Fig. 1: Phonon anomalies across magnetic phase transitions in MnBi₂Te₄.

a Crystal structure of MnBi₂Te₄. b Eigendisplacements of the A_1g⁽¹⁾ and A_1g⁽²⁾ modes, with arrows denoting displacement of ions. c, d Raman spectra of A_1g⁽¹⁾ (c) and A_1g⁽²⁾ (d) modes in the paramagnetic (PM) and antiferromagnetic (AFM) phases at 0 T, shown in red and blue respectively. e, f Raman spectra of A_1g⁽¹⁾ (e) and A_1g⁽²⁾ (f) modes in the AFM and ferromagnetic (FM) phases at 5 K, shown in blue, and purple respectively. (g, h) The difference between spectra in the AFM and FM phases. i, j Contour plots of the difference upon subtracting the 9 T spectrum, as a function of magnetic field. The dotted lines denote the FM and spin-flop critical fields.