Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Magnetic nodal-line semimetal and semiconductor.
Fig. 2: Nodal-line band degeneracy of the chiral orbital states in Mn3Si2Te6.
Fig. 3: Metal–insulator transition by spin orientation.
Fig. 4: Colossal angular MR.

Similar content being viewed by others

Data availability

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


  1. Žutić, I., Fabian, J. & Das Sarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    Article  ADS  Google Scholar 

  2. Fert, A. Nobel lecture: Origin, development, and future of spintronics. Rev. Mod. Phys. 80, 1517–1530 (2008).

    Article  ADS  CAS  Google Scholar 

  3. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  CAS  Google Scholar 

  4. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    Article  ADS  CAS  Google Scholar 

  5. Wang, J. & Zhang, S. C. Topological states of condensed matter. Nat. Mater. 16, 1062–1067 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Manna, K., Sun, Y., Muechler, L., Kübler, J. & Felser, C. Heusler, Weyl and Berry. Nat. Rev. Mater. 3, 244–256 (2018).

    Article  ADS  CAS  Google Scholar 

  8. Nagaosa, N., Morimoto, T. & Tokura, Y. Transport, magnetic and optical properties of Weyl materials. Nat. Rev. Mater. 5, 621–636 (2020).

    Article  ADS  CAS  Google Scholar 

  9. Kumar, N., Guin, S. N., Manna, K., Shekhar, C. & Felser, C. Topological quantum materials from the viewpoint of chemistry. Chem. Rev. 121, 2780–2815 (2021).

    Article  CAS  PubMed  Google Scholar 

  10. Narang, P., Garcia, C. A. & Felser, C. The topology of electronic band structures. Nat. Mater. 20, 293–300 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Okamura, Y. et al. Giant magneto-optical responses in magnetic Weyl semimetal Co3Sn2S2. Nat. Commun. 11, 4619 (2020).

  13. Ding, L. et al. Intrinsic anomalous Nernst effect amplified by disorder in a half-metallic semimetal. Phys. Rev. X 91, 041061 (2019).

    Google Scholar 

  14. Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119–1124 (2018).

    Article  CAS  Google Scholar 

  15. Xu, L. et al. Anomalous transverse response of Co2MnGa and universality of the room-temperature \({\alpha }_{ij}^{A}/{\sigma }_{ij}^{A}\) ratio across topological magnets. Phys. Rev. B 101, 180404 (2020).

    Article  ADS  CAS  Google Scholar 

  16. Li, P. et al. Giant room temperature anomalous Hall effect and tunable topology in a ferromagnetic topological semimetal Co2MnAl. Nat. Commun. 11, 3476 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  17. Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Kim, K. et al. Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal. Nat. Mater. 17, 794–799 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Suzuki, T. et al. Singular angular magnetoresistance in a magnetic nodal semimetal. Science 365, 377–381 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Sakai, A. et al. Iron-based binary ferromagnets for transverse thermoelectric conversion. Nature 581, 53–57 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Chang, C. Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014).

    Article  CAS  Google Scholar 

  23. Yasuda, K. et al. Quantized chiral edge conduction on domain walls of a magnetic topological insulator. Science 358, 1311–1314 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Yasuda, K. et al. Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states. Nat. Nanotechnol. 15, 831–835 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Chang, C. Z. et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  27. Rimet, R., Schlenker, C. & Vincent, H. A new semiconducting ferrimagnet: a silicon manganese telluride. J. Magn. Magn. Mater. 25, 7–10 (1981).

    Article  ADS  CAS  Google Scholar 

  28. Vincent, H., Leroux, D., Bijaoui, D., Rimet, R. & Schlenker, C. Crystal structure of Mn3Si2Te6. J. Solid State Chem. 63, 349–352 (1986).

    Article  ADS  CAS  Google Scholar 

  29. May, A. F. et al. Magnetic order and interactions in ferrimagnetic Mn3Si2Te6. Phys. Rev. B 95, 174440 (2017).

    Article  ADS  Google Scholar 

  30. Kanamori, J. & Terakura, K. A general mechanism underlying ferromagnetism in transition metal compounds. J. Phys. Soc. Jpn 70, 1433–1434 (2001).

    Article  ADS  CAS  Google Scholar 

  31. Jungwirth, T., Sinova, J., Mašek, J., Kučera, J. & MacDonald, A. H. Theory of ferromagnetic (III,Mn)V semiconductors. Rev. Mod. Phys. 78, 809–864 (2006).

    Article  ADS  CAS  Google Scholar 

  32. Yu, P. Y. & Cardona, M. Fundamentals of Semiconductors (Springer, 2005).

  33. Sharma, S. K., Sagar, P., Gupta, H., Kumar, R. & Mehra, R. M. Meyer–Neldel rule in Se and S-doped hydrogenated amorphous silicon. Solid State Electron. 51, 1124–1128 (2007).

    Article  ADS  CAS  Google Scholar 

  34. Durá, O. J. et al. Transport, electronic, and structural properties of nanocrystalline CuAlO2 delafossites. Phys. Rev. B 83, 045202 (2011).

