Abstract
Current-driven domain wall dynamics is studied theoretically in the spin-valve nanostrips with parallel, perpendicular and tilted polarizers by Lagrangian formalism. In this description, the Slonczewski and field-like spin-transfer torques act as a Coulomb-type dissipation and an effective magnetic field, respectively. Considering a Walker profile, the wall behavior is governed by the dynamic equations about the center position, the out-of-plane angle, and the width of walls. It is found that the wall precesses after the steady motion breaks down for the parallel polarizer. The field-like spin-transfer torque favors a rapid increase of the steady velocity. The average velocity in the precession is nearly proportional to the current density. On the other hand, there is no precession for the perpendicular and tilted polarizers. Under the perpendicular polarizer, the wall stops when increasing current density. Moreover, there exist hysteresis and tri-stability for a large spin polarization. Under the tilted polarizer, it can be observed hysteretic, linear and nonlinear dependence of the wall velocity on the increasing current density. In the hysteresis, the wall experiences a switching of polarity or a reversal of motion.
Similar content being viewed by others
References
S. Parkin, M. Hayashi, L. Thomas, Science 320, 190 (2008)
D. Allwood, G. Xiong, C. Faulkner, D. Atkinson, D. Petit, R. Cowburn, Science 309, 1688 (2005)
L. Berger, Phys. Rev. B 54, 9353 (1996)
J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996)
J. Grollier, P. Boulenc, V. Cros, A. Hamzic, A. Vaurès, A. Fert, G. Faini, Appl. Phys. Lett. 83, 509 (2003)
A. Yamaguchi, T. Ono, S. Nasu, K. Miyake, K. Mibu, T. Shinjo, Phys. Rev. Lett. 92, 077205 (2004)
N. Vernier, D.A. Allwood, D. Atkinson, M.D. Cooke, R.P. Cowburn, Europhys. Lett. 65, 526 (2004)
M. Hayashi, L. Thomas, C. Rettner, R. Moriya, S.S.P. Parkin, Nat. Phys. 3, 21 (2006)
S. Pizzini, V. Uhlíř, J. Vogel, N. Rougemaille, S. Laribi, V. Cros, E. Jiménez, C. Tieg, E. Bonet, M. Bonfim, R. Mattana, C. Deranlot, F. Petroff, C. Ulysse, A. Fert, Appl. Phys. Express 2, 023003 (2009)
Ya.B. Bazaliy, B.A. Jones, S.C. Zhang, Phys. Rev. B 57, R3213 (1998)
Z. Li, S. Zhang, Phys. Rev. Lett. 92, 207203 (2004)
Z. Li, S. Zhang, Phys. Rev. B 70, 024417 (2004)
S. Zhang, Z. Li, Phys. Rev. Lett. 93, 127204 (2004)
G. Tatara, H. Kohno, Phys. Rev. Lett. 92, 086601 (2004)
X. Waintal, M. Viret, Europhys. Lett. 65, 427 (2004)
A. Thiaville, Y. Nakatani, J. Miltat, Y. Suzuki, Europhys. Lett. 69, 990 (2005)
P.B. He, X.C. Xie, W.M. Liu, Phys. Rev. B 72, 172411 (2005)
A. Mougin, M. Cormier, J.P. Adam, P.J. Metaxas, J. Ferre, Europhys. Lett. 78, 57007 (2007)
Z.Z. Sun, J. Schliemann, P. Yan, X.R. Wang, Eur. Phys. J. B 79, 449 (2011)
J. Grollier, A. Chanthbouala, R. Matsumoto, A. Anane, V. Cros, F. Nguyen van Dau, A. Fert, C.R. Physique 12, 309 (2011)
D. Claudio-Gonzalez, A. Thiaville, J. Miltat, Phys. Rev. Lett. 108, 227208 (2012)
S. Zhang, P.M. Levy, A. Fert, Phys. Rev. Lett. 88, 236601 (2002)
M.A. Zimmler, B. Özyilmaz, W. Chen, A.D. Kent, J.Z. Sun, M.J. Rooks, R.H. Koch, Phys. Rev. B 70, 184438 (2004)
J. Xiao, A. Zangwill, M.D. Stiles, Phys. Rev. B 72, 014446 (2005)
