Spin-orbit torques from interfacial spin-orbit coupling for various interfaces

Kyoung Whan Kim, Kyung Jin Lee, Jairo Sinova, Hyun Woo Lee, M. D. Stiles

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66 Citations (Scopus)


We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal-metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.

Original languageEnglish
Article number104438
JournalPhysical Review B
Issue number10
Publication statusPublished - 2017 Sept 26

Bibliographical note

Funding Information:
The authors acknowledge J. McClelland, P. Haney, and O. Gomonay for critical reading of the manuscript. K.-W.K acknowledges V. Amin and D.-S. Han for fruitful discussion. K.-W.K. was supported by the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology, Center for Nanoscale Science and Technology (Grant No. 70NANB10H193), through the University of Maryland. K.-W.K also acknowledges support by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2016R1A6A3A03008831). K.-W.K and J.S. are supported by Alexander von Humboldt Foundation, the ERC Synergy Grant SC2 (Grant No. 610115), and the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X. K.-J.L was supported by the National Research Foundation of Korea (Grants No. 2015M3D1A1070465 and No. 2017R1A2B2006119). H.-W.L. was supported by the SBS Culture Foundation (Grant No. 15-009).

Publisher Copyright:
© 2017 American Physical Society.

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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