Skip to main content
Log in

Spin transfer torque in non-collinear magnetic tunnel junctions exhibiting quasiparticle bands: a non-equilibrium Green’s function study

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

A non-equilibrium Green’s function formulation to study the spin transfer torque (STT) in non-collinear magnetic tunnel junctions (MTJs) exhibiting quasiparticle bands is developed. The formulation can be used to study the magnetoresistance and spin current too. The formulation is used to study the STT in model tunnel junctions exhibiting multiple layers and quasiparticle bands. The many body interaction that gives rise to quasiparticle bands is assumed to be a sf exchange interaction at the electrode regions of the MTJ. The quasiparticle bands are obtained using a many body procedure and the single particle band structure is obtained using the tight binding model. The bias dependence of the STT as well as the influence of band occupancy and sf exchange coupling strength on the STT are studied. We find from our studies that the band occupancy plays a significant role in deciding the STT and the sf interaction strength too influences the STT significantly. Anomalous behavior in both the parallel and perpendicular components of the STT is obtained from our studies. Our results obtained for certain values of the band occupation are found to show the trend observed from the experimental measurements of STT.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.C. Slonczewski, Phys. Rev. B 39, 6995 (1989)

    Article  ADS  Google Scholar 

  2. A. Kalitsov, I. Theodonis, M. Chshiev, W.H. Butler, A. Vedyayev, J. Appl. Phys. 99, 08G501 (2006)

    Article  Google Scholar 

  3. J.C. Sankay, T.-T. Cui, J.Z. Sun, J.C. Slonczewski, R.A. Buhrman, D.C. Ralph, Nat. Phys. 4, 67 (2008)

    Article  Google Scholar 

  4. H. Kubota, A. Fukushima, K. Yakushiji, T. Nagahama, S. Yuasa, K. Ando, H. Maehara, Y. Nagamine, K. Tsunekawa, D.D. Djayaprawira, N. Watanabe, Y. Suzuki, Nat. Phys. 4, 37 (2008)

