Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems
American Journal of Physics and Applications
Volume 7, Issue 2, March 2019, Pages: 55-60
Received: Jan. 11, 2019;
Accepted: May 23, 2019;
Published: Jun. 12, 2019
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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
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.
Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems, American Journal of Physics and Applications.
Vol. 7, No. 2,
2019, pp. 55-60.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Chi-Feng Pai, Luqiao Liu, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, “Spin transfer torque devices utilizing the giant spin Hall effect of tungsten,” Appl. Phys. Lett. 101, 122404 (2012).
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.
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).
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).
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)
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
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).
D. V. Berkova, J. Miltat, “Spin-torque driven magnetization dynamics: Micromagnetic modeling,” Journal of Magnetism and Magnetic Materials 320 (2008) 1238–1259.
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).
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.
J. He, J. Z. Sun, S. Zhang, “Switching speed distribution of spin-torque-induced magnetic reversal,” J. Appl. Phys. 101, 09A501 (2007).
Zhu-Xi Wang, Dun-Ren Guo, Introduction of Special functions (in Chinese), Peking University Press, Beijing, 2010.