Piezoelectricity and rotostriction through polar and non-polar coupled instabilities in bismuth-based piezoceramics

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 field depending on grain
orientation. The strain of grains oriented along a specific 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 findings were confirmed with
electromechanical experiments, in situ neutron diffraction, 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
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cooperate to provide colossal functional responses.