Fig. 2: High-temperature evolution of lattice vibrations and elastic properties.

a A_g-mode Raman spectrum of SmFeO₃ at room temperature in z(yy)z̅ configuration using Porto’s notation³⁷ (Symbols to the left and right of the parentheses denote the propagation direction, while symbols inside the parentheses indicate polarization of incident and scattered light, respectively.). b, c Evolution of the frequency of A_g(3) and A_g(4) Raman modes from 300 to 850 K, across the spin reorientation T_SR and Néel T_N temperatures. For the temperature evolution of the complete Raman spectra, the phonon frequencies and FWHM, please refer to Supplementary Note 1+2. d Temperature evolution of a representative resonance peak in RUS spectra from room temperature to 700 K, thus above the magnetic ordering (this behavior is alike for all ultrasound resonance bands; see Supplementary Figs. 5 and 6). e Magnification of the RUS spectra across the spin reorientation interval revealing a significant deviation in elastic moduli. f Evolution of the square of the frequency, f², which scales with some combination of single crystal elastic moduli, showing a softening through the reorientation transition. g The associated acoustic loss data, showing a peak in Q⁻¹ through the reorientation typical of mobile microstructure. For a further analysis of the elastic anomalies see Supplementary Note 4.