Spin relaxation and the Elliott-Yafet parameter in W(001) ultrathin films: Surface states, anisotropy, and oscillation effects

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 22, 2013, Pages

  Long, Nguyen H ^a   Mavropoulos, Phivos ^a   Zimmermann, Bernd ^a   Heers, Swantje ^a   Bauer, David S G ^a   Blügel, Stefan ^a   Mokrousov, Yuriy ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84879762950     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.224420     Document Type: Article

References (57)

1. I. Zutic, J. Fabian, and D. Sarma, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.323 76, 323 (2004). (Pubitemid 39063520)
2. T. Valet and A. Fert, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48. 7099 48, 7099 (1993).
3. J. Bass and W. P. Pratt Jr., J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/18/183201 19, 183201 (2007). (Pubitemid 46589320)
4. S. O. Valenzuela and M. Tinkham, Nature (London) NATUAS 0028-0836 10.1038/nature04937 442, 176 (2006). (Pubitemid 44086560)
5. T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.156601 98, 156601 (2007). (Pubitemid 46582696)
6. T. Seki, Y. Hasegawa, S. Mitani, S. Takahashi, H. Imamura, S. Maekawa, J. Nitta, and K. Takanashi, Nat. Mater. 1476-1122 10.1038/nmat2098 7, 125 (2008). (Pubitemid 351161342)
7. F. Freimuth, S. Blügel, and Y. Mokrousov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.246602 105, 246602 (2010).
8. M. Gradhand, D. V. Fedorov, P. Zahn, and I. Mertig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.245109 81, 245109 (2010).
9. E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2199473 88, 182509 (2006).
10. V. P. Zhukov, E. V. Chulkov, and P. M. Echenique, Phys. Status Solidi A 1862-6300 10.1002/pssa.200778141 205, 1296 (2008).
11. M. I. Dyakonov and V. I. Perel, Fiz. Tverd. Tela 13, 3581 (1971);
12. M. I. Dyakonov and V. I. Perel, [Sov. Phys. Solid State 13, 3023 (1972)].
13. J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic, Acta Phys. Slovaca APSVCO 0323-0465 10.2478/v10155-010-0086-8 57, 565 (2007).
14. J. L. Cheng, M. W. Wu, and J. Fabian, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.016601 104, 016601 (2010).
15. R. J. Elliott, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.96.266 96, 266 (1954).
16. Y. Yafet, Solid State Physics, edited by, F. Seitz, and, D. Turnbull, (Academic, NewYork, 1963), Vol. 14, p. 1.
17. S. Heers, Ph.D. thesis, RWTH Aachen University, 2011; http://darwin.bth.rwth-aachen.de/opus3/volltexte/2011/3827/.
18. S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3419 77, 3419 (1996).
19. J. Henk, A. Ernst, and P. Bruno, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.165416 68, 165416 (2003).
20. H. A. Kramers, Proc. Amsterdam Acad. Sci. 33, 959 (1930).
21. F. Pientka, M. Gradhand, D. V. Fedorov, I. Mertig, and B. L. Györffy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.054413 86, 054413 (2012).
22. B. Zimmermann, P. Mavropoulos, S. Heers, N. H. Long, S. Blügel, and Y. Mokrousov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.236603 109, 236603 (2012).
23. Y. Mokrousov, H. Zhang, F. Freimuth, B. Zimmermann, N. H. Long, J. Weischenberg, I. Souza, P. Mavropoulos, and S. Blügel, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/25/16/163201 25, 163201 (2013).
24. P. Monod and S. Schultz, J. Pysique (Paris) JOPQAG 0302-0738 10.1051/jphys:01982004302039300 43, 393 (1982).
25. D. V. Fedorov, P. Zahn, M. Gradhand, and I. Mertig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.092406 77, 092406 (2008).
26. V. L. Safonov, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1448794 91, 8653 (2002). (Pubitemid 34636554)
27. A. Lyberatos, G. Yu, R. J. M. van de Veerdonk, and D. Weller, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1432481 91, 2236 (2002). (Pubitemid 34167763)
28. A. L. Pankratov, S. N. Vdovichev, and I. M. Nefedov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.052401 78, 052401 (2008).
29. S. L. Weng, E. W. Plummer, and T. Gustafsson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.18.1718 18, 1718 (1978).
