Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

doi:10.1088/1674-1056/ad08a3

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 47502-047502.doi: 10.1088/1674-1056/ad08a3

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

收稿日期:2023-07-30 修回日期:2023-10-09 接受日期:2023-11-02 出版日期:2024-03-19 发布日期:2024-03-19
通讯作者: De-Sheng Xue E-mail:xueds@lzu.edu.cn
基金资助:
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).

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

Received:2023-07-30 Revised:2023-10-09 Accepted:2023-11-02 Online:2024-03-19 Published:2024-03-19
Contact: De-Sheng Xue E-mail:xueds@lzu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: precession relaxation, Landau—Lifshitz—Gilbert (LLG) equation, uniaxial anisotropy, analytical solutions

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.

Key words: precession relaxation, Landau—Lifshitz—Gilbert (LLG) equation, uniaxial anisotropy, analytical solutions

中图分类号: (Magnetization dynamics)

75.78.-n

75.60.Jk (Magnetization reversal mechanisms) 75.30.Gw (Magnetic anisotropy)

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[J]. 中国物理B, 2024, 33(4): 47502-047502.

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[J]. Chin. Phys. B, 2024, 33(4): 47502-047502.

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Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

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