American Journal of Physics and Applications
Volume 7, Issue 1, January 2019, Pages: 8-13
Received: Dec. 24, 2018;
Accepted: Jan. 21, 2019;
Published: Feb. 15, 2019
Views 116 Downloads 79
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
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.
Spin Dynamics in the Ferromagnetic Resonance, American Journal of Physics and Applications.
Vol. 7, No. 1,
2019, pp. 8-13.
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/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Charles Kittel, On the Theory of Ferromagnetic Resonance Absorption. Phys. Rev. 73, 155 – Published 15 January 1948.
Michael Farle, Ferromagnetic resonance of ultrathin metallic layers. Rep. Prog. Phys. 61 (1998) 755–826.
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.
L. R. Walker, Magnetostatic Modes in Ferromagnetic Resonance, Phys. Rev. 105, 390– Published 15 January 1957.
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).
Rodrigo Arias and D. L. Mills, Extrinsic contributions to the ferromagnetic resonance response of ultrathin films, Phys. Rev. B 60, 7395.
N. Bloembergen and S. Wang, Relaxation Effects in Para- and Ferromagnetic Resonance, Phys. Rev. 93, 72
Arne Brataas, Yaroslav Tserkovnyak, Spin battery operated by ferromagnetic resonance, Phys. Rev. B 66, 060404
Sangita S. Kalarickal, Pavol Krivosik, Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods, Journal of Applied Physics 99, 093909 (2006).
J. C. Sankey, P. M. Braganca, A. G. F. Garcia, Spin-Transfer-Driven Ferromagnetic Resonance of Individual Nanomagnets, Phys. Rev. Lett. 96, 227601 (2006).
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).
Wu C, Khalfan A N, Pettiford C, Ferromagnetic resonance studies of surface and bulk spin-wave modes in a CoFe/PtMn/CoFe multilayer film. Appl. Phys. 103, 07B525 (2008).
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).
Ulban R, Woltersdorf G, Heinrich B, Gilbert Damping in Single and Multilayer Ultrathin Films: Role of Interfaces in Nonlocal Spin Dynamics Phys. Rev. Lett. 87, 217204 (2001).
Wen, H. Y, Xia, J. B, Control of spins in a nano-sized magnet using electric-current. Chin. Phys. B. 26, 047501 (2017).
Wen, H. Y, Xia, J. B, Voltage control of magnetization switching and dynamics. Chin. Phys. B. 27, 067502 (2018).