Boltzmann approach to dissipation produced by a spin-polarized current

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 1, 2011, Pages

  Tulapurkar, A A ^a,b   Suzuki, Y ^a  

^a OSAKA UNIVERSITY   (Japan)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551513217     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.012401     Document Type: Article

References (26)

1. G. A. Prinz, Science SCIEAS 0036-8075 10.1126/science.282.5394.1660 282, 1660 (1998).
2. F. J. Jedema, A. T. Filip, and B. J. van Wees, Nature (London) NATUAS 0028-0836 10.1038/35066533 410, 345 (2001).
3. Tao Yang, Takashi Kimura, and Yoshichika Otani, Nature Phys. 1745-2473 10.1038/nphys1095 4, 851.
4. S. Murakami, N. Nagaosa and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1087128 301, 1348 (2003).
5. J. Sinova, D. Culcer, Q. Niu, N.A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603 92, 126603 (2004).
6. Wunderlich, J. Kaestner, J. B. Sinova, and T. Jungwirth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.047204 94, 047204 (2005).
7. E. I. Rashba, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.68.241315 68, 241315 (2003).
8. S. Zhang and Z. Yang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.066602 94, 066602 (2005).
9. G. E. W. Bauer, A. Brataas, and Yaroslav Tserkovnyak, Appl. Phys. Lett. 0003-6951 10.1063/1.1579122 82, 3928 (2003).
10. Arne Brataas, Yaroslav Tserkovnyak, Gerrit E. W. Bauer, and Bertrand I. Halperin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.66.060404 66, 060404 (2002).
11. M. Hatami, G. E. W. Bauer, Q. F. Zhang, and P. J. Kelly, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.066603 99, 066603 (2007).
12. K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Nature (London) NATUAS 0028-0836 10.1038/nature07321 455, 778 (2008).
13. J.-E. Wegrowe, Q. Anh Nguyen, M. Al-Barki, J.-F. Dayen, T. L. Wade, and H.-J. Drouhin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.134422 73, 134422 (2006).
14. L. Gravier, S. Serrano-Guisan, F. Reuse, and J.-P. Ansermet, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.052410 73, 052410 (2006); 73, 024419 (2006).
15. A. A. Tulapurkar and Y. Suzuki, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2009.12.035 150, 466 (2010).
16. J.-E. Wegrowe, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.62.1067 62, 1067 (2000).
17. W. M. Saslow, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.76.184434 76, 184434 (2007).
18. M. Johnson and R. H. Silsbee, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.35.4959 35, 4959 (1987).
19. J. Foros, A. Brataas, G. E. W. Bauer, Y. Tserkovnyak, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.214407 79, 214407 (2009).
20. J. M. Ziman, Electrons and Phonons (Oxford University Press, Oxford, 1960).
21. T. Valet and A. Fert, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.48. 7099 48, 7099 (1993).
22. ks, s-f to 0.
23. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Orlando, Florida, 1976).
24. D. Kondepudi and I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, (Wiley, New York, 1998).
25. 0 to 0 while deriving Eq. (9).
26. F/2)(1-β).