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We present full characterisation of acoustic wave devices based on the fullysynthetic crystalline material at the liquid helium temperature range {required for the design of ultra low loss mechanical systems in many areas ofresearch including frequency control and fundamental measurements}. Temperaturecoefficients of the effective elastic tensor of Langatate (LGT) in Lagrangianrepresentation are determined for the temperature range $3.8-15$K. TheLagrangian formalism is mandatory in the analysed situation since the expansioncoefficients of the LGT are still unknown at these temperatures. Themeasurement method involves a set of high-quality resonators of various cutangles, and uses measurements of frequency-temperature relations to extract thetemperature coefficients of the elastic tensor. In addition, power sensitivityof LGT resonators at cryogenic temperatures is determined and dominant lossmechanism is identified.

Measurements of Elastic Properties of Langatate at Liquid Helium Temperatures for design of ultra low loss mechanical systems