Z. Li, S. Zhang, Z. Diao, Y. Ding, X. Tang, D.M. Apalkov, Z. Yang, K. Kawabata, Y. Huai, Phys. Rev. Lett. 100, 246602 (2008)
Y. Zhou, J. Appl. Phys. 109, 023916 (2011)
X.J. Xing, Y.P. Yu, S.W. Li, Appl. Phys. Lett. 95, 142508 (2009)
A.V. Khvalkovskiy, K.A. Zvezdin, Y.V. Gorbunov, V. Cros, J. Grollier, A. Fert, A.K. Zvezdin, Phys. Rev. Lett. 102, 067206 (2009)
C.T. Boone, J.A. Katine, M. Carey, J.R. Childress, X. Cheng, I.N. Krivorotov, Phys. Rev. Lett. 104, 097203 (2010)
C.T. Boone, I.N. Krivorotov, Phys. Rev. Lett. 104, 167205 (2010)
P. Yan, X.R. Wang, Appl. Phys. Lett. 96, 162506 (2011)
R. McMichael, M. Donahue, IEEE Trans. Magn. 33, 4167 (1997)
N. Rougemaille, V. Uhlíř, O. Fruchart, S. Pizzini, J. Vogel, J.C. Toussaint, Appl. Phys. Lett. 100, 172404 (2012)
X.C. Zhu, J.G. Zhu, IEEE Trans. Magn. 42, 2739 (2006)
C.L. Zha, J. Akerman, IEEE Trans. Magn. 45, 3491 (2009)
C.L. Zha, J. Persson, S. Bonetti, Y.Y. Fang, J. Akerman, Appl. Phys. Lett. 94, 163108 (2009)
U. Roy, H. Seinige, F. Ferdousi, J. Mantey, M. Tsoi, S.K. Banerjee, J. Appl. Phys. 111, 07C913 (2011)
R. Sbiaa, R. Law, E.-L. Tan, T. Liew, J. Appl. Phys. 105, 013910 (2009)
C.-M. Lee, J.-S. Yang, T.-H. Wu, IEEE Trans. Magn. 47, 649 (2011)
Y. Zhou, C.L. Zha, S. Bonetti, J. Persson, J. Akerman, Appl. Phys. Lett. 92, 262508 (2008)
Y. Zhou, C.L. Zha, S. Bonetti, J. Pearson, J. Akerman, J. Appl. Phys. 105, 07D116 (2009)
P.B. He, Z.D. Li, A.L. Pan, Q. Wan, Q.L. Zhang, R.X. Wang, Y.G. Wang, W.M. Liu, B.S. Zou, Phys. Rev. B 78, 054420 (2008)
P.B. He, Z.D. Li, A.L. Pan, Q.L. Zhang, Q. Wan, R.X. Wang, Y.G. Wang, W.M. Liu, B.S. Zou, J. Appl. Phys. 105, 043908 (2009)
R.X. Wang, P.B. He, Q.H. Liu, Z.D. Li, A.L. Pan, B.S. Zou, Y.G. Wang, J. Magn. Magn. Mater. 322, 2264 (2010)
Y. Zhou, S. Bonetti, C.L. Zha, J. Akerman, New J. Phys. 11, 103028 (2009)
P.B. He, R.X. Wang, Z.D. Li, Q.H. Liu, A.L. Pan, Y.G. Wang, B.S. Zou, Eur. Phys. J. B 73, 417 (2010)
R.X. Wang, P.B. He, Z.D. Li, A.L. Pan, Q.H. Liu, J. Appl. Phys. 109, 033905 (2011)
Ya.B. Bazaliy, Phys. Rev. B 85, 014431 (2012)
Y. Zhou, H. Zhang, Y.W. Liu, J. Åkerman, J. Appl. Phys. 112, 063903 (2012)
A. Thiaville, J.M. Garcia, J. Miltat, J. Magn. Magn. Mater. 242-245, 1061 (2002)
J. Miltat, G. Albuquerque, A. Thiaville, in Spin Dynamics in Confined Magnetic Structures I, edited by B. Hillebrands, K. Ounadjela (Springer, New York, 2002), p. 12
A. Thiaville, Y. Nakatani, in Spin Dynamics in Confined Magnetic Structures III, edited by B. Hillebrands, A. Thiaville (Springer, New York, 2002), p. 180
A. Thiaville, Y. Nakatani, J. Miltat, N. Vernier, J. Appl. Phys. 95, 7049 (2004)
N.L. Schryer, L.R. Walker, J. Appl. Phys. 45, 5406 (1974)
J. Angeles, Dynamic Response of Linear Mechanical Systems (Springer, New York, 2011), p. 26
G. Bertotti, I. Mayergoyz, C. Serpico, Nonlinear magnetization Dynamics in Nanosystems (Elsevier, Oxford, 2009), p. 237
A. Vanhaverbeke, A. Bischof, R. Allenspach, Phys. Rev. Lett. 101, 107202 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, PB. Current-driven domain wall dynamics in spin-valve nanostrips with parallel, perpendicular, and tilted polarizers. Eur. Phys. J. B 86, 412 (2013). https://doi.org/10.1140/epjb/e2013-40472-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2013-40472-9