We present full characterisation of acoustic wave devices based on the fully synthetic crystalline material at the liquid helium temperature range { required for the design of ultra low loss mechanical systems in many areas of research including freq
uency control and fundamental measurements}. Temperature coefficients of the effective elastic tensor of Langatate (LGT) in Lagrangian representation are determined for the temperature range $3.8-15$K. The Lagrangian formalism is mandatory in the analysed situation since the expansion coefficients of the LGT are still unknown at these temperatures. The measurement method involves a set of high-quality resonators of various cut angles, and uses measurements of frequency-temperature relations to extract the temperature coefficients of the elastic tensor. In addition, power sensitivity of LGT resonators at cryogenic temperatures is determined and dominant loss mechanism is identified.
