  The interaction between magnetic impurities and the gapless surface state is
of critical importance for realizing novel quantum phenomena and new
functionalities in topological insulators. By combining angle-resolved
photoemission spectroscopic experiments with density functional theory
calculations, we show that surface deposition of Cr atoms on Bi$_2$Se$_3$ does
not lead to gap opening of the surface state at the Dirac point, indicating the
absence of long-range out-of-plane ferromagnetism down to our measurement
temperature of 15 K. This is in sharp contrast to bulk Cr doping, and the
origin is attributed to different Cr occupation sites. These results highlight
the importance of nanoscale configuration of doped magnetic impurities in
determining the electronic and magnetic properties of topological insulators.
