Abstract
We calculate the electric field-induced damping-like spin–orbit torque in a ferromagnetic metal/topological insulator bilayer using the tight-binding method and the Kubo formula. The effective damping-like spin Hall conductivity converted from the spin accumulation in a ferromagnetic metal is comparable to the reported experimental values. We find that hybridized states emerge at the interface between a ferromagnetic metal and a topological insulator and these states are crucial for the large damping-like spin Hall conductivity. Our result provides one possible way to explain experimentally reported large damping-like spin–orbit torque in a ferromagnetic metal/topological insulator bilayer.
Similar content being viewed by others
References
I.M. Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. Vogel, P. Gambardella, Nat. Mater. 9, 230 (2010). https://doi.org/10.1038/nmat2613
L. Liu, O.J. Lee, T.J. Gudmundsen, D.C. Ralph, R.A. Buhrman, Phys. Rev. Lett. 109, 096602 (2012). https://doi.org/10.1103/PhysRevLett.109.096602
L. Liu, C.-F. Pai, Y. Li, H.W. Tseng, D.C. Ralph, R.A. Buhrman, Science 336, 555 (2012) https://doi.org/10.1126/science.1218197https://www.science.org/doi/pdf/10.1126/science.1218197
K.-W. Kim, S.-M. Seo, J. Ryu, K.-J. Lee, H.-W. Lee, Phys. Rev. B 85, 180404 (2012). https://doi.org/10.1103/PhysRevB.85.180404
P.M. Haney, H.-W. Lee, K.-J. Lee, A. Manchon, M.D. Stiles, Phys. Rev. B 87, 174411 (2013). https://doi.org/10.1103/PhysRevB.87.174411
P.M. Haney, H.-W. Lee, K.-J. Lee, A. Manchon, M.D. Stiles, Phys. Rev. B 88, 214417 (2013). https://doi.org/10.1103/PhysRevB.88.214417
G. Yu, P. Upadhyaya, Y. Fan, J.G. Alzate, W. Jiang, K.L. Wong, S. Takei, S.A. Bender, L.-T. Chang, Y. Jiang, M. Lang, J. Tang, Y. Wang, Y. Tserkovnyak, P.K. Amiri, K.L. Wang, Nat. Nanotechnol. 9, 548 (2014). https://doi.org/10.1038/nnano.2014.94
K. Garello, C.O. Avci, I.M. Miron, M. Baumgartner, A. Ghosh, S. Auffret, O. Boulle, G. Gaudin, P. Gambardella, Appl. Phys. Lett. 105, 212402 (2014)
J. Sinova, S.O. Valenzuela, J. Wunderlich, C.H. Back, T. Jungwirth, Rev. Mod. Phys. 87, 1213 (2015). https://doi.org/10.1103/RevModPhys.87.1213
T. Shiino, S.-H. Oh, P.M. Haney, S.-W. Lee, G. Go, B.-G. Park, K.-J. Lee, Phys. Rev. Lett. 117, 087203 (2016). https://doi.org/10.1103/PhysRevLett.117.087203
K. Garello, I.M. Miron, C.O. Avci, F. Freimuth, Y. Mokrousov, S. Blügel, S. Auffret, O. Boulle, G. Gaudin, P. Gambardella, Nat. Nanotechnol. 8, 587 (2013). https://doi.org/10.1038/nnano.2013.145
H. Kurebayashi, J. Sinova, D. Fang, A.C. Irvine, T.D. Skinner, J. Wunderlich, V. Novák, R.P. Campion, B.L. Gallagher, E.K. Vehstedt, L.P. Zârbo, K. Výborný, A.J. Ferguson, T. Jungwirth, Nat. Nanotechnol. 9, 211 (2014). https://doi.org/10.1038/nnano.2014.15
F. Freimuth, S. Blügel, Y. Mokrousov, Phys. Rev. B 90, 174423 (2014). https://doi.org/10.1103/PhysRevB.90.174423
K.-W. Kim, K.-J. Lee, J. Sinova, H.-W. Lee, M.D. Stiles, Phys. Rev. B 96, 104438 (2017). https://doi.org/10.1103/PhysRevB.96.104438
R. Ramaswamy, J.M. Lee, K. Cai, H. Yang, Appl. Phys. Rev. 5, 031107 (2018). https://doi.org/10.1063/1.5041793
F. Mahfouzi, N. Kioussis, Phys. Rev. B 97, 224426 (2018). https://doi.org/10.1103/PhysRevB.97.224426
A. Manchon, J. Železný, I.M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, P. Gambardella, Rev. Mod. Phys. 91, 035004 (2019). https://doi.org/10.1103/RevModPhys.91.035004
A.R. Mellnik, J.S. Lee, A. Richardella, J.L. Grab, P.J. Mintun, M.H. Fischer, A. Vaezi, A. Manchon, E.A. Kim, N. Samarth, D.C. Ralph, Nature 511, 449 (2014). https://doi.org/10.1038/nature13534
Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L.-T. Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R.N. Schwartz, Y. Tserkovnyak, K.L. Wang, Nat. Mater. 13, 699 (2014). https://doi.org/10.1038/nmat3973
Y. Wang, P. Deorani, K. Banerjee, N. Koirala, M. Brahlek, S. Oh, H. Yang, Phys. Rev. Lett. 114, 257202 (2015). https://doi.org/10.1103/PhysRevLett.114.257202
N.H.D. Khang, Y. Ueda, P.N. Hai, Nat. Mater. 17, 808 (2018). https://doi.org/10.1038/s41563-018-0137-y
Y. Wang, D. Zhu, Y. Wu, Y. Yang, J. Yu, R. Ramaswamy, R. Mishra, S. Shi, M. Elyasi, K.-L. Teo, Y. Wu, H. Yang, Nat. Commun. 8, 1364 (2017). https://doi.org/10.1038/s41467-017-01583-4
J. Han, A. Richardella, S.A. Siddiqui, J. Finley, N. Samarth, L. Liu, Phys. Rev. Lett. 119, 077702 (2017). https://doi.org/10.1103/PhysRevLett.119.077702
M. Dc, R. Grassi, J.-Y. Chen, M. Jamali, D. ReifsnyderHickey, D. Zhang, Z. Zhao, H. Li, P. Quarterman, Y. Lv, M. Li, A. Manchon, K.A. Mkhoyan, T. Low, J.-P. Wang, Nat. Mater. 17, 800 (2018). https://doi.org/10.1038/s41563-018-0136-z
C. Şahin, M.E. Flatté, Phys. Rev. Lett. 114, 107201 (2015). https://doi.org/10.1103/PhysRevLett.114.107201
S. Ghosh, A. Manchon, Phys. Rev. B 97, 134402 (2018). https://doi.org/10.1103/PhysRevB.97.134402
S.M. Farzaneh, S. Rakheja, Phys. Rev. Mater. 4, 114202 (2020). https://doi.org/10.1103/PhysRevMaterials.4.114202
K. Kondou, R. Yoshimi, A. Tsukazaki, Y. Fukuma, J. Matsuno, K.S. Takahashi, M. Kawasaki, Y. Tokura, Y. Otani, Nat. Phys. 12, 1027 (2016). https://doi.org/10.1038/nphys3833
I. Garate, M. Franz, Phys. Rev. Lett. 104, 146802 (2010). https://doi.org/10.1103/PhysRevLett.104.146802
A. Sakai, H. Kohno, Phys. Rev. B 89, 165307 (2014). https://doi.org/10.1103/PhysRevB.89.165307
F. Mahfouzi, N. Nagaosa, B.K. Nikolić, Phys. Rev. B 90, 115432 (2014). https://doi.org/10.1103/PhysRevB.90.115432
F. Mahfouzi, B.K. Nikolić, N. Kioussis, Phys. Rev. B 93, 115419 (2016). https://doi.org/10.1103/PhysRevB.93.115419
M.H. Fischer, A. Vaezi, A. Manchon, E.-A. Kim, Phys. Rev. B 93, 125303 (2016). https://doi.org/10.1103/PhysRevB.93.125303
P.B. Ndiaye, C.A. Akosa, M.H. Fischer, A. Vaezi, E.-A. Kim, A. Manchon, Phys. Rev. B 96, 014408 (2017). https://doi.org/10.1103/PhysRevB.96.014408
W. Wang, T. Wang, V.P. Amin, Y. Wang, A. Radhakrishnan, A. Davidson, S.R. Allen, T.J. Silva, H. Ohldag, D. Balzar, B.L. Zink, P.M. Haney, J.Q. Xiao, D.G. Cahill, V.O. Lorenz, X. Fan, Nat. Nanotechnol. 14, 819 (2019). https://doi.org/10.1038/s41565-019-0504-0
D. Go, H.-W. Lee, Phys. Rev. Res. 2, 013177 (2020). https://doi.org/10.1103/PhysRevResearch.2.013177
K. Kobayashi, Phys. Rev. B 84, 205424 (2011). https://doi.org/10.1103/PhysRevB.84.205424
J. Zhang, J.P. Velev, X. Dang, E.Y. Tsymbal, Phys. Rev. B 94, 014435 (2016). https://doi.org/10.1103/PhysRevB.94.014435
Y.-T. Hsu, K. Park, E.-A. Kim, Phys. Rev. B 96, 235433 (2017). https://doi.org/10.1103/PhysRevB.96.235433
Y. Zhang, K. He, C.-Z. Chang, C.-L. Song, L.-L. Wang, X. Chen, J.-F. Jia, Z. Fang, X. Dai, W.-Y. Shan, S.-Q. Shen, Q. Niu, X.-L. Qi, S.-C. Zhang, X.-C. Ma, Q.-K. Xue, Nat. Phys. 6, 584 (2010). https://doi.org/10.1038/nphys1689
C.S. Ho, Y. Wang, Z.B. Siu, S.G. Tan, M.B.A. Jalil, H. Yang, Sci. Rep. 7, 792 (2017). https://doi.org/10.1038/s41598-017-00911-4
Acknowledgements
S.S. and H.W.L. were supported by the Samsung Science and Technology Foundation (Grant No. BA-1501-51).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shin, S., Lee, HW. Large damping-like spin–orbit torque in a ferromagnet/topological insulator bilayer from localized interfacial states. J. Korean Phys. Soc. 80, 241–246 (2022). https://doi.org/10.1007/s40042-021-00378-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40042-021-00378-7