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# Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors

## Abstract

Efficient magnetic control of electronic conduction is at the heart of spintronic functionality for memory and logic applications1,2. Magnets with topological band crossings serve as a good material platform for such control, because their topological band degeneracy can be readily tuned by spin configurations, dramatically modulating electronic conduction3,4,5,6,7,8,9,10. Here we propose that the topological nodal-line degeneracy of spin-polarized bands in magnetic semiconductors induces an extremely large angular response of magnetotransport. Taking a layered ferrimagnet, Mn3Si2Te6, and its derived compounds as a model system, we show that the topological band degeneracy, driven by chiral molecular orbital states, is lifted depending on spin orientation, which leads to a metal–insulator transition in the same ferrimagnetic phase. The resulting variation of angular magnetoresistance with rotating magnetization exceeds a trillion per cent per radian, which we call colossal angular magnetoresistance. Our findings demonstrate that magnetic nodal-line semiconductors are a promising platform for realizing extremely sensitive spin- and orbital-dependent functionalities.

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## Data availability

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

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## Acknowledgements

We thank H. W. Lee and J. Y. Kim for productive discussion. We also thank H. G. Kim from the Pohang Accelerator Laboratory (PAL) for technical support. This work was supported by the Institute for Basic Science (IBS) through the Center for Artificial Low Dimensional Electronic Systems (no. IBS-R014-D1), and by the National Research Foundation of Korea (NRF) through the SRC (grant no. 2018R1A5A6075964), and the Max Planck-POSTECH Center for Complex Phase Materials (grant no. 2016K1A4A4A01922028). H.H. was supported by Samsung Science and Technology Foundation under project number SSTF-BA2002-06. The pulsed field work was supported by the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL). K.K. was supported by the NRF (grant no. 2016R1D1A1B02008461), and the internal R&D programme at KAERI (no. 524460-21). B.-J.Y. was supported by the Institute for Basic Science in Korea (grant no. IBS-R009-D1), Samsung Science and Technology Foundation under project number SSTF-BA2002-06, and NRF grants funded by the Korea government (MSIT; no. 2021R1A2C4002773 and no. NRF-2021R1A5A1032996). J.H.K. acknowledges financial support from the NRF through grant no. NRF-2021R1A2C3004989 and grant no. 2017R1A5A1014862 (vdWMRC SRC Program). B.K. acknowledges support by the NRF through grant no. 2021R1C1C1007017. S.-W.C. was partially supported by the Center for Quantum Materials Synthesis (cQMS), funded by the Gordon and Betty Moore Foundation’s EPiQS initiative through grant GBMF10104, and by Rutgers University. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative agreement no. DMR-1644779 and the State of Florida.

## Author information

Authors

### Contributions

J.S.K., J.S. and C.D. conceived the projects. J.S. and S.P. performed the transport measurements on bulk crystals. C.D., under the guidance of S.W.-C., synthesized the bulk crystals. H.H., B.K., K.K., G.Y.C. and B.-J.Y. performed the electronic-structure calculations and the band analysis. J.E.L. and J.H.K. conducted terahertz spectroscopy measurements and spectral analysis. J.P., Y.S. and E.S.C. conducted high-field experiments. G.Y.C. and H.W.Y. contributed to the data analysis. J.S., C.D., H.H., J.H.K., B.-J.Y., K.K. and J.S.K. co-wrote the manuscript. All authors discussed the results and commented on the paper.

### Corresponding authors

Correspondence to Jae Hoon Kim, Bohm-Jung Yang, Kyoo Kim or Jun Sung Kim.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Yong Xu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Single crystal growth.

a, X-ray diffraction pattern of the undoped, Ge- and Se-doped Mn3Si2Te6 crystals recorded on (0 0 L) plane at room temperature. The insets show a typical crystal image and a magnified X-ray diffraction data for Bragg peak (004). b–d, The energy dispersive spectroscopy images on a selected area of Mn3Si2Te6 crystal, taken at Mn $$K\alpha 1$$ (b), Si $$K\alpha 1$$ (c) and Te $$L\alpha 1$$ (d) edges. e, Combined Mn, Si and Te EDS image, showing a spatially uniform stoichiometry of Mn3Si2Te6 crystal.

### Extended Data Fig. 2 Magnetic properties of Mn3Si2Te6.

a–c, Temperature dependent magnetic susceptibility $$\chi (T)$$ of undoped, Ge-doped and Se-doped Mn3Si2Te6 single crystals for $$H\parallel c$$ (green) and $$H\parallel ab$$ (red) at H = 1 kOe. d–f, Magnetic field-dependent magnetization $$M(H)$$ of undoped, Ge-doped and Se-doped Mn3Si2Te6 single crystals for $$H\parallel c$$ (green) and $$H\parallel ab$$ (red) taken at T = 2 or 5 K.

### Extended Data Fig. 3 Electronic conduction of Mn3Si2Te6 at zero magnetic field.

a–c, In-plane resistivity $${\rho }_{ab}$$ as a function of the inverse temperature for undoped (a), Ge-doped (b) and Se-doped (c) Mn3Si2Te6 single crystals. Above and below Tc, $${\rho }_{ab}(T)$$ follows the thermally activated semiconducting behaviour, described by $${\rho }_{ab}(T)$$ $$\exp (\Delta /{k}_{B}T)$$ (red line), with different transport gap Δ (Extended Data Table 1). d–f, Variable-range hopping (VRH) conduction at low temperatures for undoped (d), Ge-doped (e) and Se-doped (f) Mn3Si2Te6 single crystals. The in-plane resistivity $${\rho }_{ab}(T)$$ is plotted as a function of 1/$${T}^{p}$$ with exponents p = 1/4 (left), 1/3 (middle), and 1/2 (right), corresponding to the Mott-VRH models with three- and two-dimensions and the Efros-Shklovskii (ES) VRH model, respectively.

### Extended Data Fig. 4 Electronic conduction of Mn3Si2Te6 under magnetic fields.

a–f, Temperature dependent in-plane resistivity $${\rho }_{ab}(T)$$ (left panel) and its first derivative $$d{\rho }_{ab}(T)/dT$$ (rigth panel) for undoped (upper), Ge-doped (middle) and Se-doped (lower) Mn3Si2Te6 at different magnetic fields and orientations, $$H\parallel ab$$ (a–c) and $$H\parallel c$$ (d–f). The estimated Tc is indicated by the arrows. g–i, Magnetic field dependent Tc for $$H\parallel ab$$ and $$H\parallel c$$. The errors in the experimental data are smaller than the size of the points.

### Extended Data Fig. 5 Magnetic field dependent semiconducting conduction in Mn3Si2Te6.

a–c, Arrhenius plot of $${\rho }_{ab}(T)$$ for $$H\parallel ab$$ (left panel) and $$H\parallel c$$ (right panel) at various magnetic fields for the undoped (a), Ge-doped (b) and Se-doped (c) Mn3Si2Te6. d–f, Magnetic field dependent activation gap $$\Delta (H)$$, extracted from the Arrhenius plot of $${\rho }_{ab}(T)$$, for $$H\parallel c$$ (solid symbols) and $$H\parallel ab$$ (open symbols). The errors in the experimental data are smaller than the size of the points.

### Extended Data Fig. 6 Magnetic and magnetotransport properties of Mn3Si2Te6 at high magnetic fields.

a, Magnetic field dependent torque magnetometry $$\tau (H)$$ for different field angle θ with respect to the ab-plane. No signature of the ferrimagentic-to-ferromagentic transition is observed up to H ~ 70 T. b, Magnetic field dependent magnetization $$M({\rm{H}})$$, taken under pulsed magnetic fields at T = 4.2 K (black line). Magnetization M(H) under static magnetic fields is also plotted for comparison (orange symbol). c, Magnetic field dependent in-plane resistivity $${\rho }_{ab}(H)$$ for $$H\parallel ab$$ and $$H\parallel c$$. For $$H\parallel ab$$, the resistivity $${\rho }_{ab}(H)$$ exhibits a relatively slow decrease with magnetic fields up to ~ 30 T, while rapid reduction of $${\rho }_{ab}(H)$$ for $$H\parallel c$$ induces the insulator-to metal-transition at H~ 4 T.

### Extended Data Fig. 7 Temperature- and magnetic field-dependent angular magnetoresistance.

a–i, Angle dependent resistivity $${\rho }_{ab}(\theta )$$ at various temperatures and magnetic fields for undoped (a–c), Ge-doped (d–f) and Se-doped (h, i) samples. The tilting angle of the external magnetic field (θ) with respect to the ab-plane and its azimuthal angle ϕ against the current direction are illustrated in g. For the undoped sample, $${\rho }_{ab}(\theta )$$ taken for two different azimuthal angle ϕ = 0° ($$M\parallel J$$, open symbol) and 90° ($$M\perp J$$, solid symbol) are almost identical. j, Angular magnetoresistance (MR) $$(1/{\rho }_{{\rm{\min }}})$$ $$d\rho (\theta )/d\theta$$ as a function of temperature under H = 5 T (undoped), 6 T (Ge-doped) and 10 T (Se-doped). The arrows indicate Tc at zero magnetic field. k, Angular MR of the undoped and doped Mn3Si2Te6 as a function of magnetic field. Angular MR of Eu-based antiferromagnets and topological magnet candidate CeAlGe are also plotted for comparison19,41,42,44.

### Extended Data Fig. 8 Terahertz absorption spectroscopy.

a–i, Absorption coefficient as a function of energy under zero magnetic field for undoped, Ge-doped and Se-doped Mn3Si2Te6 taken at various temperatures. j–o, Absorption coefficient as a function of energy for the undoped (upper panel), Ge-doped (middle panel) and Se-doped (lower panel) Mn3Si2Te6 taken at T = 1.5 K for $$H\parallel ab$$ (j–l) and $$H\parallel c$$ (m–o). The peaks that appear in the case of the doped samples are infrared-active transverse optical (TO) phonon modes.

## Supplementary information

### Supplementary Information

This file contains Supplementary Notes 1–5, Figs. 1–6 and References.

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Seo, J., De, C., Ha, H. et al. Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors. Nature 599, 576–581 (2021). https://doi.org/10.1038/s41586-021-04028-7

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