30. M. Posternak, H. Krakauer, A. J. Freeman, and D. D. Koelling, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.21.5601 21, 5601 (1980).
31. L. F. Mattheiss and D. R. Hamann, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.29.5372 29, 5372 (1984).
32. T. E. Felter, R. A. Barker, and P. J. Estrup, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.38.1138 38, 1138 (1977).
33. M. K. Debe and D. A. King, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.39.708 39, 708 (1977).
34. D. Singh, S. H. Wei, and H. Krakauer, Phys. Rev. Lett PRLTAO 0031-9007 10.1103/PhysRevLett.57.3292 57, 3292 (1986).
35. Z. Y. Li, R. N. Lamb, W. Allison, and R. F. Willis, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(89)90859-5 211-212, 931 (1989).
36. G. A. Gaudin and M. J. G. Lee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.5575 49, 5575 (1994).
37. J. Almanstoötter, T. Firies, and B. Eberhard, J. App. Phys. JAPIAU 0021-8979 10.1063/1.370732 86, 325 (1999).
38. P. Ferriani, K. von Bergmann, E. Y. Vedmedenko, S. Heinze, M. Bode, M. Heide, G. Bihlmayer, A. Kubetzka, A. Kubetzka, and S. Blügel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.027201 101, 027201 (2008);
39. P. Ferriani, K. von Bergmann, E. Y. Vedmedenko, S. Heinze, M. Bode, M. Heide, G. Bihlmayer, A. Kubetzka, A. Kubetzka, and S. Blügel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.019901 102, 019901 (E) (2009).
40. L. W. Swanson and L. C. Crouser, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.16.389 16, 389 (1966)
41. B. J. Waclawski and E. W. Plummer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.29.783 29, 783 (1972).
42. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. CJPHAD 0008-4204 10.1139/p80-159 58, 1200 (1980).
43. N. Papanikolaou, R. Zeller, and P. H. Dederichs, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/14/11/304 14, 2799 (2002); (Pubitemid 34288364)
44. see also http://www.kkr-gf.org
45. N. Stefanou and R. Zeller, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/3/39/006 3, 7599 (1991);
46. N. Stefanou, H. Akai, and R. Zeller, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(90)90009-P 60, 231 (1990).
47. In Refs. and, the fully relativistic KKR method is used, solving the Dirac equation during self-consistency, but in the atomic sphere approximation.
48. M. Gradhand, M. Czerner, D. V. Fedorov, P. Zahn, B. Y. Yavorsky, L. Szunyogh, and I. Mertig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80. 224413 80, 224413 (2009).
49. M. Gradhand, D. V. Fedorov, P. Zahn, and I. Mertig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.020403 81, 020403 (2010).
50. D. Bauer, Ph.D. thesis, RWTH Aachen University, 2013.
51. E. I. Rashba, Sov. Phys. Solid State 2, 1109 (1960).
52. O. Krupin, G. Bihlmayer, K. Starke, S. Gorovikov, J. E. Prieto, K. Döbrich, S. Blügel, and G. Kaindl, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.201403 71, 201403 (R) (2005). (Pubitemid 43285176)
53. M. Heide, G. Bihlmayer, P. Mavropoulos, A. Bringer, and S. Blügel, Psi-k scientific highlight No. 78 (2006), http://www.psi-k.org/newsletters/News- 78/Highlight-78.pdf.
54. A. Eiguren and C. Ambrosch-Draxl, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/1/013056 11, 013056 (2009).
55. The approach was inspired from the work on giant Rashba splitting in Bi ultrathin films by T. Hirahara, K. Miyamoto, A. Kimura, Y. Niinuma, G. Bihlmayer, E. V. Chulkov, T. Nagao, I. Matsuda, S. Qiao, K. Shimada, H. Namatame, M. Taniguchi, and. S. Hasegawa, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/8/083038 10, 083038 (2008).
56. P. Mavropoulos, Spintronics: From GMR to Quantum Information, Lecture Notes of the 40th Spring School, edited by, S. Blügel, D. Bürgler, M. Morgenstern, C. M. Schneider, and, R. Waser, (Forschungszentrum Jülich, Jülich, 2009), Chap. B6.
57. G. Nicolay, F. Reinert, S. Hüfner, and P. Blaha, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.033407 65, 033407 (2001).