DOI QR코드

DOI QR Code

Non-Equilibrium Green Function Method in Spin Transfer Torque

  • Published : 2007.06.30

Abstract

We investigate the spin transfer torque in metallic multilayer system by employing Keldysh non-equilibrium Green function method. We study the dependences of the spin transfer torque on the detailed energy configuration of ferromagnetic, spacer, and lead layers. With Keldysh non-equilibrium Green function method applied to a single band model, we explore spin transfer torque effect in various layer structures and for various material parameters.

Keywords

References

  1. J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996)
  2. L. Berger, Phys. Rev. B 54, 9353 (1996)
  3. E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 285, 867 (1999) https://doi.org/10.1126/science.285.5430.999
  4. S. I. Kiselev, J. C. Sankey, I. N. Krivorotov, N. C. Emley, R. J. Schoelkopf, R. A. Buhrman, and D. C. Ralph, Nature 425, 380 (2003) https://doi.org/10.1038/425003a
  5. Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin, Rev. of Mod. Phys. 77, 1375 (2005)
  6. A. Brataas, G. E. W. Bauer, and P. J. Kelly, Phys. Rep. 427, 157 (2006) https://doi.org/10.1016/j.physrep.2006.01.001
  7. J. C. Lee, M. G. Chun, W. H. Park, C.-Y. You, S.-B. Choe, W. Y. Yung, and K. Y. Kim, J. Appl. Phys. 99, 08G517 (2006)
  8. M. Hosomi et al., Electron Devices Meeting, 2005. IEDM Technical Digest, IEEE International, 459 (2005)
  9. L. V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)
  10. D. M. Edwards, F. Federici, J. Mathon, and A. Umerski, Phys. Rev. B. 71, 054407 (2005)
  11. A. Kalitsov, I. Theodonis, N. Kioussis, M. Chshiev, W. H. Butler, and A. Vedyayev, J. Appl. Phys. 99, 08G501 (2006)
  12. I. Theodonis, N. Kioussis, A. Kalitsov, M. Chshiev, and W. H. Butler, Phys. Rev. Lett. 97, 237205 (2006)
  13. J. Mathon, Phys. Rev. B. 56, 11810 (1997) https://doi.org/10.1103/PhysRevB.56.997
  14. J. Mathon, A. Umerski, and Murielle Villeret, Phys. Rev. B. 55, 14378 (1997)
  15. J. Mathon, Murielle Villeret, A. Umerski, R. B. Muniz, J. d'Albuquerque e Castro, and D. M. Edwards, Phys. Rev. B. 56, 11797 (1997) https://doi.org/10.1103/PhysRevB.56.997
  16. M. D. Stiles, J. Magn. Magn. Mater. 200, 322 (1999)
  17. M .D. Stiles and A. Zangwill, Phys. Rev. B. 66, 014407 (2002)