# Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states

## Abstract

Surface states of three-dimensional topological insulators exhibit the phenomenon of spin–momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, but the main technique currently available is spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magnetoresistance, which depends on the relative orientation of the current with respect to the magnetic field as well as the crystallographic axes, and scales linearly with both the applied electric and magnetic fields. This bilinear magnetoelectric resistance can be used to map the spin texture of topological surface states by simple transport measurements. For a prototypical Bi2Se3 single layer, we can map both the in-plane and out-of-plane components of the spin texture (the latter arising from hexagonal warping). Theoretical calculations suggest that the bilinear magnetoelectric resistance originates from conversion of a non-equilibrium spin current into a charge current under application of the external magnetic field.

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## Acknowledgements

This work was partially supported by A*STAR’s Pharos Programme on Topological Insulators, Ministry of Education–Singapore Academic Research Fund Tier 1 (R-263-000-B47-112). The work by S.S.-L.Z. and G.V. was supported by National Science Foundation (NSF) grant DMR-1406568, and work on the revised manuscript by S.S.-L.Z. at Argonne National Laboratory was supported by Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. S.S.-L.Z. thanks O. Heinonen, A. Hoffmann, G. Bian, A. Fert, X. Jin, D. Loss and S. Zhang for helpful discussions.

## Author information

Authors

### Contributions

P.H. and H.Y. planned the study. D.Z. and P.H. fabricated devices. P.H. and D.Z. measured transport properties. Y.L., Y.W. and J.Y. helped with characterization. S.S.-L.Z. and G.V. devised the theory. All authors discussed the results. P.H., S.S.-L.Z., D.Z., G.V. and H.Y. wrote the manuscript. H.Y. supervised the project.

### Corresponding author

Correspondence to Hyunsoo Yang.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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## Supplementary information

### Supplementary information

Additional data, including 12 figures and 26 references.

## Rights and permissions

Reprints and Permissions

He, P., Zhang, S.SL., Zhu, D. et al. Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states. Nature Phys 14, 495–499 (2018). https://doi.org/10.1038/s41567-017-0039-y

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