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Proximity-induced magnetic effects on the surface Dirac spectra oftopological insulators are investigated by scanning tunneling spectroscopic(STS) studies of bilayer structures consisting of undoped Bi2Se3 thin films ontop of Cr-doped Bi2Se3 layers. For thickness of the top Bi2Se3 layer equal toor smaller than 3 quintuple layers (QL), a spatially inhomogeneous surfacespectral gap \Delta opens up below T_c^{2D}, which is much higher than the bulkCurie temperature T_c^{3D}. The mean value and spatial homogeneity of the gap\Delta generally increase with increasing c-axis magnetic field (H) andincreasing Cr doping level (x), suggesting that the physical origin of thissurface gap is associated with proximity-induced c-axis ferromagnetism. On theother hand, the temperature (T) dependence of \Delta is non-monotonic, showingan initial increase below T_c^{2D} followed by a dip and then reaching maximumat T << T_c^{3D}. These phenomena may be attributed to proximity magnetisminduced by two types of contributions with different temperature dependence: a3D contribution from the bulk magnetism that dominates at low T, and a 2Dcontribution associated with the RKKY interactions mediated by surface Diracfermions, which dominates at T_c^{3D} << T < T_c^{2D}. Additionally, spatiallylocalized sharp resonant spectra are found along the boundaries of gapped andgapless regions. These spectral resonances are long-lived at H = 0 and becomesuppressed under strong c-axis magnetic fields, and are attributed to magneticimpurity-induced topological defects in the spin texture of surface Diracfermions.

Magnetism-induced massive Dirac spectra and topological defects in the surface state of Cr-doped Bi$_2$Se$_3$-bilayer topological insulators