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Some explicit solutions of the Landau‐Lifshitz equation for anisotropic ferromagnets
Author(s) -
Han Fangyu,
Yang Ganshan
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5246
Subject(s) - landau–lifshitz–gilbert equation , anisotropy , mathematics , ferromagnetism , field (mathematics) , magnetization , transformation (genetics) , condensed matter physics , mathematical physics , physics , magnetic field , quantum mechanics , pure mathematics , biochemistry , chemistry , gene
The aim of this paper is to construct explicit solutions of the Landau‐Lifshitz equation for anisotropic ferromagnets. Firstly, we present some explicit solutions for n ‐dimensional Landau‐Lifshitz equation with a generalized uniaxial anisotropy field (depending only on time) under a suitable transformation, where the generalized uniaxial anisotropy field contains the classical easy‐axis case and the important higher‐order approximations. Some relevant examples are indicated that contains the cubic system proposed by Landau and Lifshitz in 1960. Secondly, an explicit plane‐wave solution of Landau‐Lifshitz equation for the completely anisotropic case is obtained. Finally, some properties of magnetization for ferromagnets are provided by analysis of the solutions.