Spectral analysis of resonance ultrasonic spectroscopy: Kramers–Kronig analysis, Fano profiles, and the case of precursor softening in SnTe:Cr

The analysis of resonant ultrasound spectroscopy (RUS) spectra is exemplified by the study of elastic softening in single-crystal Sn0.995Cr0.005Te near the ferroelastic phase transition at T ≃ 100 K. Kramers–Kronig analysis of the resonance peaks shows that the elastic response is linear over the entire temperature range. In the paraelastic phase the Cole–Cole plots of the RUS spectra are circles with small gaps that are related to linear damping. In the ferroelastic phase strong coupling with domain boundary movement occurs, and results in distortion of the Cole–Cole circles. The RUS line profiles in the ferroelastic phase are well-described by the sum of a resonance term and a Fano spectrum with a Fano parameter of q = 0.46. The general equations and some simple approximations, which can conveniently be used to analyze RUS spectra, are summarized. We expect that this analysis is transportable to a large parameter space and can be applied to most RUS spectra for both ferroic and nonferroic materials