with elastic constants and ultrasonic attenuation measured by resonant ultrasound spectroscopy*

Elastic constants are ideal to study phase transitions because they are the thermodynamic susceptibility of strain. Strain, being a second-rank tensor quantity, can couple to order parameters in ways that are inaccessible to thermal, electric, or magnetic fields alone. As such, ultrasound measurements have been used to great effect to study changes in elastic constants and attenuation at phase transitions under applied magnetic fields. Such approaches have often been based on pulse-echo techniques which require multiple sample-transducer combinations to obtain the complete elastic constant tensor. This can be prohibitive for low symmetry materials and introduce systematic errors.

Here, we share recent advances in resonant ultrasound spectroscopy (RUS) which enable the non-destructive determination of the entire elastic constant tensor with high accuracy and precision from a single sample in DC magnetic fields up to 14T and temperatures down to 1.7K. We apply these developments to study phase transitions in elemental Gd and the geometrically-frustrated Shastry-Sutherland-like compound BaNd₂ZnS₅. Clear thermodynamic signatures of phase transitions are identified in both elastic constants and ultrasonic attenuation as a function of temperature and magnetic field. These results clarify the rich phase diagram of BaNd₂ZnS₅ and demonstrate our ability to perform RUS in high magnetic fields.