Dzyaloshinskii-Moriya interaction accounting for the orientation of magnetic domains in ultrathin films: Fe/W(110)

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 14, 2008, Pages

  Heide, M ^a   Bihlmayer, G ^a   Blugel S ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55149113996     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.140403     Document Type: Article

References (29)

1. S. S. P. Parkin, U.S. Patent No. 6834005 (2004).
2. D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, Science 10.1126/science.1108813 309, 1688 (2005).
3. C. Kittel, Rev. Mod. Phys. 10.1103/RevModPhys.21.541 21, 541 (1949).
4. M. Hehn, K. Ounadjela, J.-P. Bucher, F. Rousseaux, D. Decanini, B. Bartenlian, and C. Chappert, Science 10.1126/science.272.5269.1782 272, 1782 (1996).
5. J. Kin Ha, R. Hertel, and J. Kirschner, Europhys. Lett. 10.1209/epl/i2003-00630-6 64, 810 (2003).
6. D. M. Schaadt, R. Engel-Herbert, and T. Hesjedal, Phys. Status Solidi B 10.1002/pssb.200642613 244, 1271 (2007).
7. K. D. Belashchenko, J. Magn. Magn. Mater. 10.1016/j.jmmm.2003.09.017 270, 413 (2004).
8. S. Cherifi, R. Hertel, A. Locatelli, Y. Watanabe, G. Potdevin, A. Ballestrazzi, M. Balboni, and S. Heun, Appl. Phys. Lett. 10.1063/1.2778466 91, 092502 (2007).
9. I. E. Dzyaloshinskii, Sov. Phys. JETP 5, 1259 (1957).
10. T. Moriya, Phys. Rev. 10.1103/PhysRev.120.91 120, 91 (1960).
11. A. Fert, Mater. Sci. Forum 59-60, 439 (1990).
12. M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubetzka, O. Pietzsch, S. Blügel, and R. Wiesendanger, Nature (London) 10.1038/nature05802 447, 190 (2007).
13. A. Kubetzka, M. Bode, O. Pietzsch, and R. Wiesendanger, Phys. Rev. Lett. 10.1103/PhysRevLett.88.057201 88, 057201 (2002).
14. O. Pietzsch, A. Kubetzka, M. Bode, and R. Wiesendanger, Phys. Rev. Lett. 10.1103/PhysRevLett.84.5212 84, 5212 (2000).
15. O. Pietzsch, A. Kubetzka, M. Bode, and R. Wiesendanger, Science 10.1126/science.1060513 292, 2053 (2001).
16. M. Pratzer, H. J. Elmers, M. Bode, O. Pietzsch, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 10.1103/PhysRevLett.87.127201 87, 127201 (2001).
17. A. Kubetzka, Ph.D. thesis, Universität Hamburg, 2002.
18. A. Kubetzka, O. Pietzsch, M. Bode, and R. Wiesendanger, Phys. Rev. B 10.1103/PhysRevB.67.020401 67, 020401 (R) (2003).
19. M. Bode, Rep. Prog. Phys. 10.1088/0034-4885/66/4/203 66, 523 (2003).
20. E. Y. Vedmedenko, A. Kubetzka, K. von Bergmann, O. Pietzsch, M. Bode, J. Kirschner, H. P. Oepen, and R. Wiesendanger, Phys. Rev. Lett. 10.1103/PhysRevLett.92.077207 92, 077207 (2004).
21. E. Y. Vedmedenko, L. Udvardi, P. Weinberger, and R. Wiesendanger, Phys. Rev. B 10.1103/PhysRevB.75.104431 75, 104431 (2007).
22. I. E. Dzyaloshinskiǐ, Sov. Phys. JETP 20, 665 (1965).
23. L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjetunion 8, 153 (1935).
24. The two Bloch walls shown in Fig. 2 are energetically degenerate if the crystal structure possesses a mirror plane parallel to the propagation direction. In order to see this, note that the spin-orbit Hamiltonian in the absence of an external magnetic field commutes with a symmetry operation that simultaneously transforms (rx, ry, rz) → (rx, - ry, rz) in real space and (Mx, My, Mz) → (Mx, - My, Mz) in spin space
25. E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 10.1103/PhysRevB.24.864 24, 864 (1981).
26. For program description see http://www.flapw.de
27. M. Heide, G. Bihlmayer, and S. Blügel (unpublished).
28. The even part of the SOC-induced corrections to E (λ-1) is negligible compared to the scalar-relativistic values given in Fig. 4
29. H. J. G. Draaisma and W. J. M. de Jonge, J. Appl. Phys. 10.1063/1.341397 64, 3610 (1988).