Steady one-dimensional domain wall motion in biaxial ferromagnets: mapping of the Landau-Lifshitz equation to the sine-Gordon equation

Motivated by the difference between the dynamics of magnetization textures in ferromagnets and antiferromagnets, the Landau-Lifshitz equation of motion is explored. A typical one-dimensional domain wall in a bulk ferromagnet with biaxial magnetic anisotropy is considered. In the framework of Walker-...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Rama-Eiroa, Ricardo, Otxoa, Rubén M, Roy, Pierre E, Guslienko, Konstantin Y
Format: Article
Language:English
Subjects:
Antiferromagnetism
Critical velocity
Dependence
Domain walls
Equations of motion
Ferromagnetism
Magnetic anisotropy
Mapping
Solitary waves
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Summary:Motivated by the difference between the dynamics of magnetization textures in ferromagnets and antiferromagnets, the Landau-Lifshitz equation of motion is explored. A typical one-dimensional domain wall in a bulk ferromagnet with biaxial magnetic anisotropy is considered. In the framework of Walker-type of solutions of steady-state ferromagnetic domain wall motion, the reduction of the non-linear Landau-Lifshitz equation to a Lorentz-invariant sine-Gordon equation typical for antiferromagnets is formally possible for velocities lower than a critical velocity of the topological soliton. The velocity dependence of the domain wall energy and the domain wall width are expressed in the relativistic-like form in the limit of large ratio of the easy-plane/easy-axis anisotropy constants. It is shown that the mapping of the Landau-Lifshitz equation of motion to the sine-Gordon equation can be performed only by going beyond the steady-motion Walker-type of solutions.
ISSN:2331-8422
DOI:10.48550/arxiv.1910.13266