Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems

Xia Jianbai; Wen Hongyu

doi:doi:10.11648/j.ajpa.20190702.14

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Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems

Xia Jianbai, Wen Hongyu

Published in American Journal of Physics and Applications (Volume 7, Issue 2)

Received: 11 January 2019 Accepted: 23 May 2019 Published: 12 June 2019

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Abstract

A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ₀)₁ and (λτ₀)₂ as functions of I/Ic and H_k are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ₀)₂ can become complex, that means that the probability density P not only decays with time, but also oscillates with time.

Published in	American Journal of Physics and Applications (Volume 7, Issue 2)
DOI	10.11648/j.ajpa.20190702.14
Page(s)	55-60
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

Fokker-Plank Equation, Legendre Function, Thermal Fluctuation, Magnetic Reversal

References

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[2]	Xiao-binWang, Yi-ran Chen, Hai-wen Xi, Hai Li, Dimitar Dimitrov, “Spintronic Memristor Through Spin-Torque-Induced Magnetization Motion,” IEEE ELECTRON DEVICE LETTERS, VOL. 30, NO. 3, MARCH 2009.
[3]	J. Z. Sun, S. L. Brown, W. Chen, E. A. Delenia, “Spin-torque switching efficiency in CoFeB-MgO based tunnel junctions,” PHYSICAL REVIEW B 88, 104426 (2013).
[4]	Xiao-bin Wang, Yuan-kai Zheng, Hai-wen Xi, and Dimitar Dimitrov, “Thermal fluctuation effects on spin torque induced switching: Mean and variations,” J. Appl. Phys. 103, 034507 (2008).
[5]	Xiao-bin Wang, H. Neal Bertram, and Vladimir L. Safonov, “Thermal-dynamic reversal of fine magnetic grains with arbitrary anisotropy axes orientation,” Journal of Applied Physics 92, 2064 (2002)
[6]	R. Bonina, G. Bertottia, C. Serpicob, I. D. Mayergo- yz, “Effect of thermal fluctuations in spin-torque driven magnetization dynamics,” Journal of Magnetism and Magnetic Materials 316 (2007) e919–e922
[7]	Xiao-bin Wang, Wen-zhong Zhu, and Dimitar Dimitrov, “Current fluctuations and magnetization dynamics symmetry in spin-torque-induced magnetization switching,” PHYSICAL REVIEW B 78, 024417 (2008).
[8]	D. V. Berkova, J. Miltat, “Spin-torque driven magnetization dynamics: Micromagnetic modeling,” Journal of Magnetism and Magnetic Materials 320 (2008) 1238–1259.
[9]	J. Z. Sun, R. P. Robertazzi, J. Nowak, et al. “Effect of subvolume excitation and pin-torque efficiency on magnetic switching,” Phys. Rev. B 84, 064413 (2011).
[10]	J. Z. Sun, Physical Principles of Spin Torque, in Handbook of Spintronics, Eds. Y. B. Xu, D. D. Awschalom, J. Nitta, Springer, 2016, Vol. IV, p. 1339.
[11]	J. He, J. Z. Sun, S. Zhang, “Switching speed distribution of spin-torque-induced magnetic reversal,” J. Appl. Phys. 101, 09A501 (2007).
[12]	Zhu-Xi Wang, Dun-Ren Guo, Introduction of Special functions (in Chinese), Peking University Press, Beijing, 2010.

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APA Style

Xia Jianbai, Wen Hongyu. (2019). Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. American Journal of Physics and Applications, 7(2), 55-60. https://doi.org/10.11648/j.ajpa.20190702.14

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ACS Style

Xia Jianbai; Wen Hongyu. Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. Am. J. Phys. Appl. 2019, 7(2), 55-60. doi: 10.11648/j.ajpa.20190702.14

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AMA Style

Xia Jianbai, Wen Hongyu. Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. Am J Phys Appl. 2019;7(2):55-60. doi: 10.11648/j.ajpa.20190702.14

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@article{10.11648/j.ajpa.20190702.14,
  author = {Xia Jianbai and Wen Hongyu},
  title = {Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems},
  journal = {American Journal of Physics and Applications},
  volume = {7},
  number = {2},
  pages = {55-60},
  doi = {10.11648/j.ajpa.20190702.14},
  url = {https://doi.org/10.11648/j.ajpa.20190702.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20190702.14},
  abstract = {A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ0)1 and (λτ0)2 as functions of I/Ic and Hk are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ0)2 can become complex, that means that the probability density P not only decays with time, but also oscillates with time.},
 year = {2019}
}

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TY  - JOUR
T1  - Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems
AU  - Xia Jianbai
AU  - Wen Hongyu
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ajpa.20190702.14
DO  - 10.11648/j.ajpa.20190702.14
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 55
EP  - 60
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20190702.14
AB  - A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ0)1 and (λτ0)2 as functions of I/Ic and Hk are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ0)2 can become complex, that means that the probability density P not only decays with time, but also oscillates with time.
VL  - 7
IS  - 2
ER  -

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Author Information

Xia Jianbai

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

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

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APA Style

Xia Jianbai, Wen Hongyu. (2019). Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. American Journal of Physics and Applications, 7(2), 55-60. https://doi.org/10.11648/j.ajpa.20190702.14

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ACS Style

Xia Jianbai; Wen Hongyu. Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. Am. J. Phys. Appl. 2019, 7(2), 55-60. doi: 10.11648/j.ajpa.20190702.14

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AMA Style

Xia Jianbai, Wen Hongyu. Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems. Am J Phys Appl. 2019;7(2):55-60. doi: 10.11648/j.ajpa.20190702.14

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@article{10.11648/j.ajpa.20190702.14,
  author = {Xia Jianbai and Wen Hongyu},
  title = {Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems},
  journal = {American Journal of Physics and Applications},
  volume = {7},
  number = {2},
  pages = {55-60},
  doi = {10.11648/j.ajpa.20190702.14},
  url = {https://doi.org/10.11648/j.ajpa.20190702.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20190702.14},
  abstract = {A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ0)1 and (λτ0)2 as functions of I/Ic and Hk are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ0)2 can become complex, that means that the probability density P not only decays with time, but also oscillates with time.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems
AU  - Xia Jianbai
AU  - Wen Hongyu
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ajpa.20190702.14
DO  - 10.11648/j.ajpa.20190702.14
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 55
EP  - 60
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20190702.14
AB  - A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ0)1 and (λτ0)2 as functions of I/Ic and Hk are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ0)2 can become complex, that means that the probability density P not only decays with time, but also oscillates with time.
VL  - 7
IS  - 2
ER  -

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