Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$, the $n=$ 1 and 2 members of a modular (Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series, which were recently established as intrinsic magnetic topological insulators. We observe topological surface states (TSS), whose Dirac-like dispersion is strongly perturbed by hybridization with valence-band states for Bi$_2$Te$_3$-terminated surfaces but remains preserved for MnBi$_2$Te$_4$-terminated surfaces. Using polarization- and photon-energy-dependent measurements we unveil a complex momentum-dependent orbital-texture evolution of the surface bands, which is supported by calculations based on density functional theory. By means of circular dichroism in ARPES we provide evidence for an inversion of orbital angular momentum at the Dirac point as a characteristic signature of a helical TSS, firmly establishing the topologically non-trivial nature of the surface electronic structure in these magnetic van der Waals materials.