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Quantum Anomalous Hall Effect in Topological Insulators
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Abhinav Kandala, Anthony Richardella, Nitin Samarth
Jackiw and Rebbi predicted long ago that the mass domain wall of a 1D Dirac system carries a bound state [11]. A simple generalization to a 2D Dirac system predicts the presence of a 1D chiral (one-way propagating) mode at the mass domain wall. The 2D Dirac surface states of 3D TIs are a natural test bed for these predictions. This is illustrated in Figure 15.1. Consider a 3D TI thin film in proximity with two oppositely oriented, perpendicular-to-plane magnetized domains of a ferromagnet. The surface states under the magnetic domains can be gapped by exchange coupling, and acquire a mass, whose sign is dependent on the direction of magnetization of the overlying domain. Therefore, the region underneath the magnetic domain wall is expected to create a mass domain wall that carries a chiral mode. This 1D mode exists within the magnetic gap, moves in one direction, protected from backscattering, and is therefore dissipationless. Practically, however, this requires that the chemical potential be placed inside the magnetic gap, and that there are no other states at the chemical potential to scatter into. Obviously, using a metallic ferromagnet on top of the TI is therefore problematic. One way to accomplish this is to make the TI itself ferromagnetic by magnetic doping, and to control the carrier density so that chemical potential lies inside the magnetic gap. If the magnetization points up, it will point outward from the top surface, and inward through the bottom surface, resulting in a 1D edge mode around the outside edges of the sample. This is the origin of the quantum anomalous Hall effect (QAHE), which was first observed in Cr doped (Bi1-xSbx)2Te3 [12, 13]. When two oppositely oriented magnetic domains are created in a ferromagnetic TI, as expected, quantized transport can be observed through a chiral mode localized at the domain wall [14, 15]. Another approach is using an insulating ferromagnet. As discussed later, much recent research has focused on interfacing 3D topological insulators with insulating ferromagnets, though to date such a chiral mode has not yet been observed using this method.
Recent advances in two-dimensional ferromagnetism: strain-, doping-, structural- and electric field-engineering toward spintronic applications
Published in Science and Technology of Advanced Materials, 2022
Sheng Yu, Junyu Tang, Yu Wang, Feixiang Xu, Xiaoguang Li, Xinzhong Wang
Most of spin logic devices, including spin field-effect transistor, spin valve and magnetic memory, require a high on-off ratio, which means a great distinction in spin transport properties between spin-up and spin-down electrons. However, this is a challenge for graphene and even for most 2D insulators [76,77]. One approach to overcome this obstacle is to interface 2D materials with 3D magnets (i.e. exfoliation). In comparison to this approach by using 3D magnets, a 2D van der Waals heterostructure has the following advantages: (i) The interlayer twisting angle and the various stacking orders endow the heterostructure with richer properties by the arbitrary choice of direct- or indirect-bandgap, which can broaden the applicability for high-performing magnetic devices [78]. (ii) There is no request for the lattice matching, accordingly keeping their pristine atomic layered structure without chemical bonding and interfacial damage [12]. (iii) The diverse and flexible choices of 2D magnetic materials can enable the precise control of the fabrication process and comprehensive characterization of the heterostructure [11]. (iv) The proximity coupling effect at atomically sharp interfaces between vdW materials and magnetic substrates could effectively tune the spin-related properties in pristine layer, including spin-orbit coupling, spin polarization and spin transport [79]. (v) The heterostructure can modulate the magnetic ions in 2D diluted magnetic semiconductors, and consequently raising the temperature at which the quantum anomalous hall effect (QAHE) can be observed [80]. (vi) Multiple interfacial mechanisms, including charge transfer, band alignment, symmetry breaking, orbital hybridization and layer polarizability, have been proposed as very effective tools to modulate the magnetic properties [81].