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# Efficient spin–orbit torque in magnetic trilayers using all three polarizations of a spin current

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An Author Correction to this article was published on 10 June 2022

## Abstract

Spin–orbit coupling can convert a charge current into a spin current, thereby generating a spin–orbit torque (SOT). Energy-efficient, commercially viable SOT technology requires field-free switching of perpendicular magnetization at low current. In heterostructures incorporating ferromagnets, the polarization of spin current consists, in general, of three vectors: $$( {{{{\hat{\mathrm z}}}} \times {{{\hat{\mathrm E}}}}} )$$, $${{{\hat{\mathrm m}}}}$$ and $${{{\hat{\mathrm m}}}} \times ( {{{{\hat{\mathrm z}}}} \times {{{\hat{\mathrm E}}}}} )$$, where $${{{\hat{\mathrm z}}}}$$ is the film normal, $${{{\hat{\mathrm E}}}}$$ is the electric-field direction and $${{{\hat{\mathrm m}}}}$$ is the magnetization direction. Previous studies on SOT have used only part of all the three polarizations, because the two $${{{\hat{\mathrm m}}}}$$-dependent polarizations are mutually orthogonal. Here we show that all the three polarizations can be exploited in systems with ferromagnet/non-magnet/ferromagnet trilayers, having a bottom epitaxial ferromagnet layer with a tilted magnetic easy axis. The approach reduces the field-free SOT switching current compared with approaches that exploit only part of all the three polarizations. We also show that this technique can be used with a sputtered polycrystalline trilayer, illustrating its potential applicability to mass production.

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## Data availability

Source data are provided with this paper. The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

This work was supported by Samsung Electronics (IO200721-07533-01 and IO201019-07699-01) (Development of interfacial SOT materials, theory and modelling of SOT). B.-G.P. acknowledges financial support from the National Research Foundation of Korea (NRF-2020R1A2C2010309). K.-J.L. acknowledges financial support from the National Research Foundation of Korea (NRF-2020M3F3A2A01082591). R.T. was supported by the Graduate Program in Spintronics at Tohoku University. M.K. and J.N. acknowledges financial support from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Grant-in-Aid for Scientific Research (grant no. 15H05699). J.M.Y. was supported by KAIST-funded Global Singularity Research Program for 2019 and the Wearable Platform Materials Technology Center (WMC) funded by the National Research Foundation of Korea (NRF-2016R1A5A1009926). J.Y.P. specially thanks NRF funded by the Korean Government for scholarship support through the Global PhD Fellowship Program (2018H1A2A1060105).

## Author information

Authors

### Contributions

B.-G.P. and J.R. planned the study. J.R., R.T., M.K. and J.N. grew the epitaxial samples. J.R., R.T., G.C. and J.K. fabricated the devices and performed the electrical and magnetic measurements. J.Y.P., H.B.J. and J.M.Y. performed the crystallographic characterization. S.-J.K. and K.-J.L. carried out the theoretical calculations. J.R., B.-G.P. and K.-J.L. performed the data analysis. J.R., K.-J.L. and B.-G.P. wrote the manuscript with comments from all the co-authors.

### Corresponding authors

Correspondence to Kyung-Jin Lee or Byong-Guk Park.

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### Competing interests

The authors declare no competing interests.

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Nature Electronics thanks Jingsheng Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–25, Discussion and Table 1.

## Source data

### Source Data Fig. 1

Statistical source data.

### Source Data Fig. 2

Statistical source data.

### Source Data Fig. 3

Statistical source data.

### Source Data Fig. 4

Statistical source data.

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Ryu, J., Thompson, R., Park, J.Y. et al. Efficient spin–orbit torque in magnetic trilayers using all three polarizations of a spin current. Nat Electron 5, 217–223 (2022). https://doi.org/10.1038/s41928-022-00735-9

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• DOI: https://doi.org/10.1038/s41928-022-00735-9