CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Prev
Next
|
|
|
Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy |
Ze-Nan Zhang(张泽南), Zhen-Lin Jia(贾镇林), and De-Sheng Xue(薛德胜)† |
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China |
|
|
Abstract Based on the Landau--Lifshitz--Gilbert (LLG) equation, the precession relaxation of magnetization is studied when the external field ${{\bm H}}$ is parallel to the uniaxial anisotropic field ${{\bm H}}_{\rm k}$. The evolution of three-component magnetization is solved analytically under the condition of $H=nH_{\rm k}$ ($n =3$, 1 and 0). It is found that with an increase of ${{\bm H}}$ or a decrease of the initial polar angle of magnetization, the relaxation time decreases and the angular frequency of magnetization increases. For comparison, the analytical solution for $H_{\rm k}=0$ is also given. When the magnetization becomes stable, the angular frequency is proportional to the total effective field acting on the magnetization. The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization, but also can be used as a standard model to test the numerical calculation of LLG equation.
|
Received: 30 July 2023
Revised: 09 October 2023
Accepted manuscript online: 02 November 2023
|
PACS:
|
75.78.-n
|
(Magnetization dynamics)
|
|
75.60.Jk
|
(Magnetization reversal mechanisms)
|
|
75.30.Gw
|
(Magnetic anisotropy)
|
|
Fund: Project supported by the National Key R&D Program of China (Grant No. 2021YFB3501300), the National Natural Science Foundation of China (Grant Nos. 91963201 and 12174163), and the 111 Project (Grant No. B20063). |
Corresponding Authors:
De-Sheng Xue
E-mail: xueds@lzu.edu.cn
|
Cite this article:
Ze-Nan Zhang(张泽南), Zhen-Lin Jia(贾镇林), and De-Sheng Xue(薛德胜) Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy 2024 Chin. Phys. B 33 047502
|
[1] Zhong W D 2017 Ferromagnetism (Vol. 2) (Beijing:Science Press) pp. 142——145 (in Chinese) [2] Wood R 2009 J. Magn. Magn. Mater. 321 555 [3] Suto H, Kudo K, Nagasawa T, Kanao T, Mizushima K and Sato R 2016 Jpn. J. Appl. Phys. 55 119204 [4] Bishnoi R, Ebrahimi M, Oboril F and Tahoori M B 2016 IEEE Trans. Magn. 52 3401611 [5] Lenz J and Edelstein A S 2006 IEEE Sens. J. 6 631 [6] Silveyra J M, Ferrara E, Huber D L and Monson T C 2018 Science 362 eaao0195 [7] Lin X M and Samia A C S 2006 J. Magn. Magn. Mater. 305 100 [8] Singamaneni S, Bliznyuk V N, Binek C and Tsymbal E Y 2011 J. Mater. Chem. 21 16819 [9] Landau L and Lifshitz E 1992 Perspectives in Theoretical Physics:The Collected Papers of E. M. Lifshitz (Oxford:Pergamon Press) pp. 51——65 [10] Gilbert T L 2004 IEEE Trans. Magn. 40 3443 [11] Kikuchi R 1956 J. Appl. Phys. 27 1352 [12] Gillette P R and Oshima K 1958 J. Appl. Phys. 29 529 [13] He L, Doyle W D and Fujiwara H 1994 IEEE Trans. Magn. 30 4086 [14] Mallinson J C 2000 IEEE Trans. on Magn. 36 1976 [15] Bertotti G, Mayergoyz I and Seroico C 2009 Nonlinear Magnetization Dynamics in Nanosystems (Oxford:Elsevise) pp. 91——100 [16] Okamoto S, Kikuchi N and Kitakami O 2008 Appl. Phys. Lett. 93 102506 [17] Koch R H, Deak J G, Abraham D W, Trouilloud P L, Altman R A, Lu Y, Gallagher W J, Scheuerlein R E, Roche K P and Parkin S S P 1998 Phys. Rev. Lett. 81 4512 [18] Shah S A, Reeves D B, Ferguson R M, Weaver J B and Krishnan K M 2015 Phys. Rev. B 92 094438 [19] Oezelt H, Qu L, Kovacs A, Fischbacher J, Gusenbauer M, Beigelbeck R, Praetorious D, Yano M, Shoji T, Kato A, Chantrell R, Winklhofer M and Zimanyi G T 2022 NPJ Comput. Mater. 8 35 [20] Kinii S, Masuzawa K, Fogiatto A L, Mitsumata C and Kotsugi M 2022 Sci. Rep. 12 19892 [21] Neeraj K, Pancaldi M, Scalera V, Perna S, d'Aquino M, Serpico C and Bonetti S 2022 Phys. Rev. B 105 054415 [22] Müller M, Scheufele M, Gückelhorn J, Flacke L, Weiler M, Huebl H, Gepraegs S, Gross R and Althammer M 2022 J. Appl. Phys. 132 233905 [23] Lévy M, Wilhelm C, Siaugue J M, Horner O, Bacri J C and Gazeau F 2008 J. Phys.:Condens. Matter 20 204133 [24] Sun Z Z and Wang X R 2006 Phys. Rev. B 73 092416 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|