Spin Dynamics in the Ferromagnetic Resonance

Hongyu Wen; Jianbai Xia

doi:doi:10.11648/j.ajpa.20190701.12

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Spin Dynamics in the Ferromagnetic Resonance

Hongyu Wen, Jianbai Xia

Published in American Journal of Physics and Applications (Volume 7, Issue 1)

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 ω₀≈h_e + 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 m_x and m_y 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 m_z reversed, and m_x and m_y decreased.

Published in	American Journal of Physics and Applications (Volume 7, Issue 1)
DOI	10.11648/j.ajpa.20190701.12
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), 2019. Published by Science Publishing Group

Keywords

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

References

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[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).
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[7]	N. Bloembergen and S. Wang, Relaxation Effects in Para- and Ferromagnetic Resonance, Phys. Rev. 93, 72
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APA Style

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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ACS 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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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://article.sciencepublishinggroup.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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Author Information

Hongyu Wen

Institute of Semiconductors, University of Chinese Academy of Sciences, Beijing, China
Jianbai Xia

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

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APA Style

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

Copy | Download

ACS 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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

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  -

Copy | Download