A comparative study of the electronic and optical properties of Mn-Bi-Te layered compounds was carried out using spectroscopic ellipsometry (SE) over a photon energy range of 0.7–6.5 eV at room temperature and density functional theory (DFT)-based first-principle calculations within the general gradient approximation with Hubbard like correction (GGA+U) and allowance for a spin-orbital coupling. The total energies of the above compounds in ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations are obtained by taking the long-range van der Waals interaction into account. The stability of the AFM state of MnBi2Te4 and MnBi4Te7 over the corresponding FM counterpart is disclosed. The SE-based and calculated dielectric functions are compared. It is shown that interband optical transitions in the accessed photon energy range mainly occur between Mn 3d + Te 5p states of the valence band and Bi 6p + Te 5p with a small admixture of Mn 3d states of the conduction band.

Further to the structure of the intrinsic magnetic topological insulators $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4·n\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)$ with $n<4$, where index $n$ is the number of quintuple Te-Bi-Te-Bi-Te building blocks inserted between the neighboring septuple Te-Bi-Te-Mn-Te-Bi-Te building blocks, the structure of the members with $n=4$, 5, and 6 was studied using x-ray powder diffraction. The unit-cell parameters and atomic positions were obtained. The obtained and available structural data were summarized to show that the crystal structure of all members of $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4·n\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)$ follows the cubic close-packing principle, independently of the space group of the given member. Confocal Raman spectroscopy was then applied. Comparative analysis of the number, frequency, symmetry, and broadening of the vibration modes responsible for the lines in the Raman spectra of the systems with $n=1$,…,6, as well as $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4\left(n=0\right)$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ ($n=\infty$) has shown that lattice dynamics of $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4·n\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)$ with $n>0$ overwhelmingly dominates by the cooperative atomic displacements in the quintuple building blocks.

With infrared spectroscopy, we studied the bulk electronic properties of the topological antiferromagnet $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ with $T_N\simeq 25\mathrm{K}$. With the support of band-structure calculations, we assign the intra- and interband excitations and determine the band gap of $E_g\approx 0.17$ eV. We also obtain evidence for two types of conduction bands with light and very heavy carriers. The multiband free-carrier response gives rise to an unusually strong increase of the combined plasma frequency, ${\omega }_{\mathrm{pl}}$, below 300 K. The band reconstruction below $T_N$ yields an additional increase of ${\omega }_{\mathrm{pl}}$ and a splitting of the transition between the two conduction bands by about 54 meV. Our study thus reveals a complex and strongly temperature-dependent multiband low-energy response that has important implications for the study of the surface states and device applications.

This work is devoted to the experimental study and symmetry analysis of the Raman-active vibration modes in MnBi₂Te₄·n(Bi₂Te₃) van der Waals topological insulators, where n is the number of Te–Bi–Te–Bi–Te quintuple layers between two neighboring Te–Bi–Te–Mn–Te–Bi–Te septuple layers. Confocal Raman spectroscopy is applied to study Raman spectra of crystal structures with $$n = 0,1,2,3,4,5,6$$ , and ∞. The experimental frequencies of vibration modes of the same symmetry in the structures with different n are compared. The lattice dynamics of free-standing one, three, and four quintuple layers, as well as of bulk Bi₂Те₃ $$(n = \infty )$$ and MnBi₂Te₄ $$(n = 0)$$ , is considered theoretically. Vibrational modes of the last two systems have the same symmetry, but different displacement fields. These fields in the case of a Raman-active mode do not contain displacements of manganese atoms for any finite $$n$$ . It is shown that two vibrational modes in the low-frequency region of the spectrum (35–70 cm^–1) of structures with $$n = 1,\;2,\;3,\;4,\;5$$ , and 6 practically correspond to the lattice dynamics of n free quintuple Bi₂Те₃ layers. For this reason, the remaining two vibration modes, which are observed in the high-frequency region of the spectrum (100–140 cm^–1) and are experimentally indistinguishable in the sense of belonging to quintuple or septuple layer or to both layers simultaneously, should also be assigned to vibrations in quintuple layers under immobile atoms of septuple layers.