Two dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator (Bi$_{0.95}$Mn$_{0.05}$)$_{2}$Te$_{3}$

Employing elastic and inelastic neutron scattering (INS) techniques, we report on detailed microscopic properties of the ferromagnetism in he magnetic topological insulator (Bi$_{0.95}$Mn$_{0.05}$)$_{2}$Te$_{3}$. Neutron diffraction of polycrystalline samples show the ferromagnetic (FM) ordering is long-range within the basal plane, and mainly 2D in character with short-range correlations between layers below $T_{\mathrm{C}} \approx 13$ K. Despite the random distribution of the dliute Mn atoms, we find that the 2D-like magnetic peaks are commensurate with the chemical structure, and the absence of (00L) magnetic peaks denote that the Mn$^{2+}$ magnetic moments are normal to the basal planes. Surprisingly, we observed collective magnetic excitations, in this dilute magnetic system. Despite the dilute nature, the excitations are typical of quasi-2D FM systems, albeit are severely broadened at short wavelengths, likely due to the random spatial distribution of Mn atoms in the Bi planes. Detailed analysis of the INS provide energy scales of the exchange couplings and the single ion anisotropy.