American Institute of Mathematical Sciences

Advanced
October  2010, 14(3): 1251-1263. doi: 10.3934/dcdsb.2010.14.1251

Dynamics of domain wall in thin film driven by spin current

Lei Yang 1, and  Xiao-Ping Wang 2,

1. 

Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
2. 

Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received  October 2009 Revised  February 2010 Published  July 2010

The dynamics of magnetization under the applied spin current is modeled by the generalized Landau-Lifshitz-Gilbert equation with a spin transfer torque term. Using matched asymptotic expansion with the domain wall thickness $\epsilon$ as the small parameter, we derive analytically the dynamic law for the domain wall motion induced by the spin current. We show that the domain wall driven by adiabatic current spin-transfer torque moves with a decreasing velocity and eventually stops. With a pinning potential, the domain wall motion is a damped oscillation around the pinning site with an intrinsic frequency which is independent of the strength of the current. When the AC current is applied, the dynamic law shows that the frequency of the applied current can be turned to maximize the amplitude of the oscillation. The results obtained are consistent with the recent experimental and numerical results.
Keywords: domain wall dynamics, Spin current, Landau-Lifshitz-Gilbert..
Mathematics Subject Classification: 35R05, 58J35, 35Q6.
Citation: Lei Yang, Xiao-Ping Wang. Dynamics of domain wall in thin film driven by spin current. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1251-1263. doi: 10.3934/dcdsb.2010.14.1251
[1]

Catherine Choquet, Mohammed Moumni, Mouhcine Tilioua. Homogenization of the Landau-Lifshitz-Gilbert equation in a contrasted composite medium. Discrete and Continuous Dynamical Systems - S, 2018, 11 (1) : 35-57. doi: 10.3934/dcdss.2018003
[2]

Gaël Bonithon. Landau-Lifschitz-Gilbert equation with applied eletric current. Conference Publications, 2007, 2007 (Special) : 138-144. doi: 10.3934/proc.2007.2007.138
[3]

Tram Thi Ngoc Nguyen, Anne Wald. On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging. Inverse Problems and Imaging, 2022, 16 (1) : 89-117. doi: 10.3934/ipi.2021042
[4]

Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867
[5]

Wei Deng, Baisheng Yan. On Landau-Lifshitz equations of no-exchange energy models in ferromagnetics. Evolution Equations and Control Theory, 2013, 2 (4) : 599-620. doi: 10.3934/eect.2013.2.599
[6]

Xiao-Ping Wang, Ke Wang, Weinan E. Simulations of 3-D domain wall structures in thin films. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 373-389. doi: 10.3934/dcdsb.2006.6.373
[7]

Zonglin Jia, Youde Wang. Global weak solutions to Landau-Lifshtiz systems with spin-polarized transport. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1903-1935. doi: 10.3934/dcds.2020099
[8]

Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure and Applied Analysis, 2021, 20 (1) : 319-338. doi: 10.3934/cpaa.2020268
[9]

Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133
[10]

Xueke Pu, Boling Guo, Jingjun Zhang. Global weak solutions to the 1-D fractional Landau-Lifshitz equation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 199-207. doi: 10.3934/dcdsb.2010.14.199
[11]

Ze Li, Lifeng Zhao. Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 607-638. doi: 10.3934/dcds.2019025
[12]

Jian Zhai, Zhihui Cai. $\Gamma$-convergence with Dirichlet boundary condition and Landau-Lifshitz functional for thin film. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 1071-1085. doi: 10.3934/dcdsb.2009.11.1071
[13]

Tetsuya Ishiwata, Kota Kumazaki. Structure preserving finite difference scheme for the Landau-Lifshitz equation with applied magnetic field. Conference Publications, 2015, 2015 (special) : 644-651. doi: 10.3934/proc.2015.0644
[14]

Boling Guo, Fangfang Li. Global smooth solution for the Sipn-Polarized transport equation with Landau-Lifshitz-Bloch equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2825-2840. doi: 10.3934/dcdsb.2020034
[15]

Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized Landau-Lifshitz-Bloch equation in high dimensions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1345-1360. doi: 10.3934/dcdsb.2019230
[16]

Leonid Berlyand, Petru Mironescu. Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain. Networks and Heterogeneous Media, 2008, 3 (3) : 461-487. doi: 10.3934/nhm.2008.3.461
[17]

Ko-Shin Chen, Peter Sternberg. Dynamics of Ginzburg-Landau and Gross-Pitaevskii vortices on manifolds. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1905-1931. doi: 10.3934/dcds.2014.34.1905
[18]

Feng-Bin Wang, Junping Shi, Xingfu Zou. Dynamics of a host-pathogen system on a bounded spatial domain. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2535-2560. doi: 10.3934/cpaa.2015.14.2535
[19]

Wenrui Hao, King-Yeung Lam, Yuan Lou. Ecological and evolutionary dynamics in advective environments: Critical domain size and boundary conditions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 367-400. doi: 10.3934/dcdsb.2020283
[20]

Hong Lu, Mingji Zhang. Dynamics of non-autonomous fractional Ginzburg-Landau equations driven by colored noise. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3553-3576. doi: 10.3934/dcdsb.2020072

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (55)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy