Dirac-fermion-mediated ferromagnetism in a topological insulator

Journal name:
Nature Physics
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Topological insulators are a newly discovered class of materials in which helical conducting modes exist on the surface of a bulk insulator1, 2, 3, 4, 5, 6. Recently, theoretical works have shown that breaking gauge symmetry7 or time-reversal symmetry8 in these materials produces exotic states that, if realized, represent substantial steps towards realizing new magnetoelectric effects9, 10 and tools useful for quantum computing11. Here we demonstrate the latter symmetry breaking in the form of ferromagnetism arising from the interaction between magnetic impurities and the Dirac fermions12, 13. Using devices based on cleaved single crystals of Mn-doped Bi2Te3−ySey, the application of both solid-dielectric and ionic-liquid gating allows us to measure the transport response of the surface states within the bulk bandgap in the presence of magnetic ions. By tracking the anomalous Hall effect we find that the surface modes support robust ferromagnetism as well as magnetoconductance that is consistent with enhanced one-dimensional edge-state transport on the magnetic domain wall. Observation of this evidence for quantum transport phenomena demonstrates the accessibility of these exotics states in devices and may serve to focus the wide range of proposed methods for experimentally realizing the quantum anomalous Hall effect8, 10 and states required for quantum computing14, 15.

At a glance


  1. Ferromagnetism in a magnetically doped topological insulator.
    Figure 1: Ferromagnetism in a magnetically doped topological insulator.

    a, Schematic of a Dirac electron with spin σ and momentum k on the surface of a topological insulator with an average z component of local spins . In the TRS broken state, the competition between the exchange interaction and the Rashba-like surface texture yields a finite component of σ in the z direction. b, Breaking of TRS opens a gap in the surface state spectrum starting at the Dirac point located at the time reversal invariant momentum Γ. c, Bulk crystals of MnxBi2−xTe3−ySey show ferromagnetic ordering below TC=13K, as seen in M(T). Both σxx and Δσxy (the spontaneous component of σxy) show anomalies at TC. The inset shows scaling of M and the anomalous part of the Hall conductivity σxyA. d, Device structure for measurement of microcrystals. A back gate is formed by the SiO2/Si substrate and a top gate with the deposition of ionic liquid. e, Atomic force micrograph (false colour) of Ti/Au contacts made by electron beam lithography for device B. The crystal thickness is 7nm. f, Measurements of Δσxy for device A indicate a ferromagnetic transition. Application of the back-gate voltage V B is shown to tune the magnetic response with varying of the transition temperature TC.

  2. AHE and
TC tuned by carrier density.
    Figure 2: AHE and TC tuned by carrier density.

    a, Hall conductivity σxy at T=2K for device A at several back-gate voltages V B, offset vertically 0.04 e2/h. The observed anomalous Hall response grows on depletion of carriers. b, After application of V T=−3V, device B shows a further enhanced spontaneous σxy whereas the ordinary Hall response σxyN changes from n-type to p-type at the most negative V B. Here, a vertical offset of 0.4 e2/h is used. c, Temperature dependence of σxy in device C. There is a sharp onset of σxyA below 12K. See Fig. 1f for the case of device A. d, Estimates of TC for devices A–E. Contrary to conventional dilute magnetic semiconductors, the transition is suppressed on increasing the carrier density. The error bars reflect the discreteness of the measurement in T. The inset depicts the critical chemical potential position μc for the onset of ferromagnetic behaviour, as estimated from σxyN relative to the conduction band (CB), valence band (VB) and surface states (SS).

  3. Sign reversal in magnetoconductivity driven by gating for device A.
    Figure 3: Sign reversal in magnetoconductivity driven by gating for device A.

    a, Back-gate voltage V B dependence of σxx, showing the onset of enhanced conductivity at the reversal of M on depletion of carriers at T=2K. b, Virgin curve and trained behaviour for V B=−100V (n2D=1.5×1013e−2cm−2). c, Schematic depiction of the domain structure in a magnetic topological insulator; domain walls across the opposite M domains support a chiral mode (shown in green). dT dependence of σxx(B) through the ferromagnetic transition gated with V B=−100V. The enhanced conductivity can be seen to track the M reversal. eσxx(B) at high carrier density shows hysteresis of the conventional form, that is, suppressed conductivity attributed to carrier scattering at magnetic domain walls. f, The difference between the virgin and trained σxx (≡σxxv) exhibits a crossover from positive to negative values on increased carrier density.


