  Proximity-induced magnetic effects on the surface Dirac spectra of
topological insulators are investigated by scanning tunneling spectroscopic
(STS) studies of bilayer structures consisting of undoped Bi2Se3 thin films on
top of Cr-doped Bi2Se3 layers. For thickness of the top Bi2Se3 layer equal to
or smaller than 3 quintuple layers (QL), a spatially inhomogeneous surface
spectral gap \Delta opens up below T_c^{2D}, which is much higher than the bulk
Curie temperature T_c^{3D}. The mean value and spatial homogeneity of the gap
\Delta generally increase with increasing c-axis magnetic field (H) and
increasing Cr doping level (x), suggesting that the physical origin of this
surface gap is associated with proximity-induced c-axis ferromagnetism. On the
other hand, the temperature (T) dependence of \Delta is non-monotonic, showing
an initial increase below T_c^{2D} followed by a dip and then reaching maximum
at T << T_c^{3D}. These phenomena may be attributed to proximity magnetism
induced by two types of contributions with different temperature dependence: a
3D contribution from the bulk magnetism that dominates at low T, and a 2D
contribution associated with the RKKY interactions mediated by surface Dirac
fermions, which dominates at T_c^{3D} << T < T_c^{2D}. Additionally, spatially
localized sharp resonant spectra are found along the boundaries of gapped and
gapless regions. These spectral resonances are long-lived at H = 0 and become
suppressed under strong c-axis magnetic fields, and are attributed to magnetic
impurity-induced topological defects in the spin texture of surface Dirac
fermions.
