American Journal of Physics and Applications

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Spin Dynamics in the Ferromagnetic Resonance

Received: 24 December 2018    Accepted: 21 January 2019    Published: 15 February 2019
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Abstract

The LLG equation including the spin-transfer torque term, and the frequency spectrum analysis method are used to study the dynamic process of ferromagnetic resonance. The effects of damping factor α, internal anisotropic field, magnetic field inclination, and spin-transfer torque caused by the spin current are studied. The following results are found as follows. The ferromagnetic resonance spectra as functions of the frequency ω for fixed magnetic field, and functions of magnetic field for fixed frequency are obtained, and it is found that the internal magnetic field also has contribution to the resonance field or frequency, and we know that the resonant frequency ω0he + h1 (in unit of γH0). In addition, when the damping factor increases from 0.01 to 0.03, the resonance frequencies increases slightly, and the resonance strength decreases. And the oscillatory waves of mx and my reach their stable values more quickly. Furthermore, the internal field perpendicular to the external field h0 as well as it parallel to h0 also has the effect to the resonant frequency. The positive and negative internal field will have reversed effects to the resonance field or frequency. And in the end when the spin current becomes larger the STT effect becomes stronger, even exceeds the ferromagnetic resonance effect, makes mz reversed, and mx and my decreased.

DOI 10.11648/j.ajpa.20190701.12
Published in American Journal of Physics and Applications (Volume 7, Issue 1, January 2019)
Page(s) 8-13
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ferromagnetic Resonance, Frequency Spectrum, Spin-transfer Torque, Internal Anisotropic Field

References
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[3] Luqiao Liu, Takahiro Moriyama, D. C. Ralph, and R. A. Buhrman, Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect. Phys. Rev. Lett. 106, 036601.
[4] L. R. Walker, Magnetostatic Modes in Ferromagnetic Resonance, Phys. Rev. 105, 390– Published 15 January 1957.
[5] Nick S. Norberg†, Kevin R. Kittilstved†, Synthesis of Colloidal Mn2+:ZnO Quantum Dots and High-TC Ferromagnetic Nanocrystalline Thin Films. J. Am. Chem. Soc., 126 (30), pp 9387–9398 (2004).
[6] Rodrigo Arias and D. L. Mills, Extrinsic contributions to the ferromagnetic resonance response of ultrathin films, Phys. Rev. B 60, 7395.
[7] N. Bloembergen and S. Wang, Relaxation Effects in Para- and Ferromagnetic Resonance, Phys. Rev. 93, 72
[8] Arne Brataas, Yaroslav Tserkovnyak, Spin battery operated by ferromagnetic resonance, Phys. Rev. B 66, 060404
[9] Sangita S. Kalarickal, Pavol Krivosik, Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods, Journal of Applied Physics 99, 093909 (2006).
[10] J. C. Sankey, P. M. Braganca, A. G. F. Garcia, Spin-Transfer-Driven Ferromagnetic Resonance of Individual Nanomagnets, Phys. Rev. Lett. 96, 227601 (2006).
[11] Beaujour, J. M. L., Kent, A. D., Abraham, D. W., Sun, J. Z., Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films. Journal of Applied Physics 103, 07B519 (2008).
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[13] Kakazei G N, Martin P P, Ruiz A, et al. Ferromagnetic resonance of ultrathin Co/Ag superlattices on Si (111) J. Appl. Phys. 103, 07B527 (2008).
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Author Information
  • Institute of Semiconductors, University of Chinese Academy of Sciences, Beijing, China

  • Institute of Semiconductors, University of Chinese Academy of Sciences, Beijing, China

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    Hongyu Wen, Jianbai Xia. (2019). Spin Dynamics in the Ferromagnetic Resonance. American Journal of Physics and Applications, 7(1), 8-13. https://doi.org/10.11648/j.ajpa.20190701.12

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    Hongyu Wen; Jianbai Xia. Spin Dynamics in the Ferromagnetic Resonance. Am. J. Phys. Appl. 2019, 7(1), 8-13. doi: 10.11648/j.ajpa.20190701.12

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    AMA Style

    Hongyu Wen, Jianbai Xia. Spin Dynamics in the Ferromagnetic Resonance. Am J Phys Appl. 2019;7(1):8-13. doi: 10.11648/j.ajpa.20190701.12

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  • @article{10.11648/j.ajpa.20190701.12,
      author = {Hongyu Wen and Jianbai Xia},
      title = {Spin Dynamics in the Ferromagnetic Resonance},
      journal = {American Journal of Physics and Applications},
      volume = {7},
      number = {1},
      pages = {8-13},
      doi = {10.11648/j.ajpa.20190701.12},
      url = {https://doi.org/10.11648/j.ajpa.20190701.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpa.20190701.12},
      abstract = {The LLG equation including the spin-transfer torque term, and the frequency spectrum analysis method are used to study the dynamic process of ferromagnetic resonance. The effects of damping factor α, internal anisotropic field, magnetic field inclination, and spin-transfer torque caused by the spin current are studied. The following results are found as follows. The ferromagnetic resonance spectra as functions of the frequency ω for fixed magnetic field, and functions of magnetic field for fixed frequency are obtained, and it is found that the internal magnetic field also has contribution to the resonance field or frequency, and we know that the resonant frequency ω0≈he + h1 (in unit of γH0). In addition, when the damping factor increases from 0.01 to 0.03, the resonance frequencies increases slightly, and the resonance strength decreases. And the oscillatory waves of mx and my reach their stable values more quickly. Furthermore, the internal field perpendicular to the external field h0 as well as it parallel to h0 also has the effect to the resonant frequency. The positive and negative internal field will have reversed effects to the resonance field or frequency. And in the end when the spin current becomes larger the STT effect becomes stronger, even exceeds the ferromagnetic resonance effect, makes mz reversed, and mx and my decreased.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Spin Dynamics in the Ferromagnetic Resonance
    AU  - Hongyu Wen
    AU  - Jianbai Xia
    Y1  - 2019/02/15
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ajpa.20190701.12
    DO  - 10.11648/j.ajpa.20190701.12
    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
    SP  - 8
    EP  - 13
    PB  - Science Publishing Group
    SN  - 2330-4308
    UR  - https://doi.org/10.11648/j.ajpa.20190701.12
    AB  - The LLG equation including the spin-transfer torque term, and the frequency spectrum analysis method are used to study the dynamic process of ferromagnetic resonance. The effects of damping factor α, internal anisotropic field, magnetic field inclination, and spin-transfer torque caused by the spin current are studied. The following results are found as follows. The ferromagnetic resonance spectra as functions of the frequency ω for fixed magnetic field, and functions of magnetic field for fixed frequency are obtained, and it is found that the internal magnetic field also has contribution to the resonance field or frequency, and we know that the resonant frequency ω0≈he + h1 (in unit of γH0). In addition, when the damping factor increases from 0.01 to 0.03, the resonance frequencies increases slightly, and the resonance strength decreases. And the oscillatory waves of mx and my reach their stable values more quickly. Furthermore, the internal field perpendicular to the external field h0 as well as it parallel to h0 also has the effect to the resonant frequency. The positive and negative internal field will have reversed effects to the resonance field or frequency. And in the end when the spin current becomes larger the STT effect becomes stronger, even exceeds the ferromagnetic resonance effect, makes mz reversed, and mx and my decreased.
    VL  - 7
    IS  - 1
    ER  - 

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