In ferroelectric materials the maximum electrostrain effect usually occurs at a phase boundary (often referred to as a “morphotropic phase boundary”) between two or more different phases due to lattice instability at such compositions. As a result it is not expected that the electrostrain maximum can appear in a single ferroelectric phase regime which is away from lattice instability. In this Rapid Communication we report an unexpected finding that the electrostrain maximum occurs in a single rhombohedral phase region of the $(1-x\%)\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{0.8}\mathrm{H}{\mathrm{f}}_{0.2}\right){\mathrm{O}}_3-x\%\left(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\right)\mathrm{Ti}{\mathrm{O}}_3$ system. The composition showing the maximum electrostrain corresponds to an “invisible boundary” within the single ferroelectric phase, which is a vertical line starting from the quadruple point of the system. At the invisible boundary other anomalies, such as maximum spontaneous polarization also appear. The origin of electrostrain enhancement at the invisible boundary is considered to correlate with an easy polarization extension inherited from the quadruple point. The electrostrain enhancement effect at the invisible boundary has the advantage of having better temperature stability as compared with that at a phase boundary and thus may provide a way for designing high-electrostrain materials with improved temperature stability.

• Received 20 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.020101