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3. Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

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4. Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures

   https://doi.org/10.1038/s41467-023-43474-x  

   Zhuo, Deyi; Yan, Zi-Jie; Sun, Zi-Ting; Zhou, Ling-Jie; Zhao, Yi-Fan; Zhang, Ruoxi; Mei, Ruobing; Yi, Hemian; Wang, Ke; Chan, Moses H. W.; et al (November 2023, Nature Communications)

   Abstract An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi₂Te₄flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase. 

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5. Fermi level dependent spin pumping from a magnetic insulator into a topological insulator

   https://doi.org/10.1103/PhysRevResearch.1.012014  

   Wang, Hailong; Kally, James; Şahin, Cüneyt; Liu, Tao; Yanez, Wilson; Kamp, Eric J.; Richardella, Anthony; Wu, Mingzhong; Flatté, Michael E.; Samarth, Nitin (August 2019, Physical Review Research)