Measurements of elastic properties of langatate at liquid helium temperatures for design of ultra low loss mechanical systems

Abstract

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 − 15K. 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.Recently low temperature applications of piezoelectric Bulk Acoustic Wave (BAW) devices has drawn serious attention due to their extraordinary quality factors [1][2][3]. Such applications include but not limited to frequency control systems [4], quantum hybrid devices[2, 5, 6] and atomic force spectroscopy. It is demonstrated [7,8] that in most of these applications, and in frequency control in particular [9], thermal response of such devices is critical and requires further improvement. For this purpose, thermal coefficient of the utilised material have to be identified at the liquid helium temperature range.Although langasite-type materials were initially developed as laser crystals, some of their properties make them very good candidates for frequency control applications. Like other compounds of this crystal family, Lanthanum gallium tantalite (La 3 Ga 5.5 Ta 0.5 O 14 ) or Langatate (LGT) belongs to the same trigonal crystal class 32 as quartz, and as a consequence exhibits similar properties. First, it is piezoelectric with an electromechanical coupling coefficient two to three times greater than that of quartz. These properties make Langatate ideal for variety of frequency-control applications including BAW and surface acoustic wave (SAW) resonators and filters [10]. BAW LGT resonators have already demonstrated their efficiency as master resonators in very stable oscillators [11]. Since LGT-based devices exhibit similar low phase noise and high Q regimes as quartz devices, they can also be classified as a low-loss material [12]. Nevertheless, such applications require careful selection of the material in terms of crystal quality. It should also be pointed out that LGT crystal can be made according to a purely synthetic process of growth whereas quartz crystal cannot be reproduce infinitely from synthetic seeds. Indeed, the crystalline quartz quality de-