Current-induced spin flip scattering at interfaces in noncollinear magnetic multilayers

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 13, 2004, Pages

  Levy, Peter M ^a   Zhang, Jianwei ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ARTICLE; ELECTRIC CURRENT; MAGNETISM; MATHEMATICAL ANALYSIS; STEADY STATE;

EID: 42749105153     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.132406     Document Type: Article

References (26)

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4. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
5. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
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7. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
8. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
9. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
10. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
11. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
12. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
13. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
14. J. G. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996); 195, L261 (1999); L. Berger, Phys. Rev. B 54, 9353 (1996); J. Appl. Phys. 89, 5521 (2001); A. Brataas, Yu. V. Nazarov, and G. E. W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); D. H. Hernando, Y. V. Nazarov, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 62, 5700 (2000); Alexey Kovalev, Arne Brataas, and Gerrit E. W. Bauer, ibid. 66, 224424 (2002); M. D. Stiles and A. Zangwill, ibid. 66, 014407 (2002); J. Appl. Phys. 91, 6812 (2002); J. C. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Phys. Rev. B 67, 094421 (2003); M. Zwierzycki, Y. Tserkovnyak, P. J. Kelly, A. Brataas, and G. E. W. Bauer, cond-mat/0402088.
15. Jianwei Zhang and Peter M. Levy, Phys. Rev. B (to be published).
16. X. Waintal, E. B. Myers, P. W. Brouwer, and D. C. Ralph, Phys. Rev. B 62, 12 317 (2000); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Adv. Solid State Phys. 43, 383 (2003). Note only states accessible in equilibrium [see Eqs. (10) and (15)] are considered in these references.
17. X. Waintal, E. B. Myers, P. W. Brouwer, and D. C. Ralph, Phys. Rev. B 62, 12 317 (2000); Gerrit E. W. Bauer, Yaroslav Tserkovnyak, Daniel Huertas-Hernando, and Arne Brataas, Adv. Solid State Phys. 43, 383 (2003). Note only states accessible in equilibrium [see Eqs. (10) and (15)] are considered in these references.
18. Coherences in the distribution function are the off-diagonal elements of statistical density matrix; here, we are interested in those induced by currents across noncollinear magnetic structures at the Fermi surface.
19. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1962), Vol. II, Chap. XIX, Secs. 11-13.
20. A realistic evaluation of the transmission coefficient, Eq. (14), is being undertaken by using spin-polarized single-electron states for a Cu/Co interface; I. Mertig (private communication).
21. In the situation envisaged in Figs. 3(c) and 3(d) of M. D. Stiles and A. Zangwill, J. Appl. Phys. 91, 6812 (2002), we see that the transverse components of the spin fluxes are annihilated on opposite sides of the normal spacer layer between two noncollinear magnetic layers.
22. Jianwei Zhang, Peter M. Levy, Shufeng Zhang, and Vladimir Antropov (unpublished).
23. The possibility for spin-flip scattering at interfaces was envisaged in the papers of Bauer's group [see Refs. 2, 4, and A. Brataas, Y. V. Nazarov, and G. E. W. Bauer, Eur. Phys. J. B 22, 99 (2001)], but their origin was not discussed nor was their role included in the analyses.
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