  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 frequency 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.
