Geometric frustration in compositionally modulated ferroelectrics

TL;DR

This paper demonstrates that compositionally graded ferroelectrics exhibit geometric frustration, leading to degenerate energy states, exotic stripe phases, and complex spatial orderings, thus expanding the understanding of frustration beyond magnetic systems.

Contribution

It reveals, through first-principles calculations, that ferroelectrics can display geometric frustration, previously mainly studied in magnetic materials, with unique critical phenomena and complex orderings.

Findings

Presence of highly degenerate energy surface

Exhibition of exotic stripe phases with spiral states

Observation of topological defects and curvature in ferroelectrics

Abstract

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1-7. 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 glasses1-7. It has also led to interesting findings of fractional charge quantization and magnetic monopoles5,6. Geometric frustration related mechanisms have been proposed to understand the origins of relaxor behavior in some multiferroics, colossal magnetocapacitive coupling and unusual and novel mechanisms of high Tc superconductivity1-5. Although geometric frustration has been particularly well studied in magnetic systems in the last 20 years or so, its manifestation in the important class formed by ferroelectric materials (that are compounds exhibiting electric rather than magnetic dipoles) is basically unknown. Here, we show, via the use of a first-principles-based technique, that compositionally graded ferroelectrics possess the characteristic "fingerprints" associated with geometric frustration. These systems have a highly degenerate energy surface and exhibit original 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 as the "missing" link that brings ferroelectrics into the broad category of materials able to exhibit geometric frustration. Our ab-initio calculations allow a deep microscopic insight into this novel geometrically frustrated system.