Shear piezoelectric coefficients of PZT, LiNbO$_3$ and PMN-PT at cryogenic temperatures

Piezoelectric transducers are widely used as sensitive detectors of stress and to generate nanometer scale displacements. However, their piezoelectric coefficients often decrease substantially at cryogenic temperatures, limiting their performance in, e.g., low temperature STMs. We have recently used PZT shear transducers to measure the elastic modulus of solid $^4$He at very low strains and to plastically deform the helium at high strains. From our elastic measurements, we inferred a shear piezoelectric coefficient d$_{15} = $1.0x10$^{-10}$ m/V at temperatures below 1 K. This is about 6 times smaller than the room temperature value for PZT and comparable to d$_{15}$ for single crystal LiNbO${_3}$ transducers (7x10$^{-11}$ m/V). We have developed a capacitive technique and have directly measured the temperature dependence of d$_{15}$ for ceramic (PZT) and single crystal (LiNbO$_3$ and PMN-PT) shear transducers. PMN-PT has an extremely large d$_{15}$ at room temperature (4x10$^{-9}$ m/V) but it decreases rapidly below 100 K. LiNbO$_3$ has the smallest room temperature d$_{15}$, but it is nearly temperature-independent. At 4 K, the three types of transducers have similar piezoelectric shear coefficients.