Time-dependent spintronic transport and current-induced spin transfer torque in magnetic tunnel junctions

Physical Review B - Condensed Matter and Materials Physics

Volumn 68, Issue 22, 2003, Pages

  Zhu, Zhen Gang ^a   Su, Gang ^a   Zheng, Qing Rong ^a   Jin, Biao ^a  

^a UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ELECTRIC CURRENT; ELECTRIC RESISTANCE; ENERGY; FOURIER TRANSFORMATION; MAGNETIC FIELD; MATHEMATICAL ANALYSIS; MODEL; TIME;

EID: 1542293438     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.68.224413     Document Type: Article

References (44)

1. S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, and D.M. Treger, Science 294, 1488 (2001);
2. J.S. Moodera, J. Nassar, and G. Mathon, Annu. Rev. Mater. Sci. 29, 381 (1999);
3. G.A. Prinz, Science 282, 1660 (1998).
4. C. Heide, A.I. Krikunov, Yu.F. Ogrin, P.E. Zilberman, and R.J. Elliott, J. Appl. Phys. 87, 5221 (2000).
5. J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).
6. L. Berger, J. Appl. Phys. 55, 1954 (1984);
7. L. Berger Phys. Rev. B 54, 9353 (1996).
8. M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, M. Seck, V. Tsoi, and P. Wyder, Phys. Rev. Lett. 80, 4281 (1998).
9. J.-E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J.-Ph. Ansermet, Europhys. Lett. 45, 626 (1999).
10. J.Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999).
11. E.B. Myers, D.C. Ralph, J.A. Katine, R.N. Louie, and R.A. Buhrman, Science 285, 867 (1999).
12. A. Asamitsu, Y. Tomioka, H. Kuwahara, and Y. Tokura, Nature (London) 388, 50 (1997).
13. J.A. Katine, F.J. Albert, R.A. Buhrman, E.B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000);
14. J. Grollier, V. Cros, A. Hamzic, J.M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and H. Legall, Appl. Phys. Lett. 78, 3663 (2001);
15. Appl. Phys. Lett. J.Z. Sun, D.J. Monsma, D.W. Abraham, M.J. Rooks, and R.H. Koch, 81, 2202 (2002).
16. E.B. Myers, F.J. Albert, J.C. Sankey, E. Bonet, R.A. Buhrman, and D.C. Ralph, Phys. Rev. Lett. 89, 196801 (2002).
17. J.C. Slonczewski, Phys. Rev. B 39, 6995 (1989).
18. Ya.B. Bazaliy, B.A. Jones, and Shou-Cheng Zhang, Phys. Rev. B 57, R3213 (1998).
19. K.B. Hathaway and J.R. Cullen, J. Magn. Magn. Mater. 104-107, 1840 (1992);
20. A. Brataas, Yu.V. Nazarov, and G.E.W. Bauer, Eur. Phys. J. B 22, 99 (2001);
21. M.D. Stiles and A. Zangwill, J. Appl. Phys. 91, 6812 (2002).
22. X. Waintal, E.B. Myers, P.W. Brouwer, and D.C. Ralph, Phys. Rev. B 62, 12317 (2000).
23. Y. Tserkovnyak and A. Brataas, Phys. Rev. B 65, 094517 (2002).
24. X. Waintal and P.W. Brouwer, Phys. Rev. B 63, 220407 (2001).
25. X. Waintal and P.W. Brouwer, Phys. Rev. B 65, 054407 (2002).
26. C. Heide, P.E. Zilberman, and R.J. Elliott, Phys. Rev. B 63, 064424 (2001);
27. C. Heide, Phys. Rev. Lett. 87, 197201 (2001).
28. S. Zhang, P.M. Levy, and A. Fert, Phys. Rev. Lett. 88, 236601 (2002).
29. Z. Li and S. Zhang, cond-mat/0302337 (unpublished);
30. Z. Li S. Zhang cond-mat/0302339(unpublished).
31. For a detailed discussion, see Zhen-Gang Zhu, Gang Su, Biao Jin, and Qing-Rong Zheng, Phys. Lett. A 306, 249 (2003).
32. Gang Su and M. Suzuki, Mod. Phys. Lett. B 16, 711 (2002).
33. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1998).
34. A.P. Jauho, N.S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994).
35. M.P. Anantram and S. Datta, Phys. Rev. B 51, 7632 (1995).
36. Baigeng Wang, Jian Wang, and Hong Guo, Phys. Rev. Lett. 82, 398 (1999).
37. As the calculations here are quite involved, for the purpose of illustration we may assume that the elements of the tunneling matrix do not depend on the momentum for simplicity, which is also a reasonable assumption in a wide-band limit. The k and q dependence of the tunneling matrix will be left for future study.
38. Tai-Kai Ng, Phys. Rev. Lett. 76, 487 (1996).
39. Zhen-Gang Zhu, Gang Su, Qing-Rong Zheng, and Biao Jin, Phys. Lett. A 300, 658 (2002).
40. J.R. Tucker and M.J. Felman, Rev. Mod. Phys. 57, 1055 (1985).
41. A.P. Jauho, cond-mat/9711141 (unpublished).
42. J.S. Moodera, M.E. Taylor, and R. Meservey, Phys. Rev. B 40, 11980 (1989).
43. J. Miltat et al., J. Appl. Phys. 89, 6982 (2001).
44. Ya.B. Bazaliy, B.A. Jones, and S.C. Zhang, J. Appl. Phys. 89, 6793 (2001).