Realizing the quantum anomalous Hall effect in materials with in-plane magnetization

Abstract

When an electric current flows through a confined two-dimensional (2D) electron gas, which is under an external high magnetic field (H) along the z direction, themagnetic fieldwill deflect the current. A transverse quantizedHall conductance can then be observed across the sample. This effect, known as the quantum Hall effect (QHE), was discovered in 1980 by Klaus von Klitzing who won the 1985 Nobel Prize in Physics for this fundamental discovery. However, the large externalmagnetic field required to observe the QHE strongly hampers its practical application. In the last few years, people have realized that even without the externalH, the quantizedHall conductance could also be induced by magnetization, dubbed as the quantum anomalous Hall (QAH) effect.Thiswas first observed this year in magnetically doped topological insulator thin films. As the QAH system carries dissipationless currents, its realization could pave the way for the field of dissipationless electronics. It is commonly believed that the QAH effect, just like the QHE, also requires out-of-plane magnetization. Recently, Chao-Xing Liu and his colleagues from the Pennsylvania State University predicted that, for the QAH system, the out-of-plane magnetization is not a must, whereas the most essential point is to break all the reflection symmetries [1]. By using general symmetry analysis, Liu et al. found that the presence of the reflection symmetry (RS), or time reversal symmetry in a 2D lattice, can bring the Hall conductance to zero. For a 2D system with in-plane magnetization, RS, with the reflection plane normal to the magnetization direction, is still preserved. Therefore, the remaining RS needs to be broken in order to achieve a non-zero Hall conductance. Following this idea, Liu et al. proposed the experimental setups in two realistic systems, including magnetically doped Bi2Te3 thin films and HgMnTe quantum wells. For magnetically doped Bi2Te3 thin films, they demonstrated that when in-plane magnetization is aligned along proper directions, the warping effects, which originate from the microscopic crystalline structure, can break the remaining RS and yield the QAH effect. More interestingly, they revealed that the sign of the quantized Hall conductance depends on the angle between the magnetization and the crystalline orientation. Thus, by rotating the inplane magnetization, one can easily distinguish the in-plane-magnetizationinduced QAH effect from that caused by out-of-plane magnetization. Moreover, Liu et al. predicted that the similar effect also occurs in HgMnTe quantum wells with the shear strain, indicating that the proposed effects should exist generally. Furthermore, based on two concrete examples, Liu et al. suggested that in a QAH system, a pseudo-scalar can always be constructed to break all the RSs in 2D point groups. Guided by this strategy, it is possible to search newQAH systems in hybrid structures with the ferromagnetic insulator substrates, such as EuO and GdN thin films, which host in-plane magnetization. Liu et al.’s proposal completely excludes the orbital effect from Landau levels induced by the out-of-plane magnetic field and provides a clear experimental signature to distinguish the orbital effect of magnetic fields from the exchange effect of magnetic ions.