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One analytical approach of Rashba–Edelstein magnetoresistance in 2D materials

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Abstract

We study analytically the Rashba–Edelstein magnetoresistance in a structure made from an insulator ferromagnet, such as yttrium iron garnet, and a 2D material with direct and inverse Rashba–Edelstein effects, such as SLG and MoS\(_2\). Our results represent an efficient way of analyzing the Rashba–Edelstein effects. In addition, it also presents a concrete analysis of the exchange field acting on the accumulation of spins.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data will be made available on reasonable request to the authors. Thus, the authors understand that there is no need to deposit the data.].

References

  1. A. Soumyanarayanan, N. Reyren, A. Fert, C. Panagopoulos, Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces. Nature (London) 539, 509 (2016)

    Google Scholar 

  2. F. Hellman, A. Hoffmann, Y. Tserkovnyak, G.S.D. Beach, E.E. Fullerton, C. Leighton, A.H. MacDonald, D.C. Ralph, D.A. Arena, H.A. Dürr et al., Interface-induced phenomena in magnetism. Rev. Mod. Phys. 89, 025006 (2017)

    ADS  MathSciNet  Google Scholar 

  3. W. Han, Y. Otani, S. Maekawa, Quantum materials for spin and charge conversion. NPJ Quant. Mater. 3, 27 (2018)

    ADS  Google Scholar 

  4. J.C. Rojas-Sánchez, A. Fert, Compared efficiencies of conversions between charge and spin current by spin-orbit interactions in two- and three-dimensional systems. Phys. Rev. Appl. 11, 054049 (2019)

    ADS  Google Scholar 

  5. J.C. Leutenantsmeyer, A.A. Kaverzin, M. Wojtaszek, B.J. van Wees, Proximity induced room temperature ferromagnetism in graphene probed with spin currents. 2D Mater. 4, 014001 (2017)

    Google Scholar 

  6. Y. Wang, Y. Huang, Y. Song, X. Zhang, Y. Ma, J. Liang, Y. Chen, Room temperature ferromagnetism of graphene. Nano Lett. 9, 220 (2008)

    ADS  Google Scholar 

  7. K.M. McCreary, A.G. Swartz, W. Han, J. Fabian, R.K. Kawakami, Magnetic moment formation in graphene detected by scattering of pure spin currents. Phys. Rev. Lett. 109, 186604 (2012)

    ADS  Google Scholar 

  8. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167 (2013)

    ADS  Google Scholar 

  9. P. Wei, F. Katmis, B.A. Assaf, H. Steinberg, P. Jarillo-Herrero, D. Heiman, J.S. Moodera, Exchange-coupling-induced symmetry breaking in topological insulators. Phys. Rev. Lett. 110, 186807 (2013)

    ADS  Google Scholar 

  10. Z. Wang, C. Tang, R. Sachs, Y. Barlas, J. Shi, Proximity induced ferromagnetism in graphene revealed by the anomalous Hall effect. Phys. Rev. Lett. 114, 016603 (2015)

    ADS  Google Scholar 

  11. C. Tang, Z. Zhang, S. Lai, Q. Tan, W.-B. Gao, Magnetic proximity effect in graphene/\(\text{ CrBr}_3\) van der Waals heterostructures. Adv. Mater. 32, 1908498 (2020)

    Google Scholar 

  12. C. Gong, X. Zhang, Two-dimensional magnetic crystals and emergent heterostructure devices. Science 363, eaav4450 (2019)

    Google Scholar 

  13. D. Zhong, K.L. Seyler, X. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M.A. McGuire et al., Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics. Sci. Adv. 3, e1603113 (2017)

    ADS  Google Scholar 

  14. K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010)

    ADS  Google Scholar 

  15. W.S. Paz, J.J. Palacios, A theoretical study of the electrical contact between metallic and semiconducting phases in monolayer \(\text{ MoS}_2\). 2D Mater. 4, 015014 (2016)

    Google Scholar 

  16. M. Amani et al., Near-unity photoluminescence quantum yield in \(\text{ MoS}_2\). Science 350, 1065 (2015)

    ADS  Google Scholar 

  17. J.B.S. Mendes, A. Aparecido-Ferreira, J. Holanda, A. Azevedo, S.M. Rezende, Efficient spin to charge current conversion in the 2D semiconductor \(\text{ MoS}_2\) by spin pumping from yttrium iron garnet. Appl. Phys. Lett. 112, 242407 (2018)

