| Summary: | An intrinsic antiferromagnetic topological insulator MnBi_{2}Te_{4} arises when intercalating a Mn-Te bilayer chain in a topological insulator, Bi_{2}Te_{3}. We present observations on the inter- and intralayer phonon modes of the generalized MnBi_{2n}Te_{3n+1}(n=1,2,3,4) family using cryogenic low-frequency Raman spectroscopy with various polarization configurations. Two peaks at 66 and 112cm^{–1} show abnormal perturbation in Raman linewidths below magnetic transition temperature due to spin-phonon coupling. In MnBi_{4}Te_{7}, Bi_{2}Te_{3} layers induce Davydov splitting of the A_{1g} mode around 137cm^{–1} at 5 K. The out-of-plane interlayer force constant estimated using the linear chain model was (3.98±0.14)×10^{19}N/m^{3}, three times weaker than that of Bi_{2}Te_{3}. Adding more Bi_{2}Te_{3} layers, such as MnBi_{6}Te_{10} and MnBi_{8}Te_{13}, makes Bi_{2}Te_{3} properties more dominant than magnetic properties. Our work experimentally and theoretically discovers the dynamics of phonon modes of MnBi_{2n}Te_{3n+1} family, facilitating utilization of magnetic topological heterostructures.
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