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Recently discovered magnetic topological insulators $T$Bi$_{2}$Te$_{4}$($T=$Mn, Fe) crystallize into the $R\bar{3}m$ rhombohedral structure andexhibit the antiferromagnetic order. Here, we discuss the lattice dynamics ofthese compounds to confirm the stability of these systems. We show that thephonon dispersion does not contain soft modes, so both compounds aredynamically stable in the $R\bar{3}m$ phase. We perform theoretical analyses ofthe mode activity at $\Gamma$ point for the discussed compounds. In the case ofthe Raman active modes, our results are in agreement with the experimentallyobserved frequencies. Finally, we also discuss the possibility of realizationof chiral phonons.

physical review. b./physical review. b

Dynamical properties of magnetic topological insulator  $T$Bi$_{2}$Te$_{4}$ ($T=$Mn, Fe): phonons dispersion, Raman active modes, and  chiral phonons study