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1. Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2

   https://doi.org/10.1038/s41524-019-0257-1  

   Wang, Hua ; Qian, Xiaofeng ( December 2019 , npj Computational Materials)

   Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials – an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a remarkable ferroelectric nonlinear anomalous Hall effect in time-reversal invariant few-layer WTe₂where nonlinear anomalous Hall current switches in odd-layer WTe₂except 1T′ monolayer while remaining invariant in even-layer WTe₂upon ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear anomalous Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe₂. Our work not only treats Berry curvature dipole and shift dipole on an equal footing to account for intraband and interband contributions to nonlinear anomalous Hall effect, but also establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials. The present findings suggest that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics.

    

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2. Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

   https://doi.org/10.1002/adma.202001460  

   Pan, Lei ; Grutter, Alexander ; Zhang, Peng ; Che, Xiaoyu ; Nozaki, Tomohiro ; Stern, Alex ; Street, Mike ; Zhang, Bing ; Casas, Brian ; He, Qing Lin ; et al ( July 2020 , Advanced Materials)

   Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically‐doped topological insulator grown on the antiferromagnetic insulator Cr₂O₃. The exchange coupling between the two materials is investigated using field‐cooling‐dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂O₃and the magnetic topological insulator, manifested as an exchange bias when the sample is field‐cooled under an out‐of‐plane magnetic field, and an exchange spring‐like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.

    

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3. Revealing Fermi surface evolution and Berry curvature in an ideal type-II Weyl semimetal

   https://doi.org/10.1038/s41467-024-46633-w  

   Jiang, Qianni ; Palmstrom, Johanna C. ; Singleton, John ; Chikara, Shalinee ; Graf, David ; Wang, Chong ; Shi, Yue ; Malinowski, Paul ; Wang, Aaron ; Lin, Zhong ; et al ( March 2024 , Nature Communications)

   In type-II Weyl semimetals (WSMs), the tilting of the Weyl cones leads to the coexistence of electron and hole pockets that touch at the Weyl nodes. These electrons and holes experience the Berry curvature generated by the Weyl nodes, leading to an anomalous Hall effect that is highly sensitive to the Fermi level position. Here we have identified field-induced ferromagnetic MnBi_2-xSb_xTe₄as an ideal type-II WSM with a single pair of Weyl nodes. By employing a combination of quantum oscillations and high-field Hall measurements, we have resolved the evolution of Fermi-surface sections as the Fermi level is tuned across the charge neutrality point, precisely matching the band structure of an ideal type-II WSM. Furthermore, the anomalous Hall conductivity exhibits a heartbeat-like behavior as the Fermi level is tuned across the Weyl nodes, a feature of type-II WSMs that was long predicted by theory. Our work uncovers a large free carrier contribution to the anomalous Hall effect resulting from the unique interplay between the Fermi surface and diverging Berry curvature in magnetic type-II WSMs.

    

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4. Exchange‐Biased Quantum Anomalous Hall Effect

   https://doi.org/10.1002/adma.202300391  

   Zhang, Peng ; Balakrishnan, Purnima P. ; Eckberg, Christopher ; Deng, Peng ; Nozaki, Tomohiro ; Chong, Su Kong ; Quarterman, Patrick ; Holtz, Megan E. ; Maranville, Brian B. ; Qiu, Gang ; et al ( June 2023 , Advanced Materials)

   The quantum anomalous Hall (QAH) effect is characterized by a dissipationless chiral edge state with a quantized Hall resistance at zero magnetic field. Manipulating the QAH state is of great importance in both the understanding of topological quantum physics and the implementation of dissipationless electronics. Here, the QAH effect is realized in the magnetic topological insulator Cr‐doped (Bi,Sb)₂Te₃(CBST) grown on an uncompensated antiferromagnetic insulator Al‐doped Cr₂O₃. Through polarized neutron reflectometry (PNR), a strong exchange coupling is found between CBST and Al‐Cr₂O₃surface spins fixing interfacial magnetic moments perpendicular to the film plane. The interfacial coupling results in an exchange‐biased QAH effect. This study further demonstrates that the magnitude and sign of the exchange bias can be effectively controlled using a field training process to set the magnetization of the Al‐Cr₂O₃layer. It demonstrates the use of the exchange bias effect to effectively manipulate the QAH state, opening new possibilities in QAH‐based spintronics.

    

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5. Imaging orbital ferromagnetism in a moiré Chern insulator

   https://doi.org/10.1126/science.abd3190  

   Tschirhart, C. L. ; Serlin, M. ; Polshyn, H. ; Shragai, A. ; Xia, Z. ; Zhu, J. ; Zhang, Y. ; Watanabe, K. ; Taniguchi, T. ; Huber, M. E. ; et al ( May 2021 , Science)

   Electrons in moiré flat band systems can spontaneously break time-reversal symmetry, giving rise to a quantized anomalous Hall effect. In this study, we use a superconducting quantum interference device to image stray magnetic fields in twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap, consistent with the expected contribution of chiral edge states to the magnetization of an orbital Chern insulator. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micrometer-scale domains pinned to structural disorder.

    

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