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# Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet

## Abstract

Owing to the unusual geometry of kagome lattices—lattices made of corner-sharing triangles—their electrons are useful for studying the physics of frustrated, correlated and topological quantum electronic states1,2,3,4,5,6,7,8,9. In the presence of strong spin–orbit coupling, the magnetic and electronic structures of kagome lattices are further entangled, which can lead to hitherto unknown spin–orbit phenomena. Here we use a combination of vector-magnetic-field capability and scanning tunnelling microscopy to elucidate the spin–orbit nature of the kagome ferromagnet Fe3Sn2 and explore the associated exotic correlated phenomena. We discover that a many-body electronic state from the kagome lattice couples strongly to the vector field with three-dimensional anisotropy, exhibiting a magnetization-driven giant nematic (two-fold-symmetric) energy shift. Probing the fermionic quasi-particle interference reveals consistent spontaneous nematicity—a clear indication of electron correlation—and vector magnetization is capable of altering this state, thus controlling the many-body electronic symmetry. These spin-driven giant electronic responses go well beyond Zeeman physics and point to the realization of an underlying correlated magnetic topological phase. The tunability of this kagome magnet reveals a strong interplay between an externally applied field, electronic excitations and nematicity, providing new ways of controlling spin–orbit properties and exploring emergent phenomena in topological or quantum materials10,11,12.

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## Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.

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## Acknowledgements

Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547/Hasan) and the United States Department of Energy (US DOE) under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200). Work at the Institute of Physics of the Chinese Academy of Science (IOP CAS) was supported by the National Key R&D Program of China (grant number 2017YFA0206303). Work at Boston College is supported by US DOE grant DE-FG02-99ER45747. We also acknowledge the Natural Science Foundation of China (grant numbers 11790313, 11774422 and 11774424), National Key R&D Program of China (numbers 2016YFA0300403 and 2017YFA0302903), the Key Research Program of the Chinese Academy of Sciences (number XDPB08-1), Princeton Center for Theoretical Science (PCTS) and Princeton Institute for the Science and Technology of Materials (PRISM)’s Imaging and Analysis Center at Princeton University. T.-R.C. was supported by the Ministry of Science and Technology under a MOST Young Scholar Fellowship (MOST Grant for the Columbus Program number 107-2636-M-006-004-), the National Cheng Kung University, Taiwan, and the National Center for Theoretical Sciences (NCTS), Taiwan. M.Z.H. acknowledges support from Lawrence Berkeley National Laboratory and the Miller Institute of Basic Research in Science at the University of California, Berkeley in the form of a Visiting Miller Professorship. We thank D. Huse and T. Neupert for discussions.

### Reviewer information

Nature thanks S. Sachdev and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Author notes

1. These authors contributed equally: Jia-Xin Yin, Songtian S. Zhang, Hang Li

### Affiliations

1. #### Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, NJ, USA

• Jia-Xin Yin
• , Songtian S. Zhang
• , Guoqing Chang
• , Ilya Belopolski
• , Hao Zheng
• , Tyler A. Cochran
• , Su-Yang Xu
• , Guang Bian
•  & M. Zahid Hasan
2. #### Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China

• Hang Li
•  & Wenhong Wang
3. #### Department of Physics, Boston College, Chestnut Hill, MA, USA

• Kun Jiang
•  & Ziqiang Wang
4. #### Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China

• Bingjing Zhang
• , Kai Liu
•  & Zhong-Yi Lu

• Biao Lian
6. #### International Center for Quantum Materials and School of Physics, Peking University, Beijing, China

• Cheng Xiang
•  & Shuang Jia
7. #### CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China

• Cheng Xiang
•  & Shuang Jia
8. #### Department of Physics, National Cheng Kung University, Tainan, Taiwan

• Tay-Rong Chang

• Hsin Lin
10. #### Lawrence Berkeley National Laboratory, Berkeley, CA, USA

• M. Zahid Hasan

### Contributions

J.-X.Y. and S.S.Z. conducted the STM and STS experiments in consultation with M.Z.H.; H.L.,W.W., C.X. and S.J. synthesized and characterized the sequence of samples; K.J., G.C., B.Z., B.L., K.L., T-R.C., H.L., Z.-Y.L. and Z.W. carried out theoretical analysis in consultation with J.Y. and M.Z.H.; I.B., T.A.C., H.Z., S.-Y.X. and G.B. contributed to sample characterization and instrument calibration; J.-X.Y., S.S.Z. and M.Z.H performed the data analysis and figure development and wrote the paper with contributions from all authors; M.Z.H. supervised the project. All authors discussed the results, interpretation and conclusion.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to M. Zahid Hasan.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Longitudinal resistivity measurement.

