Recently, Associate Professor Lü Baiqing from the Li Zhengdao Institute/School of Physics and Astronomy/Zhangjiang Advanced Research Institute at Shanghai Jiao Tong University, Professor Ding Hong from the Li Zhengdao Institute at Shanghai Jiao Tong University, Researcher Huang Yaobo from the Shanghai Advanced Research Institute of the Chinese Academy of Sciences, Researcher Shang Tian from East China Normal University, Associate Professor Tan Hengxin from the School of Physics and Astronomy at Shanghai Jiao Tong University, Professor Wang Ziqiang from Boston College, USA, and Researcher He Lunhua from the Institute of Physics, Chinese Academy of Sciences, have jointly achieved significant progress in the novel antiferromagnetic cage-lattice metal material TbTi₃Bi₄. They have for the first time directly observed a peculiar orbital-selective double-periodic modulation phenomenon: within the antiferromagnetic state, distinct electron orbitals within the material exhibit a ‘division of labour,’ reconstructing the electronic band structure at specific wave vectors (~1/3, 0.28, 0). This reconstruction induces a topological phase transition, forming a Dirac cone at specific momentum points. This discovery unveils a novel microscopic mechanism for magnetic field generation and provides a crucial key to understanding the enigmatic one-third magnetisation plateau phenomenon in this material. The findings have been published in the premier international journal Physical Review X [Physical Review X, 15, 031012 (2025)].

Employing a multi-dimensional experimental approach combining angle-resolved photoemission spectroscopy (ARPES), neutron powder diffraction (NPD), and scanning tunnelling microscopy (STM), alongside density functional theory (DFT) calculations, the research team discovered that when the material cools below approximately 20.4 K into its antiferromagnetic state, its electronic structure undergoes a highly anisotropic double-period modulation: Fermi surface nesting instability with wave vectors 1/3 a* and 0.28 b* occurs along directions parallel (a-axis) and perpendicular (b-axis) to the terbium atomic zigzag chains, respectively, accompanied by corresponding band folding (Figures 1 and 2). Moreover, the energy gap in the a* direction is three times that in the b* direction, exhibiting strong anisotropy. STM measurements rule out charge density waves, confirming the origin lies in antiferromagnetism. Neutron diffraction further confirms the emergence of a magnetic structural modulation at (1/3 a*, 0.28 b*, 0) below the antiferromagnetic phase transition temperature in TbTi₃Bi₄, indicating this magnetic modulation arises from RKKY interactions induced by Fermi surface nesting (Figure 3). Notably, the cascade of band folding induces a symmetry-protected Dirac cone structure at the Brillouin zone edge [Figure 1(b)], signifying a magnetic phase transition-driven topological phase transition occurring in the antiferromagnetic state.

Theoretical calculations clearly indicate that this highly anisotropic dual modulation is primarily driven by the specific 5dxz electronic orbital of the terbium atom (Figure IV). This orbital exhibits high concentration in a specific region of the Fermi surface (along the A-L₁ direction), and its instability induces Fermi surface nesting, ultimately leading to the observed anisotropic antiferromagnetic order (1/3 a*, 0.28 b*, 0).

TbTi₃Bi₄ has attracted considerable attention due to its unique one-third magnetisation plateau exhibited under magnetic fields. The proposed orbital-selective anisotropic dual-modulation model and corresponding antiferromagnetic structure provide a rational explanation. Owing to the pronounced anisotropy of the energy gap both parallel and perpendicular to the quasi-one-dimensional terbium atomic zigzag chain in TbTi₃Bi₄, the 1/3 a* antiferromagnetic order becomes more stable under external fields, thereby establishing a dominant 3a-periodic unidirectional antiferromagnetic order. Based on the 3a-periodic magnetic moment reversal model, the formation of the 1/3 fractional magnetisation plateau can be naturally explained (Figure 5). Furthermore, during magnetic moment reversal, the generation of scattering leads to dramatic changes in electrical properties such as resistivity, consistent with experimental observations.

This work provides the first clear demonstration of how the orbital degrees of freedom of electrons selectively couple with local magnetic moments. It demonstrates that designing anisotropic structures—such as inserting quasi-one-dimensional chains—can enhance orbital selectivity, thereby enabling the manipulation of magnetic properties (e.g., inducing magnetic ordering at specific wavevectors or fractional magnetisation plateaus). This offers novel insights for developing novel magnetic quantum materials, such as more stable magnetic skyrmions and exotic topological states.

Zhang Renjie, a joint PhD candidate from the Li Zhengdao Institute at Shanghai Jiao Tong University and the Institute of Physics, Chinese Academy of Sciences; Yu Bocheng, a PhD candidate from East China Normal University; Tan Hengxin, Associate Professor at the School of Physics and Astronomy, Shanghai Jiao Tong University; and Cheng Yiwei, a joint PhD candidate from the Shanghai Advanced Research Institute of the Chinese Academy of Sciences and the Li Zhengdao Institute at Shanghai Jiao Tong University, are the co-first authors of this paper. Associate Professor Lü Baiqing from the Li Zhengdao Institute/School of Physics and Astronomy/Zhangjiang Advanced Research Institute at Shanghai Jiao Tong University, Researcher Huang Yaobo from the Advanced Research Institute of the Chinese Academy of Sciences, and Researcher Shang Tian from East China Normal University served as co-corresponding authors. This work received support from the Ministry of Science and Technology, the National Natural Science Foundation of China, and the Shanghai Municipal Government.

Paper link: https://journals.aps.org/prx/abstract/10.1103/c3tg-1lxl