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Pinning Effect on Current-Induced Domain Wall Motion in Nanostrip

Part of: Equations of mathematical physics and other areas of application Miscellaneous topics - Partial differential equations Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  31 January 2018

Lei Yang
Lei Yang*
Affiliation:
Faculty of Information and Technology, Macau University of Science and Technology, Macao SAR
*
*Corresponding author. Email address:leiyang@must.edu.mo (L. Yang)
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Abstract

Pinning effect on current-induced magnetic transverse domain wall dynamics in nanostrip is studied for its potential application to new magnetic memory devices. In this study, we carry out a series of calculations by solving generalized Landau-Lifshitz equation involving a current spin transfer torque in one and two dimensional models. The critical current for the transverse wall depinning in nanostrip depends on the size of artificial rectangular defects on the edges of nanostrip. We show that there is intrinsic pinning potential for a defect such that the transverse wall oscillates damply around the pinning site with an intrinsic frequency if the applied current is below critical value. The amplification of the transverse wall oscillation for both displacement and maximum value of m3 is significant by applying AC current and current pulses with appropriate frequency. We show that for given pinning potential, the oscillation amplitude as a function of the frequency of the AC current behaves like a Gaussian distribution in our numerical study, which is helpful to reduce strength of current to drive the transverse wall motion.

Keywords

Spin currentdomain wall motionLandau-Lifshitz equation

MSC classification

Secondary: 35R05: Partial differential equations with discontinuous coefficients or data 58J35: Heat and other parabolic equation methods 35Q60: PDEs in connection with optics and electromagnetic theory
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017 , pp. 837 - 851
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Chen, J., Yang, L. and Wang, X.P., The sharp interface limit of domain wall dynamics in Landau-Lifshitz equation and Walker's ansatz, Commun. Math. Sci., Under review.Google Scholar
[2] Chen, Y., Huang, F., Spectral method approximation of flow optimal control problems with H1 - norm state contraint, Numer. Math.-Theory Methods Appl. 10, 614–638 (2017)Google Scholar
[3] E, W.N. and Wang, X.P., Numerical methods for the Landau-Lifshitz equation, SIAM J. Numer. Anal. 38, 1647–1665 (2001).Google Scholar
[4] Gibson, N.L., A Polynomial Chaos Method for Dispersive Electromagnetics, Commun. Comput. Phys. 18, 1234–1263 (2015).Google Scholar
[5] Grollier, J., Cros, V., Hamzic, A., George, J.M., Jaffres, H., Fert, A., Faini, G., Ben Youssef, J. and Legall, H., Spin-polarized current induced switching in Co/Cu/Co pillars, Appl. Phys. Lett. 78, 3663 (2001).Google Scholar
[6] He, J., Li, Z. and Zhang, S., Current-driven domain-wall depinning, J. Appl. Phys. 98, 016108 (2005).Google Scholar
[7] Ilgaz, D., Nievendick, J., Heyne, L., Backes, D., Rhensius, J., Moore, T.A., M.á. Niño, Locatelli, A., Menteş, T.O., Schmidsfeld, A.v., Bieren, A.v., Krzyk, S., Heyderman, L.J. and M. Kläui, Domain-wall depinning assisted by pure spin currents, Phys. Rev. Lett. 105, 076601 (2010).Google Scholar
[8] Katine, J.A., Albert, F.J., Buhrman, R.A., Myers, E.B. and Ralph, D.C., Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars, Phys. Rev. Lett. 84, 3149 (2000).Google Scholar
[9] Kim, S.D., Chun, B.S. and Kim, Y.K., Domain wall width and velocity behaviors in notched magnetic devices, J. Appl. Phys. 101, 09F504 (2007).Google Scholar
[10] Li, Z. and Zhang, S., Domain-wall dynamics driven by adiabatic spin-transfer torques, Phys. Rev. B 70, 024417 (2004).Google Scholar
[11] Ono, T., Miyajima, H., Shigeto, K. and Shinjo, T., Magnetization reversal in submicron magnetic wire studied by using giant magnetoresistance effect, Appl. Phys. Lett. 72, 1116 (1998).Google Scholar
[12] Poluektov, M., Eriksson, O., Kreiss, G., Scale transitions in magnetisation dynamics, Commun. Comput. Phys. 20, 969–988 (2016).Google Scholar
[13] Parkin, S., Hayashi, M. and Thomas, L., Magnetic domain-wall racetrack memory, Science 320, 190–194 (2008).Google Scholar
[14] Parkin, S. and Yang, S.H., Memory on the racetrack, Nature Nanotechnol. 10, 195–198 (2015).Google Scholar
[15] Sun, J.Z., Current-driven magnetic switching in manganite trilayer junctions, J. Magn. Magn. Mater. 202, 157–162 (1999).Google Scholar
[16] Thomas, L., Hayashi, M., Jiang, X., Moriya, R., Rettner, C. and Parkin, S., Oscillatory dependence of current-driven magnetic domain wall motion on current pulse length, Nature 443, 197 (2006).Google Scholar
[17] Thomas, L., Hayashi, M., Jiang, X., R.Moriya, Rettner, C. and Parkin, S., Resonant amplification of magnetic domain-wall motion by a train of current pulses, Science Reports, 315, 1553 (2007).Google Scholar
[18] Thiaville, A., Nakatani, Y., J.Miltat and Suzuki, Y., Micromagnetic understanding of current-driven domain wall motion in patterned nanowires, Europhys. Lett. 69, 990–996 (2005).Google Scholar
[19] Thomas, L., Rettner, C., Hayashi, M., Samant, M.G., Parki, S.S.P., Doran, A. and Scholl, A., Observation of injection and pinning of domain walls in magnetic nanowires using photoemission electron microscopy, Appl. Phys. Lett. 87, 262501 (2005).Google Scholar
[20] Wang, X.P., Garcia-Cervera, C.J. and E, W.N., A Gauss-Seidel projection method for micromagnetics simulations, J. Comput. Phys. 171, 357–372 (2001).Google Scholar
[21] Wegrowe, J.E., Kelly, D., Truong, T., Guittienne, Ph. and Ansermet, J.Ph., Magnetization reversal triggered by spin-polarized current in magnetic nanowires, Europhys. Lett. 56, 748–754 (2001).Google Scholar
[22] Han, X., Li, Y. and Xie, H., A multilevel correction method for Steklov eigenvalue problem by non-conforming finite element methods, Numer. Math.-Theory Methods Appl. 8, 383–405 (2015).Google Scholar
[23] Yang, L., Current Induced Domain Wall Motion: Analysis and Simulation, Ph.D Thesis, 2008.Google Scholar
[24] Yuan, H.Y. and Wang, X.R., Domain wall pinning in notched nanowires, Phys. Rev. B 89, 054423 (2014).Google Scholar
[25] Yang, L. and Wang, X.P., Dynamics of domain wall in thin film driven by spin current, Discrete Contin. Dynam. Syst. Ser. B 14, 1251–1263 (2010).Google Scholar
[26] Zhang, S., Levy, P.M. and Fert, A., Mechanisms of spin-polarized current-driven magnetization switching, Phys. Rev. Lett. 88, 236601 (2002).Google Scholar
[27] Zhang, S. and Li, Z., Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets, Phys. Rev. Lett. 93, 127204 (2004).Google Scholar