1 Scientific RepoRts | 6:28742 | DOI: 10.1038/srep28742 www.nature.com/scientificreports piezoelectricity and rotostriction through polar and non-polar coupled instabilities in bismuth- based piezoceramics Matias Acosta 1 , Ljubomira A. schmitt 1 , Claudio Cazorla 2 , Andrew studer 3 , Alexander Zintler 1 , Julia Glaum 2,4 , Hans-Joachim Kleebe 1 , Wolfgang Donner 1 , Mark Hofman 2 , Jürgen Rödel 1 & Manuel Hinterstein 2,5 Coupling of order parameters provides a means to tune functionality in advanced materials including multiferroics, superconductors, and ionic conductors. We demonstrate that the response of a frustrated ferroelectric state leads to coupling between order parameters under electric ield depending on grain orientation. The strain of grains oriented along a speciic crystallographic direction, 〈h00〉, is caused by converse piezoelectricity originating from a ferrodistortive tetragonal phase. For 〈hhh〉 oriented grains, the strain results from converse piezoelectricity and rotostriction, as indicated by an antiferrodistortive instability that promotes octahedral tilting in a rhombohedral phase. Both strain mechanisms combined lead to a colossal local strain of (2.4 ± 0.1) % and indicate coupling between oxygen octahedral tilting and polarization, here termed “rotopolarization”. These indings were conirmed with electromechanical experiments, in situ neutron difraction, and in situ transmission electron microscopy in 0.75Bi 1/2 Na 1/2 tio 3 -0.25SrTiO 3 . this work demonstrates that polar and non-polar instabilities can cooperate to provide colossal functional responses. Multifunctional ceramics deine breakthrough technologies due to their unique ability of transducing electrical, mechanical, optical, and magnetic signals 1 . his is a consequence of the rich and complex interplay between their order parameters and conjugated ields 2 . In ferroelectric and ferroelastic materials, for instance, polarization and strain are typical order parameters that can be controlled through the application of an electric ield and stress, respectively (see Fig. 1). he development of polarization and its reorientation with electric ield are considered ingerprints of ferroelectricity (FE) and are ascribed to the sotening of a zone-center polar phonon mode in the reference centrosymmetric phase the electromechanical response generally considered in ferroelectrics is piezoelectricity and electrostriction, which indicate that the strain and polarization are coupled order parame- ters (Fig. 1(1)). Another order parameter in perovskites is provided by the oxygen octahedral tilts ϕ. hese tilts occur due to a structural instability in the reference centrosymmetric coniguration that involves the sotening of a non-polar zone-boundary vibrational mode and are termed antiferrodistortive (AFD). he development of octahedral tilts leading to strain, which indicates their coupling, is allowed by fundamental crystal symmetry arguments and is termed rotostriction (Fig. 1(2)) 3 . he coupling or combined action of piezoelectricity and roto- striction, however, has remained mostly elusive. FE and AFD instabilities in general compete with each other. Cases in which both distortions are mutually coupled are rare (Fig. 1(3)) 4–10 . Research on superlattices has revealed remarkable examples where octahedral tilts can strongly enhance or even induce a ferroelectric distortion in materials that would otherwise be non-polar 11,12 . heoretical studies have shed light on ways to manipulate and design FE-AFD couplings that could potentially 1 Department of Geo- and Materials Science, Technische Universität Darmstadt, Alarich-Weiss-Strasse 2, 64287 Darmstadt, Germany. 2 School of Materials Science and engineering, UnSW Australia, Sydney, new South Wales 2052, Australia. 3 Bragg Institute, Australian Nuclear Science and Technology Organization, Locked Bag 2001, Kirrawee DC NSW 2232, Australia. 4 Department of Materials Science and engineering, norwegian University of Science and Technology, Trondheim, 7491, Norway. 5 institute for Applied Materials, Karlsruhe institute for Technology, P.O. Box 3640, 76021 Karlsruhe, Germany. Correspondence and requests for materials should be addressed to J.R. (email: roedel@ceramics.tu-darmstadt.de) Received: 20 April 2016 Accepted: 07 June 2016 Published: 01 July 2016 opeN