    Article  Google Scholar 

  5. D.M. Edwards, F. Federici, J. Mathon, A. Umerski, Phys. Rev. B 71, 054407 (2005)

    Article  ADS  Google Scholar 

  6. I. Theodonis, N. Kioussis, A. Kalitsov, M. Chshiev, W.H. Butler, Phys. Rev. Lett. 97, 237205 (2006)

    Article  ADS  Google Scholar 

  7. I. Theodonis, A. Kalitsov, N. Kioussis, Phys. Rev. B 76, 224406 (2007)

    Article  ADS  Google Scholar 

  8. C. Heiliger, M.D. Stiles, Phys. Rev. Lett. 100, 186805 (2008)

    Article  ADS  Google Scholar 

  9. A. Kalitsov, M. Chshiev, I. Theodonis, N. Kioussis, W.H. Butler, Phys. Rev. B 79, 174416 (2009)

    Article  ADS  Google Scholar 

  10. A. Manchon, S. Zhang, Phys. Rev. B 79, 174401 (2009)

    Article  ADS  Google Scholar 

  11. A. Kalitsov, W. Silvestre, M. Chshiev, J.P. Velev, Phys. Rev. B 88, 104430 (2013)

    Article  ADS  Google Scholar 

  12. Y.-H. Tang, N. Kioussis, A. Kalitsov, W.H. Butler, R. Car, Phys. Rev. B 81, 054437 (2010)

    Article  ADS  Google Scholar 

  13. U. Roy, H. Seinige, F. Ferdousi, J. Mantey, M. Tsoi, S.K. Banerjee, J. Appl. Phys. 111, 07C913 (2012)

    Article  Google Scholar 

  14. J.-I. Inoue, J. Appl. Phys. 111, 07C902 (2012)

    Article  Google Scholar 

  15. C.O. Pauyac, A. Kalitsov, A. Manchon, M. Chshiev, Phys. Rev. B 90, 235417 (2014)

    Article  ADS  Google Scholar 

  16. X. Zhang, C. Wang, Y. Liu, Z. Zhang, Q.Y. Jin, C.-G. Duan, Sci. Rep. 6, 18719 (2016)

    Article  ADS  Google Scholar 

  17. S.-Z. Wang, K. Xia, Phys. Rev. B 93, 184414 (2016)

    Article  ADS  Google Scholar 

  18. M. Stamenova, R. Mohebbi, J.S. Yazdi, I. Rungger, S. Sanvito, Phys. Rev. B 95, 060403(R) (2017)

    Article  ADS  Google Scholar 

  19. A. Useinov, L.-X. Ye, N. Useinov, T.-H. Wu, C.-H. La, Sci. Rep. 5, 18026 (2015)

    Article  ADS  Google Scholar 

  20. P.-Y. Clment, C. Baraduc, C. Ducruet, L. Vila, M. Chshiev, B. Diny, Appl. Phys. Lett. 107, 102405 (2015)

    Article  ADS  Google Scholar 

  21. C. Franz, M. Czerner, C. Heiliger, Phys. Rev. B 88, 094421 (2013)

    Article  ADS  Google Scholar 

  22. L. Tang, Z. Yang, J. Appl. Phys. 114, 193703 (2013)

    Article  ADS  Google Scholar 

  23. Y.-H. Tang, F.-C. Chu, J. Appl. Phys. 117, 093901 (2015)

    Article  ADS  Google Scholar 

  24. W. Nolting, R. Rex, S. Mathi Jaya, J. Phys.: Condens. Matter 9, 1301 (1997)

    ADS  Google Scholar 

  25. S. Rex, V. Eyert, W. Nolting, J. Magn. Magn. Mater. 192, 529 (1999)

    Article  ADS  Google Scholar 

  26. C. Santos, V. Eyert, W. Nolting, J. Magn. Magn. Mater. 272–276, e371 (2004)

    Article  Google Scholar 

  27. S. Mathi Jaya, W. Nolting, Phys. Status Solidi B 208, 497 (1998)

    Article  ADS  Google Scholar 

  28. S. Mathi Jaya, W. Nolting, Physica B 292, 359 (2000)

    Article  ADS  Google Scholar 

  29. S. Bhattacharjee, S. Mathi Jaya, Eur. Phys. J. B 49, 305 (2006)

    Article  ADS  Google Scholar 

  30. W. Nolting, S. Mathi Jaya, R. Rex, Phys. Rev. B 54, 14455 (1996)

    Article  ADS  Google Scholar 

  31. S. Mathi Jaya, M.C. Valsakumar, Eur. Phys. J. B 72, 41 (2009)

    Article  ADS  Google Scholar 

  32. S. Mathi Jaya, M.C. Valsakumar, J. Magn. Magn. Mater. 323, 2554 (2011)

    Article  ADS  Google Scholar 

  33. C. Caroli, R. Combescot, P. Nozieres, D. Saint-James, J. Phys. C 4, 916 (1971)

    Article  ADS  Google Scholar 

  34. N.S. Wingreen, A.P. Jauho, Y. Meir, Phys. Rev. B 48, 8487 (1993)

    Article  ADS  Google Scholar 

  35. A.P. Jauho, N.S. Wingreen, Y. Meir, Phys. Rev. B 50, 5528 (1994)

    Article  ADS  Google Scholar 

  36. S. Mathi Jaya, M.C. Valsakumar, Europhys. Lett. 102, 57006 (2013)

    Article  ADS  Google Scholar 

  37. L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)

    MathSciNet  Google Scholar 

  38. D.C. Langreth, J.W. Wilkins, Phys. Rev. B 6, 3189 (1972)

    Article  ADS  Google Scholar 

  39. S. Mathi Jaya, M.C. Valsakumar, Europhys. Lett. 110, 47005 (2015)

    Article  ADS  Google Scholar 

  40. M.D. Stiles, A. Zangwill, Phys. Rev. B 66, 014407 (2002)

    Article  ADS  Google Scholar 

  41. P.M. Haney, C. Heiliger, M.D. Stiles, Phys. Rev. B 79, 054405 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Selvaraj Mathi Jaya.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jaya, S.M. Spin transfer torque in non-collinear magnetic tunnel junctions exhibiting quasiparticle bands: a non-equilibrium Green’s function study. Eur. Phys. J. B 90, 122 (2017). https://doi.org/10.1140/epjb/e2017-80069-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2017-80069-8

Keywords

Navigation