    ADS  Google Scholar 

  18. W. Zhang, J. Sklenar, B. Hsu, W. Jiang, M.B. Jungfleisch, J. Xiao, F.Y. Fradin, Y. Liu, J.E. Pearson, J.B. Ketterson, Z. Yang, A. Hoffmann, Perspective: Interface generation of spin-orbit torques featured. APL Mater. 4, 032302 (2016)

    ADS  Google Scholar 

  19. Q. Shao, G. Yu, Y.-W. Lan, Y. Shi, M.-Y. Li, C. Zheng, X. Zhu, L.-J. Li, P.K. Amiri, K.L. Wang, Strong Rashba–Edelstein effect-induced spin-orbit torques in monolayer transition metal dichalcogenide/ferromagnet bilayers. Nano Lett. 16, 7514 (2016)

    ADS  Google Scholar 

  20. D.B. de Araújo, R.Q. Almeida, A.C. Gadelha, N.P. Rezende, F.C.C.S. Salomo, F.W.N. Silva, L.C. Campos, E.B. Barros, Controlling the electronic bands of a 2D semiconductor by force microscopy. 2D Mater. 7, 045029 (2020)

    Google Scholar 

  21. D. Pesin, A. MacDonald, Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409 (2012)

    ADS  Google Scholar 

  22. J.B.S. Mendes, O. Alves Santos, L.M. Meireles, R.G. Lacerda, L.H. Vilela-Leão, F.L.A. Machado, R.L. Rodríguez-Suárez, A. Azevedo, S.M. Rezende, Spin current to charge-current conversion and magnetoresistance in a hybrid structure of graphene and yttrium iron garnet. Phys. Rev. Lett. 115, 226601 (2015)

    ADS  Google Scholar 

  23. R. Vidyasagar, O. Alves Santos, J. Holanda, R.O. Cunha, F.L.A. Machado, P.R.T. Ribeiro, A.R. Rodrigues, J.B.S. Mendes, A. Azevedo, S.M. Rezende, Giant Zeeman shifts in the optical transitions of yttrium iron garnet thin films. Appl. Phys. Lett. 109, 122402 (2016)

    ADS  Google Scholar 

  24. J.C. Rojas-Sanchez, L. Vila, G. Desfonds, S. Gambarelli, J.P. Attane, J.M. De Teresa, C. Magen, A. Fert, Spin-to-charge conversion using Rashba coupling at the interface between nonmagnetic materials. Nat. Commun. 4, 2944 (2013)

    ADS  Google Scholar 

  25. J. B. S. Mendes, O. Alves Santos, J. Holanda, R. P. Loreto, C. I. L. de Araujo, C.-Z. Chang, J. S. Moodera, A. Azevedo, and S. M. Rezende, Dirac-surface-state-dominated spin to charge current conversion in the topological insulator (\(\text{ Bi}_{0.22}\text{ Sb}_{0.78})_2\text{ Te}_3\) films at room temperature. Phys. Rev. B 96, 180415(R) (2017)

  26. J.B.S. Mendes, O. Alves Santos, T. Chagas, R. MagalhãesPaniago, T.J.A. Mori, J. Holanda, L.M. Meireles, R.G. Lacerda, A. Azevedo, S.M. Rezende, Direct detection of induced magnetic moment and efficient spin-to-charge conversion in graphene/ferromagnetic structures. Phys. Rev. B 99, 214446 (2019)

    ADS  Google Scholar 

  27. J. Holanda, H. Saglam, V. Karakas, Z. Zang, Y. Li, R. Divan, Y. Liu, O. Ozatay, V. Novosad, J.E. Pearson, A. Hoffmann, Magnetic damping modulation in \(\text{ IrMn}_3\)/\(\text{ Ni}_{80}\)\(\text{ Fe}_{20}\) via the magnetic spin Hall effect. Phys. Rev. Lett. 124, 087204 (2020)

    ADS  Google Scholar 

  28. S.Y. Huang, X. Fan, D. Qu, Y.P. Chen, W.G. Wang, J. Wu, T.Y. Chen, J.Q. Xiao, C.L. Chien, Transport magnetic proximity effects in platinum. Phys. Rev. Lett. 109, 107204 (2012)

