Temperature studies of raman spectra in MnBi$_2$Te$_4$ and MnSb$_2$Te$_4$ magnetic topological insulators

Raman spectra of magnetic topological crystalline insulators in a wide temperature range including the magnetic ordering region are studied in detail. The anharmonicity parameters and Grüneisen mode parameters of Raman-active phonons in the studied crystals have been determined. It has been shown that the temperature dependence of the frequency of the $A^{(1)}_{\text{1g}}$ (${\sim}\,48$ cm$^{-1}$) phonon in MnSb$_2$Te$_4$ coincides within $\sim 0.1$ cm$^{-1}$ with the standard anharmonic model disregarding the spin–phonon coupling. The polarization dependences of Raman spectra in the MnSb2Te4 crystals indicate that Sb and Mn atoms are strongly mixed in them unlike the isostructural MnBi$_2$Te$_4$ crystals.