Abstract
The problem of magnetization change across the direction of magnetic field for a magnetic layer with non-symmetric boundary conditions was treated. The exact solution of the problem for the magnetization components mx and my was written in the form of complex combination of Jacobian elliptic functions and elliptic integrals. This allows one to demonstrate both the static mode and all dynamic modes for the mag-netization distribution across the layer thickness. The static mode and several dynamic modes, as well as the first and second derivatives of the magnetization components, were calculated. Also, average values of the magnetization components ?mx? and amy? for the static mode and three dynamic modes were calculated in dependence on the magnetic field. The obtained results can represent an interest in the large amount of ap-plications of magnetic devices such as recording media, memory chips, and computer disks. The results are also useful for checking different numerical methods recently applied to study the problem, because it is thought that any numerical method cannot demonstrate solutions for the dynamic modes.
Highlights
The Landau-Lifshits equations first derived by Landau and Lifshits on a phenomenological ground in [1,2] are fundamental equations in the theory of ferromagnetism
Average values of the magnetization components mx and my for the static mode and three dynamic modes were calculated in dependence on the magnetic field
This paper demonstrated the magnetization distribution in a magnetically-soft layer on a magnetically-hard substrate when the applied magnetic field is perpendicular to the initial magnetization
Summary
The Landau-Lifshits equations first derived by Landau and Lifshits on a phenomenological ground in [1,2] are fundamental equations in the theory of ferromagnetism. It is thought that any numerical treatment can not demonstrate existence of a set of additional solutions These solutions can improve understanding of magnetization distributions in a ferromagnetic layer when different regimes of application of magnetic fields can be realized for a domain in the layer. Some interesting experimental data can be found in the review paper [23] for the novel evaluation of the problem This theoretical study of the magnetization distribution provides exact solutions leading to existence possibility of infinite number of dynamic modes in addition to the single static mode. The fourth section provides the magnetization distribution in the case when the magnetic anisotropy is accounted
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