Radiation-spin interaction, gilbert damping, and spin torque

Physical Review Letters

Volumn 92, Issue 9, 2004, Pages

  Ho, Jeongwon ^a   Khanna, F C ^b,c   Choi, B C ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

^b UNIVERSITY OF ALBERTA   (Canada)

^c TRIUMF   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; DEMAGNETIZATION; EQUATIONS OF MOTION; FERROMAGNETIC MATERIALS; HAMILTONIANS; MAGNETIZATION; MATHEMATICAL MODELS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; THIN FILMS; TORQUE;

GILBERT DAMPING; MICROMAGNETIC STRUCTURES; RADIATION-SPIN INTERACTION; SPIN TORQUE;

RELAXATION PROCESSES;

EID: 2442661598     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.92.097601     Document Type: Article

References (46)

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3. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
4. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
5. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
6. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
7. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
8. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
9. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
10. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
11. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
12. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
13. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
14. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
15. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
16. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
17. For the spin-orbit coupling model, V. Kambersky, Can. J. Phys. 48, 2906 (1970); V. Korenman and R. E. Prange, Phys. Rev. B 6, 2769 (1972); B. Heinrich, D. J. Meredith, and J. F. Cochran, J. Appl. Phys. 50, 7726 (1979). For the two-magnon model, M. Sparks, Ferromagnetic-Relaxation Theory, Advanced Physics Monograph Series (McGraw-Hill, New York, 1964); C.E. Patton, C. H. Wilts, and B. Humphrey, J. Appl. Phys. 38, 1358 (1967); B. Heinrich, J. F. Cochran, and R. Hasegawa, J. Appl. Phys. 57, 3690 (1985); M.J. Hurben, D.R. Franklin, and C. E. Patton, J. Appl. Phys. 81, 7458 (1997); R. Arias and D.L. Mills, Phys. Rev. B 60, 7395 (1999); A. Azevedo, A. B. Oliveira, F. M. de Aguiar, and S. M. Rezende, Phys. Rev. B 62, 5331 (2000); R. Urban, B. Heinrich, G. Woltersdorf, K. Ajdari, K. Myrtle, J. F. Cochran, and E. Rozenberg, Phys. Rev. B 65, 020402(R) (2002); R. D. McMichael and D. J. Twisselmann, Phys. Rev. Lett. 90, 227601 (2003). For other descriptions of magnetization relaxation process, see V. G. Baryakhtar, B. A. Ivanov, A. L. Sukstanskii, and E.Yu. Melikhov, Phys. Rev. B 56, 619 (1997); H. Suhl, IEEE Trans. Magn. 34, 1834 (1998); V.L. Safonov and H.N. Bertram, J. Appl. Phys. 85, 5072 (1999); E.D. Boerner, H.N. Bertram, and H. Suhl, J. Appl. Phys. 87, 5389 (2000); N. Smith and P. Arnett, Appl. Phys. Lett. 78, 1448 (2001).
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22. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
23. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
24. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
25. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
26. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
27. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
28. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
29. M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seek, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998); E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 258, 867 (1999); J. Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); M. Tsoi, A.G.M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Nature (London) 406, 46 (2000); J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D.C. Ralph, Phys. Rev. Lett. 84, 3149 (2000); J. Grollier, V. Gros, A. Hamzic, J. M. George, H. Jaffres, A. Fert, G. Faini, J. Ben Youssef, and K Legall, Appl. Phys. Lett 78, 3663 (2001); R. Urban, G. Woltersdorf, and B. Heinrich, Phys. Rev. Lett. 87, 217204 (2001); J. Z. Sun, D. J. Monsma, M.J. Rooks, and R.H. Koch, Appl. Phys. Lett. 81, 2202 (2002); in magnetic nanowires, J. E. Wegrowe, D. Kelly, Y. Jaccard, Ph. Guittienne, and J. Ph. Ansermet, Europhys. Lett 45, 626 (1999); J.E. Wegrowe, X. Hoffer, Ph. Guittienne, A. Fabian, L. Gravier, T. Wade, and J. Ph. Ansermet, J. Appl. Phys. 91, 6806 (2002).
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