show, using a technique based on first principles, that compositionally graded ferroelectrics possess the characteristic ‘fingerprints’ associated with geometric frustration. These systems have a highly degenerate energy surface and display critical phenomena. They further reveal exotic orderings with novel stripe phases involving complex spatial organization. These stripes display spiral states, topological defects and curvature. Compositionally graded ferroelectrics can thus be considered the ‘missing link’ that brings ferroelectrics into the broad category of materials able to exhibit geometric frustration. Our ab initio calculations allow deep microscopic insight into this novel geometrically frustrated system.