| Summary: | Proximity-induced magnetic effects on the surface Dirac spectra of topological insulators are investigated by scanning tunneling spectroscopic studies of bilayer structures consisting of undoped Bi _2 Se _3 thin films on top of Cr-doped Bi _2 Se _3 layers. For thickness of the top Bi _2 Se _3 layer equal to or smaller than 3 quintuple layers, a spatially inhomogeneous surface spectral gap Δ opens up below a characteristic temperature ${{T}_{{\rm{c}}}}^{2{\rm{D}}},$ which is much higher than the bulk Curie temperature ${{T}_{{\rm{c}}}}^{3{\rm{D}}}$ determined from the anomalous Hall resistance. The mean value and spatial homogeneity of the gap Δ 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 Δ is non-monotonic, showing initial increase below ${{T}_{{\rm{c}}}}^{2{\rm{D}}},$ which is followed by a ‘dip’ and then rises again, reaching maximum at T ≪ ${{T}_{{\rm{c}}}}^{3{\rm{D}}}.$ These phenomena may be attributed to proximity magnetism induced by two types of contributions with different temperature dependences: a three-dimensional contribution from the bulk magnetism that dominates at low T , and a two-dimensional contribution associated with the RKKY interactions mediated by surface Dirac fermions, which dominates at ${{T}_{{\rm{c}}}}^{3{\rm{D}}}$ ≪ T < ${{T}_{{\rm{c}}}}^{2{\rm{D}}}.$ In addition to the observed proximity magnetism, spatially localized sharp resonant spectra are found along the boundaries of gapped and gapless regions. These spectral resonances are long-lived at H = 0, with their occurrences being most prominent near ${{T}_{{\rm{c}}}}^{2{\rm{D}}}$ and becoming suppressed under strong c -axis magnetic fields. We attribute these phenomena to magnetic impurity-induced topological defects in the spin texture of surface Dirac fermions, with the magnetic impurities being isolated Cr impurities distributed near the interface of the bilayer system. The long-term stability of these topologically protected two-level states may find potential applications to quantum information technology.
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