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Geometric frustration in compositionally modulated ferroelectrics


Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1,2,3,4,5,6,7. 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 glasses1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17. It has also led to interesting findings of fractional charge quantization and magnetic monopoles5,6. 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 superconductivity3,4,5,12,16. 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.

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Figure 1: Characteristics and material properties.
Figure 2: Ground-state microstructures.
Figure 3: Frustrated ground-state microstructure and dipolar orientational correlations in phase II.
Figure 4: Frustrated ground-state microstructure and spiral states in phase I.


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This work was supported by the US National Science Foundation, Office of Naval Research and Department of Energy. We gratefully acknowledge extensive use of the supercomputing resources of the University of Arkansas High Performance Computing Center as well as the Center for Piezoelectrics by Design, College of William and Mary, Virginia. We thank A. Apon, D. Chaffin, J. Pummill and E. J. Walter for computational support.

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This work is an outgrowth of an ongoing project on compositionally modulated ferroelectrics at the University of Arkansas. L.W., S.L. and L.B. developed an effective-Hamiltonian implementation for BST systems. N.C. carried out the present Monte Carlo simulations using these effective-Hamiltonian and code implementations. N.C. found exotic degenerate ground states and spiral domains and suggested that these complex results can be explained in terms of geometric frustration. L.B. proposed further studies of critical behaviours and size dependency, and these additional simulations were carried out by N.C. Various complex details were jointly analysed by N.C. and L.B. and together they wrote the paper, with feedback from L.W. and S.L.

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Correspondence to Narayani Choudhury.

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The authors declare no competing financial interests.

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Choudhury, N., Walizer, L., Lisenkov, S. et al. Geometric frustration in compositionally modulated ferroelectrics. Nature 470, 513–517 (2011).

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