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Geometric Berry phase can be induced either by spin-orbit coupling, giving rise to the anomalous Hall effect in ferromagnetic materials, or by chiral spin texture, such as skyrmions, leading to the topological Hall effect. Recent experiments have revealed that both phenomena can occur in topological insulator films with magnetic doping, thus providing us with an intriguing platform to study the interplay between these two phenomena. In this work, we numerically study the anomalous Hall and topological Hall effects in a four-band model that can properly describe the quantum well states in the magnetic topological insulator films by combining Landauer-Buttiker formula and the iterative Greens function method. Our numerical results suggest that spin-orbit coupling in this model plays a different role in the quantum transport in the clean and disordered limits. In the clean limit, spin-orbit coupling mainly influences the longitudinal transport but does not have much effect on topological Hall conductance. Such behavior is further studied through the analytical calculation of scattering cross-section due to skyrmion within the four-band model. In the disordered limit, the longitudinal transport is determined by disorder scattering and spin-orbit coupling is found to affect strongly the topological Hall conductance. This sharp contrast unveils a dramatic interplay between spin-orbit coupling and disorder effect in topological Hall effect in magnetic topological insulator systems.
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The quantum anomalous Hall (QAH) state is a two-dimensional bulk insulator with a non-zero Chern number in absence of external magnetic fields. Protected gapless chiral edge states enable dissipationless current transport in electronic devices. Doping topological insulators with random magnetic impurities could realize the QAH state, but magnetic order is difficult to establish experimentally in the bulk insulating limit. Here we predict that the single quintuple layer of GdBiTe3 film could be a stoichiometric QAH insulator based on ab-initio calculations, which explicitly demonstrate ferromagnetic order and chiral edge states inside the bulk gap. We further investigate the topological quantum phase transition by tuning the lattice constant and interactions. A simple low-energy effective model is presented to capture the salient physical feature of this topological material.
High quality chromium (Cr) doped three-dimensional topological insulator (TI) Sb2Te3 films are grown via molecular beam epitaxy on heat-treated insulating SrTiO3(111) substrates. We report that the Dirac surface states are insensitive to Cr doping, and a perfect robust long-range ferromagnetic order is unveiled in epitaxial Sb2-xCrxTe3 films. The anomalous Hall effect is modulated by applying a bottom gate, contrary to the ferromagnetism in conventional diluted magnetic semiconductors (DMSs), here the coercivity field is not significantly changed with decreasing carrier density. Carrier-independent ferromagnetism heralds Sb2-xCrxTe3 films as the base candidate TI material to realize the quantum anomalous Hall (QAH) effect. These results also indicate the potential of controlling anomalous Hall voltage in future TI-based magneto-electronics and spintronics.
The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicates the coexistence of both bulk and surface states. The magnetization shows the induced antiferromagnetic ordering with Cu doping and the observed quantum oscillation in it indicates that magnetization in Sb1.90Cu0.10Te3 is the bulk property. The non linearity in Hall data suggests the existence of anomalous and topological Hall effect. The anomalous and topological Hall effect (THE) from measured hall data of Cu doped Sb2Te3 topological insulator have been evaluated.
A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This article reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T=2-3 K and an AHE at T=80-300 K. Over T=3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to an interfacial DMI interaction. The DMI strength estimated is substantially higher than that in heavy metal-based systems.
The quantized version of anomalous Hall effect realized in magnetic topological insulators (MTIs) has great potential for the development of topological quantum physics and low-power electronic/spintronic applications. To enable dissipationless chiral edge conduction at zero magnetic field, effective exchange field arisen from the aligned magnetic dopants needs to be large enough to yield specific spin sub-band configurations. Here we report the thickness-tailored quantum anomalous Hall (QAH) effect in Cr-doped (Bi,Sb)2Te3 thin films by tuning the system across the two-dimensional (2D) limit. In addition to the Chern number-related metal-to-insulator QAH phase transition, we also demonstrate that the induced hybridization gap plays an indispensable role in determining the ground magnetic state of the MTIs, namely the spontaneous magnetization owning to considerable Van Vleck spin susceptibility guarantees the zero-field QAH state with unitary scaling law in thick samples, while the quantization of the Hall conductance can only be achieved with the assistance of external magnetic fields in ultra-thin films. The modulation of topology and magnetism through structural engineering may provide a useful guidance for the pursuit of QAH-based new phase diagrams and functionalities.
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