Crystal structure and Raman-active lattice vibrations of magnetic topological insulators <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Mn</mml:mi><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Te</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>·</mml:mo><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Te</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo…

Further to the structure of intrinsic magnetic topological insulators $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}n({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})$ with $n&lt;4$, where index $n$ is number quintuple Te-Bi-Te-Bi-Te building blocks inserted between neighboring septuple Te-Bi-Te-Mn-Te-Bi-Te blocks, members $n=4$, 5, and 6 was studied using x-ray powder diffraction. The unit-cell parameters atomic positions were obtained. obtained available structural data summarized show that crystal all follows cubic close-packing principle, independently space group given member. Confocal Raman spectroscopy then applied. Comparative analysis number, frequency, symmetry, broadening vibration modes responsible for lines in spectra systems $n=1$,\dots{},6, as well $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\phantom{\rule{0.16em}{0ex}}(n=0)$ ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ ($n=\ensuremath{\infty}$) has shown lattice dynamics $n&gt;0$ overwhelmingly dominates by cooperative displacements blocks.