Abstract
Compound phases often display properties that are symmetry forbidden relative to their nominal, average crystallographic symmetry, even if extrinsic reasons (defects, strain, or imperfections) are not apparent. Specifically, breaking the macroscopic inversion symmetry of a centrosymmetric phase can dominate or significantly change its observed properties while the detailed mechanisms and magnitudes of the deviations of symmetry breaking are often obscure. Here, we choose piezoelectricity as a tool to investigate macroscopic inversion-symmetry breaking in nominally centrosymmetric materials as a prominent example and measure resonant piezoelectric spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect concentrations, i.e., NaCl, fused silica, and ${\mathrm{CaF}}_{2}$. We exclude the flexoelectric effect as a source of the observed piezoelectricity yet observe piezoelectricity in all nominally cubic phases of these samples. By scaling the RPS intensities with those of RUS, we calibrate the effective piezoelectric coefficients using single-crystal quartz as standard. Using this scaling we determine the effective piezoelectric modulus in nominally nonpiezoelectric phases, finding that the ``symmetry-forbidden'' piezoelectric effect ranges from $\ensuremath{\sim}1$ to ${10}^{\ensuremath{-}5}$ pm/V ($\ensuremath{\sim}0.5%$ to $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}%$ of the piezoelectric coefficient of poled ferroelectric lead zirconate titanate). The values for the unpoled ferroelectric phase are only slightly higher than those in the paraelectric phase. The extremely low coefficients are well below the detection limit of conventional piezoelectric measurements and demonstrate RPS as a convenient and ultrahighly sensitive method to measure piezoelectricity. We suggest that symmetry-breaking piezoelectricity in nominally centrosymmetric materials and disordered, unpoled ferroelectrics is a common phenomenon.
Highlights
Along with chiral dichroism, second harmonic generation, and Rashba spin splitting, the classic effects of piezoelectricity and pyroelectricity belong to a group of functionalities enabled by specific crystal class (CC) symmetries
We choose piezoelectricity as a tool to investigate macroscopic inversion-symmetry breaking in nominally centrosymmetric materials as a prominent example and measure resonant piezoelectric spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect concentrations, i.e., NaCl, fused silica, and CaF2
To have access to piezoelectric coefficients that are beyond the resolution of direct piezoelectric measurements, we develop a method based on RPS and RUS
Summary
Second harmonic generation, and Rashba spin splitting, the classic effects of piezoelectricity and pyroelectricity belong to a group of functionalities enabled by specific crystal class (CC) symmetries. We measured the resonant piezoelectric spectroscopy (RPS) [5,10,36] of five unpoled ferroelectric compounds (characterized by ferroelectric domains) and their paraelectric phases (with local polar structures including ferroelectric precursors), ferroelastic LaAlO3 (with polar twin walls), four relaxor ferroelectrics (with PNRs) above their freezing temperature, incipient ferroelectrics KTaO3 and SrTiO3 with no known polar clusters at room temperature, and materials with low concentrations of defects, namely, NaCl, CaF2, and silica glass. We show that nominally centrosymmetric phases of materials with local polar entities and chemical defects, like dopants, possess measurable piezoelectric effects that vary by seven orders of magnitude in comparison with poled ferroelectrics that have high piezoelectric coefficients. The small deviations from centrosymmetry are well reflected by piezoelectric coefficients that are as low as 0.1% to 0.001% of that of piezoelectric quartz
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