  1. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).
  2. Bernevig, B. A., Hughes, T. L. & Zhang, S-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 17571761 (2006).
  3. Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766770 (2007).
  4. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
  5. Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306(R) (2007).
  6. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970974 (2008).
  7. Linder, J., Tanaka, Y., Yokoyama, T., Sudbo, A. & Nagaosa, N. Unconventional superconductivity on a topological insulator. Phys. Rev. Lett. 104, 067001 (2010).
  8. Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 6164 (2010).
  9. Qi, X-L., Hughes, T. L. & Zhang, S-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
  10. Nomura, K. & Nagaosa, N. Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators. Phys. Rev. Lett. 106, 166802 (2011).
  11. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
  12. Liu, Q., Liu, C-X., Xu, C., Qi, X-L. & Zhang, S-C. Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett. 102, 156603 (2009).
  13. Abanin, D. A. & Pesin, D. A. Ordering of magnetic impurities and tunable electronic properties of topological insulators. Phys. Rev. Lett. 106, 136802 (2011).
  14. Fu, L. & Kane, C. L. Probing neutral majorana fermion edge modes with charge transport. Phys. Rev. Lett. 102, 216403 (2009).
  15. Akhmerov, A., Nilsson, J. & Beenakker, C. Electrically detected interferometry of Majorana fermions in a topological insulator. Phys. Rev. Lett. 102, 216404 (2009).
  16. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398402 (2009).
  17. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178181 (2009).
  18. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 30453067 (2010).
  19. Chen, Y. L. et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329, 659662 (2010).
  20. Dietl, T., Haury, A. & Merle d’ Aubigne, Y. Free carrier-induced ferromagnetism in structures of diluted magnetic semiconductors. Phys. Rev. B 55, 33473350(R) (1997).
  21. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 15391592 (2010).
  22. Ye, J. T. et al. Liquid-gated interface superconductivity on an atomically flat film. Nature Mater. 9, 125128 (2010).
  23. Checkelsky, J. G., Hor, Y. S., Cava, R. J. & Ong, N. P. Bulk band gap and surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3. Phys. Rev. Lett. 106, 196801 (2011).
  24. Choi, J. et al. Single crystal growth and magnetic properties of Mn-doped Bi2Se3 and Sb2Se3. J. Magn. 9, 125127 (2004).
  25. Dietl, T., Ohno, H., Matsukura, F., Cibert, J. & Ferrand, D. Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science 287, 10191022 (2000).
  26. Ohno, H. et al. Electric-field control of ferromagnetism. Nature 408, 944946 (2000).
  27. Chiba, D., Matsukura, F. & Ohno, H. Electric-field control of ferromagnetism in (Ga,Mn)As. Appl. Phys. Lett. 89, 162505 (2006).
  28. Kim, D. et al. Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3. Nature Phys. 8, 460464 (2012).
  29. Levy, P. M. & Zhang, S. Resistivity due to domain wall scattering. Phys. Rev. Lett. 79, 51105113 (1997).
  30. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 16981701 (1979).

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  1. Cross-Correlated Materials Research Group (CMRG) and Correlated Electron Research Group (CERG), RIKEN-ASI, Wako 351-0198, Japan

    • Joseph G. Checkelsky,
    • Yoshihiro Iwasa &
    • Yoshinori Tokura
  2. Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Hongo, Tokyo 113-8656, Japan

    • Jianting Ye,
    • Yoshinori Onose,
    • Yoshihiro Iwasa &
    • Yoshinori Tokura
  3. Multiferroics Project, ERATO, Japan Science and Technology Agency (JST), c/o University of Tokyo, Hongo, Tokyo 113-8656, Japan

    • Yoshinori Onose &
    • Yoshinori Tokura


J.G.C. and Y.O. performed the single-crystal growth and experiments. J.G.C. and J.Y. made devices and performed device experiments aided by Y.O. J.G.C. analysed the data and wrote the manuscript with contributions from all authors. Y.I. and Y.T. contributed to discussion of the results and guided the project. Y.T. conceived and coordinated the project.

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