    Article  ADS  Google Scholar 

  35. Hauser, A. J. et al. Electronic and magnetic tunability of Sr2CrReO6 films by growth-mediated oxygen modulation. Appl. Phys. Lett. 102, 032403 (2013).

    Article  ADS  Google Scholar 

  36. Kokado, S., Tsunoda, M., Harigaya, K. & Sakuma, A. Anisotropic magnetoresistance effects in Fe, Co, Ni, Fe4N, and half-metallic ferromagnet: a systematic analysis. J. Phys. Soc. Jpn 81, 024705 (2012).

    Article  ADS  Google Scholar 

  37. Wang, H. et al. Giant anisotropic magnetoresistance and nonvolatile memory in canted antiferromagnet Sr2IrO4. Nat. Commun. 10, 2280 (2019).

  38. Endo, T., Kubota, H. & Miyazaki, T. Magnetoresistance of Co2MnAl1-xSix Heusler alloys. J. Magn. Soc. Jpn 23, 1129–1132 (1999).

    Article  CAS  Google Scholar 

  39. Eckstein, J. N., Bozovic, I., O’Donnell, J., Onellion, M. & Rzchowski, M. S. Anisotropic magnetoresistance in tetragonal La1-xCaxMnO3 thin films. Appl. Phys. Lett. 69, 1312 (1996).

    Article  ADS  CAS  Google Scholar 

  40. Li, R.-W. et al. Anomalously large anisotropic magnetoresistance in a perovskite manganite. Proc. Natl Acad. Sci. USA 106, 14224–14229 (2009).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  41. Wang, Z.-C. et al. Colossal magnetoresistance without mixed valence in a layered phosphide crystal. Adv. Mater. 33, 2005755 (2021).

    Article  CAS  Google Scholar 

  42. Soh, J.-R. et al. Magnetic and electronic structure of Dirac semimetal candidate EuMnSb2. Phys. Rev. B 100, 174406 (2019).

    Article  ADS  CAS  Google Scholar 

  43. Yin, J. et al. Large negative magnetoresistance in the antiferromagnetic rare-earth dichalcogenide EuTe2. Phys. Rev. Mater. 4, 013405 (2020).

    Article  ADS  CAS  Google Scholar 

  44. Yang, H. et al. Observation of an unusual colossal anisotropic magnetoresistance effect in an antiferromagnetic semiconductor. Preprint at (2021).

  45. Ni, Y. et al. Colossal magnetoresistance via avoiding fully polarized magnetization in the ferrimagnetic insulator Mn3Si2Te6. Phys. Rev. B 103, L161105 (2021).

    Article  ADS  CAS  Google Scholar 

  46. Manyala, N. et al. Magnetoresistance from quantum interference effects in ferromagnets. Nature 404, 581–584 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Tsujii, N., Nishide, A., Hayakawa, J. & Mori, T. Observation of enhanced thermopower due to spin fluctuation in weak itinerant ferromagnet. Sci. Adv. 5, eaat5935 (2019).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  48. Lu, C. et al. Crossover of conduction mechanism in Sr2IrO4 epitaxial thin films. Appl. Phys. Lett. 105, 082407 (2014).

    Article  ADS  Google Scholar 

  49. Yildiz, A., Serin, N., Serin, T. & Kasap, M. Crossover from nearest-neighbor hopping conduction to Efros–Shklovskii variable-range hopping conduction in hydrogenated amorphous silicon films. Jpn. J. Appl. Phys. 48, 111203 (2009).

    Article  ADS  Google Scholar 

  50. Li, Z. et al. Transition between Efros–Shklovskii and Mott variable-range hopping conduction in polycrystalline ermanium thin films. Semicond. Sci. Technol. 32, 035010 (2017).

    Article  ADS  Google Scholar 

  51. Koepernik, K. & Eschrig, H. Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 59, 1743–1757 (1999).

    Article  ADS  CAS  Google Scholar 

  52. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  PubMed  Google Scholar 

  53. Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014).

    Article  ADS  CAS  MATH  Google Scholar 

  54. Tsirkin, S. S. High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code. npj Comput. Mater. 7, 33 (2021).

    Article  ADS  Google Scholar 

Download references


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 and Affiliations



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.

Additional information

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.

Extended Data Table 1 Characteristic parameters of the undoped, Ge-doped and Se-doped Mn3Si2Te6 including the ferrimagnetic transition temperature (Tc), the saturated magnetization \(({M}_{{\rm{sat}}})\) and fields \(({H}_{{\rm{sat}}})\) along the c-axis and the ab-plane, the magnetocrystalline anisotropy energy (K), the activation gap above Tc \(({\Delta }_{{\rm{P}}M})\) and below Tc (Δ), and the temperature scale T0 of the ES-VRH model
Extended Data Table 2 Magnetoresistance (MR) and angular MR of various magnetic materials. For each case, the magnetic phase, the magnetic ordering temperature (Tc or TN), the MR, the angular MR, and the corresponding temperature (T) and magnetic field (H) are listed

Supplementary information

Supplementary Information

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

Peer Review File

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seo, J., De, C., Ha, H. et al. Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors. Nature 599, 576–581 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing