  Metal and magnetic overlayers alter the surface of the topological insulator
(TI) bismuth selenide (Bi$_2$Se$_3$) through proximity effects but also by
changing the composition and chemical structure of the Bi$_2$Se$_3$
sub-surface. The interface between Bi$_2$Se$_3$ and Mn metal or manganese
selenide was explored using x-ray photoelectron spectroscopy (XPS) revealing
chemical and electronic changes at the interface. Depositing Mn metal on
Bi$_2$Se$_3$ without an external source of Se shows unexpected bonding within
the Mn layer due to Mn-Se bonding as Se diffuses out of the Bi$_2$Se$_3$ layer
into the growing Mn film. The Se out-diffusion is further evidenced by changes
in Bi core levels within the Bi$_2$Se$_3$ layers indicating primarily Bi-Bi
bonding over Bi-Se bonding. No out-diffusion of Se occurred when excess Se is
supplied with Mn, indicating the importance of supplying enough chalcogen atoms
with deposited metals. However, Bi$_2$Se$_3$ core level photoelectrons
exhibited a rigid chemical shift toward higher binding energy after depositing
a monolayer of MnSe$_{2-x}$, indicating a dipole within the overlayer.
Stoichiometry calculations indicated that the monolayer forms MnSe
preferentially over the transition metal dichalcogenide (TMD) phase MnSe$_2$,
providing a consistent picture of the dipole formation in which a plane of Se
anions sits above Mn cations. This study shows that chemical diffusion and
dipole formation are important for Mn-Bi$_2$Se$_3$ and
MnSe$_{2-x}$-Bi$_2$Se$_3$ and should be considered carefully for TMD/TI
interfaces more generally.