    ADS  Google Scholar 

  29. R.H. Mckenzie, J.S. Qualls, S.Y. Han, J.S. Brooks, Violation of Kohler’s rule by the magnetoresistance of a quasi two-dimensional metal. Phys. Rev. B 57, 11854 (1998)

    ADS  Google Scholar 

  30. J. Holanda, Analyzing the magnetic interactions in nanostructures that are candidates for applications in spintronics. J. Phys. D Appl. Phys. 54, 245004 (2021)

    ADS  Google Scholar 

  31. H. Nakayama et al., Spin Hall magnetoresistance induced by a nonequilibrium proximity effect. Phys. Rev. Lett. 110, 206601 (2013)

    ADS  Google Scholar 

  32. M. Althammer, S. Meyer, H. Nakayama, M. Schreier, S. Altmannshofer, M. Weiler, H. Huebl, S. Geprägs, M. Opel, R. Gross et al., Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids. Phys. Rev. B 87, 224401 (2013)

    ADS  Google Scholar 

  33. Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S.T.B. Goennenwein, E. Saitoh, G.E.W. Bauer, Theory of spin Hall magnetoresistance. Phys. Rev. B 87, 144411 (2013)

    ADS  Google Scholar 

  34. V.M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 233, 73 (1990)

    Google Scholar 

  35. H. Nakayama, Y. Kanno, H. An, T. Tashiro, S. Haku, A. Nomura, K. Ando, Rashba–Edelstein magnetoresistance in metallic heterostructures. Phys. Rev. Lett. 117, 116602 (2016)

    ADS  Google Scholar 

  36. K. Uchida, J. Xiao, H. Adachi et al., Spin Seebeck insulator. Nat. Mater. 9, 894–897 (2010)

    ADS  Google Scholar 

  37. J.B.S. Mendes, S.M. Rezende, J. Holanda, Rashba–Edelstein magnetoresistance in two-dimensional materials at room temperature. Phys. Rev. B 104, 014408 (2021)

    ADS  Google Scholar 

  38. S. Liang, H. Yang, P. Renucci, B. Tao, P. Laczkowski, S. McMurtry, G. Wang, X. Marie, J.-M. George, S. Petit-Watelot, A. Djeffal, S. Mangin, H. Jaffrès, Y. Lu, Electrical spin injection and detection in molybdenum disulfide multilayer channel. Nat. Commun. 8, 14947 (2017)

    ADS  Google Scholar 

  39. X. Jia, K. Liu, K. Xia, G. E. W. Bauer. Spin transfer torque on magnetic insulators. EPL (Europhysics Letters), 96, 17005 (2011)

  40. S.M. Rezende, R.L. Rodríguez-Suarez, A. Azevedo, Magnetic relaxation due to spin pumping in thick ferromagnetic films in contact with normal metals. Phys. Rev. B 88, 014404 (2013)

    ADS  Google Scholar 

  41. D. Ghazaryan, M.T. Greenaway, Z. Wang et al., Magnon-assisted tunneling in van der Waals heterostructures based on CrBr 3. Nat. Electron. 1, 344–349 (2018)

    Google Scholar 

  42. P. Wei, S. Lee, F. Lemaitre et al., Strong interfacial exchange field in the graphene/EuS heterostructure. Nat. Mater. 15, 711–716 (2016)

    ADS  Google Scholar 

  43. Y.T. Fanchiang, K.H.M. Chen, C.C. Tseng et al., Strongly exchange-coupled and surface-state-modulated magnetization dynamics in Bi2Se3/yttrium iron garnet heterostructures. Nat. Commun. 9, 223 (2018)

    ADS  Google Scholar 

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Acknowledgements

This research was supported by the Brazilian National Council for Scientific and Technological Development (CNPq), Coordination for the Improvement of Higher Education Personnel - Federal Rural University of Pernambuco (CAPES-UFRPE), Financier of Studies and Projects (FINEP) and Foundation for Support to Science and Technology of the State of Pernambuco (FACEPE).

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Correspondence to José Holanda.

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Resubmitted to The European Physical Journal B - Condensed Matter and Complex Systems in December 2022.

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Silva, W.W.G., Holanda, J. One analytical approach of Rashba–Edelstein magnetoresistance in 2D materials. Eur. Phys. J. B 96, 47 (2023). https://doi.org/10.1140/epjb/s10051-023-00516-z

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