Ballistic current induced effective force on magnetic domain wall
Corresponding Author: K. Xia
Nano-Micro Letters,
Vol. 1 No. 1 (2009), Article Number: 34-39
Abstract
The collective dynamics of magnetic domain wall under electric current is studied in the form of spin transfer torque (STT). The out-of-plane STT induced effective force is obtained based on the Landau-Lifshitz-Gilbert (LLG) equation including microscopic STT terms. The relation between microscopic calculations and collective description of the domain wall motion is established. With our numerical calculations based on tight binding free electron model, we find that the non adiabatic out-of-plane torque components have considerable non-local properties. It turns out that the calculated effective forces decay significantly with increasing domain wall widths.
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- S. A. Wolf, D. D. Awschalom, R.A. Buhrman, J. M. Daughton and S. Von Molnar, Science 294, 1488 (2001); I. Zutic, J. Fabian and S. Das Sarma, Rev. Mod. Phys. 76, 2 (2004).
- Berger, Phys. Rev. B 54, 9353 (1996). doi:10.1103/PhysRevB.54.9353
- J. Slonczewski and J. Magn. Magn. Mater. 159, L1 (1996). doi:10.1016/0304-8853(96)00062-5
- G. S. D. Beach, C. Knutson, C. Nistor, M. Tsoi and J. L. Erskine, Phys. Rev. Lett. 97, 057203 (2006). doi:10.1103/PhysRevLett.97.057203
- M. Tsoi, Nature Phys. 4, 17 (2008). doi:10.1038/nphys822
- J. C. Sankey, P. M. Braganca, A. G. F. Garcia, I. N. Krivorotov, R. A. Buhrman and D. C. Ralph, Phys. Rev. Lett. 96, 227601 (2006). doi:10.1103/PhysRevLett.96.227601
- S. Stuart and P. Parkin, Science 320, 190 (2008). doi:10.1126/science.1145799
- J. Shibata, G. Tarara and H. Kohno, Phys. Rev. Lett. 94, 076601 (2005). doi:10.1103/PhysRevLett.94.076601
- G. Tatara, H. Kohno and J. Shibata, Phys. Rep. 468, 6 (2008). doi:10.1016/j.physrep.2008.07.003
- Z. Li and S. Zhang, Phys. Rev. Lett. 93, 127204 (2004). doi:10.1103/PhysRevLett.93.127204
- S. Zhang and Z. Li, Phys. Rev. Lett 92, 207203 (2004). doi:10.1103/PhysRevLett.92.207203
- J. Xiao, A. Zangwill and M. D. Stiles, Phys. Rev. B. 73, 054428 (2006). doi:10.1103/PhysRevB.73.054428
- I. Turek, V. Drchal, J. Kudrnovsky, M. Sob and P. Weinberger, Electronic Structure of Disordered Alloys: Surface sand Interfaces (Kluwer, Boston-London-Dordrecht, 1997).
- O. K. Andersen, O. Jepsen and D. Glotzel, in Highlights in Condensed Matter Theory, edited by F. Bassani, F. Fumi and M. P. Tosi (North-Holland, Amsterdam, 1985), p. 59.
- S. Wang, Y. Xu and K. Xia, Phys. Rev. B 77, 184430 (2008). doi:10.1103/PhysRevB.77.184430
- N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 (1974). doi:10.1063/1.1663252
- X. R. Wang, P. Yan, J. Lu and C. He, Ann. Phys. 324, 8 (2009). doi:10.1016/j.aop.2009.05.004
References
S. A. Wolf, D. D. Awschalom, R.A. Buhrman, J. M. Daughton and S. Von Molnar, Science 294, 1488 (2001); I. Zutic, J. Fabian and S. Das Sarma, Rev. Mod. Phys. 76, 2 (2004).
Berger, Phys. Rev. B 54, 9353 (1996). doi:10.1103/PhysRevB.54.9353
J. Slonczewski and J. Magn. Magn. Mater. 159, L1 (1996). doi:10.1016/0304-8853(96)00062-5
G. S. D. Beach, C. Knutson, C. Nistor, M. Tsoi and J. L. Erskine, Phys. Rev. Lett. 97, 057203 (2006). doi:10.1103/PhysRevLett.97.057203
M. Tsoi, Nature Phys. 4, 17 (2008). doi:10.1038/nphys822
J. C. Sankey, P. M. Braganca, A. G. F. Garcia, I. N. Krivorotov, R. A. Buhrman and D. C. Ralph, Phys. Rev. Lett. 96, 227601 (2006). doi:10.1103/PhysRevLett.96.227601
S. Stuart and P. Parkin, Science 320, 190 (2008). doi:10.1126/science.1145799
J. Shibata, G. Tarara and H. Kohno, Phys. Rev. Lett. 94, 076601 (2005). doi:10.1103/PhysRevLett.94.076601
G. Tatara, H. Kohno and J. Shibata, Phys. Rep. 468, 6 (2008). doi:10.1016/j.physrep.2008.07.003
Z. Li and S. Zhang, Phys. Rev. Lett. 93, 127204 (2004). doi:10.1103/PhysRevLett.93.127204
S. Zhang and Z. Li, Phys. Rev. Lett 92, 207203 (2004). doi:10.1103/PhysRevLett.92.207203
J. Xiao, A. Zangwill and M. D. Stiles, Phys. Rev. B. 73, 054428 (2006). doi:10.1103/PhysRevB.73.054428
I. Turek, V. Drchal, J. Kudrnovsky, M. Sob and P. Weinberger, Electronic Structure of Disordered Alloys: Surface sand Interfaces (Kluwer, Boston-London-Dordrecht, 1997).
O. K. Andersen, O. Jepsen and D. Glotzel, in Highlights in Condensed Matter Theory, edited by F. Bassani, F. Fumi and M. P. Tosi (North-Holland, Amsterdam, 1985), p. 59.
S. Wang, Y. Xu and K. Xia, Phys. Rev. B 77, 184430 (2008). doi:10.1103/PhysRevB.77.184430
N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 (1974). doi:10.1063/1.1663252
X. R. Wang, P. Yan, J. Lu and C. He, Ann. Phys. 324, 8 (2009). doi:10.1016/j.aop.2009.05.004