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# Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator

## Abstract

Understanding and control of spin degrees of freedom on the surfaces of topological materials are key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal (TR) symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi2Se3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies, which directly demonstrate the mechanics of TR symmetry breaking on the surface. We further show that an insulating gap induced by quantum tunnelling between surfaces exhibits spin texture modulation at low energies but respects TR invariance. These spin phenomena and the control of their Fermi surface geometrical phase first demonstrated in our experiments pave the way for the future realization of many predicted exotic magnetic phenomena of topological origin.

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## Acknowledgements

Work at Princeton University is supported by the US National Science Foundation Grant, NSF-DMR-1006492. M.Z.H. acknowledges visiting-scientist support from Lawrence Berkeley National Laboratory and additional partial support from the A. P. Sloan Foundation and NSF-DMR-0819860. The spin-resolved and spin-integrated photoemission measurements using synchrotron X-ray facilities are supported by the Swedish Research Council, the Knut and Alice Wallenberg Foundation, the Swiss Light Source, the Swiss National Science Foundation, the German Federal Ministry of Education and Research, and the Basic Energy Sciences of the US Department of Energy. Theoretical computations are supported by the US Department of Energy (DE-FG02-07ER46352 and AC03-76SF00098) as well as the National Science Council and Academia Sinica in Taiwan, and benefited from the allocation of supercomputer time at NERSC and Northeastern University’s Advanced Scientific Computation Center. Sample growth and characterization are supported by US DARPA (N66001-11-1-4110). We gratefully acknowledge A. Preobrajenski for beamline assistance on XMCD measurements (supported by DE-FG02-05ER46200) at the D1011 beamline at Maxlab in Lund, Sweden. We acknowledge helpful discussions with S-Q. Shen and L. Balents. We also thank S-K. Mo and A. Fedorov for beamline assistance on spin-integrated photoemission measurements (supported by DE-FG02-05ER46200) at Lawrence Berkeley National Laboratory (The synchrotron facility is supported by the US DOE).

## Author information

Authors

### Contributions

S-Y.X. performed the experiments with assistance from M.N., C.L., L.A.W., N.A. and M.Z.H.; D.Z., A.R. and N.S. provided samples; M.L., T.B., J.S-B., O.R., G.L., B.S., J.H.D. and J.O. provided beamline assistance; T-R.C., H-T.J., H.L. and A.B. carried out the theoretical calculations; M.Z.H. was responsible for the overall direction, planning and integration among the different research units.

### Corresponding author

Correspondence to M. Zahid Hasan.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Information (PDF 5584 kb)

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Xu, SY., Neupane, M., Liu, C. et al. Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator. Nature Phys 8, 616–622 (2012). https://doi.org/10.1038/nphys2351

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