Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

doi:10.1088/1674-1056/ad08a3

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.

Keywords: precession relaxation Landau—Lifshitz—Gilbert (LLG) equation uniaxial anisotropy analytical solutions

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

[1]	Theoretical investigation of ferromagnetic resonance in a ferromagnetic thin film with external stress anisotropy Jieyu Zhou(周婕妤), Jianhong Rong(荣建红), Huan Wang(王焕), Guohong Yun(云国宏), Yanan Wang(王娅男), and Shufei Zhang(张舒飞). Chin. Phys. B, 2022, 31(1): 017601.
[2]	Continuum states of modified Morse potential Wei Gao-Feng(卫高峰) and Chen Wen-Li(陈文利). Chin. Phys. B, 2010, 19(9): 090308.
[3]	Exact analytical solutions to the mean-field model depicting microcavity containing semiconductor quantum wells Song Pei-Jun(宋佩君), Lü Xin-You (吕新友), Liu Ji-Bing(刘继兵), and Hao Xiang-Ying(郝向英). Chin. Phys. B, 2010, 19(5): 050503.
[4]	The scattering states of the generalized Hulthén potential with an improved new approximate scheme to the centrifugal term Wei Gao-Feng(卫高峰), Chen Wen-Li(陈文利), Wang Hong-Ying(王红英), and Li Yuan-Yuan(李院院). Chin. Phys. B, 2009, 18(9): 3663-3669.
[5]	Mössbauer study of the field induced uniaxial anisotropy in electro-deposited FeCo alloy films Li Zhi-Wei(李志伟), Yang Xu(杨旭), Wang Hai-Bo(王海波), Liu Xin(刘忻), and Li Fa-Shen(李发伸). Chin. Phys. B, 2009, 18(11): 4829-4833.
[6]	Evolution of structure and magnetic properties of nanocrystalline FeXN thin films via Ta and Al addition Wu Guo-Guang (伍国光), Wu Dong-Ping (吴东平), Zheng Kuo-Hai (郑阔海), Wei Fu-Lin (魏福林), Yang Zheng (杨正), Kamzin A. S.. Chin. Phys. B, 2005, 14(6): 1238-1242.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Cite this article:

Online attention