The longitudinal resistivity ρxx was measured from 380 K to 5 K at zero magnetic field. The current was applied along the ab plane.

2. ### Extended Data Fig. 2 Magnetization at 5 K in different magnetic field directions.

The sharp saturation of the magnetization curve for the in-plane field suggests that the easy magnetization axis lies in the ab plane.

3. ### Extended Data Fig. 3 Interlayer resistivity evolution as a function of in-plane field azimuth angle.

The black line is the fitting curve. The inset shows a schematic of the sample (black hexagon) with the concentric electrical contacts used in such measurements (inner blue circle, voltage contacts; outer blue ring, current contacts).

4. ### Extended Data Fig. 4 Spectroscopic maps with vector-field conditions.

a, Topography of a large FeSn surface. b, Differential conductance map taken in the area shown in a at the energy of the side peak. c, Differential conductance maps with various vector-field conditions taken in the area shown in a at the energy of the side peak. The black arrow indicates the a axis and the red arrow represents the field vector. Their corresponding FFT images (known as QPI signals) are shown in Fig. 3.

5. ### Extended Data Fig. 5 Topographic image of a FeSn surface, showing two kinds of dark-spot defect.

The centres of the defects are located at Fe and Sn sites, based on the atomic assignment from Fig. 1.

6. ### Extended Data Fig. 6 Nonmagnetic scattering channels for helical spin–momentum texture with different magnetization directions.

a, The upper panel shows that spins cant towards the c axis to generate a net c-axis magnetization. The lower panel shows that backscattering is allowed in all directions. b, c, To generate a net in-plane magnetization, the momentum of the band shifts perpendicular to the in-plane direction and the spins reorganize their directions (similar to the Edelstein effect31), as shown in the upper panels (the faded red arrows represent helical spin texture without magnetization for reference). The spins are still locked perpendicular to the original momentum centre31 (black circle). The lower panels show that backscattering is allowed only in the magnetization direction and forbidden in the perpendicular direction owing to spin reversal.

7. ### Extended Data Fig. 7 Lorentz transmission electron microscopy images of the magnetic domain structures taken at different temperatures after turning off the external 0.7-T magnetic field applied along the c axis.

The measurement is taken in the ab plane in these images and the different shades indicate the different orientation of the spin relative to the ab plane. The skyrmions and stripe domains gradually disappear when the temperature drops to 130 K.

8. ### Extended Data Fig. 8 STM results on Mn3Sn.

a, b, Single crystals of Mn3Sn and Fe3Sn2, respectively. c, d, Typical STM images of the cleavage surface of Mn3Sn showing no clear atomic lattice structure.

9. ### Extended Data Fig. 9 Kagome lattice model.

a, Kagome lattice with Kane–Mele SOI. Here, $${v}_{{\rm{A}}{\rm{B}}}=2({{\boldsymbol{d}}}_{1}\times {{\boldsymbol{d}}}_{2})\cdot {\boldsymbol{z}}/\sqrt{3}=-1$$, where d1 is the unit vector from A to C and d2 is the unit vector from C to B. b, Flux Ω enclosed by the fundamental plaquette formed by sites A, B and C on the kagome lattice.

10. ### Extended Data Fig. 10 Band dispersion from the kagome model.

a, Red lines are the band structure for Mi along the z direction (Mc) with a Dirac mass generated by λ. Blue lines are the band structure for Mi in the xy plane (Mab), showing a vanishing Dirac mass gap even in the presence of λ. b, Similar to a but including bilayer splitting due to interlayer coupling. Only the spin minority bands are shown.

11. ### Extended Data Fig. 11 Effect of spin Berry phase.

a, The spin Berry phase Ωijk is equal to half the solid angle formed by spins Si, Sj and Sk. b, An electron hopping in the chiral spin background is equivalent to hopping in the presence of a gauge flux Ω. c, Band structures in the presence of both λand chiral flux Ω, when the magnetic field and the magnetization are along the xy plane (Mab) and the z direction (Mc).