Abstract.
We present numerical calculations of the spin transfer torque resulting in current-induced domain wall motion. Rather than the conventional micromagnetic finite difference or finite element method, we use an atomistic/classical Heisenberg spin model approach, which is well suited to study geometrically confined domain walls. We compute the behaviour of domain walls in a one dimensional chain when currents are injected using adiabatic and non-adiabatic spin torque terms. Our results are compared to analytical calculations and are found to agree very well for small current densities. At larger current densities deviations are observed, which can be attributed to the approximations used in the analytical calculations.
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References
R.D. McMichael, M.J. Donahue, IEEE Trans. Magn. 33, 4167 (1997)
M. Laufenberg et al., Appl. Phys. Lett. 88, 52507 (2006)
P. Bruno, Phys. Rev. Lett. 83, 2425 (1999)
N. Kazantseva, R. Wieser, U. Nowak, Phys. Rev. Lett. 94, 37206 (2005)
M. Kläui et al., Phys. Rev. Lett. 90, 97202 (2003)
C.C. Faulkner et al., J. Appl. Phys. 95, 6716 (2004)
M. Kläui et al., Appl. Phys. Lett. 87, 102509 (2005)
A. Himeno et al., J. Appl. Phys. 99, 08G304 (2006)
G.S.D. Beach et al., Nature Mater. 4, 741 (2005)
Y. Nakatani et al., Nature Mater. 2, 521 (2003)
R.P. Cowburn, Patents PCT/GB2003/001266, PCT/GB2004/000840 (2004)
D.A. Allwood et al., Science 309, 1688 (2005)
L. Berger, J. Appl. Phys. 55, 1954 (1984)
J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996)
P.P. Freitas, L. Berger, J. Appl. Phys. 57, 1266 (1985)
A. Yamaguchi et al., Phys. Rev. Lett. 92, 77205 (2004)
M. Kläui et al., Phys. Rev. Lett. 95, 26601 (2005); M. Kläui et al., Appl. Phys. Lett. 88, 232507 (2006)
J. Grollier et al., Appl. Phys. Lett. 83, 509 (2003)
N. Vernier et al., Europhys. Lett. 65, 526 (2004)
M. Kläui et al., Phys. Rev. Lett. 94, 106601 (2005)
D. Ravelosona et al., Phys. Rev. Lett. 95, 117203 (2005)
S.S.P. Parkin, U.S. patent 6,834,005 (2003)
A. Yamaguchi et al., Appl. Phys. Lett. 86, 12511 (2005)
A. Himeno, S. Kasai, T. Ono, Appl. Phys. Lett. 87, 243108 (2005)
U. Nowak, in Annual Reviews of Computational Physics IX, edited by D. Stauffer (World Scientific, Singapore, 2001), p. 105
H. Kronmüller, M. Fähnle, in: Micromagnetism and the Microstructure of Ferromagnetic Solids, Cambridge University Press (2003)
A. Aharoni, Introduction to the theory of ferromagnetism, (Clarendon Press, Oxford, 1996)
L.D. Landau, E.M. Lifshitz, Physik Z. Sowjetunion 8, 153 (1935)
The OOMMF software is available at http://math.nist.gov/oommf
M. Laufenberg et al., Phys. Rev. Lett. 97, 46602 (2006)
V.A. Gopar et al., Phys. Rev. B 69, 14426 (2004)
G. Tatara, H. Kohno, Phys. Rev. Lett. 92, 86601 (2004)
Z. Li, S. Zhang, Phys. Rev. Lett. 92, 207203 (2004)
A. Thiaville, Y. Nakatani, J. Miltat, N. Vernier, J. Appl. Phys. 95, 7049 (2004)
S. Zhang, Z. Li, Phys. Rev. Lett. 93, 127204 (2004)
A. Thiaville, Y. Nakatani, J. Miltat, Y. Suzuki, Europhys. Lett. 69, 990 (2005)
J. He, Z. Li, S. Zhang, J. Appl. Phys. 98, 16108 (2005)
W.F. Brown, Phys. Rev. 130, 1677 (1963)
J.L. Garcia-Palacios, F.J. Lázaro, Phys. Rev. B 58, 14937 (1998)
C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin 1990)
Z. Li, S. Zhang, Phys. Rev. B 70, 24417 (2004)
N.L. Schryer, L.R. Walker, J. Appl. Phys. 45, 5406 (1974)
R. Wieser, U. Nowak, K.D. Usadel, Phys. Rev. B 69, 064401 (2004)
J. Xiao, A. Zangwill, M.D. Stile, Phys. Rev. B 73, 054428 (2006)
J. He, Z. Li, S. Zhang, Phys. Rev. B 73, 184408 (2006)
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Schieback, C., Kläui, M., Nowak, U. et al. Numerical investigation of spin-torque using the Heisenberg model. Eur. Phys. J. B 59, 429–433 (2007). https://doi.org/10.1140/epjb/e2007-00062-2
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DOI: https://doi.org/10.1140/epjb/e2007-00062-2