Definition of the spin current: The angular spin current and its physical consequences

Physical Review B - Condensed Matter and Materials Physics

Volumn 72, Issue 24, 2005, Pages

  Sun, Qing Feng ^a   Xie, X C ^b,c  

^a INSTITUTE OF PHYSICS   (China)

^b OKLAHOMA STATE UNIVERSITY   (United States)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29644433329     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.72.245305     Document Type: Article

References (37)

1. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. V. Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science SCIEAS 0036-8075 10.1126/science.1065389 294, 1488 (2001);
2. G. A. Prinz, Science SCIEAS 0036-8075 10.1126/science.282.5394.1660 282, 1660 (1998).
3. I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.323 76, 323 (2004).
4. S. Murakami, N. Nagaosa, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1087128 301, 1348 (2003);
5. S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.235206 69, 235206 (2004);
6. Z. F. Jiang, R. D. Li, S.-C. Zhang, and W. M. Liu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.045201 72, 045201 (2005).
7. 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);
8. B. K. Nikolic, S. Souma, L. P. Zarbo, and J. Sinova, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.046601 95, 046601 (2005).
9. S. Q. Shen, M. Ma, X. C. Xie, and F. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.256603 92, 256603 (2004);
10. S.-Q. Shen, Y.-J. Bao, M. Ma, X. C. Xie, and F. C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.155316 71, 155316 (2005);
11. S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.156804 93, 156804 (2004);
12. S.-P. Kou, X.-L. Qi, and Z.-Y. Weng, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.165114 72, 165114 (2005).
13. G. Y. Guo, Y. Yao, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.226601 94, 226601 (2005);
14. Y. Yao and Z. Fang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.156601 95, 156601 (2005);
15. X. Dai, Z. Fang, Y.-G. Yao, and F.-C. Zhang, cond-mat/0507603 (unpublished).
16. S. Datta and B. Das, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.102730 56, 665 (1990).
17. T. Matsuyama, C.-M. Hu, D. Grundler, G. Meier, and U. Merkt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.155322 65, 155322 (2002);
18. F. Mireles and G. Kirczenow, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.024426 64, 024426 (2001);
19. J. Wang, H. B. Sun, and D. Y. Xing, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.085304 69, 085304 (2004).
20. P. Zhang, J. R. Shi, D. Xiao, and Q. Niu, cond-mat/0503505 (unpublished);
21. J. Wang, B. G. Wang, W. Ren, and H. Guo, cond-mat/0507159 (unpublished).
22. F. Schätz, P. Kopietz, and M. Kollar, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00348-9 41, 557 (2004).
23. D. Culcer, J. Sinova, N. A. Sinitsyn, T. Jungwirth, A. H. MacDonald, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.046602 93, 046602 (2004).
24. S. Zhang and Z. Yang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.066602 94, 066602 (2005).
25. A. A. Burkov, A. S. Nunez, and A. H. MacDonald, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.155308 70, 155308 (2004).
26. Of course, in some special cases, one may be able to introduce a conserved current, for example see Janin Splettstoesser, M. Governale, and U. Zälicke, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.165341 68, 165341 (2003).
27. E. I. Rashba, Fiz. Tverd. Tela (Leningrad) FTVTAC 0367-3294 2, 1224 (1960)
28. E. I. Rashba, [Sov. Phys. Solid State SPSSA7 0038-5654 2, 1109 (1960)].
29. Y. A. Bychkov and E. I. Rashba, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/33/015 17, 6039 (1984).
30. Recently, Ref. has investigated the definition of the spin current in the insulating Heisenberg model. In our opinion, our definition is valid in the Heisenberg model, for which the linear spin current js is always zero since particles do not move in this insulating model.
31. J. E. Hirsch, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.4774 42, 4774 (1990);
32. J. E. Hirsch, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.14787 60, 14787 (1999);
33. F. Meier and D. Loss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.167204 90, 167204 (2003).
34. F. Schütz, M. Kollar, and P. Kopietz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.017205 91, 017205 (2003);
35. F. Schütz, M. Kollar, and P. Kopietz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.035313 69, 035313 (2004).
36. Q.-F. Sun, H. Guo, and J. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.054409 69, 054409 (2004).
37. For example, see D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1989).