Quantum Corrections Crossover and Ferromagnetism in Magnetic Topological Insulators Weiyi Wang, Yanwen Liu, Cheng Zhang, Ping Ai, Faxian Xiu Department of Physics and State Key Laboratory of Surface Physics Fudan University, Shanghai, 200433, China Introduction Quantum Corrections Crossover in CrxBi2-xTe3 Thin Films Magnetic Topological Insulators Magnetic doping x =0 x =0.08 x =0.10 x =0.14 Weak antilocalization Weak localization Hikami-Larkin-Nagaoka (HLN) model R. Yu, et al. Science 329, 61, 2010. M. König, et al. Science 318, 766, 2007. Time reversal symmetry (TRS) protected helical metallic edge/surface state. Quantum spin Hall effect in 2D TI. Broken TRS. Gapped surface state. Quantized anomalous Hall effect Weak localization: Constructive interference. enhanced magnetoresistance (MR). Weak anti-localization: Destructive interference. decreased MR. TI: Backscattering prohibited but spin-orbit interaction induced spin flip at opposite surface of crystal. Magnetic TI-Gapped Surface State Ferromagnetism in CrxBi2-xTe3 Thin Films X=0.14 X=0.27 X=0.30 X=0.32 Quasi-rectangular shaped hysteresis loop in magnetic field dependent Hall resistance curves at low magnetic fields (~0.2 T), showing ferromagnetic order is developed in these thin films. Increasing Cr concentration results in an enhancement the AHE effect. (e) Temperature-dependent Hall resistance Ryx of CrxBi2-xTe3 thin films at zero magnetic fields. (f) Temperature-dependent carrier concentration of CrxBi2-xTe3 thin films. The high carrier concentration indicates that a high bulk conduction contribution is present in the thin films (g) Curie temperature of CrxBi2-xTe3 thin films with different Cr content. The monotonic increase in Tc with increasing Cr concentration suggests an enhanced AHE upon increasing Cr doping concentration. Gap: 7 meV Y. L. Chen, et al. Science 329, 659, 2010 Magnetic TI-Quantized Anomalous Hall Effect Quantum Corrections in High Doping Regime X=0.14 X=0.27 X=0.30 C. Z. Chang, et al. Science 340, 167, 2013 Results Structural Characterization of MBE Grown CrxBi2-xTe3 Thin Films on Mica The hysteresis loop behavior in MC curves in (a) x = 0.27, (b) x = 0.30, and (c) x= 0.32, further confirming the establishment of ferromagnetism in these thin films. The MC minima in the MC curves reflect the strength of coercive force, indicating that once x reaches 0.27, the coercive force shows almost no response to the increasing Cr concentration. Figs. a-c show the representative AFM images of as-grown pure (Fig. a) and Cr-doped (Figs. b and c) Bi2Te3 thin films. The pure Bi2Te3 thin films have an atomically flat surface with micrometer sized terraces, indicating the high quality of the thin films (Fig. a). The sharp streaky lines in Fig. d indicate a layer-by-layer 2D growth mode and a flat surface morphology. Conclusion The incorporation of Cr dopants into the Bi2Te3 produces sufficient disorder to prompt a transition from WAL to WL in MC. Cr-doping is an appropriate approach to break TRS in the Bi2Te3 system. The increased carrier concentration with increasing Cr concentration suggests that introducing Cr in Bi2Te3 thin films indeed generates free carriers. The high carrier concentration in the ferromagnetic CrxBi2-xTe3 thin films indicates that the ferromagnetism is originated from bulk state. The transport signatures from the TRS-broken magnetic topological insulators in this study provides a critical reference for accessing of the gapped surface states. We gratefully acknowledge the financial support from the department. *To whom correspondence should be addressed: faxian@fudan.edu.cn